A, Lynott, D, Carter, A, Zerhouni, O, Meyer, S, Ladegaard, I, Gardner, J, O' Bouguettaya

KS Brien

Ayoub Bouguettaya

Dermot Lynott

Adrian Carter

Oulmann Zerhouni

Silke Meyer

Isak Ladegaard

John Gardner

Kerry S O'brien
email: kerrykez@gmail.com

The relationship between gambling advertising and gambling attitudes, intentions and behaviours: a critical

Keywords: Gambling advertising, betting, gambling, exposure, intentions, behaviour

Gambling advertising has become ubiquitous in westernised countries in the last two decades, yet there is little understanding of the relationship between exposure to gambling advertising and gambling attitudes, intentions and behaviour. We conduct a critical and meta-analytic review of the past two decades of empirical research. The research suggests a positive association between exposure to gambling advertising and gambling-related attitudes, intentions, and behaviour. The association is greatest for gambling behaviour. There is some evidence for a dose-response relationship. The quality and breadth of research on gambling advertising is weaker than comparable areas (e.g., alcohol, tobacco), with an absence of longitudinal and experimental studies. Gaps in, and methodological problems with, the field are discussed, and research directions recommended.

Introduction

Gambling is one of the world's largest industries, generating over US$500 billion in revenue per year (1). The gambling industry has grown substantially in the past two decades due in part to technological advances [START_REF] Markham | Big gambling": the rise of the global industry-state gambling complex[END_REF]. Because of its significant social, mental health, and economic costs, gambling has become a serious public health issue, and of concern to peak bodies such as the World Health Organisation [START_REF]The epidemiology and impact of gambling disorder and other gambling-related harm[END_REF].

Along with availability and pricing, restrictions on advertising has been identified as one of the most cost-effective measures for reducing harms from products such as alcohol and tobacco [START_REF] Casswell | Reducing harm from alcohol: call to action[END_REF], and might also be effective for gambling. Restrictions of alcohol and tobacco advertising have been introduced in many countries on the back of reviews of the evidence showing an association between exposure to alcohol and tobacco advertising and greater consumption [START_REF] Anderson | Impact of alcohol advertising and media exposure on adolescent alcohol use: a systematic review of longitudinal studies[END_REF][START_REF] Smith | The effect of alcohol advertising, marketing and portrayal on drinking behaviour in young people: systematic review of prospective cohort studies[END_REF][START_REF] Lovato | Impact of tobacco advertising and promotion on increasing adolescent smoking behaviours[END_REF]. However, effective regulations have yet to be developed for gambling advertising, and this appears in large part because of a lack of understanding of the relationship between gambling advertising and gambling-related attitudes, intentions, and behaviour [START_REF] Banks | Towards global gambling[END_REF][START_REF] Derevensky | Social casino gaming and adolescents: Should we be concerned and is regulation in sight?[END_REF]. Instead, gambling industry expenditure on advertising is increasing, and remains largely free from effective regulation [START_REF]Trends in Advertising Activity -Gambling[END_REF]. The aim of this review is to examine the evidence on the relationship between gambling advertising and gambling-related attitudes, intentions, and behaviours.

The effect of gambling advertising: an understudied field

That greater exposure to advertising of addictive products is associated with more positive attitudes, use initiation and more problematic use, is established [START_REF] Anderson | Impact of alcohol advertising and media exposure on adolescent alcohol use: a systematic review of longitudinal studies[END_REF][START_REF] Smith | The effect of alcohol advertising, marketing and portrayal on drinking behaviour in young people: systematic review of prospective cohort studies[END_REF][START_REF] O'brien | Alcohol industry sponsorship and hazardous drinking in UK university students who play sport[END_REF][START_REF] Lund | Gambling Behaviour and the Prevalence of Gambling Problems in Adult EGM Gamblers when EGMs are Banned. A Natural Experiment[END_REF]. For example, a systematic review of longitudinal research found that exposure to alcohol advertising was associated with greater drinking intentions, earlier initiation of drinking, and more problematic drinking [START_REF] Anderson | Impact of alcohol advertising and media exposure on adolescent alcohol use: a systematic review of longitudinal studies[END_REF]. Similar relationships have been observed for tobacco [START_REF] Lovato | Impact of tobacco advertising and promotion on increasing adolescent smoking behaviours[END_REF].

Despite comparable potential for harm, the effect of gambling advertising has historically been understudied compared to other areas of addiction, restricted by regulatory requirements [START_REF] David | The role of public health advocacy in preventing and reducing gambling related harm: challenges, facilitators, and opportunities for change[END_REF], and potentially compromised by vested interests (e.g., industry funded studies; 14). The historical lack of research on gambling advertising means that policy makers, advocates, researchers, and intervention designs are poorly informed [START_REF] Williams | Prevention of Problem Gambling: A Comprehensive Review of the Evidence, and Identified Best Practices[END_REF]. This review seeks to address this gap by establishing the relationship between exposure to gambling advertising and gambling-related attitudes, intentions, and behaviour.

Methodology

Following PRISMA guidelines (Figure 1), a literature search for studies published since 1999 (completed 20 July 2019) examining the effect of, or relationship between gambling advertising and attitudes, intentions, and behaviour was conducted using research databases (i.e., ISI Web of Knowledge, PsychInfo, PubMed, Scopus) and Google Scholar.

Searches used Boolean operators to identify all papers and used combinations of the terms gambl* bet* casino* lott* promot* advert* market* intent* expect* behav* activit* spons* attitud* belie*. The lack of empirical research necessitated an inclusive approach to the review. We included research that did not report a statistical relationship (i.e., qualitative research) between gambling advertising and gambling outcomes, but which provided insights for the field. . We also did not use a strict definition for what constituted gambling attitudes, intentions, or expectancies, but instead included any papers that described their outcomes as such. Papers were deemed eligible for inclusion (and further screening) if they were in English, published after 1999, and fit a combination of advertising keywords and outcome keywords. Reference lists of gambling advertising publications were examined for additional research sources. Experts were also contacted to identify additional work. The search strategies yielded N=255 results. Physical inspection of abstracts and results to ensure the studies were empirical in nature, not review articles, established associations between gambling advertising/marketing and attitudes, intentions and behaviour, resulted in the exclusion of N=229 papers. A total 28 studies were identified and reviewed (Table 1). After examining the full text, we excluded one qualitative study conducted in young children (6year olds) because of queries regarding cognitive capacity to recall gambling advertising [START_REF] Bestman | Children's implicit recall of junk food, alcohol and gambling sponsorship in Australian sport[END_REF]. We describe the reported statistical and non-statistical relationships (qualitative) in text.

Raw effect sizes for each study are reported in Table 1. Meta-analyses were conducted for studies where sufficient statistical information was provided, and effect sizes and confidence intervals calculated for attitudes, intentions, and behaviour (see Figures 2,[START_REF]The epidemiology and impact of gambling disorder and other gambling-related harm[END_REF][START_REF] Casswell | Reducing harm from alcohol: call to action[END_REF]respectively).

In each case we converted available effect sizes to r's and submitted these values to a random-effects analysis using MAVIS (an R statistical tool). A sufficient number of studies were identified to allow for tests of publication bias for gambling behaviour research. There was no statistical indication of publication bias in research on gambling intentions and advertising studies (funnel plot asymmetry, t(5)=1. 46, p=.20), although the publication bias estimate should be treated with caution due to the smaller number of studies. There was no statistical indication of publication bias in gambling advertising and behaviour studies (funnel plot asymmetry, t(13)=1. 11, p=.29).

Gambling advertising and gambling attitudes

Eleven studies have examined the link between gambling advertising and gamblingrelated attitudes (see Table 1; [START_REF] Derevensky | An Empirical Study Examining the Impact of Gambling Advertisements on Adolescent Gambling Attitudes and Behaviors[END_REF][START_REF] Hing | Gambling sponsorship of sport: an exploratory study of links with gambling attitudes and intentions[END_REF][START_REF] Hing | Promotion of gambling and live betting odds during televised sport: Influences on gambling participation and problem gambling[END_REF][START_REF] Hing | Sports-Embedded Gambling Promotions: A Study of Exposure, Sports Betting Intention and Problem Gambling Amongst Adults[END_REF][START_REF] Korn | Commercial gambling advertising: Understanding the youth connection[END_REF][START_REF] Lee | Role of gambling media exposure in influencing trajectories among college students[END_REF][START_REF] Lamont | Affective response to gambling promotions during televised sport: A qualitative analysis[END_REF][START_REF] Pitt | What do children observe and learn from televised sports betting advertisements? A qualitative study among Australian children[END_REF][START_REF] Thomas | They are working every angle'. A qualitative study of Australian adults' attitudes towards, and interactions with, gambling industry marketing strategies[END_REF][START_REF] Clarke | Key indicators of the transition from social to problem gambling[END_REF][START_REF] Hing | Understanding persuasive attributes of sports betting advertisements: A conjoint analysis of selected elements[END_REF]. Attitude assessment included measures of affect, favourability, and interest. Five studies adopted quantitative methods, four reported significant associations between exposure to gambling advertising and more positive gambling-related attitudes. Only two studies correctly reported statistics to allow estimates of overall effect size. Effect sizes ranged from r=.12 to r=.62; Mean r=.40). Five qualitative studies reported a link between gambling advertising and gambling-related attitudes. For example, in qualitative work Thomas and colleagues [START_REF] Thomas | They are working every angle'. A qualitative study of Australian adults' attitudes towards, and interactions with, gambling industry marketing strategies[END_REF] found that participants perceived gambling advertising to be saturating, normalised gambling, and that advertising seeking to incentivise gambling (betting promotions) was effective in influencing gambling-related attitudes.

There was some evidence for a dose-response relationship between gambling advertising and attitudes similar to that observed for alcohol marketing [START_REF] Anderson | Impact of alcohol advertising and media exposure on adolescent alcohol use: a systematic review of longitudinal studies[END_REF][START_REF] Austin | How does alcohol advertising influence underage drinking? The role of desirability, identification and skepticism[END_REF][START_REF] Goodall | Automatically activated attitudes as mechanisms for message effects: The case of alcohol advertisements[END_REF], although this is primarily based on retrospective self-report. Cross-sectional work in the United States (US; N=229) found that greater self-reported exposure to gambling advertisements was related to more positive gambling attitudes [START_REF] Lee | Role of gambling media exposure in influencing trajectories among college students[END_REF]. Cross-sectional research from Australia found that exposure to gambling sponsorship of sporting events was related to favourable attitudes toward gambling [START_REF] Hing | Gambling sponsorship of sport: an exploratory study of links with gambling attitudes and intentions[END_REF]. Research with adolescents (N=1,195) also suggests that exposure to lottery advertisements increases adolescents' perceptions of success and likelihood of large cash prizes [START_REF] Monaghan | Impact of gambling advertisements and marketing on children and adolescents: Policy recommendations to minimise harm[END_REF]. A large Canadian survey of adolescents (N=1,147), found that gambling-related advertising is more likely to influence established gamblers and problem gamblers' attitudes by prompting gambling. Counter-intuitively, participants did not believe that advertising would create new gamblers [START_REF] Derevensky | An Empirical Study Examining the Impact of Gambling Advertisements on Adolescent Gambling Attitudes and Behaviors[END_REF].

Gambling advertising appears to influence gambling attitudes by normalising and/or glamorising gambling [START_REF] Deans | The role of peer influences on the normalisation of sports wagering: a qualitative study of Australian men[END_REF]. For example, research from Europe and Australia suggests that valued forms of entertainment, especially sport, are used to normalise betting and create positive attitudes toward gambling by seeing gambling as an interactive part of sport participation/viewing [START_REF] Thomas | They are working every angle'. A qualitative study of Australian adults' attitudes towards, and interactions with, gambling industry marketing strategies[END_REF][START_REF] Deans | Creating symbolic cultures of consumption: an analysis of the content of sports wagering advertisements in Australia[END_REF][START_REF] Lopez-Gonzalez | A content analysis of how 'normal'sports betting behaviour is represented in gambling advertising[END_REF][START_REF] Lopez-Gonzalez | Enhancing Media Sport Consumption: Online Gambling in European Football[END_REF]. In other countries (e.g., Canada) advertisements function to normalise and romanticize lottery ticket purchases [START_REF] Lopez-Gonzalez | Enhancing Media Sport Consumption: Online Gambling in European Football[END_REF]. However, whether lottery advertisements are successful in changing attitudes remains unclear [START_REF] Binde | Selling dreams-causing nightmares? On gambling advertising and problem gambling[END_REF][START_REF] Binde | Exploring the impact of gambling advertising: An interview study of problem gamblers[END_REF][START_REF] Binde | Gambling advertising: A critical research review[END_REF].

Gambling advertising and gambling intentions

Only eight studies have examined the link between exposure to gambling advertising and gambling-related intentions or expectancies (see Table 1; 18-20, 22, 38, 39-41). Most studies assessed intentions in a rudimentary manner by asking participants if they were going to engage in gambling behaviour, and/or within a set time period. All except three studies were cross-sectional (quantitative), and all studies except two [START_REF] Ho | The relationship between gambling accessibility and Hong Kong people's participation in gambling activities[END_REF][START_REF] Browne | The impact of exposure to wagering advertisements and inducements on intended and actual betting expenditure: An ecological momentary assessment study[END_REF] reported an overall positive association between exposure to gambling advertising and gambling intentions. Only five reported sufficient statistics details to allow effect size calculations (effects sizes ranged from r=.00 to r=.20, Mean r=.05). This small (but significant) effect size suggests there is link, although caution is warranted here as there are very few studies included in this calculation. Consistent with the findings on gambling attitudes, three studies found that participants who reported watching sports programs containing large amounts of gambling advertisements expressed greater intentions to gamble [START_REF] Hing | Gambling sponsorship of sport: an exploratory study of links with gambling attitudes and intentions[END_REF][START_REF] Hing | Sports-Embedded Gambling Promotions: A Study of Exposure, Sports Betting Intention and Problem Gambling Amongst Adults[END_REF]. Notably, this work also suggests a dose-response relationship whereby higher self-reported exposure was related to greater intentions to gamble, particularly in riskier gamblers. Gambling intentions were also associated with gambling attitudes [START_REF] Hing | Gambling sponsorship of sport: an exploratory study of links with gambling attitudes and intentions[END_REF][START_REF] Hing | Sports-Embedded Gambling Promotions: A Study of Exposure, Sports Betting Intention and Problem Gambling Amongst Adults[END_REF].

Two studies used ecological momentary assessment techniques to reduce problems with recall [START_REF] Browne | The impact of exposure to wagering advertisements and inducements on intended and actual betting expenditure: An ecological momentary assessment study[END_REF][START_REF] Russell | Are direct messages (texts and emails) from wagering operators associated with betting intention and behavior? An ecological momentary assessment study[END_REF], and both found that receipt of direct messaging (e.g., email and text prompts and promotions) was associated with greater gambling intent. And although there were no experimental studies on gambling advertising, one large population study in Hong Kong (N=4,208) found that gambling intentions were not changed (but gambling behaviour increased, see below) following a large increase in gambling advertising due to the removal of gambling marketing restrictions in neighbouring Macau [START_REF] Ho | The relationship between gambling accessibility and Hong Kong people's participation in gambling activities[END_REF]. Similarly experiments with alcohol advertising suggest that young people's exposure increases intentions to buy and consume alcohol [START_REF] Litt | Adolescent alcohol-related risk cognitions: the roles of social norms and social networking sites[END_REF][START_REF] Alhabash | Saw it on Facebook, drank it at the bar! Effects of exposure to Facebook alcohol ads on alcoholrelated behaviors[END_REF]. It is reasonable to expect that gambling advertisements would increase gambling intentions in a similar fashion.

Gambling advertising and gambling behaviour

Our review found 23 studies examining relationships between gambling advertising and gambling behaviour (12, 17-21, 26, 36, 38, 40, 41, 44-55), with 14 studies using crosssectional methods to assess the relationship. One study sought to conduct a longitudinal analysis of EMA data collected across one week in regular gamblers [START_REF] Russell | Are direct messages (texts and emails) from wagering operators associated with betting intention and behavior? An ecological momentary assessment study[END_REF], with one experimental study and three quasi-experimental studies (i.e., naturalistic studies). Overall, 16 studies assessed the relationship between gambling advertising and gambling behaviours generally, and five studies examined the relationship with problem gambling exclusively.

Because problem gambling measures also included measures of gambling frequency (a potential confound), and the overall number of studies is small, we simply treated these studies as having evidence for a gambling behaviour. All but one study suggested a statistically significant link between advertising and gambling behaviours (effects sizes ranged from r=-.08 to r=.68, Mean r=. [START_REF] Pitt | What do children observe and learn from televised sports betting advertisements? A qualitative study among Australian children[END_REF]. Five studies used qualitative methods to assess gambling advertising impact on behaviour. For example, a Norwegian study (N=25) presented gambling advertising to gamblers and asked whether they felt the advert would affect their gambling [START_REF] Binde | Exploring the impact of gambling advertising: An interview study of problem gamblers[END_REF]. Approximately half of these gamblers indicated that the advertising would increase their gambling behaviour.

Quantitative cross-sectional research in Norwegian (N=6,034; 47), Australian (N=544; 48), and US samples (N=1,813; 50) show that greater exposure to gambling advertising (both self-report and proxy measures) is associated with gambling or problem gambling behaviour. US research analysing the link between gambling advertising expenditure and lottery scratch card revenue (sales) shows a dose-response relationship between the two whereby greater advertising expenditure is associated with greater purchasing of scratch cards [START_REF] Munoz | An investigation into the sales-advertising relationship: The state lottery case[END_REF][START_REF] Stone | An analysis of selected determinants of Texas Lottery revenue[END_REF]. Notably, a study involving three US states found that for each 1% increase in advertising expenditure there was a 0.1-0.24% increase in revenue due to increased gambling [START_REF] Zhang | Over-or under-advertising by state lotteries[END_REF]. Novel work from Norway (N=1,293) examining the effect of a ban of electronic gambling machines (EMG's), which because of their attractive built-in lighting and sound functions as advertising, found a drop-off in all gambling behaviour following the government ban on EMG's [START_REF] Lund | Gambling Behaviour and the Prevalence of Gambling Problems in Adult EGM Gamblers when EGMs are Banned. A Natural Experiment[END_REF]. While it is possible that this reduction in gambling behaviour was due to a loss of accessibility to a familiar gambling method, the ban did not cover other forms of gambling which were normally located in the same place (i.e., supermarkets), which likely means the loss of EGMs lighting and built in advertising acted a loss in advertising, rather than just a loss of access. Furthermore, both studies using ecological momentary assessment (one using a longitudinal analysis; 41) found an association between advertising exposure, gambling frequency, and gambling expenditure [START_REF] Browne | The impact of exposure to wagering advertisements and inducements on intended and actual betting expenditure: An ecological momentary assessment study[END_REF][START_REF] Russell | Are direct messages (texts and emails) from wagering operators associated with betting intention and behavior? An ecological momentary assessment study[END_REF].

Ultimately, the goal of gambling advertisements is to increase gambling behaviour frequency and/or expenditure amongst established gamblers, and develop new gamblers [START_REF] Deans | Creating symbolic cultures of consumption: an analysis of the content of sports wagering advertisements in Australia[END_REF][START_REF] Lopez-Gonzalez | A content analysis of how 'normal'sports betting behaviour is represented in gambling advertising[END_REF][START_REF] Abarbanel | Gambling games on social platforms: How do advertisements for social casino games target young adults?[END_REF]. Overall, the research suggests a significant positive relationship between exposure to gambling advertising and gambling-related behaviour. Effects vary, but suggest greater exposure equals more gambling.

Conclusions

Despite decades of research detailing the increasing harm caused by gambling (3) and the rapid increase in gambling advertising [START_REF] Banks | Towards global gambling[END_REF][START_REF] Derevensky | Social casino gaming and adolescents: Should we be concerned and is regulation in sight?[END_REF], there has been a paucity of quality research, particularly longitudinal and experimental research, examining the relationship between gambling advertising and gambling-related attitudes, intentions and behaviour. . Almost half the studies were qualitative, making it harder to apply the results to the research question.

Quantitative studies on attitudes and intentions were rare, and even when they were available, many studies did not explain their measurement methods in enough detail nor provide enough statistics for measures of effect size. The research was also diverse, as some chose purely to focus on problem gamblers, or certain types of gambling, or on a particular form of gambling advertising in certain areas. This lack of high-quality research has hampered previous reviews and policy makers. Even with these limitations, this research review of the past two decades, using available evidence shows that exposure to gambling-related advertising is likely associated with more positive gambling related-attitudes, greater gambling intentions, and increases in gambling and problem gambling behaviour.

The pattern of results is consistent with those found in the fields of alcohol and tobacco

(5-7), however, the research on gambling advertising is considerably less developed than for alcohol and tobacco. In particular, there is an absence of longitudinal and experimental studies. The most convincing research on the association between advertising and attitudes, intentions and behaviour, comes from the large naturalistic quasi-experimental studies where due to government interventions gambling advertising is either banned, permitted, or increased [START_REF] Lund | Gambling Behaviour and the Prevalence of Gambling Problems in Adult EGM Gamblers when EGMs are Banned. A Natural Experiment[END_REF][START_REF] Ho | The relationship between gambling accessibility and Hong Kong people's participation in gambling activities[END_REF][START_REF] Zhang | Over-or under-advertising by state lotteries[END_REF]. This work shows a dose-response relationship between advertising and behaviour, suggesting increases in advertising leads to increases in behaviours. As with research in alcohol and tobacco advertising, cross-sectional studies show that people reporting more exposure to gambling advertising were more likely to report positive gambling attitudes, intentions, and being gamblers. Although there are challenges in conducting largescale longitudinal studies in representative population samples, the absence of such research is hampering policy makers and advocates from developing effective policies and regulations regarding gambling advertising.

Gambling advertising research needs to address a number of significant design and measurement issues. Notably, poor methodological and statistical reporting is common.

There is little justification and psychometric support for the choice of measures of exposure, attitudes, intentions, and indeed gambling behaviour. For example, one study [START_REF] Hing | Adolescent exposure to gambling promotions during televised sport: an exploratory study of links with gambling intentions[END_REF] used different Likert scales to assess attitudes to promotion of gambling during televised sport, but also used a scale developed in marketing to measure attitude to gambling sponsors of televised sport. Furthermore, links between measures of intention and behaviour have already been questioned in psychological research [START_REF] Youn | Restricting gambling advertising and the third-person effect[END_REF][START_REF] Sniehotta | Time to retire the theory of planned behaviour[END_REF], suggesting validity issues for measuring intent as a predictor of gambling behaviour. Accordingly, there is little consistency in measurement across studies, potentially compromising the integrity of the meta-analytic component of this study as it is unknown how much these measurement methods show convergent validity.

Lack of comprehensive analytical and statistical information and reporting makes assessment of the quality of evidence difficult, and undermines the credibility of the field.

Sample selection and study designs utilised in the field (largely cross-sectional), mean that reverse causation cannot be ruled out. Sample selection needs to be better to avoid bias as it is known that the gambling industry advertises in areas, and to populations, where gambling is already common and problematic (e.g., young men, those with poor impulse control, low socioeconomic status areas; 59). Although experimental designs are impractical because of the ubiquitous nature of gambling advertising, longitudinal studies in young populations who may be less exposed can overcome inherent problems with establishing causal inferences [START_REF] Anderson | Impact of alcohol advertising and media exposure on adolescent alcohol use: a systematic review of longitudinal studies[END_REF].

Direct measurements of gambling activity after observing gambling advertisements are more likely to be a valid measure of their impact. For example, a study could track gambling advertising in mobile phones compared to the installing and use of gambling applications, which appear to be a significant form of gambling [START_REF] Deans | I can sit on the beach and punt through my mobile phone": the influence of physical and online environments on the gambling risk behaviours of young men[END_REF].

Use of standardised definitions and measurement of advertising exposure and gambling behaviours would lead to better understanding of the causal mechanisms involved.

For example, most studies developed their own definitions and measures to assess the impact of diverse forms of advertising against varying definitions of gambling attitudes, intentions, and behaviour. Notably, the studies on behaviour often use scales on problem gambling to assess gambling, masking potential associations between gambling advertising and a broader range of gambling behaviours.

Overall, the breadth and quality of research in this area needs to be improved.

Governments and non-gambling funded bodies need to invest in quality research on the effect of gambling advertising. In the absence of government funding for research in this area, it is possible that the gambling industry funded research, as found with the tobacco and alcohol industry, could result in a biased and/or unreliable evidence base [START_REF] Mccambridge | Vested interests in addiction research and policy. The challenge corporate lobbying poses to reducing society's alcohol problems: insights from UK evidence on minimum unit pricing[END_REF][START_REF] Adams | Ways in which gambling researchers receive funding from gambling industry sources[END_REF][START_REF] Chapman | Research from tobacco industry affiliated authors: need for particular vigilance[END_REF]. Although our research did not find evidence of publication bias in behaviour links to gambling advertising, it is worth remembering that much of the research examined in this review used problem gamblers as the sample of interest, which in turn, pathologizes the issue rather than discuss social harm. Therefore, industry funded studies may have an actual incentive to report a relationship in these studies, while divesting or downplaying any studies that use the general population. This may mask findings which are unfavourable to the gambling industry, while also showing no publication bias. To conduct these studies, public funding is required.

Governments at state and/or federal/national levels gather considerable revenue from gambling, and disproportionately from those most at risk of being problem gamblers.

Accordingly, it is their responsibility that they need to ensure that the societal harms associated with gambling are minimised by supporting research that can inform best practice for reducing gambling harms.

Gambling is a growing problem for most western societies [START_REF] Banks | Towards global gambling[END_REF], and the gambling industry's profit motive means that they now spend record amounts on gambling advertising [START_REF]Trends in Advertising Activity -Gambling[END_REF]. The past two decades of research suggests that the gambling industries investment in advertising is effective. The more people are exposed to gambling advertising, the more likely they are to become gamblers and problem gamblers. In the absence of effective government regulation, gambling advertising is likely to increase and be more influential, and lead to greater societal harm. Within this climate it is important that more and higher quality research on this issue is conducted in order to inform regulations and interventions that can reduce gambling harms.

Figure 2 :Figure 3 :

 23 Figure 2: Coefficients and confidence intervals for relations between gambling advertising

Table 1 .

 1 Summary of studies reviewed

	Authors	N's	Setting	Population	Study Design	Independent	Outcome	Relationship	Recall	Self-	Raw	Attitude	Intent link	Behaviour
						variables	variables*	found	of	report for	measures	link and	and average	link and
						(IVs)	(DVs)		adverts	outcome	reported for	average	effect size	average effect
											effect size	effect size		size
	Browne,	597	Australia	Regular	Cross-	advertising	Intent AND	Yes and no;	No	Yes	IV: gambling	N/A	Yes and No:	Yes; sports
	Hing,			gamblers	sectional	observed	Problem	exposure to			exposure		Sports betting	betting r=.06,
	Russell,			(18+ years)	(repeated	(recall-but	Gambling	advertising			DV for race		r=.01, Race	race betting
	Thomas,				measure/ecol	immediate	AND	associated			betting, all		betting r=.00	.03
	Jenkinson				ogical	through	Gambling	with higher			odd ratios:
	(2019) (40)				momentary	ecological	Behaviour	betting and			intent:1.00
					assessments)	assessment)	(actual	spend, but not			Behav (actual
							betting,	with			spend): 1.24
							amount	intentions
							spent-split	(with some			DV for race
							on race vs	exceptions of			betting, all
							sport bet)	direct			odds ratio:
								advertising)			intent:1.03
											Behav (actual
											spend): 1.13
	Clemens,	4617	Germany	Adolescent	Cross-	Presented	Gambling	Yes, top	No,	Yes	IV: correct	N/A	N/A	Yes:
	Hanewinke			s and young	sectional	masked	behaviour	quartile of	Recogn		recall rate			r=0.28
	l,&			adults 13-		advertising		exposure had	ition		DVs and their
	Morgenster			25 years				higher			Ds from ORs,
	n, (2017)							gambling			comparing
	(43)							rates than			bottom
								lowest			quartile to top
											quartile of
											exposure to
											advertising:
											Lifetime prev
											of gambling
											(.468)
											12-month
											prevalence
											(.473)
											Current
											gambling
											(called once a
											week): (.692)


Fanny Lalot
email: fanny.lalot@unige.ch

Alain Quiamzade

Oulmann Zerhouni

Regulatory focus and self-determination motives interact to predict students' nutrition habit intentions

Keywords: self-determination, regulatory focus, extrinsic and intrinsic motives, health behaviour, nutrition Public Significance

 are two motivation theories widely applied in health intervention research but never conjointly, despite sharing a number of theoretical similarities. In three studies (N = 578), we investigated how university students' self-determination motives to act upon their nutrition interact with induced regulatory focus and also regulatory message framing to predict their behaviour or intention to improve their eating habits. Results revealed a fit between extrinsic motives and prevention focus: intention increased with extrinsic motives in a prevention but not promotion focus. The effect of intrinsic motives, however, was independent of the focus, which suggests that these motives drive intention and behaviour independently of external cues. Hence, the results advocate for simultaneously taking into consideration self-determination and regulatory focus when planning a health intervention relying on motivation.

Regulatory focus and self-determination motives interact to predict students' nutrition habit intentions Poor and unbalanced nutrition rates are currently increasing in the Western societies according to health specialists. The whole population is concerned (World Health Organization, 2011), but some groups are more at risk than others. For example, it has recently been highlighted that university students were especially likely to develop and maintain an unhealthy diet [START_REF] Racette | Changes in weight and health behaviors from freshman through senior year of college[END_REF][START_REF] Vella-Zarb | The 'Freshman 5': A Meta-Analysis of Weight Gain in the Freshman Year of College[END_REF]. If these students benefit from a fair amount of knowledge about nutrition, they lack time and money to engage in a healthy lifestyle. Intervention programs have started tackling the issue but results are still limited (see [START_REF] Franko | Motivation, self-efficacy, physical activity and nutrition in college students: Randomized controlled trial of an Internet-based education program[END_REF][START_REF] Kelly | Systematic Review of Dietary Interventions With College Students: Directions for Future Research and Practice[END_REF][START_REF] Milkman | Behavior Change for Good Initiative[END_REF].

The success of an intervention relies on complex interactions between the individuals' characteristics and the context in which the intervention takes place, the intervention itself (style and content) being considered as a crucial element of the context. In this view, motivational states have a key role to play and have been investigated through two lenses.

First, motivational states are taken into account as a chronic disposition that will determine a person's responsiveness to an intervention (e.g., [START_REF] Maes | Self-Regulation Assessment and Intervention in Physical Health and Illness: A Review[END_REF]. Second, the intervention itself can be designed so that it induces a specific motivational state, which, in turn, increase the intervention's effectiveness (e.g., [START_REF] Noar | Tailored Health Communication to Change Lifestyle Behaviors[END_REF].

As such, two motivation theories have been widely applied to help create efficient messages and interventions: self-determination theory [START_REF] Deci | The 'what' and 'why' of goal pursuits: Human needs and the selfdetermination of behavior[END_REF] and regulatory focus theory [START_REF] Higgins | Beyond pleasure and pain[END_REF]. They have, however, always been considered independently from one another but for one notable, purely theoretical exception. [START_REF] Meyer | Employee commitment and motivation: a conceptual analysis and integrative model[END_REF] present regulatory focus and self-determination as two parallel ways of considering motivational states. They propose that both autonomous regulation and promotion focus will increase as a result of a greater salience of what they call "internal drives", whereas controlled regulation and prevention focus will increase when "external demands" are made more salient [START_REF] Meyer | Employee commitment and motivation: a conceptual analysis and integrative model[END_REF](Meyer et al., , p. 1000)). We propose to extend the idea of a link between self-determination and regulatory focus one step forward by suggesting that they could interact and should therefore be considered together, rather than separately. The present paper proposes a first step towards the investigation of the combined effect of the person's intrinsic and extrinsic motives to act upon their eating habits and the framing of the intervention message in terms of promotion versus prevention focus.

Self-Determination Theory and Applications

Two behavioural motives

Self-determination theory proposes that an intrinsic motivation arises when three basic psychological needs (i.e., autonomy, competence, and relatedness) are fulfilled; this intrinsic -or autonomous-motivation represents the pursuit of an activity because it is interesting, enjoyable, and challenging [START_REF] Deci | The Empirical Exploration of Intrinsic Motivational Processes[END_REF], 2000, 2008). By opposition, extrinsic -or controlled-motivation represents the pursuit of an activity for more external reasons.

Motivations are organised on a continuum of increasing self-determination [START_REF] Deci | The 'what' and 'why' of goal pursuits: Human needs and the selfdetermination of behavior[END_REF], from completely external (e.g., reward and punishment) to introjected (e.g., pride and shame) to identified (i.e., the behaviour is internalised but still pursued as a mean and not an end) to integrated (i.e., fully internalised). Individual differences in self-determination have been investigated in two different ways. The first is causality orientation, that is, one's general motivational orientation in life (autonomous, controlled, or impersonal; [START_REF] Deci | The general causality orientations scale: Self-determination in personality[END_REF].

The second concerns one's motives to pursue an action, which are labelled as intrinsic (e.g., affiliation, generativity, and personal development) versus extrinsic (e.g., wealth, fame, social approbation; [START_REF] Deci | The 'what' and 'why' of goal pursuits: Human needs and the selfdetermination of behavior[END_REF][START_REF] Kasser | Further Examining the American Dream: Differential Correlates of Intrinsic and Extrinsic Goals[END_REF].

Intrinsic and extrinsic motivation and health behaviour

Self-determination theory has been widely applied to health interventions (see [START_REF] Ng | Self-Determination Theory Applied to Health Contexts: A Meta-Analysis[END_REF][START_REF] Teixeira | Exercise, physical activity, and self-determination theory: A systematic review[END_REF], for reviews) with three main scopes. First, programs insisting on individuals' autonomous regulation yield better results, for example regarding weight loss amongst obese patients [START_REF] Silva | Using self-determination theory to promote physical activity and weight control: a randomized controlled trial in women[END_REF][START_REF] Williams | Motivational predictors of weight loss and weight-loss maintenance[END_REF]. Second, individuals with a stronger autonomous orientation have more success in modifying their habits in the longer run [START_REF] Deci | The Empirical Exploration of Intrinsic Motivational Processes[END_REF], for example in maintaining weight loss [START_REF] Williams | Motivational predictors of weight loss and weight-loss maintenance[END_REF]. Third, intrinsic motives have a positive effect on the adoption of health behaviour, notably regarding exercise and weight loss. Extrinsic motives, however, yield mixed findings [START_REF] Teixeira | Exercise, physical activity, and self-determination theory: A systematic review[END_REF], having sometimes a positive impact, sometimes no impact and, more rarely, a negative impact.

An explanation for those mixed findings could be that extrinsic motives need to be articulated with other elements to be effective. For example, their impact might depend on the nature of the task: extrinsic motivators such as rewards can increase task enjoyment and performance when the task is considered boring or aversive [START_REF] Deci | The Empirical Exploration of Intrinsic Motivational Processes[END_REF]. The task is still considered as a mean and not an end but commitment can be high nonetheless. Moreover, the same behaviour can be produced because of several coexisting reasons. For example, one can adopt a goal of exercising often because it is a mean to lose weight, to improve one's body-image, to maintain cardiac health, or because it provides an occasion to socialise in a sport club, or still because one enjoys exercisingor for any and all these reasons [START_REF] Ingledew | Three Levels of Exercise Motivation[END_REF]. This implies that motives do not exclude each other. As such, one could first engage in a behaviour for extrinsic motives and then learn to enjoy it and pursue it for more intrinsic motives. Accordingly, [START_REF] Teixeira | Exercise, physical activity, and self-determination theory: A systematic review[END_REF] recommend avoiding denigrating a patient's motives even when those are extrinsic (see also [START_REF] Ingledew | The role of motives in exercise participation[END_REF].

Finally, some research suggests that interventions are more efficient when they fit to the individual's motives. Investigating safer sexual activity amongst adolescents, [START_REF] Sanderson | Social dating goals in late adolescence: implications for safer sexual activity[END_REF] found that interventions focusing on communication skills were more efficient for adolescents who pursue social dating for intrinsic motives (here, intimacy goals), while interventions focusing on technical skills were more efficient for those endorsing extrinsic motives (here, identity goals). In the present paper, we aim to pursue this view and suggest that interventions framed in terms of promotion versus prevention (i.e., regulatory focus; [START_REF] Higgins | Beyond pleasure and pain[END_REF] could be more or less effective depending on the person's intrinsic and extrinsic motives for action. In the next section, we briefly describe regulatory focus theory before exposing how it relates to self-determination.

Regulatory Focus Theory and Applications

Regulatory focus and regulatory fit theory

Regulatory focus theory [START_REF] Higgins | Beyond pleasure and pain[END_REF] distinguishes two independent motivational systems: A prevention focus arises from security needs and is related to "ought" goals (obligations and duties). It implies a particular attention to potential negative outcomes and a preference for vigilant means and strategies [START_REF] Crowe | Regulatory focus and strategic inclinations: Promotion and prevention in decision-making[END_REF][START_REF] Friedman | The effects of promotion and prevention cues on creativity[END_REF]. A promotion focus arises from nurturance needs and is related to ideal goals (hopes and aspirations). Attention is drawn to potential positive outcomes and eager means and strategies are favoured. Regulatory focus is a motivational disposition that can be reliably measured (e.g. [START_REF] Higgins | Achievement orientations from subjective histories of success: Promotion pride versus prevention pride[END_REF][START_REF] Lockwood | Motivation by positive or negative role models: Regulatory focus determines who will best inspire us[END_REF]. Nonetheless, it can also be induced by contextual factors. For example, a person can intermittently focus on their current ideal versus ought goals, which would put them in a promotion versus prevention mind-set, respectively (see [START_REF] Freitas | Enjoying goal-directed action: The role of regulatory fit[END_REF][START_REF] Guo | Regulatory focus affects predictions of the future[END_REF]. They can also be led to think about a particular issue in a given mind-set, i.e., a framing of the issue in terms of ideal versus obligation, safety versus growth, and gain versus loss (e.g., [START_REF] Falomir-Pichastor | A regulatory fit perspective in majority versus minority support to attitudes toward homosexuals[END_REF]. Message framing can similarly induce a promotion versus prevention mind-set [START_REF] Cesario | A self-regulatory framework for message framing[END_REF].

A notion of regulatory fit was subsequently derived from regulatory focus theory [START_REF] Higgins | Making a good decision: Value from fit[END_REF][START_REF] Higgins | Value From Regulatory Fit[END_REF]. Regulatory fit research proposes that a "feeling right" experience arises when there is a fitor correspondencebetween different aspects of the situation and the individual, which results in higher commitment, persuasion, behaviour change, and performance [START_REF] Freitas | Enjoying goal-directed action: The role of regulatory fit[END_REF][START_REF] Higgins | Transfer of value from fit[END_REF][START_REF] Plessner | Regulatory fit as a determinant of sport performance: How to succeed in a soccer penalty-shooting[END_REF]. As such, perceived persuasiveness of a message and subsequent intention to act are higher when the person's focus fits with the framing of a persuasion message [START_REF] Cesario | Regulatory Fit and Persuasion: Transfer From 'Feeling Right[END_REF], as well as when the different aspects of the message fit one another (see [START_REF] Cesario | A self-regulatory framework for message framing[END_REF][START_REF] Cesario | Regulatory Fit and Persuasion: Basic Principles and Remaining Questions[END_REF]; for reviews). Fit effects have also been identified between a promotion versus prevention framing and other situational elements, such as perceived risk [START_REF] Lee | Bringing the Frame Into Focus: The Influence of Regulatory Fit on Processing Fluency and Persuasion[END_REF]) and behavioural control [START_REF] Haddad | Persuading young car drivers to take part in a driving skills test: The influence of regulatory fit on informational-assessment value and persuasion[END_REF].

Regulatory focus and fit, and health behaviour

Literature suggests that promotion and prevention underpin different behaviours and can lead to both healthy and unhealthy conducts via different routes. For example, eating behaviour under a promotion (prevention) focus relies more on internal cues such as satiation (external cues such as social approbation; [START_REF] Florack | The moderating role of regulatory focus on the social modeling of food intake[END_REF]. Neither this study nor numerous others yielded a main effect of the focus on behavioural outcomes (e.g., [START_REF] Avraham | Regulatory focus and adherence to self-care behaviors among adults with type 2 diabetes[END_REF][START_REF] Berezowska | The interplay between regulatory focus and temporal distance in the health context[END_REF][START_REF] Cesario | Regulatory Fit and Persuasion: Transfer From 'Feeling Right[END_REF] for one exception showing an advantage of promotion focus, see [START_REF] Joireman | Promotion Orientation Explains Why Future-Oriented People Exercise and Eat Healthy: Evidence From the Two-Factor Consideration of Future Consequences-14 Scale[END_REF]. In other words, health behaviours one ultimately adopts can be underpinned by different motivations, such as preventing illness versus promoting health [START_REF] Gomez | Avoiding poor health or approaching good health: Does it matter? The conceptualization, measurement, and consequences of health regulatory focus[END_REF]. Accordingly, most studies find a regulatory focus effect that is moderated by another factor, conceptualised as an effect of regulatory fit. Individuals adopt more behaviours that are supposed to be beneficial for their health when the persuasion message fits with the person's focus: participants reported a greater intention to increase their fruits and vegetables intake when an eagerness (vigilance) message framing matched their promotion (prevention) focus [START_REF] Cesario | Regulatory Fit and Persuasion: Transfer From 'Feeling Right[END_REF], and when the emphasis was put on benefits versus costs, respectively [START_REF] Spiegel | How regulatory fit enhances motivational strength during goal pursuit[END_REF]. Similarly, intention to adhere to medical care regimens was higher amongst prevention-oriented patients when the message framing fit their orientation [START_REF] Avraham | Regulatory focus and adherence to self-care behaviors among adults with type 2 diabetes[END_REF]. Regulatory focus also interacts with temporal distance of the highlighted health outcomes: a promotion focus increases intention and behaviour when distant outcomes are highlighted whereas a prevention focus proves more efficient when immediate outcomes are highlighted [START_REF] Berezowska | The interplay between regulatory focus and temporal distance in the health context[END_REF]. Finally, promotion and prevention are differentially related to behavioural initiation and behavioural maintenance. Drawing from Rothman and colleagues' model [START_REF] Rothman | Toward a theory-based analysis of behavioral maintenance[END_REF][START_REF] Rothman | Self-regulation and behavior change: Disentangling behavioral initiation and behavioral maintenance[END_REF], [START_REF] Fuglestad | Getting there and hanging on: the effect of regulatory focus on performance in smoking and weight loss interventions[END_REF] observed that promotion-oriented participants were more efficient in initiating behaviour change (quitting smoking and losing weight) whereas prevention-oriented participants were more efficient in maintaining their efforts in the long run. A promotion focus also predicted a more stable weight loss at two years amongst people who were far from their weight goal; conversely, a prevention focus proved more efficient amongst people who were close from their goal [START_REF] Fuglestad | Regulatory Focus, Proximity to Goal Weight, and Weight Loss Maintenance[END_REF]; see also [START_REF] Bullard | How Goal Distance Influences Regulatory Focus in Goal Pursuit[END_REF][START_REF] Bullard | How goal progress influences regulatory focus in goal pursuit[END_REF].

A Fit between Regulatory Focus and Intrinsic-Extrinsic Motives

In sum, several investigations have identified a fit between regulatory focus and other contents in the health domain. However, to the best of our knowledge, no work has yet studied such a fit with self-determination motives. We propose here that individuals' intrinsic and extrinsic motives for acting upon their health could fit with regulatory focus because they share a number of core constituents, and that such a fit potentially increases commitment to health-related behaviour. Indeed, past research has shown that the motives could make the individual more receptive to certain features of an intervention [START_REF] Sanderson | Social dating goals in late adolescence: implications for safer sexual activity[END_REF].

We propose that they could determine the persuasiveness of a message framed in promotion versus prevention terms. We investigate here, specifically, how the person's intrinsic and extrinsic motives interact with a message framing in terms of promotion versus prevention.

First, prevention focus and extrinsic motives share a preoccupation about obligations and ought, i.e., goals pursued because of a certain normative pressure and need for social acceptance. In this vein, an aforementioned study found people to rely more on cues of social approbation (i.e., an extrinsic motive) to regulate their eating behaviour under a prevention focus [START_REF] Florack | The moderating role of regulatory focus on the social modeling of food intake[END_REF]. Similarly, discrepancies between the actual and the "ought" self [START_REF] Higgins | Self-discrepancy: a theory relating self and affect[END_REF] result in emotions of shame and guilt as well as fear of punishmentall features that correspond to extrinsic motives for action. Deci and Ryan themselves wrote that, in their view, "the 'ought self' is a set of introjected values or standards that can affect the self and motivate behaviour but is not the basis for self-determined action" (Deci & Ryan, 2000, p. 248). From such similarities, one can expect a fit when the person holds strong extrinsic motives and the intervention or the message adopts a prevention, rather than promotion, framing. As they are per definition externally driven, extrinsic motives should be highly sensitive to contextual changes; as a result, the person's commitment would greatly depend on the situation of fit versus non-fit, as a function of the message framing. Hence, when there is a fit, one would expect that the higher the extrinsic motives, the higher the commitment towards healthier behaviourswhile no such result would appear when there is a non-fit.

Second, promotion and intrinsic motives both relate to a need for personal development ("nurturance" or "growth") and as such, they imply the pursuit of an ideal. Indeed, the "ideal" self [START_REF] Higgins | Self-discrepancy: a theory relating self and affect[END_REF]) is an integrated self-schema that relies on the person's internal values as self-guides and, as such, would underlie autonomous motivation [START_REF] Deci | The 'what' and 'why' of goal pursuits: Human needs and the selfdetermination of behavior[END_REF]. Promotion-related emotions (i.e., cheerfulness and dejection) similarly refer to an intrapersonal rather than interpersonal (or external) perspective [START_REF] Higgins | Emotional responses to goal attainment: Strength of regulatory focus as moderator[END_REF]. In direct relation with health, individuals in a promotion focus were also found to rely more on internal cues (e.g., satiation) to regulate their eating behaviour [START_REF] Florack | The moderating role of regulatory focus on the social modeling of food intake[END_REF]. As such, one could expect a fit when the person holds strong intrinsic motives and the intervention or message adopts a promotion, rather than prevention, framing.

However, intrinsic motives are, per definition, an internal drive to behaviour. As such, they might be less sensitive, or not at all, to external cues. The promotion-prevention framing being such a contextual cue, it could be of lesser importance in predicting subsequent commitment when intrinsic motives are prevailing. In other words, intrinsic motives are more independent from the context; hence, changing the context and implementing a fit versus nonfit situation could induce less change, if not at all, compared to extrinsic motives. Thus, the prediction for intrinsic motives is not straightforwardly symmetrical to the one for extrinsic motives. In the former case, we would expect the fit versus non-fit situation to have a weaker or even no effect on commitment.

Overview of the studies

We present three studies in which participants' motives to act upon their nutrition were assessed, and regulatory focus was manipulated either as a general mind-set (Study 1), the framing of an intervention message (Study 2) or a specific mind-set regarding nutrition (Study 3). Dependent variables included personal behavioural intention (Study 1), willingness to participate in an online health program (Study 2) and information-seeking behaviour (Study 3). The research was approved by the ethics committee of the first author's university. All measures and manipulations included in the studies are reported.

Study 1

Method

Participants. University students were contacted by email to participate in an online study about students' nutrition habits. We determined the required sample size through an a priori power analysis [START_REF] Faul | G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences[END_REF]. For this first study we assumed a small-to-medium effect size (Cohen's d = .42). The analysis recommended a minimal N of 180 to ensure 80% power for our design. A total of 188 participants, amongst which 56 men and 132 women, completed the study (average age = 24.4, SD = 6.12). They were randomly assigned to one condition of regulatory focus (promotion: N = 94, prevention: N = 94).

Independent variables

Intrinsic and extrinsic motives. Drawing from the literature [START_REF] Deci | The 'what' and 'why' of goal pursuits: Human needs and the selfdetermination of behavior[END_REF][START_REF] Osbaldiston | Promoting internalized motivation for environmentally responsible behavior: A prospective study of environmental goals[END_REF][START_REF] Tabernero | Self-efficacy and intrinsic motivation guiding environmental behavior[END_REF], we first measured participants' intrinsic and extrinsic motives to act upon their eating habits through four items, two for each motivation (7-point scale, 1 = not at all, 7 = very much). We conducted an exploratory factorial analysis on the four items. As intrinsic and extrinsic motives are not fully independent but can, instead, correlate, we use an oblique rotation (i.e., Oblimin method; [START_REF] Abdi | Factor Rotations in Factor Analyses[END_REF], which revealed two independent factors corresponding to intrinsic and extrinsic motives, accounting for 76% of variance (interfactor correlation: r(186) = -.01, p = .93).

Hence, we computed separate scores of intrinsic and extrinsic motives. Items, loadings, and descriptive statistics are reported in Table 1. In this study as well as the two following ones, we also assessed participants' current eating habits (e.g., consumption of sweets, calorific food, alcohol, coffee, fruits and vegetables, read and white meat). The variable, however, did not interact with the independent variables nor did it change the effects when entered as covariable in the statistical models.

Hence, we do not discuss it. Additional analyses can be obtained upon request from the corresponding author.

Regulatory focus induction.

We induced regulatory focus through the "current ideals or ought procedure" described by [START_REF] Freitas | Enjoying goal-directed action: The role of regulatory fit[END_REF] see also [START_REF] Guo | Regulatory focus affects predictions of the future[END_REF].

Depending on the experimental promotion (vs. prevention) condition, participants read, "We

Discussion

A first study tested the idea that motives interact with regulatory focus to predict personal intention to improve eating habits. As expected, prevention focus fit with extrinsic motives: the stronger the extrinsic motives, the higher the intention to act, in the prevention condition. In the promotion condition, intention was independent from extrinsic motives.

Regarding intrinsic motives, results -with all caution related to interpreting null findingsseem to support the idea that intrinsic motives drive behaviour independently from contextual cues, in this case from the regulatory focus mind-set manipulation; hence, a fit does not lead to any benefit compare to a non-fit for those motives.

Extrinsic motives

Personal behavioural intention

Prevention focus

Promotion focus

Two limitations of this first study must be noted. First, the regulatory focus induction corresponded to a general focus that was not directly related to nutrition. Second, the dependent variable was limited to a rather abstract personal intention to put in more efforts regarding one's nutrition. To address these limitations, a second study adopted a more ecological design where regulatory focus was induced through the framing of a text depicting the issues of an unhealthy diet amongst students, and where the dependent measure assessed

Independent variables

Measures of intrinsic and extrinsic motives. Again, we started by assessing participants' intrinsic and extrinsic motives. To increase validity, we added two items to the initial set of four used in the previous study. An exploratory factorial analysis with Oblimin rotation revealed two independent factors corresponding to intrinsic and extrinsic motives, and accounting for 70% of variance (interfactor correlation r(175) = .10, p = .19), and we accordingly created separate composite scores of intrinsic and extrinsic motives (see Table 1).

Regulatory focus manipulation.

After these measures, we presented participants with a one-page newspaper-like article on the topic of students' nutrition. The article described the current situation of unhealthy dieting amongst students, identified responsible factors (i.e., lack of time and money and high levels of daily stress) and reported on an intervention program that aimed to rectify the situation, with preliminary positive results. Two versions of the article were created in order to induce a prevention or a promotion focus including, respectively, a loss-versus gain-framing, vigilance versus eagerness strategies, and focusspecific emotions. Core differences are reported in Table 2, and full texts are included in a supplementary material appendix in the original language (Appendix I). program?" (7-point scale, 1 = not at all, 7 = very much). Answers loaded on a single factor in an exploratory factorial analysis and were aggregated (α = .80, M = 3.63, SD = 1.47). i

Results

Willingness to participate in the program was regressed on regulatory focus (-1 = prevention, +1 = promotion), intrinsic and extrinsic motives (both standardised) and all interactions (overall model: F(7,169) = 6.25, p < .001, R 2 adj = .17

Discussion

This second study replicated the interaction effect found in Study 1 with a different regulatory focus induction as well as a different dependent variable. This more ecological manipulation of regulatory focus increases the findings' reliability and suggests intervention directions for creating efficient messages. Although in this study the moderation effect fell just short of significance, simple effects indicated a fit effect between extrinsic motives and prevention focus: willingness to act increased with extrinsic motives in the prevention condition only. Consistent with the first study, intrinsic motives were independent from the focus, supporting the hypothesis that they drive behaviour regardless of external cues.

Before concluding, we conducted a third study in order to strengthen our results and answer a few remaining questions. In this last study we utilised yet another regulatory focus induction, manipulating participants' conception of nutrition in promotion versus prevention terms. We also moved to a more behavioural dependent measure. Indeed, it is important to

Independent variables

Measures of intrinsic and extrinsic motives. We used the same six items as in Study 2

to assess participants' intrinsic and extrinsic motives. Consistent with previous findings, items loaded on two separate factors (accounting for 70% of variance) independent from one another, r(212) < .001, p = .99, allowing to create separate scores of intrinsic and extrinsic motives (see Table 1).

Regulatory focus manipulation.

The manipulation aimed to put participants in a specific mind-set (see [START_REF] Falomir-Pichastor | A regulatory fit perspective in majority versus minority support to attitudes toward homosexuals[END_REF]study 3). Participants were instructed to think about the value of personal health and more specifically of a healthy diet. They answered three short tasks that englobed the different components of regulatory focus, namely, type of goal, type of strategy, valence of the outcomes, and focus-related emotions.

Specifically and depending on the experimental condition, participants indicated to what extent maintaining their personal health represented a personal ideal (obligation), an aspiration (ought) and a goal to attain (a requirement to respect). Second, they described two strategies allowing to promote a healthy diet (prevent an unhealthy diet) as well as the two main consequences ensuing from a healthy diet (the avoidance of an unhealthy diet), according to them. Finally, they reported to what extent they would feel a set of emotions when adopting a healthy behaviour (avoiding an unhealthy behaviour; see [START_REF] Shah | Regulatory concerns and appraisal efficiency: The general impact of promotion and prevention[END_REF] or not.

Dependent measure: information-seeking behaviour. After the manipulation, we indicated that the National Society of Nutrition (NSN) had launched a website offering nutrition tips as well as different tests (e.g., BMI and calories intake calculator). Participants indicated whether they wished to be redirected to this website at the end of the study, or not.

This binary response formed an index of information-seeking behaviour. Overall, 61% of participants asked to be redirected to the NSN website.

Results

Regulatory focus (-1 = prevention, +1 = promotion), intrinsic and extrinsic motives (standardised) and all interactions were entered in a binary logistic regression with information-seeking as the dependent variable (0 = no wish to seek information, 1 = information seeking); overall model evaluation: χ 2 (7) = 154, p = .031; Hosmer and Lemeshow goodness-of-fit test: χ 2 (8) = 12.7, p = .12; Cox and Snell R 2 = .07. The analysis revealed a main effect of both intrinsic, B = .31 (SE = .15), Wald's χ 2 (1) = 4.14, p = .042, and extrinsic motives, B = .34 (SE = .16), Wald's χ 2 (1) = 4.36, p = .037positively predicting information seeking in both cases. The expected regulatory focus × extrinsic motives was also significant, B = -.34 (SE = .16), Wald's χ 2 (1) = 4.34, p = .037. The logistic curve for extrinsic motives was positive and significant in the prevention condition, B = .62 (SE = .25), Wald's χ 2 (1) = 6.20, p = .013, but nonsignificant in the promotion condition, B = .07 (SE = .19), Wald's χ 2 (1) = 0.14, p = .71 (see Figure 3). No other effect was significant, Wald's χ 2 (1) < 2.63, p > .11, including the intrinsic motives × regulatory focus interaction, B = .02 (SE = .16), Wald's χ 2 (1) = 0.01, p = .92.

Discussion

A third study replicated our findings, showing that probability to seek health-related information increased with extrinsic motives in the prevention, but not promotion focus condition. As observed before, the effect of intrinsic motives was independent from the focus.

The present results strengthened the previous ones by ensuring that the effects replicated on a behavioural measure, beyond simple intention.

Small-Scale Meta-Analysis

Globally, findings of the three studies were consistent. However, the interaction term failed to reach significance in the second study. To better estimate the reliability of our findings and following recommendations from [START_REF] Braver | Continuously Cumulating Meta-Analysis and Replicability[END_REF], we hence conducted a small-scale meta-analysis including the findings of all three studies.

We separately considered the intrinsic motives × regulators focus and extrinsic motives × regulatory focus interaction terms. Given its common use in meta-analyses, we

General Discussion

The present paper aimed to bring together two traditions that are widely represented in health psychology and intervention research but surprisingly always considered separately, that is, regulatory focus theory [START_REF] Higgins | Beyond pleasure and pain[END_REF] and self-determination theory [START_REF] Deci | The Empirical Exploration of Intrinsic Motivational Processes[END_REF], 2000). We proposed here that promotion versus prevention focus and intrinsic versus extrinsic motives, respectively, share a number of core components that allow to expect them to fit with each other. In three studies, we tested how university student's intrinsic and extrinsic motives to act upon their nutrition interacted with a regulatory focus framing to predict intention to improve their eating habits. To increase validity, we relied on three First, it is worth noting that intrinsic and extrinsic motives did not correlate with each other in any of the studies. This supports the idea that one person can hold different motives that coexist and together drive behaviour (see [START_REF] Ingledew | The role of motives in exercise participation[END_REF][START_REF] Ingledew | Three Levels of Exercise Motivation[END_REF]Teixeira et al., 2012, for similar considerations). Moreover, regulatory focus framing per se did not produce any main effect, which is congruent with a large body of literature showing that the regulatory focus effects are seldom direct but most often moderated by another factor (e.g., [START_REF] Avraham | Regulatory focus and adherence to self-care behaviors among adults with type 2 diabetes[END_REF][START_REF] Berezowska | The interplay between regulatory focus and temporal distance in the health context[END_REF][START_REF] Florack | The moderating role of regulatory focus on the social modeling of food intake[END_REF].

Indeed, and more interestingly, results revealed that reaction to a prevention focus framing was a function of the participants' extrinsic motives: this framing worked best for participants who reported higher extrinsic motives to act upon their nutrition habits and resulted in higher personal intention to act, willingness to participate in an online program as well as interest for nutrition-related information (i.e., the fit hypothesis). Regarding intrinsic motives, it was more difficult to draw a clear prediction. On the one hand, a fit hypothesis leads to predict an interaction with the contextual regulatory focus framing. On the other hand, these motives rely by definition on an internal drive towards action, which leads to expect a reduced or even null impact of the context. Results support this latter possibility by consistently showing no interaction between intrinsic motives and regulatory focus. Caution is of course necessary when interpreting nonsignificant results. Nonetheless, the meta-analysis suggested that this effect was reliably and homogeneously null. This highlights an interesting distinction between extrinsic and intrinsic motives, which cannot simply be considered as

Limitations and future directions

Within the scope of providing experimental results that would inform intervention research, we limited our investigation to a specific question. Importantly, we systematically used self-determination theory to represent individual differences, that is, intrinsic and extrinsic motives, and regulatory focus theory to represent (induced) contextual cues.

However, both theories are rich in nuances and can be considered at the individual as well as the contextual level. Indeed, the fact that our results revealed only a half-fit (i.e., fit between prevention and extrinsic motives, but no relation with promotion and intrinsic motives) largely depends on our paradigm in which intrinsic motives, being measured, represent the person's tendency to act for internal reasons independently of the context, as discussed above.

These results do not rule out, however, that promotion and intrinsic motives could otherwise lead to better outcomes than a non-fit. First, they could naturally coexist, which means that promotion-oriented individuals would tend to hold more intrinsic motives in general. Second, reversing the role of the constructs, one could find that promotion-versus prevention-oriented individuals react more favourably to health interventions insisting on autonomy versus control, or stressing the low versus high (social) benefits of a health-related activity, specifically; in this case a complete and symmetrical fit effect could be observed, as promotion and prevention should be comparably sensitive to the context. Finally, these factors could interact when both manipulated as contextual features, that is, an intervention might be more efficient when it both insists on autonomy and relies on typical promotion features (i.e., importance of positive outcomes, eagerness strategies, ideal goals) or when it insists on control and relies on prevention features (i.e., negative outcomes, vigilance strategies, ought goals). Future research will need to investigate these different possibilities.

Moreover, in the present set of studies we relied on a simple distinction between intrinsic and extrinsic motives, which is not uncommon in empirical research (e.g., [START_REF] Osbaldiston | Promoting internalized motivation for environmentally responsible behavior: A prospective study of environmental goals[END_REF][START_REF] Tabernero | Self-efficacy and intrinsic motivation guiding environmental behavior[END_REF]. Self-determination theory, however, distinguishes different levels of extrinsic motives [START_REF] Deci | The 'what' and 'why' of goal pursuits: Human needs and the selfdetermination of behavior[END_REF]. As such, extremely external motives such as rewards/punishments are not completely similar to introjected (pride and shame) or even identified motives (behaviour pursued as a mean), and they could differently fit with the prevention focus. Indeed, prevention is related to the "ought self" [START_REF] Higgins | Self-discrepancy: a theory relating self and affect[END_REF], which, despite focusing on obligations and potential punishments, still constitutes an inner guide to behaviour. We would imagine that the intermediate level of introjected motives could be the best suitable candidate to correspond to the prevention focus.

Our studies, however, were not designed to test such a possibility. Future research will need to measure more precisely the motives along the self-determination continuum in order to disentangle between competing external motives and identity the "sweet spot" fitting with a prevention mind-set.

As another limitation, one will note that we studied here a specific population (i.e., university students) and a specific health domain (i.e., nutrition). We would expect our results to replicate on different populations and different domains and future studies will need to assure this. More importantly, literature on message framing and health has shown that the topic under investigation could be of importance, notably when considering detection versus prevention behaviour (e.g., [START_REF] Rothman | The Strategic Use of Gain-and Loss-Framed Messages to Promote Healthy Behavior: How Theory Can Inform Practice[END_REF][START_REF] Rothman | Shaping perceptions to motivate healthy behavior: The role of message framing[END_REF]. In one study comparing three persuasive messages promoting physical activity framed in terms of loss vs. gain vs. mixed, [START_REF] Latimer | Promoting participation in physical activity using framed messages: An application of prospect theory[END_REF] found an advantage of the gain-framed message over the two others, but only in the longer run (i.e., a difference appeared at 9 but not 2-week follow-up). As such, future studies will need to ensure that the interactive effect of motives and regulatory focus holds for other health concerns including those involving higher risk, and over a longer time span.

Finally, our proposition to simultaneously take into account self-determination and regulatory focus is not solely confined to health issues. Similar interactions can be expected in a variety of others domains where a fit was found to occur, as for example pro-environmental behaviour [START_REF] Bertolotti | Effects of message framing in policy communication on climate change[END_REF] or social collective action [START_REF] Zaal | Social change as an important goal or likely outcome: How regulatory focus affects commitment to collective action[END_REF]. Future research should investigate this possibility and extend knowledge of the articulation of these different motivations, a proposition that exceeds the scope of the present article.

Notes i One will note that the four questions represent increasing levels of commitment to a given action (i.e., a Guttman scale), ranked from the least engaging (petition signing) to the most engaging (actual participation in the action). As such, one might want to know how motives and message framing impact each level of commitment. For information purposes, we report the graphs of the extrinsic motives × regulatory focus interaction for each item in Appendix II.

  will now ask you to perform a mental visualization task. Please think about something you ideally would like to do (you think you ought to do). In other words, please think about the hopes or aspirations (duties or obligations) that you currently have. Please spend at least 2 or 3 minutes to think about these hopes or aspirations (duties or obligations) as this is very important for the study." Participants reported in an open field what their ought or ideal was.The questionnaire was designed so that it was not possible to continue to the next page before at least 45 seconds had elapsed. Participants spent an average of 153 seconds (SD = 262) on the task.Dependent measure: personal behavioural intention. Finally, participants rated their intention to act upon their nutrition habits. Specifically, three questions asked: "Regarding your personal nutrition, to what extent do you think (1) you should put in more efforts; (2) you ideally would like to put in more efforts; (3) you intend to put in more efforts?" (7-point scale, 1 = not at all, 7 = very much). The nuances were introduced to ensure the items would not correspond to one focus more than the other. Answers loaded on a single factor and were aggregated (α = .90, M = 4.50, SD = 1.87).ResultsRegulatory focus (-1 = prevention, +1 = promotion), intrinsic motives (standardised), extrinsic motives (standardised) and all the interactions were entered as predictors in a linear model with personal behavioural intention as the dependent variable (overall model: F(7,180) = 2.42, p = .022, R 2 adj = .05). The analysis revealed a main effect of extrinsic motives, b = .35, 95% CI [.08, .62], t(180) = 2.55, p = .012, η 2 p = .035, so that stronger extrinsic motives predicted higher personal intention. Moreover, the expected regulatory focus × extrinsic motives interaction was also significant, b = -.32, 95% CI [-.59, -.05], t(180) = -2.36, p = .019, η 2 p = .030. Decompositions showed that the simple effect of extrinsic motivation was positive and significant in the prevention condition, b = .68, 95% CI [.31, 1.04], t(180) = 3.66, p < .001; but nonsignificant in the promotion condition, b = .05, 95% CI [-.33, .43], t(180) = 0.28, p = .78 (see Figure1). No other effect was significant. Importantly, intrinsic motives produced neither a main effect, b = -.21, 95% CI [-.47, .07], t(180) = -1.48, p = .14, η 2 p =.012, nor an interaction with regulatory focus, b = -.08, 95% CI[-.35, .19], t(180) = -0.57, p = .57, η 2 p = .002.

Figure 1 .

 1 Figure 1. Personal intention to act upon one's eating habits as a function of extrinsic motives

  participants' willingness to commit to an online health program in relation to this text. As in the previous study, participants were university students recruited by email to participate in an online study. A total of 177 participants completed the study, which fulfils the same statistical power requirements as Study 1. They were 60 men and 117 women of an average age of 23.1 (SD = 4.31). Participants were randomly assigned to one regulatory focus condition (prevention: N = 91, promotion: N = 86).

  Participants spent an average of 87 seconds reading the text (SD = 101, Median = 66). Reading time was not function of the text framing, F(1,175) = 0.23, p = .64 (prevention: M = 83.5, SD = 91.4; promotion: M = 90.7, SD = 109.9).

  ). The model yielded a main effect of both intrinsic, b = .52, 95% CI[.31, .73], t(169) = 4.97, p < .001, η 2 p = .13, and extrinsic motives, b = .29, 95% CI [.09, .49], t(169) = 2.85, p = .005, η 2 p = .046, revealing positive relations with willingness to participate in both cases. The expected regulatory focus × extrinsic motives fell just short of significance, b = -.19, 95% CI [-.39, .01], t(169) = -1.90, p = .060, η 2 p = .021. Despite its marginal nature, we decomposed the interaction with respect to our hypothesis. The extrinsic motives slope was strongly significant in the prevention, b = .52, 95% CI [.23, .80], t(169) = 3.57, p < .001, but nonsignificant the promotion condition, b = .15, 95% CI [-.16, .47], t(169) = 0.97, p = .33 (see Figure 2). No other effect reach significance, ts < 1.47, ps > .14. Importantly and consistent with the first study, the regulatory focus × intrinsic motives was not significant, b = -.01, 95% CI [-.22, .19], t(169) = -0.12, p = .91, η 2 p < .001.

Figure 2 .

 2 Figure 2. Participants' willingness to participate in an online health program as a function of

  effects found on behavioural intention replicate on actual behaviour. Hence, in this study we used a measure of information-seeking behaviour. As in previous studies, participants were university students recruited by email to participate in an online study. Because we suspected that the previous study might have been underpowered, we recruited a larger number of participants than in the previous studies. A total of 213 participants, amongst which 71 men and 142 women (average age = 23.4, SD = 6.07), completed the study. Participants were randomly assigned to one condition of regulatory focus (prevention: N = 105, promotion: N = 108).

Figure 3 .

 3 Figure 3. Probability to engage in information-seeking behaviour as a function of extrinsic

  chose Cohen's d as the effect size indicator. Using R, we computed Cohen's d for each effect es package; Del Re, 2013), then ran a random-effect model with the Sidik-Jonkman method on the data (metafor package;[START_REF] Viechtbauer | Conducting meta-analyses in R with the metafor package[END_REF]. Detailed results are reported in Table3and Figure4. The analysis revealed a significant and homogenous extrinsic motives by regulatory focus interaction effect, d = -0.31[-1.15, -0.47], z = -3.76, p < .001, Q(2) = .08, ns. The intrinsic motives by regulatory focus interaction effect, for its part, was homogeneously nonsignificant, d = -0.04, 95% CI [-0.20, 0.12], z = -0.45, ns., Q(2) = .14, ns.

Figure 4 .

 4 Figure 4. Observed Cohen's d and 95% confidence intervals for the two motives × regulatory

  different regulatory focus inductions, ranging from a general mind-set induction (Study 1) to a more specific nutrition-related mind-set induction (Study 3), as well as the framing of an intervention message (Study 2). We considered different outcomes under the form of personal intention to act upon one's health (Study 1), willingness to participate in an online health program (Study 2), and information-seeking behaviour (Study 3).

Table 1

 1 Loadings of the items measuring participants' intrinsic and extrinsic motives in Studies 1 to 3.An exploratory factorial analysis with Oblimin rotation was conducted for each study.

	Descriptive statistics and interfactor correlations are also reported.
		Study 1	Study 2	Study 3
		Factor 1 Factor 2 Factor 1 Factor 2 Factor 1 Factor 2
	Item	Intrinsic Extrinsic Intrinsic Extrinsic Intrinsic Extrinsic
	…because it is
	interesting and	.91		.91		.91
	enjoyable to do it
	...because it is
	important and	.91		.87		.87
	worthwhile to me
	…because I enjoy doing it	n/a		.94		.93
	…because I feel like I have to do it		.83		.78		.81
	…because I gain social acceptance through it		.82		.78		.82
	…because I have the
	possibility to gain something (or avoid to		n/a		.68		.52
	lose something)
	M (SD)	5.05 (1.72)	2.32 (1.40)	4.74 (1.57)	2.74 (1.32)	4.89 (1.57)	2.74 (1.33)
	Interfactor correlation	r = -.01 ns	r = .10 ns	r = .00 ns

Table 2

 2 Core elements of the message manipulation in Study 2 inducing a promotion versus prevention focus.

	Text element	Promotion focus condition	Prevention focus condition
	Title	How to eat healthy as a student?	How to avoid eating unhealthy as a student?
		Students miss an opportunity to	Students develop unhealthy
	Gain-/ loss-	develop healthy eating habits that	eating habits that could likely
	frame	could likely perpetuate and create a	perpetuate and create a ground
		ground for good health in the future.	for chronical illness in the future.
		Time management strategies to free up time and enjoy a meal	Time management strategies to free up time and avoid missing a meal
	Approach /
	avoidance strategies	Tips to find healthy and cheap food	Tips to avoid unhealthy food and avoid spending too much money
		Emotion regulation strategies to	Emotion regulation strategies to
		increase well-being	decrease stress
	Focus-related emotions	First results are encouraging: students report lower feeling of discouragement and more satisfaction.	First results are reassuring: students report higher feeling of relaxation and less tension.
	Conclusion	Let's hope these programs now spread!	These programs must now spread!

Table 3

 3 Small-scale meta-analysis of the findings of the three studies.

			Extrinsic motives × regulatory focus	Intrinsic motives × regulatory focus
	Study	N	Statistic	d	95% CI	Statistic	d	95% CI
	1	188	t = -2.36	-0.34	[-0.62, -0.06]	t = -0.57	-0.08	[-0.36, 0.20]
	2	177	t = -1.90	-0.29	[-0.57, -0.01]	t = -0.12	-0.02	[-0.30, 0.26]
	3	213	χ 2 = 4.34	|0.29|	[-0.57, -0.01]	χ 2 = 0.01	|0.01|	[-0.29, 0.27]
			z	d and 95% CI	SE	z	d and 95% CI	SE
	Meta-effect		-3.76*** -0.31 [-0.47, -0.15]	.08	-0.45 ns	-0.04 [-0.20, 0.12]	.08
	Homogeneity		I 2 = 0.11%	Q(2) = .08, p = .96	I 2 = 0.33%	Q(2) = .14, p = .93

*** p < .001

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

Appendices Appendix I

Messages used in Study 2 to manipulate the promotion versus prevention regulatory focus.

Promotion condition

Prevention condition

Appendix II

Extrinsic motives × regulatory focus interaction on each item forming the measure of willingness to participate to a nutrition program in Study 2.

To what extent would you… "sign a petition supporting this program" "subscribe to a newsletter"


M Neuhauser
email: mathis.neuhauser@cesbio.cnes.fr

S Verrier

S Mangiarotti

Multiscale description of Sentinel-2/MAJA products: a spectral and structure function approach

Objective: Testing the existence of scaling properties in Sentinel-2/MAJA products based on two main tools: 2D Fourier power spectra and first order structure functions.

Sentinel-2 surface reflectances exhibit a strong spatial variability that is due to both natural variability and strong anthropogenic effects. From an image processing viewpoint, Sentinel-2 products may be seen as images that embed a hierarchy of spatial structures of different sizes and of different energy levels. Many remotesensing images of natural variables show a fractal structure that can be evidenced by various geometrical and statistical tools [1], [2]. Thus, it is tempting to check if Sentinel-2 images exhibit such scaling features.

[ 1 ]•••First

 1 Identification of fractal scaling features over specific scale ranges: • Scaling exponents coherent with literature [1] • Spectral drop close to satellite resolution: possibly due to optical sensors limitations… • Different scaling behavior according to the acquisition spectral band (as in [5]) • Clouds impacts scaling properties and anisotropy at least in the blue band • Anthropogenic effects (land cover) on scaling exponents  Further work: • Apply this analysis on time series of images during 2016-2017 • Comparison to scaling behavior of other optical products: Landsat-8, SPOT (Take5), Venμs… • Multifractal analysis [3]: finer characterization of the variability, especially on the extreme • Refine the study on anisotropy: multiple angles to estimate the structure function 5 Lovejoy et al (2008), Single-and multiscale remote sensing techniques, multifractals, and MODIS-derived vegetationand soil moisture, Vadose Zone Journal, 7(2), 533-546. [2] Neuhauser et al (2018), Propriétés statistiques multi-échelles de produits satellitaires SMOS d'humidité du sol désagrégés à la résolution kilométrique, Rencontre du Non Linéaire, 55. [3] Schertzer and Lovejoy (1987), Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. Journal of Geophysical Research: Atmospheres, 92(D8), 9693-9714. [4] Olivier Hagolle, «Using NDVI with atmospherically corrected data", http://www.cesbio.ups-tlse.fr/multitemp/?p=12746, 4 th February 2018 [5] Alonso et al (2017), Spatial and radiometric characterization of multi-spectrum satellite images through multi-fractal analysis. Nonlinear Processes in Geophysics, 24(2), 141-155. References: THEIA-MAJA Workshop, 13-14 th June 2018, Toulouse, France • Four S2 tiles selected on the region: 30TYP, 31TCJ, 31TCK, 30TYQ • Chosen dates with minimum clouds and outliers: 04/02/2016 -10/07/2016 -05/07/2017 • MAJA products available in this region (atmospheric and slope corrections, clouds detection) • Many in-situ campaigns carried out by "Observatoire Spatial Regional" -CESBIO • Work in progress on Landsat-8/MAJA products Range of scales with scaling law: l 𝒎𝒊𝒏 < l 𝒇𝒊𝒕 < l 𝒎𝒂𝒙 • Scaling exponent β • Computes 2D Fourier power spectrum 𝑷(𝒌 𝒙 , 𝒌 𝒚 ) = |𝑭𝑭𝑻 𝑹 | 𝟐 • Angle integration on x and y axis 𝑬 𝒌 = 𝒌 =𝒌 𝑷 𝒌 𝒅𝒌 2. STRUCTURE FUNCTIONS with 𝒍 = ∆𝒙 = ∆𝒚 l 𝒇𝒊𝒕 SCALING LAW ∆𝑹 𝒗 ∆𝒙 = Ф 𝒍 ∆𝒙 𝑯 𝒗 ∆𝑹 𝒉 ∆𝒚 = Ф 𝒍 ∆𝒚 𝑯 𝒉 • Computes vertical structure function ∆𝑹 𝒗 (∆𝒙) = |𝑹 𝒙 + ∆𝒙 -𝑹 𝒙 | • Computes horizontal structure function ∆𝑹 𝒉 (∆𝒚) = |𝑹 𝒚 + ∆𝒚 -𝑹 𝒚 | • Fractional integration parameters: 𝑯 𝒉 and 𝑯 𝒗 (for each axis) Impact of acquisition wavelength on the scaling exponent • Comparison of two vegetation indices NDVI vs ACORVI behavior on most scales -better "sensor noise robustness" of ACORVI at smallest scales • Cloud impact: increase of spectral slope • Urban impact: decrease of spectral slope Clouds and land cover effects on blue band spectrum Twofold scaling behavior (scale break at around 200 m) • Fractional integration at small scales (l < 200 m) • Possible cloud anisotropy created at scales l > 1 km Study area: 200x200 km² Example of analyzed image: 40x40 km²