Erkin Diyarbakirlioglu
email: ediyarbakirlioglu@gsu.edu.tr

A Portfolio Diversification Index Analysis of the Home Bias Current version: March 2011

Keywords: Portfolio diversification index, Home bias, Diversification

This paper implements a parsimonious and practical methodology to examine the diversification potential of international equity portfolios. The analysis shows that the Portfolio Diversification Index (Rudin, A.M., and Morgan, J.S., Journal of Portfolio Management [2006]) efficiently replicates a number of stylized facts associated to home bias and local investors' preference for geographically proximate destinations over a sample of 8 developed countries.

INTRODUCTION

Diversification is central to portfolio analysis. Since the development of the modern portfolio theory, it is well known that the diversification potential represented by a particular portfolio pool depends closely on the correlation structure: The weakest are the correlations between the portfolio's various constituents, the higher is the diversification potential provided by the considered investment set.

Another well-known result is that investors worldwide typically hold poorly diversified portfolios as they consider a practically limited scope among the set of all investable assets, an observation that particularly holds at an international scale. This so-called home bias in international portfolio investments is well documented by [START_REF] French | Investor Diversification and International Equity Markets[END_REF], [START_REF] Lewis | Trying to Explain Home Bias in Equities and Consumption[END_REF], and [START_REF] Karolyi | Are Financial Assets Priced Locally or Globally?[END_REF], among others. Indeed, as long as international portfolio diversification provides potentially profitable risk-return tradeoffs for stock market investors compared to domestic strategies (see, among others, [START_REF] Baele | Time-Varying Integration and International Diversification Strategies[END_REF], [START_REF] Driessen | International Portfolio Diversification Benefits: Crosscountry Evidence from a Local Perspective[END_REF]), limiting one's portfolio within locally traded stocks is perceived as an irrational behavior and likely to involve more or less important opportunity costs due to overlooking foreign markets. This paper's main objective is to reveal out these opportunity costs due to the global under-diversification of equity portfolios. Doing so, I implement an alternative technique, the portfolio diversification index (PDI), recently proposed by [START_REF] Rudin | A Portfolio Diversification Index[END_REF]. Briefly, the PDI provides a methodology that resumes the diversification potential of a given investment set via a single statistic by only making use of the information inherent to the correlation matrix of returns through a principal components analysis (PCA). Indeed, as noted by [START_REF] Rudin | A Portfolio Diversification Index[END_REF], the direct exploitation of the correlations between stock returns could be highly inefficient for portfolio analysis purposes even when the investor has to deal with a medium-sized portfolio of, say, 30 stocks, which requires the analysis of 435 different correlation coefficients. In contrast, the PDI technique constitutes a relatively parsimonious framework that can be easily implemented by practitioners.

In particular, I implement the PDI analysis to highlight the effects of home bias on the diversification potential of international stock portfolios from the perspective of investors in major developed countries (G7 countries and Australia). Based on prior research, I assume that investors exhibit equity home bias using two different portfolio selection schemes. First, investors can hold disproportionately high proportions in local stocks, thereby altering the underlying diversification scheme of their aggregate investment portfolio. Second, even though investors consider foreign markets, they are doing so in such a way that they prefer geographically close markets to their home market (see, for example, [START_REF] Lane | International Investment Patterns[END_REF], [START_REF] Portes | The Determinants of Cross-Border Equity Flows[END_REF]), a practice that ultimately mitigate the diversification potential of the international portfolio. The results show that the PDI technique can effectively take into account the effects of these investment practices, as well as the opportunity costs involved by holding poorly diversified international portfolios.

The organization of the paper is as follows. The next section is a brief overview of the PDI methodology. Section 3 shows how the PDI can be efficiently used to reveal out the diversification costs due to the home bias in international equity portfolios. Sections 4 and 5 provide two further examples regarding the implementation of the PDI technique. Specifically, I analyze the effects of local investors' preference for geographic proximity on international portfolio investments and the marginal declining value of international portfolio diversification. Section 6 concludes.

THE PORTFOLIO DIVERSIFICATION INDEX

Let ! be a matrix consisting of ! independent observations on a 1×! dimensional vector

! !• = ! !! ! !" ⋯ ! !! such that ! ! = ! ! ! ! ⋯ ! ! . Let ! ! ! denote the minor-product
moment and ! a transformation matrix consisting of the eigenvectors of ! ! !. Statistically, the principal components of the matrix ! are linear transformations of the form ! = !", designed to reduce the dimensionality of the original matrix ! while retaining a maximal portion of the variation described by the minor-product moment matrix of the raw data. Mathematically, the eigenvalues and eigenvectors of the matrix ! ! ! satisfy the following system of linear equations,

! ! !! ! = ! ! ! ! for ! = 1, … , ! (1)
Since by construction ! ! ! is positive definite and symmetric, the eigenvectors ! ! are all mutually orthogonal and ordered by declining variance ! ! ≥ ⋯ ≥ ! ! . The resulting matrix of principal components are complex linear combinations of the original matrix ! ! !, weighted by the mutually orthogonal eigenvectors ! ! . Due to the declining order of the eigenvalues, the first component captures the largest part of the variance in the data, the second one captures the largest part of the remaining variance component and so on for the remaining components.

Formally, we can express the fraction of the total variance due to the !th component by,

! ! = ! ! ! ! ! !!! (2)
such that the sum of component weights is always equal to 1.

Since eigenstructures play a central role in reorienting an original data space with correlated dimensions to uncorrelated axes, principal components analysis can also be of practical interest in portfolio selection because it technically allows to replace a large number of correlated variables by a smaller number of uncorrelated ones with negligible loss of information. Indeed, correlation or covariance matrices, both central to portfolio analysis, can be considered as special cases of the minor-product moment matrix given above with the desirable properties of being both positive definite and symmetric.

Making use of this dimension-reduction method, [START_REF] Rudin | A Portfolio Diversification Index[END_REF] have recently proposed the portfolio diversification index (PDI), a formula resuming within one single statistic the diversification potential likely to be provided by a given investment set. Specifically, for a set of ! securities for which historical return data is available, the PDI is defined as follows,

!"#$%"&'" !"#$%&"'"()*"+, !"#$% = 2 • ! • ! ! -1 ! !!! (3)
with ! ! defined as above. According to this formulation the PDI is defined as the center of mass of the component weights vector. Thus, it resumes the extent to which the vector ! is front-loaded, providing a concise measure of the potential diversification scheme likely to be obtained using the portfolio pool of interest. As underlined by [START_REF] Rudin | A Portfolio Diversification Index[END_REF], the PDI formula has a number of useful interpretations. First, it is numerically bounded within the continuous interval 1, ! . If the PDI is equal to 1, then the entire variation is attributed to only one component and the portfolio is completely non-diversified.1 Second, if the PDI is equal to !, i.e. if ! ! ≈ 1 !, then portfolio provides the ideal diversification scheme since it implies that the elements of the vector of component weights are all equal to each other, suggesting a powerful orthogonal structure across different portfolio constituents. In practice, the decision rule is simply to prefer the portfolio yielding to the highest PDI score.

PDI APPROACH TO THE EQUITY HOME BIAS

In this section, I show how the PDI technique can be implemented to replicate the opportunity costs associated to home bias in international equity portfolios from the viewpoint of local investors in different countries. I use a dataset consisting of monthly returns from 48 investable market indices in USD terms with dividends reinvested, from January 1998 to December 2007.

This also constitutes the international portfolio pool through which local investors in developed countries (i.e. G7 countries and Australia) can choose to diversify their equity portfolios. Exhibit 1 provides the sample means, standard deviations and correlations.

[Insert Exhibit 1 about here]

The last three columns show the average correlations between the returns on these eight sample countries and other countries included into the international portfolio pool. For example, the average correlation of the United States with the remaining 47 countries is 51.9%. Also, we observe that, on average, correlations with emerging countries are lower than those with other developed countries. These high-to-moderate correlations generally stand on the basis of most of the gains from international portfolio diversification.

To illustrate the implications of home bias on the diversification potential of international portfolios by means of the PDI technique, it is necessary and sufficient to weight the index returns by the actual portfolio weights. For ease of calculations, I assume that local investors allocate a constant portion of their equity investments into their home market, and that they follow an equally-weighted portfolio strategy concerning their foreign holdings. Thus, if the domestic market weight is !%, the respective portfolio weights of the remaining markets in the international portfolio pool are 100 -!% 47. Then, I compute different PDI scores as a function of increasing values of the domestic market share to replicate a home-biased investment scheme.

The PDI analysis of home bias in international equity portfolios for local investors in G7 countries and Australia is shown in Exhibit 2.

[Insert Exhibit 2 about here]

The graph points out to one common observation: The diversification potential of an international portfolio decreases sharply as the domestic investment share increases. For example, when French investors allocate 20% of their equity assets within their domestic stock market, the PDI score associated to an equally-weighted international diversification strategy is about 1.13. This score very close to unity suggests that the resulting international portfolio consists of a unique truly independent component. Indeed, when the domestic portfolio weight exceeds 20%, the resulting international portfolio of local investors in developed markets exhibits, on average, an almost non-diversified pattern as shown by the PDI scores.

PDI ANALYSIS OF THE PREFERENCE FOR GEOGRAPHIC PROXIMITY

Academics have so far established a convincing case that investors prefer geographically close investment vehicles, both domestically [START_REF] Huberman | Familiarity breeds investment[END_REF], [START_REF] Coval | Home Bias at Home: Local Equity Preference in Domestic Portfolios[END_REF]) and internationally [START_REF] Lane | International Investment Patterns[END_REF], [START_REF] Portes | The Determinants of Cross-Border Equity Flows[END_REF]). For example, [START_REF] Portes | The Determinants of Cross-Border Equity Flows[END_REF] report that when geographic distance is divided by two, foreign investment almost doubles. In this section, I employ the PDI technique to analyze the effects of this preference for geographic proximity on the diversification potential of international equity portfolios. Doing so, I first compute the PDI score associated to an international portfolio pool of ! markets, !"# ! , which always includes local investors' home market. Then, it is possible to check whether the addition of one more foreign market into the existing portfolio pool improves the international diversification potential by computing the marginal PDI score defined as,

!"#$%&"' !"# ! + 1 = !"# ! + 1 -!"#(!) (4)
As noted by [START_REF] Rudin | A Portfolio Diversification Index[END_REF], at the limit of large pool sizes, the expression above is the first derivative of the PDI with respect to the portfolio pool size.

To replicate investors' preference for geographic proximity in international portfolio investments, I proceed as follows: Starting by local investors' home country, I gradually enlarge the international portfolio pool by including the first geographically close foreign country and compute the resulting PDI score. Then, I repeat this process till the most distant foreign country in the sample is included into the international portfolio pool, which ultimately consists of 47 foreign countries plus investors' home country. 2 For example, for French investors, according to flight distances between capital cities, the first three foreign markets to be included are Belgium, the U.K. and the Netherlands. While working with the same dataset on monthly index returns for 48 countries, I standardize those returns prior to the computations and bring them to the same volatility level in order to guarantee comparability across countries. Exhibit 3 shows the marginal 2 I compute the flight distance between the capital or the main cities of countries using the Great Circle Distance formula. More details can be found in [START_REF] Coval | Home Bias at Home: Local Equity Preference in Domestic Portfolios[END_REF].

PDI scores calculated for local investors in G7 countries and Australia.

[Insert Exhibit 3 about here]

The plots clearly highlight the negative impact of investors' preference toward geographical proximity on international portfolio diversification. First, we observe that a great deal of the diversification potential result from the first 10 to 15 foreign markets: On average, adding the first 10 destinations in a ascending order of the physical distance from the source provides 70% of the total international portfolio diversification potential as measured by the PDI score. Second, the impact of adding one more foreign country into the initial international portfolio pool drops sharply as the pool size ! increases: Including the last 10 foreign countries into an existing international portfolio pool generates, on average, only 6% of the total diversification potential over the sample. Third, the preference for geographic proximity has an important negative impact on the diversification potential as shown by negative marginal PDI scores in 75 out of a total of 368 observations. For example, for German investors, adding Czech and Hungarian markets reduces the resulting PDI score of the international portfolio pool respectively by 23% and 8%.

IS MORE IS BETTER?

I provide a final illustration related to the PDI technique in international portfolio choice. I show that the PDI can also be used to emphasize the marginal declining value of diversification, a wellknown result since the early stages of modern portfolio analysis. The example provided here follows [START_REF] Rudin | A Portfolio Diversification Index[END_REF] marginal PDI analysis based upon the S&P 100 index.

Specifically, I randomly draw ! countries from the international portfolio pool, which consists of 48 countries, and compute the resulting PDI score, with local investors' home country being always included into the portfolio pool. Then, I repeat the process many times for different international portfolio pool sizes ranging from 2 to 48, and report the average PDI scores. Exhibit 4 shows the evolution of the PDI scores with respect to different portfolio pool sizes.

[Insert Exhibit 4 about here]

Exhibit 4 confirms the limits of diversification in international portfolio investments using the PDI technique, rejecting the view that more is better. Different plots drawn for developed countries' investors are clearly sublinear, which means that the increase in diversification gains are not proportional to the number of countries included into the international portfolio. In general, for pool sizes exceeding 20 countries, the incremental PDI gains are mostly limited and close to zero. For example, for Japanese and UK investors, holding an international portfolio made up by 48 instead of 24 countries (including their own home country), increases the initial PDI scores by only about 7% and 9% respectively. Overall, the results are consistent with those presented by [START_REF] Rudin | A Portfolio Diversification Index[END_REF] who also underline the declining value of diversification by means of PDI analysis using data on S&P 100 index members.

CONCLUSION

The Portfolio Diversification Index provides a practical and parsimonious tool to practitioners

willing to understand the diversification potential represented by a particular portfolio pool. It resumes the underlying correlation structure among different portfolio constituents within a single statistic, which is also comparable across various portfolio pools and over time. This study is an attempt to provide an example as to how the PDI technique can also be implemented in the context of international portfolio investments. The analysis suggests that the PDI methodology allows one to efficiently replicate a number of well-known investment patterns related to literature on international portfolio selection and the home bias, such as the opportunity costs of portfolio underdiversification or investors' preference toward geographically closer markets.

GERMANY

Notes: This exhibit shows the marginal declining value of international diversification using PDI technique. To obtain the graphs for each country, I randomly choose an international portfolio consisting of ! countries and compute the PDI score. Then, I repeat the process many times for different international portfolio pool sizes of ! = 2, … ,48 countries (horizontal axis), and report the average PDI scores (vertical axis).

  Notes: The first two columns show the sample mean and standard deviation of monthly returns over the period January 1998 -December 2007. The last three columns show the average correlation of the country returns with the remaining 47 countries in the international portfolio pool, as well as with developed and emerging countries. All numbers are expressed as percentage values Exhibit 2. Home bias: PDI by domestic investment share Notes: The plots show the dependence of the PDI scores for local investors in G7 countries and Australia as a function of the domestic portfolio share. For a given level of domestic investment share, say !% (horizontal axis), it is assumed that local investors follow an equally-weighted portfolio strategy for their foreign holdings allocated into remaining countries in the international portfolio pool (i.e. 100 -!% 47), and the resulting PDI score is reported (vertical axis). The plots show the incremental PDI scores for local investors from G7 countries and Australia. Starting with local investors' home country, I gradually enlarge the international portfolio pool by including the first geographically close foreign country and compute the resulting PDI score. The process is then repeated till the most distance foreign country is included, which ultimately consists of 47 foreign countries plus investors' home country (horizontal axis). First differences of the PDI scores as a function of the portfolio pool size are provided on the vertical axis.

	Exhibit 1. Summary statistics and correlation Exhibit 3. Marginal PDI analysis of the preference for geographic proximity
	Country Australia Canada France 1.5 2.0 2.5 3.0 --10% 0% 10% 20% 30% 3 8 13 18 23 28 33 38 43 48 Mean Standard deviation all countries Average correlation with developed countries emerging countries 1.30 5.11 51.9 57.8 46.8 1.17 5.95 53.5 61.7 47.8 0.95 5.24 52.0 68.6 37.3 --10% 3 8 13 18 23 28 33 38 43 48 --10% 0% 3 8 13 18 23 28 33 38 43 48 2 6 10 14 18 22 26 30 34 38 42 46 2 6 10 14 18 22 26 30 34 38 42 46 --10% 1 1 3 8 13 18 23 28 33 38 43 48 0% 10% 0% 2 2 10% 10% 20% 20% 3 3 30% 20% 30% 40% 4 4 30% 40% 50% 3.5 4.0 40% 50% AUSTRALIA 50% 60% CANADA 40% 5 5 60% 70% ITALY 50% JAPAN 6 AUSTRALIA 6 CANADA
	Germany Italy Japan U.K. U.S.A. 1.0 1% 2.0 2.5 3.0 3.5 4.0 --20% --30% --20% --10% 0% 10% 20% 30% 40% 50% 60% 70% 3 8 13 18 23 28 33 38 43 48 0.84 6.60 51.9 0.89 5.58 45.1 0.38 5.31 36.2 0.60 3.88 51.8 0.47 4.30 51.9 6% 11% 16% 21% Domes0c por4olio share FRANCE GERMANY ITALY 66.1 58.6 40.4 65.4 62.1 26% Interna0onal por4olio pool size --20% Interna0onal por4olio pool size FRANCE --30% --20% --10% 0% 10% 20% 30% 40% 50% 60% 70% 80% 3 8 13 18 23 28 33 38 43 48 39.5 33.2 32.6 39.8 42.9 31% UK Interna0onal por4olio pool size Interna0onal por4olio pool size GERMANY Interna0onal por4olio pool size --20% Interna0onal por4olio pool size --20% --10% 0% 10% 20% 30% 40% 50% 60% 70% 3 8 13 18 23 28 33 38 43 48 UK --10% 0% 10% 20% 30% 40% 50% 60% 3 8 13 18 23 28 33 38 43 48 USA Interna0onal por4olio pool size Interna0onal por4olio pool size 1 2 3 4 5 6 2 6 10 14 18 22 26 30 34 38 42 46 FRANCE 1 2 3 4 5 6 2 6 10 14 18 22 26 30 34 38 42 46 Notes: --20% --30% Interna0onal por4olio pool size --20% Interna0onal por4olio pool size Interna0onal por4olio pool size Interna0onal por4olio pool size
	1.5
	1.0
	1%	6%	11%	16%	21%	26%
			Domes0c por4olio share
		AUSTRALIA		CANADA	JAPAN	USA

It can be checked that for the PDI formula to be equal to 1, the first element of the component weight vector must be close to unity, i.e. ! ! ≈ 1, while the remaining elements automatically tend to have values close to zero, i.e. ! !!!!! ≈ 0.


Letizia Dal

Dr Marco Peña-Jimenez
email: marco.pena-jimenez@u-bordeaux.fr

Federica Canzan

Luisa Saiani

Adalgisa Battistelli

The Emotional Side of the E-learning Among Nursing Students: the role of the Affective Correlates on the E-Learning Satisfaction*

Keywords: E-learning environment, emotions, satisfaction with E-learning, Community of Inquiry (CoI)

On the 26th December prof. Adalgisa Battistelli passed away

Introduction

Education has been experiencing multiple changes (e.g., new learning contents, methods, applications) because of the adoption of the new digital technologies, thus transforming the way learning takes place and how people (e.g., students, teachers) interact with each other (for a review see [START_REF] Rodrigues | Tracking e-learning through published papers: A systematic review[END_REF]. As a result, this new form of learning, that uses emerging technologies (e.g., learning platforms, mobile and wearable devices) for educational purposes, also known as e-learning or online learning, has expanded significantly in recent times (for a review see [START_REF] Valverde-Berrocoso | Trends in educational research about e-learning: A systematic literature review (2009-2018)[END_REF]. The recent social distancing measures to prevent the spread of COVID-19 pandemic all over the world, have accelerated and intensified these educational changes, thus placing e-learning as an alternative (if not the unique) option to ensure training in higher education, including nursing education. Thus, it becomes important to evaluate not only the online courses' features, but also how students experience the e-learning environment [START_REF] Woolliscroft | Innovation in response to the COVID-19 pandemic crisis[END_REF].

In that regard, many scholars (e.g., [START_REF] Mayer | Where is the learning in mobile technologies for learning?[END_REF][START_REF] Loderer | Beyond cold technology: A systematic review and meta-analysis on emotions in technology-based learning environments[END_REF] have called for further research to explore the emotional side of e-learning considering that human learning involves much more than cognitive processes and outcomes. Learning environments, and more specifically e-learning environment, might trigger positive (e.g., curiosity, surprise, pride) and negative (e.g., failure, anxiety, frustration) emotions, which in turn could potentially interfere with other cognitive processes and outcomes (e.g., [START_REF] Reisenzein | The cognitive-evolutionary model of surprise: A review of the evidence[END_REF]. For instance, regarding emotional outcomes, satisfaction with a course is considered a relevant learning outcome shaping the decision to continue or withdraw from a course [START_REF] Paechter | Students' expectations of, and experiences in elearning: Their relation to learning achievements and course satisfaction[END_REF].

Studying the emotional states in the e-learning experience of students seems to be even more relevant to respond to the unplanned educational changes (e.g., synchronous virtual classrooms, online discussion forums, virtual meetings) imposed by the COVID-19 pandemic [START_REF] Carolan | COVID 19: Disruptive impacts and transformative opportunities in undergraduate nurse education[END_REF]. For example, these unforeseen changes may, themselves, trigger an emotional response, which, in turn, may impact the way students experience online learning [START_REF] Cleveland-Innes | Emotional presence, learning, and the online learning environment[END_REF]. In the nursing context, empirical evidence on how students experience distance e-learning (i.e., from face-to-face to e-learning training) during the pandemic is still scarce (e.g., [START_REF] García-González | Analysis of anxiety levels of nursing students because of e-learning during the COVID-19 Pandemic[END_REF][START_REF] Kim | Influence of learning flow and distance e-learning satisfaction on learning outcomes and the moderated mediation effect of social-evaluative anxiety in nursing college students during the COVID-19 pandemic: A cross-sectional study[END_REF].To bridge this gap, the present study aims to examine the emotional side of e-learning during the COVID-19 pandemic context by investigating the role of emotions in the relationship between perceived experiences of e-learning environment and satisfaction with e-learning. More specifically, this study addresses the following research questions (RQ): RQ1. How are nursing students' perceptions of e-learning experience (e.g., cognitive, social) related to positive and negative emotions? By addressing these research questions, we seek to contribute to research on emotions in technology-based learning contexts (and more specifically in e-learning nurse education) in two ways [START_REF] Loderer | Beyond cold technology: A systematic review and meta-analysis on emotions in technology-based learning environments[END_REF][START_REF] Carolan | COVID 19: Disruptive impacts and transformative opportunities in undergraduate nurse education[END_REF]. First, considering that the complete e-learning training imposed by the COVID-19 pandemic was a new experience for study participants, we provide evidence on how the undergraduate nursing students' evaluations of two essential aspects of educational experience (i.e., social and cognitive) are related to overall satisfaction with a fully online course. Second, we lend evidence on the mediating role of positive and negative emotions between perceived e-learning experiences and satisfaction, thus demonstrating the potential that affective mechanisms have for shaping satisfaction, but also opening up new avenues of research to study other educational outcomes.

The E-learning Educational Experience

E-learning refers to a learning system based on digital and online technologies, whose main goal is to offer learners an interactive, learner-centered and open learning environment, which can support and improve the learning processes [START_REF] Rapanta | Online university teaching during and after the COVID-19 crisis: Refocusing teacher presence and learning activity[END_REF][START_REF] Rodrigues | Tracking e-learning through published papers: A systematic review[END_REF]). E-learning has been seen for a long time as an alternative form of learning for those learners who could not have had learning opportunities otherwise [START_REF] Rhim | Teaching online: Foundational concepts of online learning and practical guidelines[END_REF]. However, it is more and more frequent to find higher-education institutions offering "online education" courses or even entire academic programs [START_REF] Rivera-Vargas | Exploring students' learning experience in online education: analysis and improvement proposals based on the case of a Spanish open learning university[END_REF].

Over the last years, considerable efforts have been made to explore the constant changes in the e-learning environment [START_REF] Loderer | Beyond cold technology: A systematic review and meta-analysis on emotions in technology-based learning environments[END_REF][START_REF] Rodrigues | Tracking e-learning through published papers: A systematic review[END_REF]. While many frameworks (e.g., [START_REF] Mayer | Where is the learning in mobile technologies for learning?[END_REF][START_REF] Paechter | Students' expectations of, and experiences in elearning: Their relation to learning achievements and course satisfaction[END_REF] propose to explore several functional facets of the learning environment (e.g., course design, student-instructor exchange, studentstudent exchange), others propose to study learning by focusing on the perception of the individuals' educational experience [START_REF] Fiock | Designing a community of inquiry in online courses[END_REF][START_REF] Garrison | The first decade of the community of inquiry framework: A retrospective[END_REF]. In this regard, we propose here to focus on the core aspects of the learning experience or "presence" within an elearning environment, based on the Community of Inquiry (CoI) theoretical framework [START_REF] Fiock | Designing a community of inquiry in online courses[END_REF][START_REF] Garrison | The first decade of the community of inquiry framework: A retrospective[END_REF].

Drawing from the CoI framework [START_REF] Fiock | Designing a community of inquiry in online courses[END_REF][START_REF] Garrison | The first decade of the community of inquiry framework: A retrospective[END_REF], the present study evaluates the e-learning educational experience by focusing on the cognitive and the social presences as two core elements of the e-learning environment. Cognitive presence is defined as the learners' ability to develop meaning through a reflective process or sustained reflection (i.e., problem identification, exploration, ideas integration, problem resolution) [START_REF] Garrison | The first decade of the community of inquiry framework: A retrospective[END_REF].

Social presence refers to the students' ability to present themselves as "real people" by using existing online communicating tools, which is determined by several social presence indicators (i.e., emotional expression, open communication, group cohesion) [START_REF] Garrison | The first decade of the community of inquiry framework: A retrospective[END_REF].

Empirical evidence suggests that learning experience involves cognitive and social presences to develop meaningful learning and shows that they are related to useful learning outcomes (e.g., overall satisfaction, perceived learning, sense of community) (Castellano-Reyes, 2020). For example, [START_REF] Garrison | Researching the community of inquiry framework: Review, issues, and future directions[END_REF] found that social and cognitive presences was positively associated with valuable learning outcomes such as learners' satisfaction, sense of community and perceived learning. More recently, [START_REF] Lim | Predictive effects of undergraduate students' perceptions of social, cognitive, and teaching presence on affective learning outcomes according to disciplines[END_REF] indicated that the student's perception of cognitive and social presence were positively related to student satisfaction. In line with this perspective, the present study's general focus is to examine how nursing students perceive cognitive and social presences, as two representative factors of a meaningful and constructive learning environment [START_REF] Fiock | Designing a community of inquiry in online courses[END_REF][START_REF] Garrison | The first decade of the community of inquiry framework: A retrospective[END_REF].

Emotions and Satisfaction With E-learning

Cognition and social interactions are considered the core elements of meaningful learning environments, including in online settings, which in turn might trigger affective and emotional processes [START_REF] Ashwin | Impact of inquiry interventions on students in e-learning and classroom environments using affective computing framework[END_REF]. Within the e-learning educational setting, emotions refer to both positive (e.g., enjoyment, curiosity) and negative (e.g., anger, sadness, anxiety) affective states, experienced by learners as parts of their e-learning experience [START_REF] D'mello | A selective meta-analysis on the relative incidence of discrete affective states during learning with technology[END_REF][START_REF] Mayer | Where is the learning in mobile technologies for learning?[END_REF].

Emotions research within educational environments has demonstrated that emotions are linked to learning outcomes such as academic achievement [START_REF] Artino | Emotions in online learning environments: Introduction to the special issue[END_REF], students' performance [START_REF] D'mello | Confusion can be beneficial for learning[END_REF] and satisfaction with the training [START_REF] Paechter | Students' expectations of, and experiences in elearning: Their relation to learning achievements and course satisfaction[END_REF]. Among all these different learning outcomes, we explored how emotions are related to overall satisfaction with e-learning for several reasons. First, satisfaction with a course is a variable, which involves a self-perceived range of fulfillment linked to the individual's wish to learn and is an indicator of a positive evaluation of a learning experience [START_REF] Arbaugh | Virtual classroom characteristics and student satisfaction with internetbased MBA courses[END_REF]. Second, satisfaction is also an affective outcome, which influences learners' decision to remain or leave a course [START_REF] Paechter | Students' expectations of, and experiences in elearning: Their relation to learning achievements and course satisfaction[END_REF]. Last, satisfaction can be considered an alternative, but relevant indicator of educational quality [START_REF] Hakim | Nursing students' satisfaction about their field of study[END_REF]. On the other hand, psychological research has also provided substantive meta-analytical evidence about the antecedents (e.g., prior knowledge, learning environment) and outcomes (e.g., engagement, achievement) of emotions within the technology-based learning context such as the e-learning training (e.g., D 'Mello, 2013;[START_REF] Loderer | Beyond cold technology: A systematic review and meta-analysis on emotions in technology-based learning environments[END_REF]. In fact, emotions are representative variables of affective states which, regulate not only the way we perceive our environment, but also how we react to a given context (e.g., [START_REF] Ashwin | Impact of inquiry interventions on students in e-learning and classroom environments using affective computing framework[END_REF][START_REF] Reisenzein | The cognitive-evolutionary model of surprise: A review of the evidence[END_REF].

Building on these observations, emotions can be considered as central affective mechanisms, which mediate the relationship between the student's evaluation of the e-learning environment and the overall satisfaction with the e-learning experience.

Aim and hypotheses

In line with the previous observations, this study aims to contribute to better understand the perception of the e-learning environment, characterized by cognitive (strategic planning) and social (interaction) factors, and the mediating role played by emotions on students' satisfaction with the e-learning training. Thus, we formulated the following hypotheses (see Figure 1): Hypothesis 1. The cognitive dimension of the e-learning environment will be positively related to positive emotions and negatively related to negative emotions.

Hypothesis 2. The social dimension of the e-learning environment will be positively related to positive emotions and negatively related to negative emotions. Hypothesis 3a. Positive emotions will be positively related to satisfaction with e-learning.

Hypothesis 3b. Negative emotions will be negatively related to satisfaction with e-learning.

Hypothesis 4a. Positive emotions will mediate the relationship between the cognitive and the social dimension of the e-learning environment and satisfaction with e-learning. Hypothesis 4b. Negative emotions will mediate the relationship between the cognitive and the social dimension of the e-learning environment and satisfaction with e-learning.

----Insert Figure 1 about here ----

Method Study Design

Through a cross-sectional design, the current study explored the affective correlates of the e-learning environment, as they were experienced by nursing students during the lockdown due to the COVID-19 pandemic. To do so, an online questionnaire was used for data collection

Sample

The sample was composed of 353 undergraduate nursing students enrolled in a public Italian university who agreed to voluntarily participate in the current study. Within this sample, the majority of the participants were female (81.9%), and students had an average mean of 22.8 years old (SD = 3.99). Students' sociodemographic and e-learning characteristics are detailed in Table 1.

----Insert Table 1 about here ----

Procedure

As part of our research protocol, we contacted the Nursing Studies Department and, after approval of the study protocol, an institutional e-mail having the online survey was sent to the target population. The criteria used to extend the invitation to take part in our study to the target population was the following: (1) students enrolled in the Nursing Studies Department, (2) second-and third-year students (bachelor's degree), and (3) students who had a fully remote training by using an online-connected learning platform (i.e., Moodle) and digital communication technologies (i.e., Zoom, Skype). Then, the target study population received an invitation from the university, where they were informed about the purpose and the characteristics of the research, as well as that their participation in the study was voluntary. The survey was administered via an online survey platform, where authors explicitly informed the above-mentioned aspects and assuring the anonymity of respondents.

Measures

Satisfaction with E-learning. Satisfaction with e-learning was assessed by using an adapted version of the short form of the Minnesota Satisfaction Questionnaire (MSQ; [START_REF] Weiss | Manual for the Minnesota satisfaction questionnaire[END_REF]. Three items measure the overall degree of satisfaction with the E-learning activities (α = .87). Items comprising this variable (e.g., "I am satisfied with the preparation I have achieved by using the distance teaching method") were rated on a 5-point Likert scale from 1 ("not at all") to 5 ("extremely").

Positive and Negative Emotions. Affective states were assessed through nine different emotional descriptors felt during the E-learning activities [START_REF] Wortha | Multiple negative emotions during learning with digital learning environments-Evidence on their detrimental effect on learning from two methodological approaches[END_REF]. Positive emotions (sample emotional descriptors were "pleasure", "hope", and "pride") and Negative emotions (illustrative emotional descriptors were "sadness", "frustration", and "anxiety") were rated on a 5-point type-Likert scale from 1 ("not at all") to 5 ("extremely").

E-Learning Environment

Perception. E-learning environment perception was assessed by using a 12-item scale derived from the John Hopkins Learning Environment Scale (JHLES; Shochetet al., 2015) and adapted for the purposes of this study. This measure assesses four dimensions of the e-learning environment perception (c.f., autonomy, programming, collaboration, communication), which capture two core aspects: (1) strategic planning (an elearning environment which develops a cognitive activation for an autonomous planning) as a cognitive presence dimension, and (2) interaction (an e-learning environment allowing relationship and communication with other students) as a social presence dimension. The goodness of the two-factor learning experiences provided adequate support for the two-factor solution (χ 2 (26) = 97.35, p < .05; CFI = 0.93; TLI = 0.91; RMSEA = 0.08, SRMR = 0.04) compared to the 1-factor solution (χ 2 (27) = 283.41, p < .05; CFI = 0.77; TLI = 0.70; RMSEA = 0.16, SRMR = 0.09). Both "strategic planning" (sample item: "The distance learning experience allowed me to organize my study times and anticipate the preparation of some exams") and "interaction" (sample item: "The distance learning experience allowed me to stay in touch with my fellow students and share teaching materials") were rated through a type-Likert scale ranging from 1 ("not at all") to 5 ("extremely").

Ethical Considerations

In accordance with the ethical principles of the Declaration of Helsinki (World Medical Association, 2013) and the ethical guidelines (Section 8) of the American Psychological Association (2020), the current research was examined and approved by the Institutional Research Board of the Nursing Studies Department before data collection.

Data Analysis

Statistical Package for Social Sciences software version 25.0 was used to analyze descriptive data and to carry out bivariate analysis. Reliability analysis was performed by using JASP software version 0.14.1 [START_REF] Mcneish | Thanks coefficient alpha, we'll take it from here[END_REF]. To assess our measurement model and test our hypotheses, structural equation modelling was performed by using Mplus 8. Regarding the analytical approach, considering that our measures used 5-point response options, we adopted a maximum likelihood approach (with a Robust Maximum Likelihood estimator, MLR in Mplus), which is considered an advisable option for 5 or more response options [START_REF] Rhemtulla | When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions[END_REF].

The goodness of fit of our research model was evaluated through different statistical indexes such as the Comparative Fit Index (CFI), the Tucker-Lewis Index (TLI), the Root Mean Square Error of Approximation (RMSEA), the Standardized Root Mean Square Residual (SRMR), the Maximum-Likelihood Chi-Square (χ 2 ) and the degrees of freedom (df), by following the traditional assessment criteria [START_REF] Keith | Multiple regression and beyond: An introduction to multiple regression and structural equation modelling[END_REF].

Results

Measurement Model

Confirmatory Factorial Analysis (CFA) was carried out to assess the measurement model. ----Insert Table 2 about here ----To provide further evidence of the convergent validity of the study variables, Table 3 presents the average variance extracted (AVE) and composite reliability (CR) of the five latent variables of our theorized model. Based on AVEs, reasonably good evidence of convergent validity is demonstrated. All AVE's values were satisfactory (> 0.50) or excellent (> 0.70), except for the e-learning environment fostering strategic planning, where value is acceptable [START_REF] Bagozzi | On the evaluation of structural equation models[END_REF]. In terms of internal consistency, all CR values are above 0.7, which indicates good levels of scale reliability [START_REF] Hair | Multivariate data analysis: A global perspective[END_REF]. It is also reported coefficient omega, which is consistent with Cronbach's alpha reported in the measures section, thus providing evidence of the satisfactory levels for reliability/internal consistency.

Means, standard deviations and correlations of the study variables are presented in Table 3. Bivariate analysis showed that the perception of the e-learning environment, fostering strategic planning and interaction, is positively correlated to positive emotions and negatively associated with negative emotions felt in the remote training, and these in turn have a significantly positive and negative relationship with satisfaction with remote training, respectively.

----Insert Table 3 about here ----

Structural Model

By using Structural Equation Modelling (SEM), the relationship between the latent variables of our theorized framework was examined and the underlying model demonstrated an adequate fit (χ 2 (181) = 428.34, p < 0.05; CFI = 0.93; TLI = 0.92; RMSEA = 0.06, SRMR = 0.06). Standardized path coefficients of the tested model are presented in Figure 2. All factors loadings and the path coefficients were significant (p < 0.01), except for the relationship between the perception of the e-learning environment fostering interaction and negative emotions.

Overall, the current findings show that the perception of the e-learning environment fostering strategic planning is significantly positively associated with positive emotions (β = 0.46, p < 0.01) and significantly negatively associated with negative emotions (β = -0.45, p < 0.01), thus lending support to hypotheses 1a and 1b, respectively. The perception of the e-learning environment fostering interaction is significantly positively related to positive emotions (β = 0.37, p < 0.01) and no significant relationship was founded with negative emotions (β = -0.09, p = 0.29). Therefore, hypothesis 2a is supported and hypothesis 2 is rejected. Positive emotions are significantly positively associated with satisfaction with e-learning (β = 0.43, p < 0.01), while negative emotions is significantly negatively related with the latter (β = -0.31, p < 0.01).

Hypothesis 3a and 3b are thus supported.

Two additional pathways were added to test the mediation hypotheses 4a and 4b, that is, the perception of the e-learning environment fostering strategic planning and interaction to satisfaction with e-learning. While the relationship between e-learning environment fostering interaction and satisfaction was not significant (β = 0.01, p = 0.83), the relationship between elearning environment fostering strategic planning and satisfaction was significant (β = 0.36, p < 0.01), and improved the model fit (Δχ 2 [Δdf = 1] = 1.00, p < 0.01). Consequently, such path was considered in the final structural model.

Moreover, in order to analyze the mediation effect, a bootstrapping technique was used by following the guidelines of [START_REF] Shrout | Mediation in experimental and nonexperimental studies: new procedures and recommendations[END_REF]. Table 4 reports the direct effects and indirect effects of the model. As can be seen, findings showed that positive emotions about remote training partially mediate the relationship between e-learning environment fostering strategic planning and satisfaction with e-learning (direct effect β = 0.36, p < 0.01; indirect effect β = 0.20, p < 0.01), and totally mediate the relationship between e-learning environment fostering interaction and satisfaction with e-learning (direct effect β = 0.01, p = 0.83; indirect effect β = 0.16, p < 0.01). Hypothesis 4a is thus partially supported. Moreover, negative emotions about remote training partially mediate the relationship between e-learning environment fostering strategic planning and satisfaction with e-learning (direct effect β = 0.36, p < 0.01; indirect effect β = 0.14, p < 0.01), and did not mediate the relationship between elearning environment fostering interaction and satisfaction with e-learning (direct effect β = 0.01, p = 0.83; indirect effect β = 0.02, p = 0.31). Therefore, hypotheses 4b is partially supported.

----Insert Figure 2 about here --------Insert Table 4 about here ----

Discussion

The current study aimed to better understand the emotional side of the fully remote elearning training during the COVID-19 pandemic context, as experienced by nursing students.

More specifically, we aim to explore the mediating role of emotions in the relationship between the perception of the e-learning environment, characterized by cognitive (i.e., strategic planning) and social (i.e., interaction) factors, and satisfaction with the e-learning. Based on the CoI theoretical framework, which claims that social and cognitive presences represent two core elements of the e-learning experience, we explore the affective correlates of the nursing students' learning experience within an e-learning environment.

Our results showed a positive relationship between cognitive (i.e., strategic planning) and social (i.e., interaction) presences and positive emotions. In other words, the cognitive effort involved in constructing knowledge and the interaction with others might trigger positive emotions such as curiosity, pride and hope. Likewise, a positive relationship between cognitive presence (i.e., strategic planning) and satisfaction with e-learning was found. These results are consistent with the CoI framework, which highlights the importance of cognitive (e.g., solving problems, connecting ideas, planning activities) and social (e.g., opportunities to exchange, collaboration) presences for developing meaningful (e.g., satisfaction with e-learning training) learning experiences within the e-learning environment (e.g., [START_REF] Rhim | Teaching online: Foundational concepts of online learning and practical guidelines[END_REF].

Our findings also indicated that cognitive (i.e., strategic planning) and social (i.e., interaction) presences are related to negative emotions in different ways. While the cognitive dimension of the learning experience showed a negative association with emotions such as frustration, anxiety and sadness, the social presence showed no relationship with these negative emotions. Previous studies have revealed that cognitive presence, and more specifically, the autonomy and the cognitive control involved in the strategic planning decreases the negative emotional activation (e.g., [START_REF] Westerlund | Negative views of out-groups and emotion regulation strategies: Evidence for an association with the tendency to suppress emotion expression, but not with cognitive reappraisal or emotion dysregulation[END_REF], but also that cognition and social interaction play different roles in the emotional states, which is consistent with emotional and affective states literature (e.g., Izard et al., 1984). Nevertheless, further research is strongly recommended to determine whether the lack of relationship between these learning experiences and negative emotions is similar in different educational environments and ways of learning.

Our research showed the partial mediating role played by positive emotions in the cognitive presence (i.e., strategic planning) and satisfaction with e-learning relationship. Put another way, the cognitive presence would activate students' satisfaction either directly and indirectly, through the intervention of positive emotions [START_REF] Garrison | The first decade of the community of inquiry framework: A retrospective[END_REF]. Likewise, the social dimension (i.e., interaction with peers) does not directly affect students' satisfaction with e-learning training directly, but rather positive emotions play the role of a fully mediating mechanism between learning experiences and learning outcomes (i.e., satisfaction with elearning training). Accordingly, our findings suggest that cognitive (e.g., planning, connecting ideas) and social (e.g., collaboration among students) presences elicit positive emotions, which in turn move students to feel fulfilled with the e-learning environment [START_REF] Hambacher | From serial monologue to deep dialogue: Designing online discussions to facilitate student learning in teacher education courses[END_REF].

Last, the current findings showed that negative emotions play a mediating role between cognitive presence (i.e., strategic planning) and satisfaction with e-learning, however, negative emotions would not play a mediating role in the relationship between social presence (e.g., interaction with other students) and satisfaction with e-learning [START_REF] Garrison | The first decade of the community of inquiry framework: A retrospective[END_REF]. In other words, negative emotions have the potential of regulating the cognitive side of the learning experience; however, this affective mechanism would act in a different way in the case of social presence (i.e., interaction). This observation suggests that other psychological processes or learning contexts might trigger negative emotions by shaping affective learning outcomes such as satisfaction with e-learning.

Theoretical Implications

Our study has some theoretical implications, which are worth mentioning. On the one hand, our results extend the knowledge about core facets of the learning experience, that is, the students' perceptions of the e-learning environment as a Community of Inquiry (Yilmaz, 2020).

In particular, we focus on the cognitive and the social presence as two core components of the online learning settings (Giannous and Kioumourtzoglou, 2016;[START_REF] Lim | Predictive effects of undergraduate students' perceptions of social, cognitive, and teaching presence on affective learning outcomes according to disciplines[END_REF]. This is in line with previous research [START_REF] Mehall | Purposeful interpersonal interaction and the point of diminishing returns for graduate learners[END_REF], which offered evidence that positive social interaction is associated with satisfaction in e-learning. In addition, strategic planning showed a positive link to students' satisfaction; this is consistent with a recent study by [START_REF] Lim | Predictive effects of undergraduate students' perceptions of social, cognitive, and teaching presence on affective learning outcomes according to disciplines[END_REF] who claimed that: "cognitive presence showed the most powerful predictive effects on students 'perceived learning outcomes and satisfaction" (p.1).

On the other hand, this study sheds light on how emotions shape e-learning processes (e.g., learning experience, learning outcomes). This has a theoretical implication, which suggests considering positive and negative emotions as mediators/moderators elements of social and cognitive presences and other learning outcomes [START_REF] Majeski | The community of inquiry and emotional presence[END_REF]. Future studies are strongly recommended to better understand the complex interplay among different kinds of presence such as emotional, cognitive, social and teaching and their links with different outcomes. Our results are consistent with previous findings claiming that emotions shape learning, including in e-learning communities [START_REF] Cleveland-Innes | Emotional presence, learning, and the online learning environment[END_REF]Marchand and Gutierrez, 2011). Indeed, the consideration of the intervening role of emotions is "… use the specific meaning of these terms to make the point that sometimes, when we are not studying emotion per se, it is the consideration of emotion that reveals the nature of the relationship between our constructs of interest…" (Zerbe and Haertel, 2000, p. 156-157). Accordingly, further research on emotional presence within an online community is strongly recommended to better understand their role and influence on the online environment's experience.

Practical Implications

Our study has some practical implications on nursing education, to develop meaningful learning experiences. Our results underline the importance of considering strategic planning and social interaction as essential aspects of e-learning. This consideration implies that educators must develop online courses, which can foster students' perception of the e-learning environment as a Community of Inquiry [START_REF] Mehall | Purposeful interpersonal interaction and the point of diminishing returns for graduate learners[END_REF]Yilmaz, 2020).

In particular, our study underlines that interaction promotes positive emotions, which in turn activate students' satisfaction. That implies that educators should foster e-learning experiences where students have the opportunities to share their thoughts and their feeling in order to find solutions together. The promotion of high quality interpersonal interactions is demonstrated to lead to better student outcomes and generally increases students' satisfaction with the online learning setting [START_REF] Mehall | Purposeful interpersonal interaction and the point of diminishing returns for graduate learners[END_REF]. It is therefore very important to facilitate communication by creating a climate of trust (e.g., through social interactions), which in turn will provide the environment for purposeful interactions [START_REF] Lim | Predictive effects of undergraduate students' perceptions of social, cognitive, and teaching presence on affective learning outcomes according to disciplines[END_REF].

Our results also show the important role of strategic planning in e-learning environments.

In this regard, educators should promote interventions, which can shape the quality of cognitive development and the optimal functioning of a community of inquiry. In the digital age, the balancing of different online educational settings or resources means educators need to be aware that the perception of the e-learning setting can be improved by the construction of a learning community [START_REF] Yuan | Guidelines for facilitating the development of learning communities in online courses[END_REF]. This implies that educators, in the online environment, play a fundamental role: a facilitator role. They are called to facilitate students to active engage, plan their learning activities and promote interaction among peers.

Limitations of the study

The current research offers some insights about the emotional correlates within an elearning environment; however, some limitations have to be pointed out. First, from a theoretical standpoint, while we focused on two central (i.e., cognition, interaction) dimensions fostered within an e-learning environment, as presented in the CoI framework. Further research is needed to explore how other presences, such as teacher presence, are involved in the learning experience of a remote training context and which is the overlapping among these different components.

Second, from a methodological viewpoint, our study used a cross-sectional design, which allowed us to evaluate specific affective states, further research is therefore needed to assess the dynamic of affective states and possible changes within the e-learning environment through longitudinal studies. Moreover, even though the measures used in the current study assess core aspects of the learning experience and affective correlates, further research is needed to make an in-depth evaluation of different facets of the learning experience and the spectrum of emotions.

Likewise, by considering the type of sampling (i.e., convenience) of the present work, future research might include participants of different educational levels and experiences with the use of e-learning devices for evaluating the potential moderating role of such educational characteristics. Last, from an educational practice view, the current study was carried out in the midst of accelerated and unexpected implementation of an e-learning training program (due to the COVID-19 pandemic), thus providing new opportunities in the future to take into account other personal and contextual variables (e.g., prior e-learning experiences) impacting the learning process.

Conclusion

The digital age, and more recently the COVID-19 pandemic, have accelerated the transformation of learning settings in higher education, by offering new opportunities to better understand and seize the opportunities of e-learning environments. Based on the CoI theoretical framework, we propose to examine the affective correlates of the fully remote e-learning as experienced by a sample of nursing students, and more specifically, how (positive, negative) emotions mediate the relationship between the learning experience (i.e., cognitive, social) and learning outcomes (i.e., satisfaction with e-learning). Our findings suggest that both cognitive (i.e., strategic planning) and social (i.e., interaction) presences impact students' emotions differently, which in turn might affect the satisfaction with e-learning training. Thus, our model sheds light on the complex interplay among cognitive, emotional and relational components, which is consistent with previous studies (e.g., [START_REF] Cleveland-Innes | Emotional presence, learning, and the online learning environment[END_REF]. a Participants were on average 22.8 years old (SD = 3.9).

b Students reported their IT and digital skills proficiency at the end of the academic semester (September 2020).

RQ2.

  How are (positive and negative) emotions of nursing students related to overall satisfaction with e-learning training? RQ3. Do nursing students' negative and positive emotions act as mediating mechanisms on the relationship between e-learning experience (e.g., cognitive, social) and satisfaction with elearning training?

  in a Graduated Nursing Program in Italy. The questionnaire was administered in September 2020, 6 months after the implementation of the fully e-learning training program (March-August 2020).

  The results obtained indicate that all underlying latent factors of the corresponding items are consistent with the 5 constructs of our research model (χ 2 (179) = 407.38, p < 0.05; CFI = 0.94; TLI = 0.93; RMSEA = 0.05, SRMR = 0.06). As can be seen in Table2, the hypothesized 5factor model was compared to model 2 (4-factor model: both e-learning environment factors were combined), model 3 (4-factor model: both emotions factors were combined), model 4 (3factor model :both emotions factors were combined, and both e-learning environment factors), model 5 (2-factor model: e-learning environment factors, emotion factors, and satisfaction were grouped), and model 6 (1-factor model). The results indicate that the 5-factor solution yielded an adequate fit to the data compared to other competing nested models, where two or more factors were combined to examine the discriminant validity of the theorized five-factor model.

  Figure 1

Table 1

 1 Students' Sociodemographic and E-learning Characteristics

	Variable	n	%
	Gender
	Female	289	81.9
	Male	60	17.0
	Did not reply	4	1.1
	Age a
	19 -20 years old	73	20.7
	21 -22 years old	162	45.9
	23 -24 years old	58	16.4
	More than 25 years old	55	15.6
	Did not reply	5	1.4
	Number of students using e-learning technologies before the pandemic
	Videoconferencing software (e.g., Zoom, Skype)	71	20.1
	for educational courses
	Videoconferencing software(e.g., Zoom, Skype)	103	29.1
	for meeting other students
	Instant messaging software (e.g., WhatsApp,	306	86.4
	Facebook messenger)
	E-mail	290	81.9
	University learning platform (i.e., Moodle)	221	62.4
	Number of students using e-learning technologies during the pandemic (Mar-Sept 2020)
	Videoconferencing software (e.g., Zoom, Skype)	353	100.0
	for educational courses
	Videoconferencing software(e.g., Zoom, Skype)	282	79.7
	for meeting other students
	Instant messaging software (e.g., WhatsApp,	323	91.5
	Facebook messenger)
	E-mail	311	88.9

Table 2

 2 Fit Indices for Confirmatory Factor AnalysisModels LESP and LEIN combinate, and PEEL and NEEL combinate); Model D: 2-factors model, (LESP and LEIN combinate, and PEEL, NEEL and OSEL combinate); Model E: 1-factor model. LESP: Learning Environment fostering Strategic Planning; LEIN: Learning Environment fostering Interaction; PEEL: Positive Emotions about E-Learning; NEEL: Negative Emotions about E-Learning; OSEL: Overall Satisfaction with E-Learning.

	Model	χ 2	df	RMSEA RMSEA 90%	CFI TLI SRMR	Model comparison (Satorra-
					CI			Bentler)
	1. Hypothesized 5-factor model 407.38 *	179	0.06	0.052 -0.068 0.94 0.93	0.05	-
	2. Model A	664.64 *	183	0.09	0.079 -0.093 0.86 0.84	0.08	2 vs. 1 = 202.35, df = 4, p < 0.01
	3. Model B	749.68 *	183	0.09	0.087 -0.101 0.84 0.82	0.08	3 vs. 1 = 267.82, df = 4, p < 0.01
	4. Model C	1005.34 * 186	0.11	0.105 -0.119 0.77 0.74	0.10	4 vs. 1 = 472.36, df = 7, p < 0.01
	5. Model D	1055.40 * 188	0.11	0.108 -0.121 0.76 0.73	0.10	5 vs. 1 = 475.55, df = 9, p < 0.01
	6. Model E	1312.60 * 189	0.13	0.123 -0.136 0.68 0.65	0.10	6 vs. 1 = 627.49, df = 10, p < 0.01
	Note. N = 353;

* p < .01; CFI: Comparative fit index; CI: Confidence interval; RMSEA: Root-mean-square error of approximation; SRMR: Standardized root mean square residual; TLI: Tucker-Lewis index. Model A: 4-factors model (LESP and LEIN combinate); Model B: 4-factors model (PEEL and NEEL combinate); Model C: 3-factors model (

Table 3

 3 Descriptive Statistics, Reliability and Correlations of Study Variables

	Variable	M	SD	AVE	CR	1	2	3	4	5
	1. LESP	3.02	0.87	0.47	0.77	(.82)
	2. LEIN	2.54	0.84	0.59	0.88	.52 **	(.88)
	3. PEEL	2.73	0.85	0.59	0.85	.56 **	.57 **	(.85)
	4. NEEL	2.85	0.98	0.56	0.87 -.40 ** .29 ** -.46 ** (.87)
	5. OSEL	2.90	0.97	0.70	0.87	.67 **	.55 **	.71 ** -.60 ** (.87)
	Note. N = 353;

** p < .01 M = mean; SD = standard deviation; AVE = Average variance extracted; CR = Composite reliability; Values in brackets are internal consistency coefficients (McDonald's omega). LESP: Learning Environment fostering Strategic Planning; LEIN: Learning Environment fostering Interaction; PEEL: Positive Emotions about E-Learning; NEEL: Negative Emotions about E-Learning; OSEL: Overall Satisfaction with E-Learning.

Table 4

 4 Note. N = 353; Bootstraping sample = 10000; Standardized coefficients are reported. 95% CI: 95% confidence interval for β; LL = lower limit; UL = upper limit.

	Mediation Analysis
	Effect	β	SE	95% CI	p
				LL	UL
	Direct effects
	LESP ➔ PEEL	0.46	0.08	0.31	0.61	< 0.01
	LESP ➔ NEEL	-0.45	0.09	-0.61	-0.27	< 0.01
	LEIN ➔ PEEL	0.37	0.07	0.22	0.51	< 0.01
	LEIN ➔ NEEL	-0.09	0.08	-0.25	0.07	0.29
	LESP ➔ OSEL	0.36	0.07	0.22	0.50	< 0.01
	LEIN ➔ OSEL	0.01	0.06	-0.11	0.12	0.83
	PEEL ➔ OSEL	0.43	0.08	0.27	0.59	< 0.01
	NEEL ➔ OSEL	-0.31	0.05	-0.41	-0.21	< 0.01
	Indirect effects
	LESP ➔ PEEL ➔ OSEL	0.20	0.05	0.11	0.31	< 0.01
	LEIN ➔ PEEL ➔ OSEL	0.16	0.05	0.08	0.26	< 0.01
	LESP ➔ NEEL ➔ OSEL	0.14	0.03	0.08	0.21	< 0.01
	LEIN ➔ NEEL ➔ OSEL	0.02	0.03	-0.02	0.09	0.31
	LESP: Learning Environment fostering Strategic Planning; LEIN: Learning Environment
	fostering Interaction; PEEL: Positive Emotions about E-Learning; NEEL: Negative Emotions
	about E-Learning; OSEL: Overall Satisfaction with E-Learning.