Dorothée Charlier

Bérangère Legendre

Olivia Ricci

Measuring fuel poverty in tropical territories: a latent class model

Keywords: fuel poverty, tropical islands, latent class model, capabilities approach JEL codes: D12, C35, O12, Q41, R21

Fuel poverty in tropical territories cannot be defined and measured using traditional indicators based on heating issues (expenditure, restriction or the sensation of cold inside houses). We propose a new framework for the identification of fuel-poor households by referring to Amartya Sen's Capability Approach. To accurately assess fuel poverty in tropical areas using observable objective characteristics of decent, safe and healthy dwellings, we use the latent class model (LCM) methodology. This approach allows us to categorize households as fuel poor or non-fuel poor. It is also possible to extend further by considering the multi-dimensional phenomenon of fuel poverty. Using three classes, we can underline a scale of fuel poverty severity with a new class of vulnerable households. Restricting fuel poverty in tropical areas to a binary phenomenon leads to the neglect of the complexity of energy deprivation.

Introduction

Fuel poverty in developed countries is a complex phenomenon resulting from a combination of the following three main factors: low income, low-energy efficient housing and high energy prices [START_REF] Epee | Project: European Fuel Poverty and Energy Efficiency, Intelligent Energy Europe. Evaluation of fuel poverty in Belgium[END_REF]Devalière, 2007;[START_REF] Palmer | Cold and Poor: An analysis of the link between fuel poverty and low income[END_REF]. These issues are quite different from those identified in developing countries, where energy poverty usually describes situations in which people have inadequate access to modern energy sources. [START_REF] Bouzarovski | A global perspective on domestic energy deprivation: Overcoming the energy poverty-fuel poverty binary[END_REF] emphasized that the term "fuel poverty" is generally used in northern and colder countries, while in less developed countries, the term "energy poverty" is preferred and encompasses broader issues (infrastructure, electrification, education and health concerns).

Fuel poverty is often defined in Europe as a situation in which household members are unable to adequately heat their homes or meet other required energy services at affordable costs. In Scotland, Wales and Ireland, fuel poverty is officially defined as having to spend more than 10% of income on fuel use to maintain a satisfactory indoor level of warmth 1 . In France, this type of heating issue also has an increased importance. Many definitions include a heating issue as a main component of fuel poverty. Devalière (2007) proposed the following definition: "one who encounters a social, economic and environmental vulnerability which prevents him from heating himself appropriately and/or paying his energy bills". The Pelletier report also highlights this issue [START_REF] De Quero | Comment prévenir la précarité énergétique ? Les leviers possibles et les risques inhérents à la libéralisation du service de l'énergie[END_REF]. A household member is considered to experience fuel poverty if he/she "has difficulty in heating their home because of the inadequacy of their resources and housing conditions."

On the one hand, in developed countries, fuel poverty is mainly related to the poor energy efficiency of housing and cold winter issues. However, on the other hand, among people living in developing countries, energy poverty concerns energy deprivation and the lack of adequate facilities. The populations in these countries face the absence of networks, which are a prerequisite for economic development. A better access to energy is therefore a key element of improving well-being [START_REF] Pachauri | On Measuring Energy Poverty in Indian Households[END_REF]. Energy poverty is strongly linked with poverty, especially consumption based measure of poverty: households do not have even a choice of 1 The satisfactory heating regime recommended by the World Health Organization is 23°C in the living room and 18°C in the other rooms, which should be maintained for 16 of every 24 hours in households with older people or people with disabilities or chronic illness and 21°C in the living room and 18°C in the other rooms for nine of every 24 hours (or 16 of 24 hours over the weekend) in other households. energy consumption level or electrical equipment to make. They do not have a physical access to electrical grid, nor physical access to markets where they could buy electrical equipment [START_REF] Pachauri | On Measuring Energy Poverty in Indian Households[END_REF]. Climatic issues are not central in energy poverty. However, according to [START_REF] Mohr | Fuel poverty in the US: Evidence using the 2009 Residential Energy Consumption Survey[END_REF], "more research is needed to understand predictors of fuel poverty and contrasts between cool and warm climates" At the crossroads of these issues, in some territories, access to energy does not seem particularly problematic, except for in the case of a major climatic event, but housing may be of poor quality. Indeed, some tropical territories have quite good energy networks; by definition, these territories do not experience winter cold but suffer from domestic energy deprivation (OREC, 2018). The geographic (islands), climatic (tropical), and socio-economic contexts in those territories induce a use of energy services that differs from that in temperate latitudes.

We focus in this paper on the French overseas territories (Guadeloupe, Martinique, Reunion Island and Guyana), which perfectly illustrate the gap between both approaches of the issue. These overseas territories are located far from mainland France. These territories, except for Guyana, are also characterized by their insularity. However, Guyana is isolated from the remainder of South America by its location between the Atlantic Ocean and Amazonia.

The climate in Guadeloupe, Martinique and Reunion Island is tropical maritime. The temperature differences between the summer and winter are low. Winter is the dry season, and summer is the wet season. In Guyana, the climate is similar but more equatorial. The temperatures slightly vary during the year. Precipitation is abundant during the summer.

However, the following climatic characteristics are rather similar across the four territories: hot temperature, very mild and humidity.

The standards of living are also significantly low in these territories. For instance, in Guadeloupe, the mean disposable income per month reaches 780 €, and 50% of the population aged older than 15 years is inactive (OREC, 2018). Monetary poverty is more important in these territories than in mainland France. In 2015, 40% of the population of Reunion Island lived under the poverty line compared to 14% of the population in mainland France (INSEE, 2018). Moreover, the prices of basic necessities are sometimes much higher (up to 35% for fuels) compared to those in mainland France (La Documentation Française, 2009). In this context, a household's energy budget may be significant. Although these territories are not developing economies, they often suffer from multidimensional precariousness (OREC, 2018). Consequently, energy is not considered a primary/basic need by household members, who adopt coping strategies and restrict their energy service consumption (OREC, 2018).

Within this context, tropical territories cannot be characterized by the current well-known fuel poverty or energy poverty issues. The phenomenon in tropical territories cannot be defined and measured by traditional indicators based on heating issues (expenditure, restriction or the sensation of cold inside houses). Moreover, indicators based on fuel expenditures and income relative to acceptable thresholds [START_REF] Boardman | Fuel Poverty: From Cold Homes to Affordable Warmth[END_REF][START_REF] Hills | An Anatomy of Economic Inequality in the UK: The Report of the National Equality Panel[END_REF][START_REF] Hills | Fuel Poverty: The problem and its measurement. Interim Report of the Fuel Poverty Review, Centre for Analysis and Social Exclusion[END_REF], 2012) can overestimate fuel-poor households given the higher rate of monetary poverty in these territories. These traditional indicators seem limited in capturing the complex and multidimensional characteristics of fuel poverty in tropical territories.

Consequently, a better understanding of the fuel poverty phenomenon in tropical territories complemented by a quantified evaluation seems necessary and original. Approaching this phenomenon in tropical areas requires overcoming the gap between the following approaches: fuel and energy poverty. Similar to [START_REF] Bouzarovski | A global perspective on domestic energy deprivation: Overcoming the energy poverty-fuel poverty binary[END_REF], we believe that in addition to heating issues, fuel and energy poverty should focus on all domestic energy services, including cooling, water heating, and cooking, as well as the hygiene, safety and sanitation of dwellings. Fuel expenditure-based indicators and definitions should capture the broader idea of energy "services" rather than simply "fuel" or even "energy". The concept of "services" captures notions of utility and adequacy rather than energy consumption [START_REF] Sovacool | Conceptualizing urban household energy use: Climbing the Energy Services Ladder[END_REF].

Recent research [START_REF] Day | Conceptualising energy use and energy poverty using a capabilities framework[END_REF] focused on the notion of energy poverty from a capabilities approach based on the pioneer work conducted by Amartya Sen and Martha Nussbaum [START_REF] Nussbaum | Capabilities as Fundamental Entitlements: Sen and Social Justice[END_REF][START_REF] Nussbaum | Creating Capabilities: The Human Development Approach[END_REF][START_REF] Nussbaumer | Measuring energy poverty: Focusing on what matters[END_REF][START_REF] Sen | Issues In the Measurement of Poverty[END_REF][START_REF] Sen | Development as Freedom[END_REF][START_REF] Sen | Development as Capability Expansion[END_REF][START_REF] Sen | Capability and Well-Being[END_REF][START_REF] Sen | Development as Capability Expansion[END_REF]. The capability approach developed by Sen considers human life a set of "doings and beings" named "functionings". Functionings vary from escaping morbidity and being adequately nourished to being integrated into a social community, achieving self-respect and receiving recognition for one's work. Sen describes functionings as a personal achievement, i.e., what a person manages to accomplish or be. The capability of a person is a derived notion that reflects the combination of functionings and the freedom to choose a way of living. Therefore, according to Sen, poverty can be understood as a deprivation in the capability to achieve crucial and valued functionings. This concept of capability deprivation can be applied to energy poverty because it allows a richer comprehension of the phenomenon. [START_REF] Day | Conceptualising energy use and energy poverty using a capabilities framework[END_REF] conceptualized the relationship among energy, energy services and capabilities to propose a definition of energy poverty based on the capabilities framework. According to these authors, domestic energy is obtained from different sources (biomass, solar energy, and gas) and provides services (lighting, refrigeration, etc.). These energy services enable people to wash clothes and store and prepare food. The authors call these daily actions secondary capabilities. Secondary capabilities are prerequisites required to access so-called basic capabilities (functionings), such as being in good health, having social respect, etc. Therefore, the authors defined energy poverty as "an inability to realize essential capabilities as a direct or indirect result of insufficient access to affordable, reliable and safe energy services, and taking into account available reasonable alternative means of realizing these capabilities" [START_REF] Day | Conceptualising energy use and energy poverty using a capabilities framework[END_REF].

In this article, we use the common term "fuel poverty" to describe energy deprivation in tropical territories as we consider this term less specific than the term energy poverty. As fuel poverty in tropical areas has never been defined or measured, our objective is to study fuel poverty as a latent phenomenon that, by definition, we cannot observe. However, the literature offers different paths to theoretically approach the observable characteristics of fuel poverty.

Therefore, we rely on the capabilities theoretical framework developed by Sen and the conceptualizing work performed by [START_REF] Day | Conceptualising energy use and energy poverty using a capabilities framework[END_REF] to identify the fuel poor in tropical territories with an innovative methodology.

To accurately assess fuel poverty in tropical areas, using observable objective characteristics, we use a latent class model (LCM) (Greene and Hansher, 2003). Assuming that objective multivariate variables describing a set of capabilities are observed, we link these variables to the following latent variable: fuel poverty in tropical areas. This methodology allows us to categorize households as fuel poor or non-fuel poor. As the main results extend the common bi-dimension phenomena, we show that defining three categories of energy-deprived people is better than defining people as only fuel poor and non-fuel poor. The most deprived represent approximately 12% of the population, while 32% of the population is expected to belong to the non-fuel poor class. An intermediate class encompassing 56% of the population represents vulnerable households that could easily be impacted by an exogenous shock. Restricting fuel poverty in tropical areas to a binary phenomenon leads to the neglect of the complexity of energy deprivation.

Our paper provides the following three key contributions to this field of research: we propose the first characterization of fuel poverty in tropical areas, we use an original methodology that has never been used to identify fuel poor households and we allow policy makers to identify a target group of households that is a top priority in fighting fuel poverty.

The paper is organized as follows. In section 2, we describe the data and variables. The class latent methodology is presented in section 3. Section 4 presents the results, and section 5 offers some concluding remarks.

Observable characteristics of fuel poverty in tropical areas: capabilities, data and variables

Capabilities

In the capability framework, energy demand can be interpreted as a services access demand. As underlined by [START_REF] Day | Conceptualising energy use and energy poverty using a capabilities framework[END_REF], households aspire to use energy services, such as cooking, lighting and cooling [START_REF] Sovacool | Deciphering energy justice and injustice[END_REF], more than they demand electricity or gas. Thus, a "capability" is the expression of the freedoms offered by the consumption of energy services.

Practical Actions (2010) outlines the following basic energy services: lighting, cooking, water heating, space heating, cooling, information and communication, and earning a living.

Lighting avoids the loss of many productive hours during the night. Cooking and water heating are strongly linked to different issues, such as the possibility of cooking nutritious food and washing oneself and the opportunity to limit deforestation and climate change from a more global perspective. Space heating enables the control of thermal comfort in cold regions, while cooling is important for lengthening the lifespan of food and maintaining spaces at reasonable temperatures in countries with hot climates. Information and communication refer to social and economic relationships to alleviate poverty. Finally, global energy access could enable a person to earn a living.

The classification of basic energy services by Practical Action and the conceptualized relationship among energy, energy services and capabilities by [START_REF] Day | Conceptualising energy use and energy poverty using a capabilities framework[END_REF] helps us identify items that could be observable characteristics of fuel poverty in tropical areas.

Moreover, the OREC (2018) technical report provides a profile of fuel-poor households living in Guadeloupe. The report shows that equipment, such as air conditioners and water systems, account for a large share of domestic energy consumption that can affect the most economically fragile households. However, some houses without air conditioners and electric water heaters also face high electricity bills, which can be explained by ageing equipment and energy-consuming practices due to the lack of device-specific technical knowledge. The presence of a cooling system remains marginal in traditional houses (wooden walls without thermal insulation and sheet metal roof construction). This type of dwelling induces significant energy losses and is an aggravating factor of high final energy consumption. Access to hot water is a preoccupation in overseas departments. Many households do not have any hot water.

Even if the lack of hot water systems does not have sanitary consequences due to warm outdoor temperatures, people should have the choice of access. In rented houses, homeowners often decide to not provide hot water to tenants. Domestic hot water, air conditioning and building insulation represent a significant proportion of over-consumption. These factors cannot be considered the only factors of fuel poverty in overseas departments because their diffusion only partially affects the most vulnerable populations. The OREC report ( 2018) also shows that it is important to integrate energy insecurity, safety and building conditions as drivers of fuel poverty in Guadeloupe.

The building quality has a direct impact on the quality of a house. Poor quality is mostly due to moisture, dampness and holes. Buildings that are very damp or very dry can have significant impacts on the occupants' health. This fact has been well established in many reports, including those published by the World Health Organization (2009). Furthermore, electricity installations in overseas departments are sometimes homemade, illegal and dangerous. Household members connect their houses to electricity poles. Regardless of whether they are installed before or after metres, electrical installations may pose risks to users if they are not up to standard.

"Homemade" and/or ageing facilities are often involved in fires. OREC (2018) also underlines the role of lighting. Lighting is not the most energy-intensive consuming item, but energy-saving margins can be achieved through better information regarding equipment and practices. Finally, some households in overseas departments do not use modern cooking equipment, which is important because indoor air pollution from the use of solid fuels leads to a high number of deaths per year according to the World Health Organization. Providing clean access to energy for cooking is a challenge in eliminating fuel poverty [START_REF] Rao | Better air for better health: Forging synergies in policies for energy access, climate change and air pollution[END_REF]; (World Bank, 2013).

Considering the literature described above and to cover all dimensions of fuel poverty, the following capabilities are analysed to characterize fuel poverty in tropical areas: lighting efficiency, security of electricity installations, access to clean energy for cooking, access to water heating, quality of building insulation and access to a cooling system.

Data

Our study is based on the 2013 French housing survey (INSEE, 2013). The purpose of the housing survey was to describe households' housing conditions and expenditures. This survey also includes a detailed description of the quality of the dwellings. Based on the survey, we have information regarding the following four French overseas departments: Guadeloupe, Martinique, Reunion Island and Guyana. To ensure consistency with the literature, we chose the following variables, which are consistent with the capabilities presented in the previous section:

-Water heating: information about water access is available. It is possible to determine whether households have only hot water or cold water or whether there is no access.

-Quality of building insulation: regarding the quality of building insulation, we consider components of the building quality, moisture and holes in the roof. A building is well insulated if there is no moisture and no holes.

-Cooling: whether a household has a cooling system is known.

-Lighting: there is no direct information about the number of lights available in a dwelling.

However, it is possible to determine whether there is sufficient brightness in a house. A good level of brightness leads to less energy consumption per day in terms of lighting.

-Electricity: information regarding the quality of the installation is available, and we introduce a dummy variable that indicates whether the electrical installation is protected.

-Cooking: based on the information in the database, the main fuel used for cooking (fossil fuels or solid fuels) is known.

For our study, additional information is available in the database to control drivers that influence fuel poverty. Even if the standard measures of fuel poverty are not relevant in this study, fuel poverty still refers to a multidimensional concept that includes the socioeconomic situation of a household according to the income level, the characteristics of the dwelling, including energy efficiency, and the energy access conditions generally reflected in energy prices. Within the same country, regional differences in climate, different socioeconomic characteristics (cost of living), and cultural factors necessarily influence the phenomenon of fuel poverty. Income elasticity is positively related to energy consumption in most studies, which is consistent with the "normal good status" of energy consumption as follows: income elasticity often lies between 0.01 and 0.15. Positive elasticity may mainly involve the purchase of more energy-efficient appliances, which could result in lower energy consumption [START_REF] Alberini | Response of residential electricity demand to price: The effect of measurement error[END_REF][START_REF] Bakaloglou | Energy Consumption in the French Residential Sector: How Much do Individual Preferences Matter? FAERE Working Paper[END_REF][START_REF] Bernard | A pseudo-panel data model of household electricity demand[END_REF][START_REF] Cayla | The role of income in energy consumption behaviour: Evidence from French households data[END_REF][START_REF] Damette | Households energy consumption and transition toward cleaner energy sources[END_REF][START_REF] Dubin | An econometric analysis of residential electric appliance holdings and consumption[END_REF][START_REF] Labandeira | A residential energy demand system for Spain (English)[END_REF][START_REF] Nesbakken | Energy Consumption for Space Heating: A Discrete-Continuous Approach[END_REF][START_REF] Parti | The Total and Appliance-Specific Conditional Demand for Electricity in the Household Sector[END_REF][START_REF] Santamouris | On the relation between the energy and social characteristics of the residential sector[END_REF]. Recently, new studies have shown that households react differently to residential energy price fluctuations as follows: fuel-poor households have the highest income elasticity [START_REF] Charlier | From Residential Energy Demand to Fuel Poverty: Income-induced Non-linearities in the Reactions of Households to Energy Price Fluctuations[END_REF]. A high education level increases the probability of being non-fuel poor [START_REF] Chaton | Does France have a fuel poverty trap?[END_REF]. Empirical research also underlines the effect of tenure status on fuel poverty as follows: renting households have a higher likelihood of experiencing fuel poverty [START_REF] Davis | Evaluating the Slow Adoption of Energy Efficient Investments: Are Renters Less Likely to Have Energy Efficient Appliances?[END_REF][START_REF] Poruschi | Densification, What Does It Mean for Fuel Poverty and Energy Justice? An Empirical Analysis[END_REF]. Tenants do not have full control of their heating consumption compared to owners [START_REF] Healy | Quantifying the severity of fuel poverty, its relationship with poor housing and reasons for non-investment in energy-saving measures in Ireland[END_REF]. Numerous studies also show that a poor energy efficiency dwelling is a main driver of fuel poverty [START_REF] Boardman | Fixing Fuel Poverty: Challenges and Solutions[END_REF][START_REF] Hills | Fuel Poverty: The problem and its measurement. Interim Report of the Fuel Poverty Review, Centre for Analysis and Social Exclusion[END_REF][START_REF] Mohr | Fuel poverty in the US: Evidence using the 2009 Residential Energy Consumption Survey[END_REF].

Experiencing mould and/or moisture problems in homes is a driver of fuel-poverty severity.

Using French data, [START_REF] Legendre | Measuring fuel poverty in France: Which households are the most fuel vulnerable?[END_REF] show that the probability of being fuel poor is higher among single persons in rented properties with inefficient roof insulation. Compared to living in an apartment, living in a single detached house increases the probability of remaining in fuel poverty [START_REF] Chaton | Does France have a fuel poverty trap?[END_REF]. These results have been confirmed in France with the empirical fuel poverty study conducted by [START_REF] Belaïd | Exposure and risk to fuel poverty in France: Examining the extent of the fuel precariousness and its salient determinants[END_REF].

Therefore, we need to control for these characteristics to determine a fuel-poor profile and the probability of living in a dwelling with poor energy services. Income, occupant status, family composition, urban area, and type of home (period of construction and type of dwelling) have to be introduced in the study. The final sample contains 5686 observations. The summary statistics of the variables included in the model are presented in Table 1.

In general, the capabilities in Guadeloupe, Martinique and Reunion Island are better than those in Guyana. The use of cooling systems in Guadeloupe is more important than that in other overseas departments. In Guyana, more households use wood and do not have a cooking system. Households include tenants with children, and those with high education levels live in rural areas. The most recent housing stock is on Reunion Island.

A latent class model defining fuel poverty in tropical areas

Latent class model versus other approaches

To identify household profiles, several methods, including a multidimensional analysis, cluster analysis [START_REF] Fizaine | On the power of indicators: how the choice of fuel poverty indicator affects the identification of the target population[END_REF] and regression analysis [START_REF] Charlier | A Multidimensional Approach to Measuring Fuel Poverty[END_REF][START_REF] Masuma | A. Modelling the Likelihood of Being Fuel Poor. Department of Energy & Climate Change Masyn[END_REF][START_REF] Thomson | Quantifying the prevalence of fuel poverty across the European Union[END_REF]) [START_REF] Belaïd | Exposure and risk to fuel poverty in France: Examining the extent of the fuel precariousness and its salient determinants[END_REF][START_REF] Waddams Price | Identifying fuel poverty using objective and subjective measures[END_REF], can be used. A regression analysis is often used to identify the drivers of fuel poverty. Generally, in the economic literature, the drivers of fuel poverty are mostly identified using a conventional binary definition of fuel poverty, such as the Low Income High Cost Indicator (LIHC) or the effort rate [START_REF] Boardman | Fuel Poverty: From Cold Homes to Affordable Warmth[END_REF][START_REF] Hills | Fuel Poverty: The problem and its measurement. Interim Report of the Fuel Poverty Review, Centre for Analysis and Social Exclusion[END_REF], which is not possible in our case because no objective measures of fuel poverty exist. Moreover, commonly in the social sciences, multiple indicators can be used to describe a phenomenon instead of a single measure of an outcome of interest. As mentioned in their report, according to Thomson and Bouzarovski (2018),"Energy poverty is a multi-dimensional concept that is not easily captured by a single indicator".

Energy poverty should be measured by a composite indicator (Llera-Sastresa, et al., 2017) [START_REF] Charlier | A Multidimensional Approach to Measuring Fuel Poverty[END_REF]. Using regression methods to analyse a composite indicator that does not currently have a formal definition in tropical areas does not seem appropriate.

Multidimensional and cluster analyses, such as Latent Class Model (LCM), are used to identify profiles and create groups, but compared to LCM, cluster analysis presents several disadvantages. First, most cluster analyses are based on the subjective distance between variables (k-means clustering and similarity). Second, the choice of the number of clusters is often subjective and biased due to the lack of objective criteria [START_REF] Ketchen | The application of cluster analysis in strategic management research: An analysis and critique[END_REF].

Indeed, [START_REF] Ketchen | The application of cluster analysis in strategic management research: An analysis and critique[END_REF] argue that cluster analyses often produce group profiles that are not meaningful considering that the number and nature of the clusters are based on the researchers' hypothesis. Third, cluster analyses can be more difficult to perform with missing data and large sample datasets. Finally, cluster analyses are not appropriate for analysing large range variables; these variables tend to skew the results if they are given more weight, and standardization can have adverse effects [START_REF] Ketchen | The application of cluster analysis in strategic management research: An analysis and critique[END_REF].

In such a context, LCM offers a "model-based clustering" approach derived from the clustering approach that uses a probabilistic model to describe the distribution of the data. In this model, it is assumed that the population consists of a number of subpopulations and that in each of population, the variables have a different multivariate probability density function. Therefore, instead of finding profiles using some arbitrary distance measure as in cluster analysis, the LCM describes the distribution of the data and assesses the probabilities that certain households are members of certain latent classes. In contrast to clustering, using a statistical model also allows for the assessment of the goodness of fit. Assuming a latent structure determining the structure of the data exists, LCM is more appropriate than clustering, which only measures some similarities. Finally, using latent class methods, we can determine the weight of each variable that contributes to the phenomenon and, thus, identify the priority attributes that could be targeted; thus, we believe that this approach can enlighten policy decision makers.

Model

In their seminal work, Lazarsfeld and Henry first proposed a latent structure analysis in 1968 [START_REF] Lazarsfeld | Latent structure analysis[END_REF], and a latent class analysis was a subdomain of this analysis. A latent class analysis is a measurement model in which the observations can be categorized into latent classes [START_REF] Goodman | Latent Class Analysis: The Empirical Study of Latent Types, Latent Variables, and Latent Structures[END_REF]. The latent variable is discrete and unobservable. The latent class model includes 1) a measurement model relating the observed variables (also called indicators or manifest variables) to the underlying latent variable and 2) a structural model characterizing the distribution of the latent variable and the impact of its antecedent variables (Masyn, 2013).

Fuel poverty in tropical areas has never been defined or measured. Consequently, this phenomenon is a good candidate as a latent variable. We assume that fuel poverty in tropical areas is a binary latent variable (i.e., typically poor and non-poor in the literature). Both identified classes are mutually exclusive and exhaustive as follows: each individual has membership in exactly one category, i.e., he is either fuel poor or non-fuel poor. The latent classes pertain to the latent heterogeneity that varies with the manifest variables.

As a first step, we are interested in building an unconditional model with only manifest variables to explain the belonging to a latent class. Consequently, we use the following observable characteristics assumed to be symptoms of this phenomenon: basic needs (Practical Actions, 2010), which are approximated by housing characteristics, and some household attributes commonly considered determinants in analyses of fuel poverty as presented in the previous section. The theoretical framework of capabilities [START_REF] Sen | Issues In the Measurement of Poverty[END_REF] allows us to theoretically identify the model. The basic needs identified in the literature and fuel poverty in tropical areas are indeed strongly linked, allowing latent class homogeneity and latent class separation [START_REF] Collins | Latent Class and Latent Transition Analysis: With Applications in the Social, Behavioral, and Health Sciences[END_REF].

Conditional or local independence is assumed (Masyn, 2013), implying that class membership explains all covariance among the manifest variables. The number and nature of the latent classes is set based on a set of associations among the observed variables.

Figure 1 represents the measurement model with the manifest variables resulting from latent class membership using diagramming conventions [START_REF] Muthén | Mplus user's guide Los Angeles: Muthén & Muthén[END_REF][START_REF] Muthén | Mplus user's guide Los Angeles: Muthén & Muthén[END_REF]. 𝑧 𝑖 represents a set of observable attributes or manifest variables that contribute to determining class membership named the "risk factor" by [START_REF] Roeder | Modeling Uncertainty in Latent Class Membership: A Case Study in Criminology[END_REF]. We denote 𝑃 𝑖 as the likelihood of individual i as follows:

𝑃 𝑖 = ∑ 𝐻 𝑖𝑞 𝑃 𝑖|𝑞 𝑄 𝑞=1
The log likelihood is as follows:

ln 𝐿 = ∑ ln 𝑃 𝑖 = ∑ ln [∑ 𝐻 𝑖𝑞 (∏ 𝑃 𝑖𝑡|𝑞 𝑇 𝑖 𝑡=1 ) 𝑄 𝑞=1 ] 𝑁 𝑖=1 𝑁 𝑖=1
This issue is usual in maximum likelihood estimation [START_REF] Greene | Econometric Analysis[END_REF]. Using the parameter estimates of 𝜃 𝑞 , the class probabilities (𝐻 ̂𝑖𝑞 ) can be obtained using Bayes Theorem as follows:

𝐻 ̂𝑞|𝑖 = 𝑃 ̂𝑖|𝑞 𝐻 ̂𝑖𝑞 ∑ 𝑃 ̂𝑖|𝑞 𝐻 ̂𝑖𝑞 𝑄 𝑞=1
𝐻 ̂𝑖𝑞 denotes the household-specific estimate of the class probability given its estimated characteristic probabilities, which differs from the unconditional class probability used in the log likelihood function.

The maximum value of 𝐻 ̂𝑖𝑞 provides an empirical estimator of the latent class to which a household belongs. Then, we can obtain estimates of the household-specific parameter vector as follows:

𝛽 ̂𝑖 = ∑ 𝐻 ̂𝑞|𝑖 𝛽 ̂𝑞 𝑄 𝑞=1
The second step involves the construction of a structural model to characterize the causal link between households' attributes and class membership. This model allows us to characterize the distribution of the latent variable. Covariates M are introduced to the mass probabilities, i.e., to the model of the distribution of latent variable Q, via a multinomial logit model. The main interests are the discrete latent variable, which is measured through the manifest variables, and how this latent variable depends on the covariates; subsequently, the covariates directly affect the probability of belonging to a given class. Thus, the regression coefficient means indicate the effect of an increase in a unit of the m-th covariate on the logit of belonging to class q with respect to the reference class (e.g., class 1). Figure 2

Results

Here, we present the results of a binary class model of fuel poverty in tropical climate to identify the fuel poor and non-fuel poor. First, we present the results of the measurement model (Table 3). Second, we present the results of the structural model (Table 4). Then, we report the class-specific marginal means of each variable (Table 5). Because the measurement model includes logistic regressions, these means are actually the predicted probabilities.

We can estimate the probabilities of being in each class. This analysis indicates that 54% of individuals are expected to be fuel poor (class 1), which can be relatively high in terms of households concerned. This class represents the statistical majority of the population living in French overseas territories. Fuel poverty can be characterized as a "normal" or "typical" situation, which can be considered substantial. The regression coefficient means measure the effect of an increase of one percent of the m-th covariate (such as income) on the logit of belonging to class2 with respect to the reference class (e.g., class 1).

In general, according to Table 3, our categories, which are chosen as capabilities, all significantly explain the probability of belonging to the fuel poor and non-fuel poor classes.

Based on this table, we only interpret the sign and statistical effect of each coefficient compared to the base outcome as a probability of being in the class considered. For example, having no roof holes or moisture compared to having roof holes or moisture significantly decreases the probability of belonging to the category of fuel poor. In general, in the non-fuel poor class (Table 4), we find high-income households and family homeowner households living in collective housing units constructed after 1999. The opposite results are found to explain the probability of being in the fuel poor classes. These results are consistent with the literature related to fuel poverty (ONPE 2014). Indeed, even in tropical climates, fuel poverty is mainly characterized by low income and tenant households [START_REF] Charlier | From Residential Energy Demand to Fuel Poverty: Income-induced Non-linearities in the Reactions of Households to Energy Price Fluctuations[END_REF][START_REF] Davis | Evaluating the Slow Adoption of Energy Efficient Investments: Are Renters Less Likely to Have Energy Efficient Appliances?[END_REF][START_REF] Poruschi | Densification, What Does It Mean for Fuel Poverty and Energy Justice? An Empirical Analysis[END_REF]. A high education level also increases the probability of being nom-fuel poor, which is consistent with the literature [START_REF] Chaton | Does France have a fuel poverty trap?[END_REF].

Furthermore, regarding the predicted probabilities (Table 5), the first column of this table reports the probabilities of being fuel poor. Experiencing mould and/or moisture problems in homes is a driver of fuel poverty, which is consistent with previous findings [START_REF] Boardman | Fixing Fuel Poverty: Challenges and Solutions[END_REF][START_REF] Hills | Fuel Poverty: The problem and its measurement. Interim Report of the Fuel Poverty Review, Centre for Analysis and Social Exclusion[END_REF][START_REF] Mohr | Fuel poverty in the US: Evidence using the 2009 Residential Energy Consumption Survey[END_REF]. In this class, the probability of having a problem with roof holes or moisture is 0.70. The probability of not having a cooling system is 0.90. This final manifest variable is the main attribute explaining the probability of being fuel poor. Generally, in the fuel poor class, there are households with poor living conditions, e.g., a higher use of wood and no cooking system, compared to the non-fuel poor (1.2% versus 0.3%, respectively). In addition, most households use cold water (42.3%). Furthermore, 26.5% of households have no protected installation. These results are interesting because they underline the profile differences in fuel poverty between northern countries and tropical islands. For instance, in a northern country, access to hot water and protected electrical installation are not questionable. However, in the same country, such as France in our case, the same phenomenon, i.e., fuel poverty, cannot be measured in the same way in metropolitan areas and overseas departments, underlining the necessity to identify another way to identify the fuel poor and non-fuel poor. Our methodology addresses this need. Recent studies raise the issue of the intensity of fuel poverty [START_REF] Charlier | A Multidimensional Approach to Measuring Fuel Poverty[END_REF] and its composite dimension [START_REF] Llera-Sastresa | Energy vulnerability composite index in social housing, from a household energy poverty perspective[END_REF] [START_REF] Charlier | A Multidimensional Approach to Measuring Fuel Poverty[END_REF] (Thomson and Bouzarovski, 2018). This question implies that fuel poverty should not be measured as a binary phenomenon but rather as a phenomenon with a continuous distribution of intensity or at least more than 2 categories. Here, our method allows us to extend further in the analysis and consider an additional class. As previously mentioned in section 3.1, this is one of the many advantages of LCM and could allow us to achieve a more detailed and discriminating level of analysis. In such a context, fuel poverty should not be defined as a binary dimension but as a phenomenon with multi-dimensions, which is very interesting since it allows us to explore whether a class of vulnerable households appears and switch households to this class. In particular, it is possible to determine whether households considered non-poor with a binary measure are actually vulnerable. This intuition is consistent with [START_REF] Charlier | A Multidimensional Approach to Measuring Fuel Poverty[END_REF] as follows: a scale of fuel poverty offers a more detailed analysis of the phenomenon and avoids exposure to threshold effects.

First, we aimed to confirm our assumption in a methodological way. In a latent class analysis, models with different numbers of classes are often compared. Following [START_REF] Goodman | Latent Class Analysis: The Empirical Study of Latent Types, Latent Variables, and Latent Structures[END_REF], we compare models including two and three latent classes. We compare both models using AIC and BIC criteria (see Table 6). Smaller AIC and BIC values are better. We prefer a model with 3 classes as the three-class model has the smallest AIC and BIC values. Thus, in a contextual way, the results show the importance of considering 3 classes, which is interesting regarding the definition of fuel poverty.

In total, 12% of individuals are expected to be fuel poor (class 1), 56% of individuals are expected to be vulnerable to fuel poverty (class 2) and 32% of individuals are expected to be non-fuel poor (class 3). This result shows that a large share of the fuel poor (previously class 1)

fall in the second class, which is also the case for some households who previously belonged to class 3 and currently belong to class 2 (12%). Vulnerable becomes the majority class.

Thus, regarding public policies, policy makers should first target the most deprived households (in class 1) and obtain information regarding who is vulnerable. With three classes, we can underline a scale of fuel poverty severity. Restricting fuel poverty in tropical areas to a binary phenomenon could lead to the neglect of the complexity of energy deprivation.

The results of the estimated coefficients and predictive variables are presented in appendix A-1.

We also present the results of the class-specific marginal means in Table 7. housing units located in rural areas. In the vulnerable class, we find homeowners with a high education level living in recently built buildings. However, these households face poor energy efficiency conditions in their dwelling. These households live mostly in dwellings with roof holes or moisture and no cooling system. In the case that their socio-economic situation deteriorates, these households can fall into a fuel poverty situation. To prove the consistency of our results, in appendix A.2, we provide additional materials. The same estimations are conducted for each overseas department separately using the same variables. Indeed, to test the robustness of the method, the class-specific marginal means were calculated using the same set of observable attributes for each overseas territory. The results of the estimation again show the existence of the following three classes: fuel-poor households, vulnerable households and households that are not fuel poor. According to the local specificities, the proportion of the fuel poor is not completely the same as that in the whole estimation. However, the results of the estimation again show the existence of the following three classes: fuel-poor households, vulnerable households and households that are not fuel This result is interesting and can be considered a tool for policy makers. Indeed, using the LCM enables policy makers to stress the main variables characterizing the probability of being in fuel poverty in each territory. If it is possible to identify those who are fuel poor within a whole sample using observable attributes, it is also possible for a community using local data to adapt policies for people who suffer the most. For example, in Guadeloupe, Martinique and Reunion island, the main tool for fighting fuel poverty is providing cooling systems. In Guyana, the quality of brightness should receive priority. Providing cold water is also a good tool for fighting fuel poverty in this territory. Finally, using LCM, the profile can be adjusted over time (if data are available) and does not depend on constant threshold measurement.

Conclusion

Recently, energy deprivation has been studied extensively. In developed countries, fuel poverty is often defined as a situation in which households are unable to adequately heat their homes or meet other required energy services at affordable costs. In developing countries, energy poverty usually describes situations in which people have inadequate access to energy. We contribute to this growing literature by exploring energy deprivation in tropical overseas areas in which the usual distinction between energy poverty and fuel poverty is no longer relevant. The energy deprivation suffered by people living in developing countries highlights access issues, and fuel poverty mainly encompasses issues linked to wintry cold conditions in Europe. However, while some tropical developed territories have good energy networks and do not experience winter cold, they still suffer from domestic energy deprivation. No definition or measure exists to understand the phenomenon in tropical overseas areas. We applied the Sen capability theoretical framework to select observable objective characteristics of a decent, safe and healthy dwelling. The capability approach focuses on the ability to achieve crucial and valued functionings, which describe an achievement of a person. This concept of capability deprivation can be applied to fuel poverty because it allows a better comprehension of the phenomenon.

Assuming that objective multivariate variables describing a set of capabilities are observed, we linked these variables to the following latent variable: fuel poverty in tropical areas. Then, the LCM methodology was used to carry out this research. Lighting, electricity security, cooking, water heating, quality of building insulation and cooling are criteria capabilities used to characterize fuel poverty in tropical areas. Based on these items, we first constructed binary classes of fuel poverty.

We identified the characteristics common to people belonging to the most energy-deprived class, i.e., "fuel poor". Facing problems with roof holes or moisture increases the probability of belonging to this class by 70%. Having access to only cold water increases the probability by 43%, and having no running water increases the probability by approximately 3.8%.

In contrast, having a cooling system increases the probability of belonging to the "non-fuel poor" class by 53%. We further our analyses by extending the common bi-dimension phenomena, and our results show that defining three categories of energy-deprived people is better than defining individuals as only fuel poor and non-fuel poor. The most deprived represent approximately 12% of the population, while 32% of the population is expected to belong to the non-fuel poor class (class 3). An intermediate class encompassing 56% of the population represents vulnerable households that could easily be impacted by an exogenous shock. Households belonging to the intermediate and non-fuel-poor classes share the following common features: on average, most households have access to hot water or protected electric installation. In contrast, vulnerable households, i.e., the intermediate class, remain exposed to roof holes or moisture and have no cooling systems. We conclude that restricting fuel poverty in tropical areas to a binary phenomenon leads to the neglect of the complexity of energy deprivation. Regarding policy recommendations, policy makers should first focus on providing cooling systems to fight fuel poverty. Moreover, using LMC, it is possible to identify the fuel poor in not only a sample but also a community using observable attributes. Thus, using local data could allow policy makers to adapt policies for people who suffer the most. This method is also flexible because it allows the government to adapt policies overtime without using a constant threshold measurement.

Finally, this research is clearly innovative as it proposes the application of capabilities to construct a categorization of the fuel poor and non-fuel poor rather than applying an existing definition that does not apply in tropical areas. Similar to previous studies, we ultimately divided the population into more than two groups and conclude that energy deprivation is much more complex and multidimensional than a binary phenomenon, implying that fuel poverty can be measured with different degrees of exposure.

Figure 1 :

 1 Figure 1: Path diagram of unconditional LCM of fuel poverty in tropical areas

  represents the complete model (including the measurement model and structural model).

Figure 2 :

 2 Figure 2: Path diagram of the complete LCM of fuel poverty in tropical areas (measurement and structural models)

Table 1 :

 1 Summary statistics

	Category	Variables	Whole sample	Guadeloupe	Martinique	Guyana		Reunion Island
			Mean	Std Dev	Mean	Std Dev	Mean	Std Dev	Mean	Std Dev	Mean	Std Dev
	Space heating and building insulation	No problem with roof holes or moisture	0.461	0.499	0.464	0.499	0.467	0.499	0.339	0.474	0.508	0.500
	Cooling	Presence of a cooling system	0.301	0.459	0.463	0.499	0.240	0.427	0.342	0.475	0.209	0.407
		Hot water supply	0.721	0.448	0.720	0.449	0.641	0.480	0.417	0.493	0.900	0.300
	Water heating	Cold water supply only	0.258	0.438	0.271	0.445	0.353	0.478	0.478	0.500	0.099	0.299
		No supply of water	0.020	0.141	0.009	0.094	0.005	0.074	0.105	0.307	0.001	0.035
		Butane/propane	0.624	0.485	0.777	0.417	0.481	0.500	0.675	0.469	0.583	0.493
		Electricity	0.279	0.449	0.182	0.386	0.418	0.493	0.252	0.434	0.273	0.446
	Cooking	Wood	0.084	0.277	0.024	0.155	0.093	0.291	0.034	0.182	0.140	0.347
		Other fuels	0.008	0.087	0.007	0.081	0.005	0.069	0.028	0.166	0.001	0.035
		No cooking system	0.006	0.079	0.010	0.100	0.003	0.058	0.011	0.103	0.003	0.057
	Electricity	Protected electrical installation	0.850	0.357	0.845	0.362	0.841	0.365	0.781	0.414	0.889	0.315
	Lighting	Good brightness level in the house	0.922	0.268	0.952	0.215	0.916	0.278	0.892	0.311	0.919	0.273
		Income	19608	18168	19398	17288	19968	16134	20327	22140	19229	18062
		Homeowner	0.551	0.497	0.607	0.489	0.566	0.496	0.441	0.497	0.549	0.498
		No children	0.580	0.494	0.642	0.480	0.678	0.468	0.477	0.500	0.521	0.500
	Other predictive variables	Diploma superior to a bachelors + 2 years	0.178	0.383	0.184	0.388	0.167	0.373	0.184	0.387	0.178	0.383
		City with more 50,000 inhabitants	0.701	0.458	0.762	0.426	0.682	0.466	0.570	0.495	0.724	0.447
		Constructed after 1999	0.273	0.446	0.282	0.450	0.214	0.410	0.247	0.432	0.314	0.464
		Individual housing unit	0.740	0.439	0.762	0.426	0.710	0.454	0.728	0.445	0.748	0.434
		Observations	6586		1675		1470		1024		2417

Note: A table of the correlations among the variables is available upon request

Table 3 :

 3 Estimated coefficients in the binary logit model of Q latent classes

	Class 1 Fuel poor	Class 2 Non-fuel poor
	Margin	Std. Err.	Margin	Std. Err.

Table 4 :

 4 Results of predictive variablesbase outcome: Class 1-fuel poor

	Coef.	Std. Err.
		No fuel poor

Table 5 :

 5 Class-specific marginal means or predicted probability

	Class 1	Class 2
	Fuel poor	Non-fuel poor
	Margin Std. Err.	Margin	Std. Err.

Table 6 :

 6 Comparison of models

			AIC	BIC	LL	df
	Model 1	2 classes	44203.67	44393.87	-22073.84	28
	Model 2	3 classes	43471.39	43783.85	-21689.69	46

Table 7 :

 7 Class-specific marginal means or predicted probability with 3 classes In general, there are poor building insulations and cooling systems. These last variables are the two main manifest variables explaining the probability of being fuel poor. There are also numerous uses of propane for cooking (21.3%) compared to the other classes. We cannot consider these households fuel poor, but we can consider them vulnerable to fuel poverty if their situation deteriorates in the future, e.g., through exogenous shock. Considering this new finding, it is possible to draw a profile of the households in each class. The members of fuel-poor households have a lower income than those of households that are non-fuel poor, do not have education diplomas or children, and live in old individual

	Class 1	Class 2	Class 3
	Fuel poor	Fuel vulnerable	Non-fuel poor
		households
	Margin Std. Err.	Margin	Std. Err.	Margin	Std. Err.

These results are interesting because our assumption is confirmed. The new intermediate class shows a median profile. These households have good brightness levels inside and mostly protected electrical installation.

Table 8 :

 8 Profile of the households in each latent class

		Class 1: fuel-poor	Class 2: fuel vulnerable	Class 3: households that
		households	households	are not fuel poor
	Items or	Problems with roof holes or	Problems with roof holes or	No problems with roof
	capabilities	moisture	moisture	holes or moisture
		No cooling system	No cooling system	Cooling system
		Wood cooking or no	Propane used for cooking	Propane used for cooking
		cooking system	Electricity used for cooking	Hot water supply
		Cold water supply or no	Hot water or cold water supply	Protected electrical
		water access	Protected electrical installation	installation
		Unprotected electrical	Good brightness level in the	Good brightness level in
		installation	house	the house
		Low brightness in the house
	Socio-	Low income	Medium income	High income
	demographic	Tenants	Homeowners	Homeowners
	characteristics	No education No children	High education level No children	High education level Families with children
		Living in rural areas	Living in a large city	Living in a large city
		Old buildings	Recently built houses	Recently built houses
		Individual housing units	Collective buildings	Collective buildings

Appendix

A.1 Results of the three latent classes

The regression coefficient means measure the effect of an increase of one percent in the m-th covariate (such as income) on the logit of belonging to class2with respect to the reference class (e.g., class 1).

A.2 Results of the three classes according to each overseas department


Bruno Chauvin
email: bruno.chauvin@unistra.fr

Etienne Mullet

Individual differences in paranormal beliefs: The differential role of personality aspects

Keywords: Personality, Big five aspect scales (BFAS), Belief in the paranormal, Confirmatory factor analysis, Path analysis

Personality is among the most studied correlates of belief in the paranormal. There is, however, some inconsistency in their association. The purpose of the present study was to provide a more clear view of how paranormal beliefs are associated with personality by (1) using a psychometrically sound instrument for assessing belief in the paranormal, and (2) investigating the differential role in paranormal beliefs of the two lower-level aspects of each Big Five domain. French citizens completed a modified version of the Revised-Paranormal Belief Scale and the Big Five Aspect Scales. A six-factor model of paranormal beliefs displaying strong psychometric properties was identified. Correlations between personality and paranormal beliefs were stronger at the aspect level than at the domain level. Consistent with our differential prediction hypothesis, the effect of one aspect was not the same as another aspect of the same broad domain of personality on belief in the paranormal. Withdrawal, Openness, Industriousness, and Assertiveness did a good job of predicting belief in the paranormal, while Volatility, Intellect, Orderliness and Enthusiasm were not predictors of such beliefs. Overall, these results emphasize the importance of considering lower levels of the personality hierarchy in attempting to understand paranormal beliefs.

Belief in paranormal phenomenadefined as anomalous experiences involving processes that in principle are physically impossible as well as outside the realm of human capabilities as presently conceived by conventional scientists [START_REF] Irwin | Belief in the paranormal: A review of the empirical literature[END_REF] is widespread around the world. According to Lindeman and Aarnio (2006), more than a third of Americans still believe in psychic powers and extrasensory perception (see also [START_REF] Irwin | The psychology of paranormal belief. A researcher's handbook[END_REF]. With such a prevalence of paranormal beliefs, attention has quickly begun to focus on the individual differences associated with such beliefs, including personality (see [START_REF] Irwin | Belief in the paranormal: A review of the empirical literature[END_REF]Irwin , 2009, for reviews), for reviews). Personality is among the most studied correlates of belief in the paranormal, probably because most of paranormal beliefs fulfill psychological needs which derive from specific patterns of personality traits and/or involve constructs conceptually related to personality. For example, religious (e.g., God existence) or superstitious (e.g., lucky charm) beliefs may provide more neurotic or less emotionally stable individuals with perceived control or resources for adjustment [START_REF] Irwin | Belief in the paranormal: A review of the empirical literature[END_REF][START_REF] Risen | Believing what we do not believe: Acquiescence to superstitious beliefs and other powerful intuitions[END_REF]). Beliefs about magical practices (e.g., witchcraft) or precognition (e.g., clairvoyance) fit fully with open-mindedness, fantasy proneness, or willingness to entertain unconventional values, all of which are characteristics typically associated with individuals high in Openness/ Intellect [START_REF] Saucier | Spiritual but not religious? Evidence for two independent dispositions[END_REF][START_REF] Smith | Personality contributions to belief in paranormal phenomena[END_REF].

What is disputed, however, is the magnitude of the relationship between personality and paranormal beliefs. Mixed evidence exists for every broad dimension of personality except for Agreeableness which is not associated with paranormal beliefs (e.g., MacDonald 2000). While some studies have found that paranormal believers score high in Neuroticism [START_REF] Wiseman | Measuring superstitious belief: Why lucky charms matter[END_REF], Openness/Intellect [START_REF] Saucier | Spiritual but not religious? Evidence for two independent dispositions[END_REF], Extraversion [START_REF] Thalbourne | Personality characteristics and sheep and goats[END_REF], and low in Conscientiousness (Zingrone et al. 1998-99), others, in contrast, have reported no such relationship between belief in the paranormal and Neuroticism [START_REF] Willging | Paranormal beliefs and personality scores of high school students[END_REF], Extraversion [START_REF] Williams | Personality and paranormal belief: A study among adolescents[END_REF], and Conscientiousness (MacDonald 2000), or even a negative relation with Openness/Intellect [START_REF] Swami | Psychology in outer-space. Personality, individual difference, and demographic predictors of beliefs about extraterrestrial life[END_REF].

Of course, inconsistency in the association between the broad-bandwidth dimensions of personality and paranormal beliefs may in part derive from differences in how studies had operationalized these constructs [START_REF] Rattet | Investigating the personality correlates of paranormal belief and precognitive experience[END_REF]. On this point, a major concern has been, and still is, related to the Revised-Paranormal Belief Scale (R-PBS, [START_REF] Tobacyk | A revised paranormal belief scale[END_REF]). Despite its widespread use across the world to assess the pattern of paranormal beliefs for a population and to examine relationships between such beliefs and various psychological features (e.g., Lindeman et al. 2015), the R-PBS has come under criticism on various psychometric fronts. First, there is a considerable debate concerning the correct dimensionality of the R-PBS. Whereas some researchers (e.g., [START_REF] Tobacyk | A revised paranormal belief scale[END_REF]) has consistently advocated seven orthogonal factors (Traditional Religious Belief, Psi belief, Witchcraft, Superstition, Spiritualism, Extraordinary Life Forms, and Precognition), others have counter-argued in favor of five oblique factorsin particular with a mixed spiritualism-psi factor (e.g., Lawrence et al. 1997), or six relatively independent factors [START_REF] Utinans | Paranormal beliefs of Latvian college students: A Latvian version of the revised paranormal belief scale[END_REF]. Still other researchers (e.g., Lindeman and Aarnio 2006) have more specifically examined whether the paranormal belief factors are manifestations of one higher-order construct or whether they express independent dimensions. Having observed high intercorrelations between factors, they showed that these beliefs could be best described by one higher-order factor indicating a general tendency to believe in paranormal phenomena. Another concern is related to the psychometric properties of the R-PBS. A less than acceptable fit between observed data and model (as recommended by Hu and Bentler 1999) has been reported for the R-PBS, regardless of the tested version (see Lawrence et al. 1997, or Utinans et al. 2015, for details). Several items had low loadings (i.e. <.40) on their intended factor (e.g., Bmind reading is not possible^); other items were associated with unjustified cross-loadings (e.g., Bthe soul continues to exist though the body may die^); still other items failed to reflect their latent construct (e.g., Bthere is life on other planets^ does not look like it taps into Extraordinary Life Forms) (see Lange et al. 2000, for details). Reliability estimates for the superstition and extraordinary life forms subscales have proven to be less than sufficient (Cronbach's α coefficients < .70 or even .60) [START_REF] Aarnio | Paranormal beliefs, education, and thinking styles[END_REF]Lange et al. 2000). In sum, key concerns about the dimensionality and the psychometric properties of the R-PBS have consistently been raised in the literature.

Additionally, another plausible explanation could be that the lower-level components of each broad dimension of personality as developed by De [START_REF] De Young | Between facets and domains: 10 aspects of the big five[END_REF] have distinct relationships with belief in the paranormal and most of its components. In their study, they showed that each of the five broad dimensions can be decomposed into two narrower aspects representing related but separable traits. The lower-order aspects of Neuroticism are Withdrawalcorresponding to anxiety, fearfulness, and vulnerability, and Volatilitycorresponding to emotional lability and irritability. For Openness/ Intellect, the two aspects are Opennessas characterized by fantasy, imagination, and artistic values, and Intellectas characterized by quickness and ingenuity. The two aspects of Conscientiousness are Industriousnessencompassing traits like purposefulness, self-discipline and deliberation, and Orderlinessencompassing traits like order and perfectionism. The lower-order aspects of Extraversion are Assertivenesscorresponding to agency, social dominance, and provocativeness, and Enthusiasmcorresponding to gregariousness and sociability. The lower-order aspects of Agreeableness are Compassioncorresponding to warmth and sympathy, and Politenesscorresponding to cooperation and straightforwardness. Consistent with this breakdown, we argue that, conceptually, belief in the paranormal involves constructs that do not correspond well to this or that personality dimension as a whole but fit better with one lower-level aspect of each broad dimension (over the other). Specifically, previous research (e.g., [START_REF] Irwin | Belief in the paranormal: A review of the empirical literature[END_REF][START_REF] Saucier | Spiritual but not religious? Evidence for two independent dispositions[END_REF] has consistently stated that paranormal beliefs (especially spiritual beliefs like reincarnation) may provide a buffer against mortality-based anxiety and thus enhance a sense of safety and security, which is much more connected with the withdrawal aspect of Neuroticism than with its volatility aspect. In addition, most of paranormal beliefs (ranging from belief in ghosts, witches, and extraordinary life forms to astrology and clairvoyance) appear to be both inherently and empirically much closer to the openness aspect of Openness/ Intellect (as characterized by fantasy proneness and imagination) than to its intellect aspect [START_REF] De Young | Ten aspects of the big five in the personality inventory for DSM-5[END_REF][START_REF] Irwin | Belief in the paranormal: A review of the empirical literature[END_REF]. Another key feature of paranormal believers is their high intuitiveness; that is, the tendency to rely heavily on their intuitive impressions or personal experiences and to engage more in intuitive thinking than in analytic thinking for processing information [START_REF] Aarnio | Paranormal beliefs, education, and thinking styles[END_REF][START_REF] Risen | Believing what we do not believe: Acquiescence to superstitious beliefs and other powerful intuitions[END_REF]). The intuitive mode of thinking coincides much more with the (low) industriousness aspect of Conscientiousness which consists of traits such as (low) purposefulness and (low) deliberation than with its (low) orderliness aspect. Finally, paranormal beliefs such as psi beliefs (e.g., psychokinesis) or precognition (e.g., ability to predict the future) challenge the conventional view about human's cognitive limitations by assigning supernatural skills to some superior beings. As such, these beliefs are more likely to represent the tendency toward provocativeness and social dominanceboth of which are traits from the assertiveness aspect of Extraversion, than the tendency toward social affiliation (Kennedy 2005).

Accordingly, the purpose of the present study is to provide a more clear view of how people's paranormal beliefs are associated with their personality. Given both reliability and validity of the R-PBS represent required conditions to examine relationship between the personality characteristics of individuals and their endorsement of paranormal beliefs [START_REF] Brown | Confirmatory factor analysis for applied research[END_REF], our first aim is to identify an alternative factor structure which represents a psychometrically sound version of the R-PBS. Our second aim is to investigate whether such relationship depends on the content of the personality measure, in particular what lower-level aspect of the personality dimension (as defined by De [START_REF] De Young | Between facets and domains: 10 aspects of the big five[END_REF]) is under consideration (except for Agreeableness for which no relationship is expected). Our first hypothesis is that stronger correlations between personality and paranormal beliefs will appear at the aspect level than at the Big Five level. Our second hypothesis states that the two lower-level aspects of each dimension will differentially predict belief in the paranormal, such that the effect of one aspect will not be the same as another aspect. Specifically, Withdrawal, Openness, Industriousness, and Assertiveness will better predict paranormal beliefs than will Volatility, Intellect, Orderliness, and Enthusiasm, respectively.

Method Participants and Procedure

Our sample consisted of 767 French citizens. They were 388 women and 379 men, ranging from 15 to 87 years (M = 38.2, SD = 16.6). These people were recruited as follows: they were contacted during daylight hours in the main streets of Nantes, a town of half-a-million inhabitants located in the west of France. The individuals approached were told that our research team was conducting a survey on belief in paranormal phenomena and were given some examples of the questions.

Data were collected individually during at-home sessions where each participant was asked to complete a French version of two questionnaires. In designing the French version, the authors followed the guidelines proposed in the literature on cross-cultural methodology [START_REF] Brislin | Some methodological concerns in intercultural and cross-cultural research[END_REF]: independent/ blind/back-translation, educated translation, small-scale pretests. A translation was executed by two bilingual translators. A first bilingual translated the English items into French, with feedback from the first author of the paper (BC). Next, a second bilingual blindly performed the back-translation from French to English. This process was reiterated until both English versions were close enough in meaning to consider that the French version was a good translation of the original English version (iterative back-translation). After the process was completed, the French version was field-tested on a small scale to insure that future participants comprehend all items.

Materials

Paranormal beliefs were measured with a modified version of [START_REF] Tobacyk | A revised paranormal belief scale[END_REF] 26-item version of the R-PBS. The R-PBS is a short scale typically used to assess belief in paranormal phenomena. It provides a self-reported measure of degree of belief in seven dimensions (Traditional Religious Belief, Psi, Witchcraft, Superstition, Spiritualism, Extraordinary Life Forms, and Precognition) which allows the researcher to examine the nature of these beliefs and their relations with various psychological constructs. Reliability indices (Cronbach's α) are not reported in [START_REF] Tobacyk | A revised paranormal belief scale[END_REF]; they ranged from .60 to .87 in [START_REF] Rattet | Investigating the personality correlates of paranormal belief and precognitive experience[END_REF] study and from .53 to .88 in [START_REF] Aarnio | Paranormal beliefs, education, and thinking styles[END_REF] study. In the present study, the R-PBS was supplemented with additional items. The rationale for including new items was that the psychometric properties of the R-PBS have been challenged in many studies (see above for details). Based on content-related considerations, and on satisfactory measurement parameters as well (e.g., high loadings, high reliability values), a set of seven items purposely selected to be semantically close to the original ones was added. Four of them were taken from [START_REF] Sjöberg | Risk perception and new age beliefs[END_REF] scale of paranormal beliefs (Bghosts exist^, Bpeople are reborn and learn something new in each life^, Bflying saucers do exist^ and Bthere are clairvoyants who can see what is happening in another place^). All of them did a good job as components of a belief in the paranormal factor (labelled Reality of the soul) by contributing to the high reliability (Cronbach's α) value for this scale. In the same vein, prior research has shown that items on belief in the possibility of contact with spirits and in life after death had strong loadings (.63 and .62, respectively) on a belief in the afterlife factor [START_REF] Thalbourne | A new instrument for measuring the sheep-goat variable: Its psychometric properties and factor structure[END_REF]. In addition, three other items were generated (Bcarrying a lucky charm is protecting from misfortunes^, Bconducting archeological excavations of the pyramids can bring bad luck^, and Bduring dark nights, spirits sometimes are appearing^). We opted for these items because (1) there are no items in the R-PBS on beliefs in amulets, rituals, or spirits (Lindeman and Aarnio 2006) while they are among the most popular paranormal beliefs (see [START_REF] Vyse | Believing in magic: The psychology of superstition[END_REF], for a review); (2) once generated, items on beliefs in amulets or rituals were associated with good reliability values in Lindeman and Aarnio's (2006) study. All participants completed the entire questionnaire. They were asked to rate the items on an 11-point scale where 0 denoted total disagreement and 10 total agreement.

The Big Five Aspect Scales (BFAS; De Young et al. 2007) was used to measure personality. It is a 100-item self-report measure designed to assess each of the Big Five factors of personality as well as two lower-level aspects of each of them. This measure asked participants to describe themselves according to statements rated on a 5-point scale ranging from 1 (very inaccurate) to 5 (very accurate). Specifically, 195 participants were presented with the 20 items of Neuroticism, 174 participants with the 20 items of Openness/Intellect, 180 participants with the 20 items of Conscientiousness, 118 participants with the 20 items of Extraversion, and 100 participants with the 20 items of Agreeableness. 1 High correlations between each BFAS factor and its counterpart from various Big Five inventories (e.g., the NEO-PI-R, [START_REF] Costa | NEO PI-R Professional Manual[END_REF] have been reported, thus providing evidence for validity of the BFAS [START_REF] De Young | Between facets and domains: 10 aspects of the big five[END_REF]. In this study, reliability (Cronbach's α) ranged from .72 to .87 for the factors and from .67 to .83 for the aspects (see Table 3 for details). Comparable values have been reported by De [START_REF] De Young | Between facets and domains: 10 aspects of the big five[END_REF]. Correlations between the two aspects within each factor of personality were varied (ranging from .11 between Openness and Intellect to .55 between Withdrawal and Volatility) and quite similar to those reported by De [START_REF] De Young | Between facets and domains: 10 aspects of the big five[END_REF].

Data Analysis

All analyses were performed using Mplus [START_REF] Muthén | Mplus User's Guide (7 th edition)[END_REF][START_REF] Muthén | Mplus User's Guide (7 th edition)[END_REF]. 2 We used Confirmatory Factor Analysis (CFA) to test and compare the fit of a number of competing structural configurations of the RPB-S. There were no missing data in any of the subsamples, likely due to the fact that data were collected individually during at-home sessions. For most items, the univariate distribution of the scores differed from no rma l ity ( ske w ne ss a nd/o r k u rtosis v a lu es >1 .0 ). Additionally, the multivariate skew and kurtosis tests of fit were both significant (p < .001), revealing a deviation from multivariate normality. Therefore, we estimated the model fit using a Maximum Likelihood estimator (abbreviated MLM in Mplus) with standard errors and a Chi-square statistic that are robust to non-normality [START_REF] Brown | Confirmatory factor analysis for applied research[END_REF]). The MLM Chi-square test statistic is also referred to as the Satorra-Bentler Chi-square (S-Bχ 2 ). In addition, we followed common practice in using multiple indices of fit and their cut-off values [START_REF] Hu | Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives[END_REF]; that is, the comparative fit index (CFI) and the Tucker-Lewis fit Index (TLI) (good fit when values are close to .95), along with the Root Mean Square Error of Approximation (RMSEA) and the Standardized Root Mean Square Residual (SRMR) (excellent fit when values are .05 or lower).

To examine the relationship between personality and paranormal beliefs, bivariate correlation and path analyses were conducted. Specifically, to test the differential prediction hypothesis, we conducted a series of four path analyses (one per Big Five factor, except for Agreeableness). For each path model, the direct effects of both aspects of each personality factor on belief in the paranormal were estimated. We then tested the difference in the standardized path coefficients (betas) for significance. As recommended by [START_REF] Brown | Confirmatory factor analysis for applied research[END_REF] 1 Participants were presented with only one set of personality items (corre-for non-normality, p-values and 95% confidence intervals (CI) of the betas as well as the difference tests (diff test) were obtained by means of 2000 bootstraps. 3Data Availability The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Results

Structure of the R-PBS

We tested a number of competing models of the R-PBS's factor structure. The first two models were the traditional 7factor model (which consisted of the 26 original itemssee Tobacyk 2004, for details) and its 6-factor alternative model (with a combination of Psi and Spiritualism into one factor). Both models were found to provide a less than acceptable fit to the data with values for CFI, TLI, RMSEA and SRMR that were outside the recommended cut-offs. Fit statistics for these models (and the following ones) are shown in Table 1.

Therefore, based on the aforementioned criticism of the RPB-S (see introduction), we investigated a new six factor conceptualization of paranormal beliefs in which Psi and Spiritualism were combined into one factor and which consisted of 21 items. Fourteen items were taken from the R-PBS (while the 12 remaining problematic items were excluded, e.g., Bmind reading is not possible^ or Bthere is life on other planets^) and seven items were new ones. Table 2 presents the model.

Fit indices indicated an excellent fit of this 6-factor model of paranormal beliefs to the data. All primary factor loadings were above .50 and significant at p < .01. Reliability was acceptable for two factors (Extraordinary Life Forms and Superstition) and good or very good for the other factors. Cross-scale correlations showed that the six paranormal belief factors were positively as well as moderately to highly correlated to each other (.43-.82). This pattern of correlations provided empirical support to proceed with a higher-order factor analysis. In this analysis, a single second-order factor indicating a general tendency to believe in paranormal phenomena was specified to account for the correlations among the six factors. The fit of the higher-order factor model was both excellent and equivalent to the fit of the 6-factor model (non-significant difference in S-B Chi-square values). This therefore supported the legitimacy of representing our six paranormal belief factors by a general index of paranormal belief, as did its excellent reliability (α = .92).

sponding to one factor) for practical reasons (e.g., length of the full questionnaire). There were no significant differences between the five subsamples regarding gender (Pearson Chi-square = .93, p = .92), age (F(4,762) = 1.07, p = .37) and belief in the paranormal (Tukey's HSD Post-Hoc test for unequal sample sizes revealed no significant pairwise comparison at p < .01). 2 Path diagrams were designed with AMOS 22. df = degree of freedom. ΔS-Bχ 2 = scaled difference between the two nested model (hierarchical and new 6-factor) S-Bχ 2 values: as the difference test is non-significant, the fit of the two tested models is considered as equivalent

Relationships between Personality Factors and Aspects and Paranormal Beliefs

Table 3 shows the zero-order correlations between personality factors and aspects and belief in the paranormal.

Inspection of this table provides strong support for our first hypothesis. For each broad domain of personality (except for Agreeableness for which no significant relationship was observed), either aspect had a higher correlation with the general index of paranormal belief than the factor. The same was true for the paranormal belief factors. The broad neuroticism factor had a lower (positive) correlation with spiritualism and psi beliefs and superstition than its withdrawal aspect. The (positive) correlations of the broad openness/intellect factor with traditional religious beliefs and precognition, as well as spiritualism and psi beliefs and witchcraft, were lower than its openness aspect. The broad conscientiousness factor correlated (negatively) with all paranormal belief factors less strongly than its industriousness aspect. The (positive) correlations of the broad extraversion factor with superstition and witchcraft were lower than its assertiveness aspect. All significant correlations were small to medium in magnitude (ranging from .15 to .30).

Our second hypothesis posited that the two lower-level aspects of each broad dimension would differentially predict belief in the paranormal. Based on the significant correlations reported in Table 3, we conducted four path analyses to test direct effects of the two aspects within each Big Five domain (except for Agreeableness) on both the general index and factors of paranormal belief. Figure 1 illustrates the resulting path models for the four broad dimensions of personality.

In the path model for the neuroticism domain (Fig. 1, diagram A), from 3 to 6% of the variance was explained in paranormal belief. Of the two aspects, we observed only significant direct effects from Withdrawal, not from Volatility. Within the openness/intellect domain (diagram B), both aspects accounted for 3 to 8% of the variance in paranormal belief. However, one can see that only the openness aspect had significant direct effects on the general index and four paranormal belief factors, not the intellect aspect. The path model for the conscientiousness domain explained from 4 to 8% of the variance in paranormal belief (diagram C). Only the industriousness aspect had significant direct effects on belief in the paranormal. Within the extraversion domain (diagram D), the two aspects contributed to explaining from 4 to 9% of the variance in paranormal belief. Again, only one aspect, namely Assertiveness, had significant direct effects on belief in the paranormal, not the other one (enthusiasm).

Table 4 shows the detailed statistics for the path modeling of each Big Five domain.

As predicted, in every case, the aspects differentially predicted belief in the paranormal; and, in most cases, the difference test was significant. So, hypothesis 2 may be considered as mostly supported by the data. Specifically, the general index and two factors of paranormal belief were positively and significantly predicted by Withdrawal but not Volatility. Openness but not Intellect emerged as a positive and significant predictor of the general index and four factors of paranormal belief. The general index and four factors of paranormal belief were negatively and significantly predicted by Industriousness but not Orderliness. Finally, the general index and two factors of paranormal belief were positively and significantly predicted by Assertiveness but not Enthusiasm. Across personality domains, the variance explained in paranormal belief was R 2 = 9% at best, indicating that the combined effects of both aspects of each personality domain were modest. 4 for detailed findings

Discussion

The first aim of this study was to identify a psychometrically sound structure of paranormal beliefs, which is a requirement for properly examining the paranormal belief-personality relationship. This step was needed because there is no consensus, but concern, about the construct validity of the leading assessment tool of such beliefs, the Tobacyk's ( 2004 1997). Empirically, compared to the traditional 7-factor model of the R-PBS, this new 6-factor model is associated with better psychometric properties. In addition, the moderate to strong correlations among the six factors allowed us to test and highlight one higher-order factor representing a general tendency to believe in paranormal phenomena. This result is fully in line with the finding from Lindeman and Aarnio's (2006) study of the dimensionality of paranormal beliefs. These authors have brought together a range of beliefs (including paranormal beliefs) and have shown that these beliefs could be best described by one higher-order factor (labelled Magico-religious beliefs), indicating a general tendency to believe in paranormal phenomena.

Having highlighted a valid model for measurement of paranormal beliefs, we were then in a position to pursue the second aim of our study which was to clarify the understanding of the association between personality and belief in the paranormal. Namely, though the Big Five factors are among the most important correlates of paranormal beliefs [START_REF] Irwin | The psychology of paranormal belief. A researcher's handbook[END_REF][START_REF] Smith | Personality contributions to belief in paranormal phenomena[END_REF]), previous studies have been mixed with regard to the magnitude of their relationships (e.g., Wiseman and Wa t t 20 04 , v er su s Wil lging a nd Lester 19 97 , f o r Neuroticism). To explain it, we argued that some lower-level aspects of the Big Five factors (as defined by De [START_REF] De Young | Between facets and domains: 10 aspects of the big five[END_REF]) are more conceptually and empirically related to paranormal beliefs than are others. Accordingly, we expected (hypothesis 1) and found that in each broad domain of personality (except for Agreeableness for which, as expected, no significant relationship was observed), one aspect correlated with the general index of paranormal belief as well as paranormal belief factors more strongly than the factor. This finding can clarify some inconsistent results found in the literature (e.g., see [START_REF] Rattet | Investigating the personality correlates of paranormal belief and precognitive experience[END_REF]. For the most part, research has adopted an omnibus approach to investigate the relations between paranormal beliefs and personality dimensions using various and broadband measures of personality (e.g., MacDonald 2000; [START_REF] Williams | Personality and paranormal belief: A study among adolescents[END_REF]. Relying only on one broad measure of personality would weaken or maskin some, but not all, studies (as a function of the measure employed)some of these relations. To our knowledge, this is the first time that such an explanation is offered for clarifying the apparent incompatibility of findings in the personalityparanormal belief relationships.

Along similar lines, we made a differential prediction hypothesis such that the effect of one aspect would not be the same as another aspect. Consistent with this second hypothesis, our resu lts sho wed th at Withd rawal, Open nes s, Industriousness, and Assertiveness did a good job of predicting belief in the paranormal, while Volatility, Intellect, Orderliness and Enthusiasm were not predictors of such beliefs. That is, the more the individuals scored high on the withdrawal, openness, or assertiveness aspect, or the less they considered themselves as industrious, the more they believed in the paranormal. Collectively, these findings are consistent with some past research (e.g., [START_REF] Aarnio | Paranormal beliefs, education, and thinking styles[END_REF]Kennedy 2005;[START_REF] Saucier | Spiritual but not religious? Evidence for two independent dispositions[END_REF]. More importantly, by showing that the De Young et al. ( 2007) aspects of each personality dimension differentially predict paranormal beliefs, this study helps in the understanding of a large number of empirical inconsistencies in the relationships between these variables. From a practical standpoint, our findings emphasize the importance of considering lower levels of the personality hierarchy in attempting to understand paranormal beliefs. This is a major thrust of our study because, as far as we know, it represents the first attempt to document the relationship between personality and belief in the paranormal at an intermediate level of personality structurebetween the narrow facets and the broad domains. As a whole, our study extends the recent literature on the merits of considering both broad and narrow representations of each Big Five domain in understanding and predicting personality-related criteria (e.g., De [START_REF] De Young | Ten aspects of the big five in the personality inventory for DSM-5[END_REF].

This study suffers, however, some limitations. First, the direct effects of the ten aspects of the Big Five on paranormal belief could not be simultaneously tested since, for practical reasons, the participants were presented with only one set of personality items corresponding to only one factor and its two lower-level aspects. As a result, it was impossible to generate the complete personality profile of the high paranormal believer (based on the combination of key personality aspects from every broad dimension) mainly because of the possible overlap in variance explained by several aspects. More extensive research using a within-subject design is needed to identify such personality profiles. A second limitation, and also an area for future research, is to include a number of important correlates of paranormal beliefs as potential moderators of the relations between personality factors and aspects and belief in the paranormal. One possible moderator is gender because a myriad of studies have shown that women tend to have more paranormal beliefs than men (e.g., [START_REF] Irwin | Belief in the paranormal: A review of the empirical literature[END_REF]Lange et al. 2000). Another interesting moderator could be the cognitive thinking styles because they have repeatedly been shown as important predictors of paranormal beliefs (e.g., Lindeman and Aarnio 2006). Third, although not the scope of the current paper, investigating paranormal beliefs as they relate to the Big Five facetsan even more narrow level of personality structurewould be a fruitful avenue of future research to explore in greater depth the paranormal belief-personality relationships. Fourth, although the results of the study supported the expected patterns of paranormal belief-personality relationships, it should be noted that the strength of association between personality and belief in the paranormal was quite small in many cases. Replication of the present study using a within-subject design (limitation 1), including some important moderators (limitation 2), and measuring personality at the facet level (limitation 3) could provide stronger support for the relationships reported in the current study.

To conclude, this study addressed some key concerns raised in the literature on the R-PBS by identifying an alternative and psychometrically sound structure of paranormal beliefs. This study also provided a more clear view of how people's paranormal beliefs are associated with their personality, by highlighting the differential role of lower-level aspects of each Big Five factor in paranormal beliefs. Only one of the two aspects within each of the Big Five predicts differences in paranormal beliefs, not the other one. Specifically, the withdrawal, openness, industriousness, and assertiveness aspects (of Neuroticism, Openness/Intellect, Conscientiousness and Extraversion, respectively) did a good job of predicting belief in the paranormal, while the volatility, intellect, orderliness and enthusiasm aspects were not predictors of such beliefs. T his c ontributes to refine our understanding of how and why people believe in paranormal phenomena, even though future work is needed to fully understand such beliefs. More broadly, using lower-level constructs of personality traits could be very helpful to disentangle, and thus better understand associations between personality and a wide variety of psychological phenomena.

Fig. 1

 1 Fig. 1 Path models for Neuroticism (diagram A), Openness/Intellect (diagram B), Conscientiousness (diagram C) and Extraversion (diagram D). The values above one-headed arrows are standardized direct effects (β), the values at double-headed arrows are correlations (r), and numbers above the rectangles reflect the amount of explained variance (R 2 ) of the associated variable by the combination of both aspects. Only significant direct effects (at least at p < .05) are shown. Refer toTable 4 for detailed findings

  ) R-PBS(Lange et al. 2000; Lindeman and Aarnio 2006). Based on the literature, we tested and provided support for a 6-factor model of the R-PBS with a combination of Psi and Spiritualism into one factor and which consisted of 21 items. Conceptually, this merger makes sense because the two factors may reflect the same human paranormal ability; namely, mind over matter. It is also congruent with existing evidence that has indicated a possible mix between these two factors (e.g., Lawrence et al.

Table 1

 1 Fit Indices for Various Models of Paranormal Beliefs

	Models

Table 2

 2 Standardized Factor Loadings (Standard Errors), Reliability [α], and Cross-scale Correlations of the New 6-factor Model of Paranormal Beliefs

	Factors

Ba^ marked items stem from the R-PBS; Bb^ marked items stem from

[START_REF] Sjöberg | Risk perception and new age beliefs[END_REF]

, non-marked items are new ones

Table 3

 3 Correlations between the Big Five Factors and Aspects and Paranormal Beliefs(Factors and General Index)

		Paranormal beliefs
	Big Five factors/aspects	Spiritualism	Supers-	Extraordinary	Witchcraft Traditional	Pre-	General Index
		and Psi beliefs	tition	Life Forms		Religious Beliefs	cognition
	Neuroticism [.86] (N = 195)	.18*	.15*	.03	.03	.00	.08	.10
	Withdrawal [.79]	.24**	.20**	.05	.07	.02	.13	.16*
	Volatility [.80]	.08	.06	.00	-.02	-.02	.02	.02
	Openness/Intellect [.72] (N = 174) .16*	-.03	.06	.12	.24**	.11	.15*
	Openness [.68]	.20**	.03	.00	.26**	.27**	.19*	.23**
	Intellect [.71]	.04	-.08	.08	-.08	.08	-.02	.00
	Conscientiousness [.87] (N = 180) -.17*	-.19*	-.18*	-.19**	-.02	-.04	-.17*
	Industriousness [.83]	-.21**	-.21**	-.21**	-.24**	-.12	-.14	-.26**
	Orderliness [.78]	-.09	-.12	-.11	-.10	.09	.07	-.05
	Extraversion [.77] (N = 118)	.15	.25**	-.03	.16	.17	.10	.17
	Assertiveness [.69]	.16	.30**	.03	.21*	.18	.16	.21*
	Enthusiasm [.69]	.10	.14	-.06	.08	.11	.02	.08
	Agreeableness [.73] (N = 100)	.04	-05	-.17	.-01	-.07	.11	-.02
	Compassion [.75]	.10	-.02	-.14	.01	-.09	.13	.01
	Politeness [.67]	-.03	-.06	-.13	-.02	-.02	.05	-.04
	Reliability [α] of the Big Five factors and aspects is given in brackets
	*p < .05; **p < .01

Bootstrapping is a resampling procedure in which multiple random samples are generated from the original data set. Because bootstrap results (e.g., parameter estimates, standard errors) are averaged across the number of bootstrapped samples -2000 in the present studythey are likely to yield more accurate estimates.

Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Informed Consent Informed consent was obtained from all individual participants included in the study.

Conflict of Interest

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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