School attachment and relatedness with parents · 2019. 3. 29. · This longitudinal study examined the role of school attachment and three sources of relatedness (friends, parents,

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School attachment and relatedness with parents, friends and teachers

as predictors of students’ intrinsic and identified regulation

Frédéric Guay, Anne-Sophie Denault, Stéphanie Renaud Université Laval, Faculty of Education, Canada

Abstract This longitudinal study examined the role of school attachment and three sources of relatedness (friends, parents, teachers) in predicting students’ intrinsic and identified regulation. A total of 946 high school students from disadvantaged neighborhoods completed self-report measures. Results of a CFA provided support for the distinctiveness of the sources of relatedness and school attachment. Results of SEM revealed that school attachment predicted intrinsic regulation, whereas relatedness to teachers predicted identified regulation. Relatedness to parents and friends did not explain a significant percentage of the variance in outcomes. All results were obtained while controlling for initial levels of the outcomes. In sum, students with low levels of intrinsic and identified regulation for learning activities may benefit from practices designed to increase school attachment and relatedness with their teachers.

1. Introduction Positive psychology stresses the importance of understanding what makes people happy with

their lives, from birth to death (Peterson, 2006), in numerous life contexts, including school (Huebner, Gilman, & Furlong, 2009). Intrinsic and identified regulation for learning activities are two positive educational characteristics that foster optimal functioning at school (Ryan & Deci, 2009) and that are affected by the quality of emotional bonds with significant others. More specifically, when students feel attached to their school and experience relatedness (i.e., close and secure emotional relationships; Deci & Ryan, 2000) with teachers, parents and friends, they derive greater pleasure from school-based learning activities (intrinsic regulation) and are also more likely to internalize the value of these activities (identified regulation).

However, few studies to date have simultaneously investigated multiple sources of relatedness (i.e., parents, teachers and friends) in predicting intrinsic and identified regulation for school-related activities among high school students. Examining various sources of relatedness is important because, if one source is found to be more relevant than another for fostering these outcomes, intervention strategies could be designed to focus on that specific source. Alternatively, if all sources of relatedness are found to be important, this could lead to systemic intervention strategies. Moreover, while the concept of school attachment has been the focus of several studies over the past decades, much of the literature on this subject comes from sociology and community psychology and includes very few comparisons with the family, classroom, or friendship contexts (Hill & Werner, 2006). No study to date has established whether these sources of relatedness and school attachment are interdependent, something that would further our understanding of intrinsic and identified regulation for learning activities. In addition, one of the dominant perspectives in the field of motivation posits that both relatedness with others and school attachment improve intrinsic and identified regulation for learning activities. Yet, the opposite perspective, positing that students’ motivational beliefs may affect their perceptions of the quality of their relationships

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with others and school attachment, has rarely been tested (see Guay, Marsh, Senécal, & Dowson, 2008 for an exception). Moreover, as proposed by some gendered models of socialization (Gilligan, 1982; Maccoby, 1998), girls are more likely than boys to value and report higher levels of relatedness with significant others (e.g., parents, teachers and friends) and school attachment. However, less is known about gender differences in the predictive associations between these sources of relatedness and school attachment and intrinsic and identified regulation. For example, while we might expect adolescent girls to report greater relatedness with their teachers than boys, it is not clear whether relatedness with teachers will predict higher motivational outcomes among girls than among boys. Looking at such gender differences is important because it could lead to the development of optimal gender-specific intervention strategies. Finally, students in disadvantaged neighborhoods may have trouble mobilizing their motivation at school. They may have restricted opportunities (Schoon, 2008). For example, their teachers might be experiencing particularly high levels of stress because they face challenges such as a higher suspension rate (O’Brennan, Pas, & Bradshaw, 2017) and academic difficulties (Fantuzzo et al., 1999) leading them to use less optimal pedagogical practices. In addition, parents work schedules in these contexts may be more inflexible compared to more affluent populations, precluding them from being actively involved in the homework setting (Cooper, Lindsay, & Nye, 2000). Moreover, students themsleves and their friends may not view school as a viable pathway to success (Oyserman, 2013). Investigating interpersonal/school factors among students living in disadvantaged neighborhoods could lead to a better understanding of what makes them resilient (Battistich et al., 1995). Taken together, there is a need to better investigate the relationships between school attachment, sources of relatedness and types of motivation for both girls and boys, and also for students who are at risk of developing low motivation due to limited neighborhood resources.

Accordingly, four goals were pursued in this longitudinal study. First, we investigated the potential effects of three sources of relatedness (parents, teachers and friends) and school attachment on intrinsic and identified regulation for school-based learning activities among high school students living in disadvantaged neighborhoods. Second, we examined whether these sources of relatedness and school attachment were interdependent. For example, students who have positive relationships with their teachers might be more highly valued by their friends at school. Third, we investigated the reciprocal associations between the three sources of relatedness and school attachment, and intrinsic and identified regulation for school-based learning activities. Fourth and lastly, we tested for gender differences in the associations between the three sources of relatedness and school attachment and intrinsic and identified regulation for school-based learning activities.

1.1. Intrinsic and identified regulation Intrinsic motivation is defined as engaging in an activity for its own sake—that is, because the

activity is interesting and enjoyable, and when there are no extrinsic motivators (Ryan & Deci, 2009). Intrinsically motivated behaviors are archetypes of autonomy. Intrinsic motivation is considered to be inherent in human nature; it is the manifestation of people’s innate proactivity. This is evident, for example, when adolescents are engaged and enthusiastic in a responsive school environment. Identified regulation, for its part, occurs when extrinsically motivated behaviors are performed with a sense of choice and volition, such as when students truly consider behaviors to be important for their own personal development. Individuals identify with the importance and value of self-regulating their behaviors, which then become part of their own values (Deci & Ryan,

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2000). Although these behaviors are considered to be instrumental, they nevertheless become integrated into the individuals’ sense of self, to the point where they are performed autonomously. These two types of regulation are differentially associated with a host of positive outcomes in adolescence, such as achievement and persistence (see Ryan & Deci, 2009). For example, Burton et al. (2006) showed that identified motivation predicted academic achievement whereas intrinsic motivation predicted psychological well-being among students.

Self-determination theory (SDT) also posits that relatedness is an essential prerequisite for the initiation of behaviors driven by intrinsic or identified motivation (Deci & Ryan, 1991). Relatedness is especially important when students are not intrinsically motivated to attend high school but nevertheless need to endorse school values (e.g., studying for exams). In this case, the internalization of external requirements is more likely to occur when students feel connected to significant others (Deci & Ryan, 1991), especially if students come from disadvantaged neighborhoods where they might have experienced various developmental challenges (Burney & Beilke, 2008). In contrast, when students feel detached from others, these external requirements have less chance of being integrated into the self. SDT thus hypothesizes that relatedness with significant others is positively related to intrinsic and identified regulation.

1.2. Various sources of relatedness, school attachment and intrinsic and identified

regulation

Relatedness is considered a basic human need in many theories (see Baumeister & Leary, 1995). Relatedness is defined within SDT as the basic psychological need to feel connected to others, to love and feel loved, to care and feel cared for (Deci & Ryan, 2000). Before reviewing studies on the associations between various sources of relatedness and intrinsic and identified regulation, it is important to describe more generally how these sources might impact students’ development during adolescence. Two different perspectives appear to emerge from the literature. The first suggests that, as adolescents grow older, they rely less on their parents or family (Scholte & van Aken, 2006). Theories such as those based on the neo-psychoanalytic, evolutionary or socio- cognitive perspective endorse this point of view, positing that increasing autonomy and individuation in adolescence cause closeness with parents to temporarily decrease, conflicts to increase, and power to progressively equalize (De Goede, Branje, & Meeus, 2008). According to this perspective, detachment sets the stage for greater self-direction and the possibility to establish new significant relationships, such as those with peers. The second perspective, on the other hand, posits that the process of separation–individuation does not occur at the expense of relatedness with parents (Youniss & Smollar, 1985). According to this perspective, attachment to parents offers the possibility to develop autonomy and establish new significant relationships with others, such as friends and teachers (Ryan, 1993). In other words, relatedness with parents and other sources of relatedness are mutually supportive.

This theoretical background could lead to different hypotheses regarding the role of each

source of relatedness in predicting intrinsic and extrinsic regulation. The first perspective would posit that relatedness with parents is less important during adolescence in terms of supporting these motivational resources whereas the second would suggest that all sources of relatedness are important. These two perspectives can also be tested in light of the additive and threshold models (see Laursen & Mooney, 2008). According to the additive model, intrinsic and identified regulation for learning activities could be cumulatively affected by all significant relationships that fulfill the need for relatedness. The additive model is in line with the sensitization-desensitization

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perspective (Moller et al., 2010) according to which people who experience relatedness satisfaction in one relationship continue to value its satisfaction in other relationships.

In contrast, the threshold model assumes that individuals do not need to perceive relatedness

in various relationships and that relational support is redundant, such that additional sources of relatedness do not improve psychological adjustment. This last perspective is in line with the satiated perspective regarding psychological needs, whereby individuals who have satisfied their need for relatedness in one relationship will not experience further benefits from other positive relationships (Baumeister & Leary, 1995). For example, students who have satisfied their need for relatedness with their peers might assign less value to time spent with their parents or teachers because their need for relatedness has already been met.

A limited number of studies have contrasted the effects of various sources of relatedness on

student outcomes. For example, Ryan, Stiller, and Lynch (1994) reported that adolescents’ relatedness with both parents and teachers were significantly associated with intrinsic and identified regulation, while their relatedness with friends was not. However, Furrer and Skinner (2003) showed that a sense of relatedness to parents, teachers and peers each predicted students’ emotional and behavioral engagement. Indeed, they found that self-reported emotional and behavioral engagement were highest when children perceived high relatedness with all these significant sources of relatedness. In a study among college students, Guay et al. (2008) tested a cross-lagged model in which they contrasted two sources of relatedness: parents and friends. Their results indicated that only relatedness with parents predicted subsequent intrinsic and identified regulation. However, their study did not include relatedness with teachers, contrary to the other two studies. Thus, among studies investigating such additive or threshold effects, no clear picture has emerged regarding the importance of one source of relatedness over the other. The question as to whether one source of relatedness is more important than the others during adolescence thus remains open, although some recent studies in social psychology have revealed the incremental value of relatedness experiences (Moller et al., 2010).

In addition, previous studies have not included school attachment, which is an emotional

feeling of affection for and enjoyment of school (Goodenow, 1993). Although conceptually related to the relatedness construct (i.e., trust and satisfaction), school attachment is different insofar as it is not evaluated in reference to a specific interpersonal relationship but rather toward school in general and thus represents a general feeling about the school experience. Moreover, it should not be confused with similar terms such as school connectedness (Niehaus et al., 2012), which also refers to specific relationships at school, or school bonding, based on a conglomerate of interpersonal experiences at school. In the current study, we used a measure that clearly assessed the students’ emotional feeling of affection for and enjoyment of school. School attachment has been linked to a host of positive outcomes, including positive social, emotional and academic adjustment. Numerous interventions have demonstrated that improving the school climate in high schools results in greater school attachment and other desirable outcomes, such as lower rates of delinquency, substance abuse and school problems (Hill & Werner, 2006). Regarding indicators of motivation, school attachment is significantly and positively associated with expectancy of success, valuing schoolwork, general school motivation, and self-reported effort (Goodenow & Grady, 1993), as well as self-efficacy and self-concept (Chiu, Chow, McBride, & Mol, 2016). As an important predictor of many positive outcomes, school attachment should be included among the possible predictors of intrinsic and identified regulation. In fact, school attachment may be more important than sources of relatedness in predicting these forms of regulation. However, to

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test this assertion rigorously, it is important to consider possible positive interdependencies among sources of relatedness and school attachment.

1.3. Positive interdependencies among sources of relatedness and school attachment The fact that various sources of relatedness and school attachment might influence one another

represents a challenge when analyzing their effects in an additive or threshold model. More specifically, if there proves to be no predictive association between relatedness to teachers and intrinsic and identified regulation, it might nevertheless be the case that relatedness to teachers has an indirect effect on these forms of regulation through school attachment (Anderman, 2003; Chiu et al., 2016). For example, students who perceive a great deal of support from their teachers might experience a higher sense of school attachment. Similarly, parents who have a positive relationship with their children may help them develop a generally positive attitude toward school, thus fostering greater school attachment. In addition, students who have a positive relationship with their teachers are more likely to be accepted by their peers (Davidson, Gest, & Welsh, 2010), which suggests that students pay attention to their relationships with the teacher and use this information in establishing positive relationships with friends. In sum, there might be many positive interdependencies among sources of relatedness and school attachment that need to be accounted for when examining their unique contribution to intrinsic and identified regulation.

1.4. Reciprocal relationships between sources of relatedness, school attachment and motivation

Most researchers endorse the view that sources of relatedness and school attachment “predict” intrinsic or identified regulation (Guay et al., 2008). However, as argued earlier, it is also possible that relatedness with significant others and school attachment are reinforced by the fact that students are motivated for intrinsic or identified reasons. Indeed, adolescents and young adults are not passive recipients of the social context. They are active agents, evoking responses from both parents and friends, which may, in turn, modify their sense of relatedness with significant others (Guay et al., 2008). For example, a student may enjoy learning activities and consider them to be important, which may subsequently affect his/her behaviors (e.g., seeking support from friends, studying more at home, being more engaged at school). In turn, his/her own behaviors might elicit behaviors from friends (e.g., giving support), and parents and teachers (e.g., giving positive feed- back), thereby leading to better representations of relatedness with these individuals. In addition, intrinsic and identified regulation for school work is likely to make one feel much more attached to school. Guay et al. (2008) tested these reciprocal relations. Their results provided good support for the effect of relatedness with parents on autonomous academic motivation but no convincing support for the effect of motivation on relatedness with parents. In addition, no significant effect was found in either direction between relatedness with friends and autonomous academic motivation. However, their study involved college students and did not consider school attachment or relatedness with teachers. Thus, it is not known whether there are reciprocal associations between these latter variables and intrinsic and identified regulation among high school students. However, based on SDT, one would expect school attachment and relatedness with teachers to be predictors of intrinsic and identified regulation rather than the reverse.

1.5. Moderating role of gender

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Gender differences are usually considered to be important when it comes to interpersonal relationships. As suggested by some developmental theories on gender differences (e.g., Gilligan, 1982; Maccoby, 1998), the differences in how girls and boys are socialized concerning social relationships lead girls to value relatedness and invest more time in their social relationships than boys. In addition, according to the gender intensification theory, this may be especially true during adolescence when the physical changes of puberty increase the pressure for sex-typed behaviors among individuals (Hill & Lynch, 1983). Moreover, girls usually value close relationships for their emotional and expressive qualities while boys value them for their instrumental features (Burleson, 2003). In the same vein, gender differences in mean levels of perceived support have been consistently documented in prior studies on concepts that are similar to relatedness. For example, in a study examining gender differences in the association between perceived social support and attitude toward school among adolescents, even though boys and girls reported the same levels of support from parents, compared to boys, girls reported significantly higher levels of support from teachers, classmates, close friends and school personnel (Rueger, Malecki, & Demaray, 2010).

Yet, the question remains as to whether boys and girls benefit equally from relatedness or school attachment. In other words, does perceiving greater relatedness with significant others have a greater tendency to increase levels of intrinsic and identified regulation among either girls or boys? SDT proposes that relatedness is a fundamental need that should provide the essential nutriments for all individuals, including both boys and girls, to develop (Deci & Ryan, 2000). Without this need it would be hard to explain why girls and boys would so readily internalize ways of interacting effectively and harmoniously with others in their peer groups. Satisfaction of the fundamental need for relatedness also helps boys and girls develop intrinsic and identified regulation (Vallerand, Fortier, & Guay, 1997). For example, intrinsic and identified regulation are likely to emerge in a school environment where boys and girls feel unconditional regard and support, allowing them to focus on their skills. Results from two longitudinal studies supported this perspective. Specifically, these studies revealed no gender differences in the associations between various sources of social support (e.g., parents, teachers, peers) and school outcomes (i.e., attitude toward school and engagement) (Rueger et al., 2010; Wang & Eccles, 2012). In line with these results, despite the existence of gender differences pertaining to some sources of relatedness or support, we believe that the functions served by these sources are more similar than different across gender. Thus, males and females are likely to have similar conceptions of close relationships and similar expectations regarding the sense of relatedness that these relationships provide (Burleson, 2003).

1.6. Overview of the present study

Using an autoregressive cross-lagged design with two measurement times, we pursued the

following four goals: First, we investigated the unique predictive associations between three sources of relatedness (parents, teachers and friends) and school attachment, on the one hand, and intrinsic and identified regulation for school-based learning activities, on the other. Based on SDT postulates regarding the nature and functions of the need for relatedness, we hypothesized that all three sources of relatedness and school attachment would be important for predicting intrinsic and identified regulation (the additive model). Second, we examined whether the sources of relatedness and school attachment were interdependent. In line with previous findings, we expected some interdependent effects to emerge, for example, relatedness with teachers leading to greater school attachment. Third, we investigated reciprocal associations between the sources of relatedness (parents, friends and teachers) and school attachment and intrinsic and identified regulation. Based

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on SDT and previous studies, we expected sources of relatedness and school attachment to predict intrinsic and identified regulation rather than the reverse. Fourth, we tested the moderating effect of gender. Based on theory and previous findings, no significant gender differences were expected at the process level, in contrast to the mean level. Mean-level differences refer to variances in a dependent variable between boys and girls, whereas process-level differences indicate a dissimilarity in the degree of association between an independent and dependent variable among boys and girls. Though we expected no difference at the process-level, we expected the following differences at the mean level based on Rueger et al. (2010) and Vallerand et al. (1997): comparatively to boys, girls will report higher levels of relatedness with friends and teachers, school attachment as well as intrinsic and identified regulations. These questions were examined among a sample of high school students from disadvantaged neighborhoods. These students are usually considered to be at greater risk of school dropout (Donnelly, 2015). Students from disadvantaged backgrounds are less likely to perceive their relationships with others as positive (Crosnoe et al., 2004). Thus, sources of relatedness and school attachment might be especially important for these students’ academic outcomes such as intrinsic and identified regulation (see Rudasill, Niehaus, Crockett, & Rakes, 2014).

2. Method

2.1. Participants, study design and procedures

The participants took part in a longitudinal research project examining extracurricular

activities and school dropout among students from disadvantaged neighborhoods. In this research project, a stratified sample of 3000 students in Grades 7 to 10 from disadvantaged neighborhoods in the province of Quebec (Canada) was formed based on sex, grade level and administrative region. To be included in the sample, students had to attend schools with a score of 8, 9 or 10 on the two indices of deprivation provided by the MELS (2007–2008). According to these indices, schools are rated on a scale from 1 to 10, where 1 is considered the most advantaged and 10, the most disadvantaged. We asked the ministry of education to provide a sample of 3000 students in order to have a large enough sample on which to perform structural equation analyses. Based on previous research (Richards et al., 2010), we estimated that approximately 33% of students would agree to take part in the study.

A questionnaire was thus mailed to the 3000 students in the stratified sample and 952 (32%) of them completed and returned the questionnaires (T1; 56% girls). One year later (T2), 639 of these students completed and returned another questionnaire (67% retention rate; 58% girls). Differences in T1 socio-demographic information between completers (i.e., those who participated at both time points) and partial completers (i.e., those who participated only at T1) revealed that the completers were more likely to be girls, younger, and from intact and more educated families than the partial completers. We conducted a series of invariance analyses to determine whether the statistical parameters (factor loadings, intercepts, uniquenesses, variances and covariances, latent means) differed between completers and partial completers. The results are presented in the data analysis section.

2.2. Measures

2.2.1. Intrinsic and identified regulation

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We assessed intrinsic and identified academic regulation using the French version of the Academic Motivation Scale (AMS; Vallerand, Blais, Briere, & Pelletier, 1989). The AMS includes seven subscales, each containing four items representing a possible reason (or regulation) for attending school. Three subscales assess types of intrinsic motivation: intrinsic motivation to know, to accomplish things, and to experience stimulation. Three other scales assess types of extrinsic motivation: identified, introjected and external regulation. The seventh subscale assesses amotivation. Items are scored on a five-point Likert scale ranging from 1 (strongly disagree) to 5 (strongly agree). Numerous studies have supported the factorial, convergent and divergent validity and internal consistency of the AMS (Vallerand et al., 1989, 1992, 1993).

As mentioned earlier, we used only the following subscales: Intrinsic Motivation to Know (i.e. intrinsic regulation) (e.g., Because I experience pleasure and satisfaction while learning new things) and Identified Regulation (e.g., Because eventually it will enable me to enter the job market in a field that I like). Correlations between these two subscales (see Table 4) were moderate and consistent with past research (e.g., Ratelle, Guay, Vallerand, Larose, & Senécal, 2007). Table 1 presents means, standard deviations, skewness and kurtosis, and minimum and maximum values for each item. Based on criteria formulated by In’nami and Koizumi (2003), all skewness (−2 to +2 range) and kurtosis (acceptable range −7 to +7) values were acceptable, except for the kurtosis values for the second identified regulation item (7.32 at T1, 10.16 at T2). This item was nevertheless retained in the analyses because the departure from the criteria values was not very high. Scale score reliability estimates were computed using the standardized parameter estimates from the confirmatory factor analysis (CFA), using McDonald’s (1970) formula: ω=(Σ|λi|)2/([Σ|λi|]2+Σδii), where λi represents the standardized factor loadings and δii represents the standardized item uniquenesses. Compared to traditional scale score reliability estimates (e.g., alpha), ω has the advantage of taking into account the strength of association between items and constructs (λi) as well as item-specific measurement errors (δii). All four scale score reliability estimates were 0.80 for identified and intrinsic regulation at both time points.

2.2.2. Sources of relatedness Relatedness with parents, teachers and friends, respectively, was measured using the French

version of the Interpersonal Relationships Quality Scale developed by Senécal, Vallerand, and Vallières (1992). This scale includes four items (e.g., “My relations with this person are satisfying”; “My relations with this person are trustworthy”) which students are asked to answer in reference to each source of relatedness, namely teachers, friends and parents. Items are scored on a five-point Likert scale ranging from 0 (strongly disagree) to 4 (strongly agree). Senécal et al.’s (1992) study supported the validity and internal consistency of this scale. In our study, the McDonald’s ω ranged between 0.79 and 0.80 for all sources at both time points. All descriptive values were acceptable (i.e., no floor or ceiling effects, sufficient variability, adequate skewness and kurtosis; see Table 1).

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2.2.3. School attachment

We used a five-item measure adapted by Hill and Werner (2006) from three instruments developed respectively by Eccles et al. (1993), Hawkins, Guo, Hill, Battin-Pearson, and Abbott (2001) and Barber and Olsen (1997). These five items are: “I am proud to be at this school”; “I am happy to be at this school”; “I feel safe in my school”; “Most mornings I look forward to going to school”; and “I like my school.” Items are scored on a five-point Likert scale ranging from 1 (strongly disagree) to 5 (strongly agree). In their study, Hill and Werner reported factor loadings ranging from 0.69 to 0.89 for these items. Also, in support of the construct validity of this measure, school attachment was negatively correlated with aggressive behaviors at school. Specifically, school attachment is expected to indicate that affiliative goals are met and increase behavioral engagement in school, which should result in less aggression in schools (Hill & Werner, 2006). In our study, the McDonald’s ω was 0.83 at T1 and 0.82 at T2. All descriptive values were acceptable (see Table 1).

2.3. Data analysis

All models were estimated using Mplus (Version 7.4; Muthén & Muthén, 2012) and tested

using standardized coefficients obtained through the maximum likelihood robust (MLR) estimation method. To ascertain the adequacy of model fit, we used the comparative fit index (CFI), non-normed fit index (NNFI, also known as the Tucker-Lewis index), root-mean-square error of approximation (RMSEA), and χ2 test statistic. The NNFI and CFI usually vary along a 0- to-1 continuum (the NNFI can be greater than 1 because of sampling, but this is rarely the case in practice) in which values greater than 0.90 and 0.95 typically reflect acceptable and excellent fit to the data, respectively (Schumacker & Lomax, 1996). Browne, Cudeck and Bollen (1993) suggest that RMSEAs below 0.05 are indicative of a “close fit” and that values of up to 0.08 represent reasonable errors of approximation. Whereas the NNFI and RMSEA contain a penalty for lack of parsimony, the CFI does not, such that the addition of new parameters leads to an improved fit that may reflect capitalization on chance. Using the Akaike Information Criteria (AIC; Akaike, 1987) and Baysian Information Criteria (BIC) also facilitates model comparison. In our study, model comparison was guided by the following criteria: (a) a decrease of more than 0.01 in CFI and NNFI values when comparing a less restrictive model to a more restrictive one is indicative of some model misfits; (b) a decrease of 0.015 in RMSEA values when comparing a less restrictive model to a more restrictive one is indicative of some model misfits; and (c) lower values for the BIC and AIC are indicative of better model fit.

Missing data ranged from less than 1% to 38% (see Table 1). As in most longitudinal studies,

there were more missing values at T2. Little’s (1988) test was computed for all individual indicators using the Missing Values Analysis add-on module in SPSS. The p value was statistically significant (χ2 [2229] = 2699.07, p = .001), indicating that the data were not missing completely at random (MCAR). In addition, because more data were missing at T2, we tested for differences in various model parameters at T1 between completers and partial completers (see Table 2). That is, those who did not participate at T2 were compared to those who participated at both time points. Overall, the invariance analyses showed no differences in the various parameters (Models 1 to 6; see Table 2), except for variances/covariances, where the CFI and NNFI values decreased by 0.01. However, no substantial latent mean differences in latent constructs across the completers and partial completers were observed, since none of the fit indices improved substantially when these means were relaxed in Model 6. This indicates that the results based on the full information

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maximum likelihood (FIML) solution for estimating subsequent models could be interpreted with a higher level of confidence. This led us to conclude that, while the data were not MCAR, there were no systematic patterns of missingness that could seriously bias subsequent results based on CFA or structural equation modeling (SEM). To account for missing data in the SEM analyses, FIML was used to compute the product of individual likelihood functions in order to estimate the analysis parameters. Using an FIML procedure under MLR to treat missing data is considered superior to using listwise deletion and other ad hoc methods, such as mean substitution (Davey, Shanahan, & Schafer, 2001; Peugh & Enders, 2004).

2.3.1. CFA models

To appropriately analyze the direction of effects or causal ordering among variables, it is important to specify CFA and SEM models that encompass the estimation of various statistical parameters. First, all latent constructs should be measured at least twice over a certain period of time. This period should make it possible to capture a sufficient amount of change. In this study, like many others in the field of educational psychology (e.g., Guay, Marsh, & Boivin, 2003), we used a one-year interval. Second, latent constructs should be measured using multiple indicators. In this study, school attachment was measured through five indicators, while other latent constructs were assessed through four indicators. Third, uniquenesses (error) of the same indicators (item) measured at two time points (T1 and T2) should be correlated to prevent an inflated stability effect (a method bias) of a latent construct measured at T1 and T2. In this study, for all latent constructs measured at two time points, uniquenesses at T1 and T2 were correlated. For example, the uniqueness of item 1 of the intrinsic motivation latent construct at T1 was correlated with the uniqueness of item 1 of the intrinsic motivation latent construct at T2. Moreover, as mentioned above, relatedness items were the same for each source (parents, friends and teachers). When the items are the same, inflated correlations (a method bias) might occur between relatedness latent constructs. To avoid such a method effect, we estimated correlated uniquenesses among items having the same wording (i.e., parallel items). For instance, the uniqueness of item 1 for relatedness with friends’ latent construct was correlated with the uniquenesses of item 1 for relatedness with teachers and parents. According to Podsakoff, MacKenzie, Lee, and Podsakoff (2003), correlated uniqueness models are quite flexible and likely to converge and produce proper parameter estimates. However, they are characterized by some weaknesses, including that method effects are orthogonal, the trait variance is possibly biased, and the trait and method effects do not interact. Because the models tested in our research involved many free parameters, this correlated uniqueness model – being much more flexible than other models used to control for potential bias (i.e., multiple-method-factor-approach) – appeared the most appropriate. In sum, considering it to be the best statistical approach, we chose the correlated uniquenesses model to control for method bias in our research. Fourth, it is important to make sure that students have the same interpretation

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of the latent construct over time. As a result, a model was estimated with an equality constraint on the factor loadings over time. We tested two CFA models: one containing all the statistical parameters described above, including all covariances among the twelve latent constructs, and another with the exact same parameters, but with factor loadings that were invariant through time.

2.3.2. SEM models The SEM models included all the statistical parameters described for the CFA models except

that latent covariances were remodeled in accordance with the hypothesized model in which correlations among independent variables at T1 and disturbances at T2 were estimated. The correlation among independent variables allows the estimation of hypothesized causal effects while controlling for stability effects. Because it is highly unlikely that independent variables will explain all the variance in the dependent variables, correlations among disturbance terms are estimated among all dependent variables. We tested four SEM models, corresponding to Models 3 to 6 in Table 3: Model 3, containing only stability paths; Model 4, containing stability paths and the effect of all sources of relatedness and school attachment on intrinsic and identified regulation; Model 5, containing reciprocal effects between sources of relatedness and school attachment, and the two types of regulation; and Model 6, containing reciprocal effects and inter-dependency effects among sources of relatedness and school attachment. Modest effect sizes for the cross-lagged paths were expected because the latent constructs were likely to be relatively stable over time. For this reason, if the NNFI containing a penalty for lack of parsimony did not decrease compared to the other more parsimonious models (e.g., stability and unidirectional), the more global model would be interpreted, especially if some significant effects were observed.

2.3.3. Gender invariance analyses

To test for possible moderating effects of gender, we built a series of five invariance models where equality constraints were imposed on various statistical parameters (Models 7 to 11; see Table 3). In the least restrictive model, factor loadings and intercepts were fixed to be equal across boys and girls. These equality constraints ensure that the results can be meaningfully compared across groups. In subsequent models, uniquenesses, correlated uniquenesses, variances and covariances, and path coefficients were constrained to equality (see Guay, Morin, Litalien, Valois, & Vallerand, 2015). Finally, we explored gender mean differences in all latent constructs by fixing

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means to 0 in one model in order to compare it to another model where means were relaxed for girls.

3. Results

3.1. CFA

Descriptive statistics for all items used in this study are presented in Table 1, and fit indices

for the various tested models are presented in Table 3. To provide an overview of the correlation pattern, we conducted a CFA in which no constraint on the various parameters were imposed. This model estimated all correlations among the uniquenesses described above. Standardized factor loadings and uniquenesses are presented in Table 1, model fit indices are presented in Table 3 (Model 1), and correlations among the six factors at T1 and T2 are presented in Table 4. First, all standardized factor loadings were above 0.40. Second, cross-sectional correlations among the sources of relatedness and school attachment at T1 and T2 were low enough to indicate that the constructs, while related, appeared to be distinct. Neither the correlations among the sources of relatedness nor those connecting these sources to school attachment exceeded 0.50. Moreover, when we used the longitudinal data measurement points in this study as a different method in order to build a multitrait-multimethod (MTMM) correlation matrix (Campbell & Fiske, 1959), we noted that convergent correlations (i.e., between two different methods, namely T1 and T2, assessing the same latent constructs) were higher than divergent ones (i.e., between two different latent constructs assessed using different methods). More specifically, the longitudinal correlations connecting various sources of relatedness or school attachment over time (divergent correlations) were weaker than the longitudinal relationships between the same constructs (relatedness or school attachment) over time. This first pattern of results is especially important because sources of relatedness or school attachment that were too strongly correlated might have compromised the first goal of this study, which was to determine which variables were most likely to predict intrinsic and identified regulation.

Third, if we look at correlations connecting both types of regulation (intrinsic and identified regulation) to sources of relatedness and school attachment, the results indicate that intrinsic and identified regulation were most strongly correlated with school attachment, followed in decreasing order by relatedness with teachers, parents and friends, respectively. This pattern of cross-sectional correlations was similar at both time points. Moreover, this pattern of results was reproduced longitudinally. For example, school attachment at T1, as compared to relatedness with friends at T1, was more strongly correlated with T2 intrinsic and identified regulation.

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A subsequent CFA model was estimated to determine whether factor loadings were invariant over time (see Model 2 in Table 3). Given that the NNFI and CFI increased, the RMSEA was identical to Model 1, and the BIC and AIC values were lower, we considered the factor loadings to be invariant across time. These results mean that, over time, students had the same understanding of items designed to measure a construct. Thus, the absence of longitudinal relationships could not be explained by the fact that students understood the construct differently over time. Based on these results, we estimated SEM models with these time-in-variant constraints.

3.2. SEM

As mentioned above, four SEM models were tested: horizontal (i.e., stability over time of a given latent variable), unidirectional (i.e., sources of relatedness and school attachment predicting types of regulation), reciprocal (i.e., both directions among sources of relatedness/ school attachment and types of regulation), and reciprocal and inter-dependency effects (see Table 3, Models 3–6). The fit indices for these four models were nearly equivalent, except for Model 6, where we observed a slight decrease (0.001) in the NNFI value. Inspection of Model 6 revealed no significant interdependencies, meaning that different sources of relatedness or school attachment were not significantly related over time. Because the NNFI of Model 5, which contains a penalty for lack of parsimony, remained unchanged by the addition of cross-lagged paths, we determined that this was the best model and based our main interpretations on it. Results of Model 5 are presented in Table 5. Inspections of path coefficients revealed that stability effects for all latent constructs were significant and ranged between 0.39 and 0.60. One cross-lagged path was statistically significant at p < .05, namely that connecting T1 school attachment to T2 intrinsic motivation (b = 0.12), and two cross-lagged paths were statistically significant at p < .10, namely that connecting T1 relatedness with teachers to T2 identified regulation (b = 0.11) and that connecting T1 relatedness with parents to T2 intrinsic motivation (b = −0.08).

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This last finding should be interpreted with caution, especially since this relationship was positive in the correlation matrix (see Table 4 for correlation coefficients). These results suggest that relatedness with parents acted as a suppressor variable in the statistical model. Suppression is a statistical phenomenon that can occur in regression analyses when predictors are strongly correlated. In such cases, the relationship between two variables will be artificially inverted (Cohen & Cohen, 1983). According to Maassen and Bakker (2001), suppression can occur in structural equation modeling and the probability of occurrence is relatively high in models that have latent variables. The fact that perceived relatedness with parents at T1 was positively correlated with intrinsic motivation at T2 at the bivariate level suggests that the negative path was probably a spurious one. In addition, three paths connecting regulation types to sources of relatedness/school attachment were marginally significant (p < .10; see Table 5), namely intrinsic regulation to relatedness with friends (b = 0.10), intrinsic regulation to school attachment (b = 0.10), and identified regulation to school attachment (b = 0.10). However, caution should be exercised when interpreting these findings because their magnitude was low (approx. 0.10) and some of them were significant at p < .10. As discussed in the next section, invariance analyses were conducted as a function of gender based on the reciprocal effect model (Model 5; see Table 3).
3.3. Gender invariance analyses

The five models (Models 7 to 11; see Table 3) indicated that factor loadings, intercepts,

uniquenesses, correlated uniquenesses and path coefficients were invariant across gender. More specifically, for Models 7 to 9, equality constraints imposed on various statistical parameters did not result in lower CFI, NNFI or RMSEA values or in higher BIC or AIC values. These results ensure that the various statistical parameters can be meaningfully compared across groups because they are not due to a different understanding of the items for boys and girls. However, imposing equality constraints on variances/covariances resulted in lower fit indices or higher AIC or BIC values. For this reason, we specified Model 12, in which variances/covariances were relaxed. Model 12 had similar fit indices to Model 7, the least restrictive model tested for invariance analyses. We thus determined that Model 12 was the best model and based our interpretations on it. Results of this model are depicted in Fig. 1 and Table 5. All coefficients depicted were standardized. First, stability paths were relatively high, ranging from 0.38 to 0.61. Second, school attachment at T1 was positively and significantly (p < .05) associated with intrinsic motivation at T2 (b = 0.11 for boys, b = 0.12 for girls). Contrary to what we observed in the general model, relatedness with teachers at T1 was now positively and significantly associated with identified regulation at T2 (b = 0.10 for boys, b = 0.13 for girls). No other cross-lagged paths were significant. These findings indicate that the results concerning the path coefficients were the same across gender. The only differences we found concerned variances and covariances. However, because these parameters are less relevant in this study, they were not interpreted.

Based on these results, we tested two subsequent CFA models (Model 13 and 14; see Table

3) to determine whether there were gender mean differences in the 12 latent constructs. Because the NNFI decreased slightly when means were set to 0 compared to a model where these gender mean differences were estimated, we decided to interpret mean differences across gender based on Model 13. When boys’ latent means at T1 were fixed to 0 for identification purposes, girls’ latent means (expressed as differences in standard deviation units) were significantly higher for T1 intrinsic motivation (M = 0.15; SE = 0.08; p < .05) and for T1 and T2 identified regulation (T1: M=0.21; SE=0.09; p < .05; T2: M=0.28; SE=0.12; p < .05), but lower for T1 and T2 relatedness

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with parents (T1: M = -19; SE=0.06; p < .05; T2: M=−0.29; SE=0.07, p < .05). There were no significant differences for school attachment or relatedness with friends.

4. Discussion

This study pursued four goals: (a) to test whether multiple sources of relatedness and school attachment predicted intrinsic and identified regulation over an one-year period; (b) to determine whether there were interdependency effects among sources of relatedness and school attachment; (c) to investigate whether there were reciprocal relationships among sources of relatedness, school attachment, and the two regulation types; and (d) to test whether gender moderated the relationships connecting sources of relatedness and school attachment to intrinsic and identified regulation. Findings based on several structural equation models indicate that, in our sample of adolescent students from disadvantaged neighborhoods, only relatedness with teachers and school attachment positively predicted intrinsic and identified regulation. More specifically, relatedness with teachers predicted identified regulation, whereas school attachment was positively linked to intrinsic regulation. In addition, no interdependency effects were observed among the sources of relatedness and school attachment, and neither regulation type was found to have significant effects on the sources of relatedness or school attachment. Finally, gender did not moderate the observed associations.

Although our hypothesis based on the additive model was not supported, our findings still

extend previous studies on sources of relatedness, school attachment and adolescents’ school-related functioning in several important ways. Indeed, our results provide evidence that school attachment and relatedness with teachers are the only two relevant predictors of intrinsic and identified regulation for school-based learning activities. Although previous research and theory have underscored the importance of relatedness with teachers in predicting autonomous regulation (Ryan et al., 1994), this study underscores the role of school attachment in intrinsic regulation, which has received less attention in previous research. In line with these ideas, our results also

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highlight that, for these regulation outcomes, different sources of relatedness play different roles, a finding that needs further consideration. It is reasonable to expect that teachers who spend a lot of time with students will create a classroom context that is more favorable to the internalization of the value of school activities (i.e., identified regulation). However, it is surprising that teachers did not play a significant role in promoting intrinsic motivation. School attachment might be a salient global feeling that helps students negotiate various school activities effectively by keeping their levels of intrinsic motivation relatively high. This feeling of attachment is developed because the school, as an independent entity per se, is able to meet students’ needs for relatedness through numerous activities (e.g., cultural and sports activities). Nevertheless, the magnitude of the effects of school attachment and relatedness with teachers was small, based on Cohen’s (1992) guidelines on effect sizes (10 = small, 0.30 = medium, 0.50 = large). Yet, our findings are particularly notable in that they were based on a cross-lagged autoregressive model controlling for prior levels of the dependent variable, whereas most other studies have used cross-sectional data or partial longitudinal models. The stability effects in autoregressive models are usually high, although they can be attenuated by correlated uniquenesses. These stability coefficients offer the possibility of testing more robust effects of one latent construct on a subsequent latent construct. However, they have an impact on the magnitude of the cross-lagged coefficients. It should be noted that a small coefficient (e.g., 0.12) obtained over a one-year period might have a cumulative impact on the outcome over several years of schooling. Although there are no clear guidelines for interpreting these autoregressive coefficients, we believe that they should be analyzed carefully in light of the stability effects and the various predictors considered simultaneously in the analyses.

It is noteworthy that neither relatedness with friends nor relatedness with parents significantly predicted the two types of regulation. Moreover, these findings do not appear to be attributable to inter-dependency effects or a degree of transference. Indeed, cross-lagged analyses revealed no effect of prior relatedness with friends or parents on school attachment or relatedness with teachers. This means that the lack of any significant predictive associations between relatedness with parents and friends and the two types of regulation were not explained by mediation processes through school attachment or relatedness with teachers. A certain degree of transference between friends and school attachment, as well as between parents and teachers, might be expected. Those who feel attached to their friends may experience greater feelings of school attachment, and those who have positive and trust-worthy relationships with their parents may experience greater relatedness with their teachers. The fact that such transference did not appear to occur increases our level of confidence regarding the lack of effect of relatedness with friends and parents on the two types of regulation. Such non-significant findings are nevertheless surprising given that many studies in the field have outlined the fundamental role of parents and friends/peers with respect to constructs akin to identified and intrinsic regulation for school activities (e.g., Vallerand et al., 1997; Wentzel, Russell, & Baker, 2015). One reason may be that the present study encompasses various sources of relatedness and school attachment, which has not always been the case in previous studies (e.g., Guay et al., 2008). Because most sources of relatedness and school attachment were positively correlated, controlling for them in a longitudinal design provided a stringent test of the threshold or additive model. More specifically, it appears that above a certain degree of school attachment and relatedness with teachers, relatedness with friends and relatedness with parents were redundant, such that these additional sources of relatedness did not improve either type of regulation. Consequently, these results might challenge the sensitization process proposed by Moller et al. (2010), who showed that relatedness leads to an incremental value of relatedness for intrinsic and identified regulation. According to this perspective, the more people experience positive relatedness in various relationships, the more they benefit from them. In contrast, our

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results are more in line with the satiety perspective. However, no definitive conclusion can yet be reached because the method used in our study was starkly different from that used by Moller et al. (2010). On the other hand, our results are in line with other studies in the field of achievement (Hattie, 2009) showing that teachers are the most significant source of influence on students’ achievement. While the influence of parents and peers is relevant, it is less important than that of teachers and school attachment.

To our knowledge, only Guay et al. (2008) have compared the effects of friends and parents

on different types of regulation in auto-regressive models involving a sample of young adults at college (18 years old). Their results indicate that only relatedness with parents predicted subsequent levels of intrinsic and identified regulation. Nevertheless, since their study did not include relatedness with teachers or attachment to college, it is not known whether the results for relatedness with parents would be corroborated if these variables were taken into account. However, it is important to note that different sources of relatedness might play different roles depending on the developmental period, as proposed by some theories (De Goede et al., 2008; Harter, 1999). Relatedness with parents might be more relevant during the elementary school years than during adolescence, and the importance of parents might subsequently be restored when adolescents develop into young adults facing important life decisions. Further studies taking a developmental approach are thus needed to answer this question.

Of additional interest is the fact that there were no effects of prior types of regulation on

subsequent sources of relatedness (i.e., no reciprocal effects), thereby providing support for our initial hypothesis based on SDT. These findings indicate that students who experienced pleasure, satisfaction and enjoyment as well as those who had internalized the importance of school did not report greater feelings of relatedness in various relationships or greater school attachment. According to Guay et al. (2008), such a lack of significant results could stem from the fact that, during adolescence, sources of relatedness and school attachment are relatively stable and thereby attenuate the possibility of various regulation types predicting these variables. However, the regulation types in our study appeared to be much more stable over time than the different sources of relatedness and school attachment, thereby providing weak support for such an interpretation. A simpler interpretation of these findings may be that the direction of the effects was from sources of relatedness and school attachment to various regulation types, which is in line with SDT (Ryan & Deci, 2009).

As expected, we found no evidence for the moderating effect of gender. Not only were boys

and girls both affected by relatedness with teachers and school attachment, but they were also affected to a very similar degree (i.e., path coefficients were not significantly different). Such results are consistent with previous findings showing that relationships between sources of relatedness and various regulation types are usually invariant (Guay et al., 2003; Rueger et al., 2010; Wang & Eccles, 2012). Based on these results, we conclude that the function served by these sources is much more similar than different across gender, as suggested by Burleson (2003). Moreover, such findings are in line with SDT (Ryan & Deci, 2009), which posits that the need for relatedness serves the same function across various groups of individuals, including males and females.

However, it is still important to keep in mind that gender differences existed at the mean level,

although such differences were not a primary focus in this investigation. More specifically, compared to boys, girls’ latent means were significantly higher for T1 intrinsic motivation and T1

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and T2 identified regulation, but lower for T1 and T2 relatedness with parents. There were no significant differences for school attachment or relatedness with friends and teachers, contrary to our initial hypothesis. The results regarding intrinsic and identified regulation were consistent with past studies showing that girls are more intrinsically motivated toward school and internalize the value of schooling more than boys (Vallerand et al., 1997). However, the gender differences pertaining to relatedness with parents are more surprising. How to explain the fact that the girls in our sample reported lower levels of relatedness with parents than the boys? Some previous studies have shown that girls experience more support from their parents than boys (Guay et al., 2003), whereas other studies have reported no significant gender differences (Rueger et al., 2010). Our sample characteristics might explain why our findings differ from past studies. More specifically, students in this sample attended schools in socio-economically disadvantaged neighborhoods. Consequently, it is possible that, in at-risk family contexts, girls experience more conflicts with their parents than boys, which may have led to lower scores on the relatedness measure. This tentative explanation should, however, be further examined in future studies. Such gender differences might, however, lead to gender-specific intervention strategies. For instance, parents of girls attenting a socioeconomically disadvantaged school might be informed that the quality of the relationship they have with their daughter is important, even if the associations connecting relatedness with parents to both types of regulations were not statistically significant in this study. Indeed, previous research has shown that positive parenting behaviors predict other important outcomes such as emotional adjustment (Ratelle, Duchesne, & Guay, 2017).

Again, it is important to note that the results were obtained among a sample of students

attending schools in disadvantaged neighborhoods. It is possible that many youth attending such schools do not view school as a relevant pathway to achieving their future goals, and thus feelings of warmth toward teachers (or attachment to school) may not be as strongly associated with academic motivation as for students attending schools in more affluent neighborhoods.

4.1. Limitations and conclusions The findings from this study should be interpreted in light of certain limitations. First,

although we used an auto-regressive longitudinal design, it is important to keep in mind that the meaning of the term “effects” remains tentative. The correlational nature of the data precludes any firm conclusion regarding the direction of causality among the constructs. Second, we asked students to self-report on various sources of relatedness and school attachment. Such self-reported measures are subject to shared method variance as well as potential bias in the estimation of scores. More specifically, this single-informant approach might have led to an inflated relationship between the sources of relatedness and school attachment and the two types of regulation. In other words, the reciprocal relationships could also be mere perceptions – when students enjoy school or value it, they are more likely to perceive their social context more positively. Third, the observed effect sizes were relatively small. However, the magnitude of the cross-lagged effects observed in this study was consistent with previous studies (e.g., Guay et al., 2008). Fourth, there were a large number of missing values in this study. Less than one third of contacted youth returned surveys at Time 1. It is possible that the two thirds of youth who chose not to participate were less attached to school, had lower school enjoyment, and valued school less than the students who participated. Yet, the results from the invariance analyses and SEM model indicated few differences between the participants who provided complete data and those for whom values were missing. In addition, we used a sophisticated approach to deal with missing values (FIML). Therefore, we believe that missing data did not compromise the validity of our study. Nevertheless, it is quite possible that

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our sample is not representative of the entire high school population from disadvantaged neighborhoods, since our students may have been more academically oriented and well adjusted than most students in this population. Finally, we only measured intrinsic and identified regulation and these motivational measures were not specific to school subjects. It is thus important to exercise caution in generalizing these results.

Further research should test the replicability of our results in different populations, including

students from different cultural and socioeconomic backgrounds. In addition, because the regression coefficients are low, perhaps there are theoretically plausible moderator or mediator variables that could be tested in future research. For example, intrinsic and identified regulations of students scoring low on neuroticism might by more positively affected by relationships with teachers, parents and peers than those high in neuroticism. Furthermore, some qualitative research may be in order to examine the experience of school attachment and sources of relatedness. In addition, it could be quite useful to study not only positive characteristics of parents, teachers and friends, but also negative characteristics, including abusive control from parents and teachers and negative peer experiences such as victimization and rejection. Indeed, some students may experience negative social experiences that could demotivate them at school.

Finally, it is important to emphasize the practical implications of our results. First, it may be

important to inform schools that they have a role to play in adolescents’ perceptions of school attachment and, subsequently, in their intrinsic motivation. To this end, schools could provide opportunities for and reward positive involvement, and enable students to develop the skills needed to take advantage of these opportunities. For example, programs intended to reduce school bullying (Schneider, O'Donnell, Stueve, & Coulter, 2012) or promote school-based extracurricular activities (Denault & Guay, 2017) might help achieve this goal. Moreover, teachers should be informed that the sense of relatedness they develop with their students is an important catalyzer of how students endorse the importance of school-related activities. In this regard, many pedagogical practices might be used to foster a positive sense of relatedness, including autonomy support (offering choices), involvement (being interested in the students experiences), and structure (providing feedback; Ryan & Deci, 2009).

In sum, this longitudinal research has moved the field forward in some meaningful ways,

theoretically, conceptually, empirically and practically. Theoretically, this study provides somewhat of a field test of the sensitization perspective proposed by SDT and shows that it is the social context that leads to inter-individual changes in motivation type, rather than the reverse. Conceptually, it also offers the possibility to delineate sources of relatedness from school attachment. Empirically, the statistical models and the method used reflect state of the art techniques in the field of applied statistics. Finally, the practical implications outlined are important for school administrators and teachers.

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cedpsych.2017.10.001

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