Associations between physical activity motives and trends in moderate-to-Vigorous physical activity among adolescents over five years

ABSTRACT This study examined the longitudinal associations between five physical activity (PA) motives and moderate-to-vigorous PA (MVPA) across a 5-year period spanning late childhood to middle adolescence. METHODS: Data (n = 937; 55% girls; mean age = 10.33 years) were drawn from the Monitoring Activities for Teenagers to Comprehend their Habits study. PA motives and MVPA were assessed 15 times over the course of 5 years. Measurement invariance for the Motives for Physical Activity Measure-Revised (MPAM-R) questionnaire was established, and sex-stratified mixed-effects regression models were analysed. MVPA increased until a mean age of 12.18 years for girls and 12.89 years for boys before decreasing through the final assessment. From late childhood to middle adolescence, for boys, enjoyment motives were positively (β(95% CI) = 6.14(3.86–8.43)), while fitness motives were negatively (β(95% CI) = −4.80(−8.0, −1.59)) associated with MVPA. Whereas, for girls, competence motives were positively β(95% CI) = 3.44(1.59–5.28)) associated with MVPA Boys may benefit from PA interventions, if these were primarily aimed at increasing ones’ enjoyment, whereas developing a girl’s competence may provide greater contributions to a girl’s future PA behaviours. PA interventions should avoid promoting the desire to be active to improve fitness, particularly among boys.

Longitudinal; measurement invariance; moderate-tovigorous; reasons; language invariance BACKGROUND Despite being associated with a plethora of health benefits (Bailey et al., 2012;Bloemers et al., 2011;Janssen & Leblanc, 2010;Poitras et al., 2016;Tremblay et al., 2011), including preventing early onset of chronic diseases and increasing life expectancy (Mintjens et al. 2018;Poitras et al., 2016;World Health Organization (WHO), 2017Ruiz et al., 2009), low levels of moderate-to-vigorous physical activity (MVPA) prevail among youth (Colley et al., 2017). As interventions aimed at increasing PA during adolescence have had limited short-term effects, (Dobbins et al., 2013;Dudley et al., 2011;Metcalf et al., 2013;Van Sluijs et al., 2007) there is a need to understand factors that explain long-term MVPA trends in youth to inform behaviour change strategies. The focus on youth is especially important given that the transition from late childhood to adolescence is a development time period with welldocumented declines in overall physical activity (PA) (Corder et al., 2019;Nader, 2008) PA motives, which reflect reasons for engaging in PA, have been studied as predictors of participation across the lifespan. Based on a number of behavioural theories (e.g., theory of planned behaviour, (Ajzen, 1991) social ecological model, (Bronfenbrenner, 1994) self-efficacy theory, (Bandura, 2010) basic psychological needs theory, (Ryan & Deci, 2000) expectancy-value model, (Wigfield & Eccles, 2000)), competence, enjoyment, and social motives are associated with PA participation. It has also been suggested that individuals engage in PA for appearance and health/fitness reasons. (Ryan et al., 1997;Sabiston et al., 2019) When people engage in PA for intrinsically motivated reasons (e.g., enjoyment and competence motives), (Frederick & Ryan, 1993;McLachlan & Hagger, 2011;Owen et al., 2014;Ryan et al., 1997;Sebire et al., 2009;Teixeira et al., 2012) they are more likely to maintain PA because they find it interesting, fun, and inherently satisfying. In contrast, when people engage in PA for extrinsically motivated reasons (e.g., fitness, appearance, and social motives) (Frederick & Ryan, 1993;Ryan et al., 1997;Teixeira et al., 2012), they engage in it to obtain some instrumentally separable outcome (e.g., attainment of a reward, achievement of some valued outcome such as social status)), and studies have made it clear that people tend to exhibit less engagement in PA.
Self-determination theory (Ryan & Deci, 2000 has emerged as the principle framework for studying motivation for PA. Motivation for PA has been assessed through self-report questionnaires that probe the extent to which PA is selfdetermined (i.e., behavioural regulations) or that probe the reasons for one's engagement in PA (i.e., specific motives). In regards to the former, studies have made it clear that intrinsic (or self-determined) motivation is positively associated with continued PA, (Teixeira et al., 2012) likely because intrinsic motivation provides the impetus for people to learn about particular subjects and to differentiate their interests, fostering the development of personal identifies that confer a sense of meaning and purpose. (Ryan & Deci, 2000) However, empirical support for the proposed associations between PA motives and PA among youth has been mixed and studies have frequently focused on the "quantity" of motives by using composite scores when assessing the associations between PA motives and PA. In a British sample of middle adolescents (ages 13-15 years; n = 580), a cross-sectional study showed that a composite score of fitness and enjoyment motives was associated with greater self-reported leisure time PA (β = 0.83), whereas appearance motives were associated with lower (β = −0.40) self-reported leisure time PA through an indirect pathway. (FB Gillison et al., 2006) In another cross-sectional study with a Spanish sample of adolescents (mean age of 15 years; n = 1098), Chicote-López et al. (Chicote-López et al., 2018) reported that a composite score of enjoyment and competence motives (β = 0.29) and a composite score of fitness and social motives (β = 0.29) were associated with greater self-reported PA; appearance motives were not assessed. Similarly, among children ages 10-12 years (n = 1272) from Belgium, a composite score of fitness, competence, and social (affiliation) motives was indirectly and positively (β = 0.68) associated with daily step counts measured with a pedometer, whereas a composite score of appearance and social (recognition) motives was indirectly and negatively (β = −0.15) associated with daily step counts. (Seghers et al., 2014) Enjoyment during PA was measured in the study but was not included as a motive for PA in associative models. (Seghers et al., 2014) In a similar age group, a longitudinal study with two measurement points with children ages 10-12 years (n = 1081 in grade 5, and n = 1011 in grade 6) from the United States of America (USA) found that enjoyment (β = 0.09) and competence (β = 0.10) motives were positively associated with accelerometer-measured MVPA, but that appearance, social, and fitness motives were not related to PA. (Dishman et al., 2013) In a cross-sectional analysis with 802 Canadian children (mean age of 10.7 years) members of our research group found that competence and enjoyment motives were significantly associated with PA, but that social, appearance, and fitness motives were not associated with PA. (Goguen Carpenter et al., 2015) Specifically, Goguen et al. (Goguen Carpenter et al., 2015) found that enjoyment motives were associated with a greater likelihood of participating in organized PA (odds ratio [OR] = 1.54), and that competence motives were associated with greater likelihood of meeting PA guidelines (OR = 1.95) and of participating in group-based PA (OR = 1.27). Additionally, in a small cross-sectional study of children (ages 7-12 years; n = 49) from the USA, enjoyment motives were ranked as a primary reason for being active, followed by competence, fitness, and social motives. (Woods et al., 2007) Collectively, these findings show that the magnitude and direction of the association between PA motives and behaviour is inconsistent across studies with youth, which may be a result of studies sampling youth of varying ages and using different methods to assess and analyse PA motives and behaviour. Nevertheless, such inconsistencies are contrary to the idea that intrinsic and extrinsic motivation are additive or synergistically positive (Atkinson, 1964) and make it challenging to identify which motives should be fostered to facilitate PA behaviour change and maintenance in youth.
Previous studies using cross-sectional designs have also found differences in the associations between PA motives and behaviour between boys and girls. For example, in one crosssectional study, (Iannotti et al., 2012) social motives were positively related with PA for girls only, fitness motives were positively associated with PA for boys only, and competence motives were positively associated with PA for both sexes. In contrast, another cross-sectional study (F Gillison et al., 2009) found that boys participated in sports for social motives, whereas girls participated in sports for fitness motives. Additionally, other cross-sectional studies have found that social and appearance motives were positively associated with PA for girls only. (Allender et al., 2006;Kopcakova et al., 2015) There are different theoretical perspectives that may help explain differences in boys' and girls' PA motives and their associations with PA behaviour. For instance, developmental perspectives suggest that competence and enjoyment are important for PA among boys and girls similarly, although boys may place more inherent value on physical competence. (Wigfield et al., 2015) Developmental perspectives also highlight that girls may place more value on the social nature of activities such as PA, and highly value appearance as part of their identity. (Harter, 2015) Additionally, motives are fostered through gender role norms and stereotypes that are inherent to identity such that boys' identity is often tied to competence and enjoyment of PA, whereas girls' identity is often tied to their appearance and social relationships. (Eccles & Harold, 1991;Kopcakova et al., 2014) Empirical data supporting or refuting such perspectives can inform recommendations for interventions targeting boys and girls.
In addition, when studying PA motives across different developmental periods, it is necessary to ensure the measure selected can be used during late childhood and adolescence. In previous studies, PA motives have been measured using different questionnaires including the Motives for Physical Activity Measure-Revised (MPAM-R) questionnaire, (Frederick & Ryan, 1993;Ryan et al., 1997) which is a multidimensional questionnaire assessing five motives for PA. (Frederick & Ryan, 1993;Owen et al., 2014;Ryan et al., 1997) To date, longitudinal invariance of the MPAM-R was tested across two time points with boys and girls transitioning from grade 5 to grade 6. (Dishman et al., 2013) Its longitudinal invariance from late childhood to adolescence (i.e. transition through two distinctive life periods) with boys and girls still needs to be tested.
Given all aforementioned gaps and inconsistent findings, the primary aim of this investigation was to examine the longitudinal associations between PA motives and MVPA over a 5-year period spanning the transition from late childhood (9-11 years), early adolescence (12-14 years), to middle adolescence (15-16 years) for boys and girls. Using a longitudinal design to examine these associations permitted the assessment of if and how these associations changed over time. Inconsistencies in previous findings did not permit the establishment of specific hypotheses prior to conducting this investigation. A secondary aim was to establish longitudinal measurement invariance for the MPAM-R.

METHODS
Data were derived from the longitudinal "Monitoring Activities of Teenagers to Comprehend their Habits" (MATCH) study. (Bélanger et al., 2013) At study inception, English-and Frenchspeaking grade 5 and grade 6 students were recruited from a convenient sample of 17 schools in New Brunswick, Canada. Efforts were made to recruit schools that were situated in a mix of rural and urban areas representing diverse socio-economic backgrounds. Participants completed self-report questionnaires during class time on a computer using a web-based survey three times per year (i.e., fall, winter, and spring) at 4-month intervals every year. These time points were specifically chosen to take into account the potential variation during the year due to seasonality (i.e., fall, winter, spring). (Bélanger et al., 2009) As per study protocol, directions given to participants before every data collection served to remind them to respond as honestly as possible and that their responses would remain confidential.
In the first year of data collection, there were 806 participants (55% girls; 65% French-speaking) who were, on average, 10.3 ± 0.6 years of age. In addition, 131 students from participating schools joined after the first year of the MATCH study, such that a total of 937 participants (56% girls; 66% Frenchspeaking) provided data at least once. Of these participants, 51.5% reported residing in an urban neighbourhood, and for all participants the mean neighbourhood income was 30 854 CAD (range 15 487-57 098 CAD). Data on PA motives and behaviour were collected during the first 15 assessments, with 118 individuals participating in all of those assessments, and 886 participating in at least three assessments. These assessments spanned the first 5 years of the MATCH study and analyses were restricted to them.

PA Motives
Participants' PA motives were assessed using the MPAM-R scale. (Frederick & Ryan, 1993;Ryan et al., 1997) This scale was available in English. To allow French-speaking MATCH study participants to complete it in French, a standard language equivalence protocol was followed to translate the questionnaire and ensure that items held similar meanings across languages. (Brislin, 1970;Chapman & Carter, 1979) Specifically, items were translated from English to French, back-translated to English, and then pilot tested with 12 French and English grade 5 and 6 students, which served to confirm that the questionnaire was comprehensible in both languages. (Bélanger et al., 2013) Participants were asked to report the extent to which 30 items representing PA motives were true for them using a 7-point Likert-type scale, with 1 representing "not at all true for me" and 7 representing "very true for me." In theory, the MPAM-R includes 7 items assessing enjoyment motives (e.g., "because it makes me happy"), 7 items assessing competence motives (e.g., "because I want to improve existing skills"), 5 items assessing social motives (e.g., "because I want to be with friends"), 5 items assessing fitness motives (e.g., "because I want be physically fit"), and 6 items assessing appearance motives (e.g., "because I want to lose or maintain weight to look better"). Score reliability and validity for the MPAM-R was demonstrated in past studies in different languages (English, Portuguese, Italian, Czech) except for French. (Albuquerque et al., 2017;Battistelli et al., 2016;Dishman et al., 2013;Vašíèková & Pernicová, 2018;Woods et al., 2007) Hence, the validity and reliability of scores obtained on the French version of the MPAM-R were evaluated in this study.

MVPA
MVPA was assessed with a 2-item measure developed specifically for adolescents. (Prochaska et al., 2001) Participants were asked to read the following statement: "Physical activity is an activity that increases your heart rate and makes you get out of breath some of the time. Physical activity can be done in sports, playing with friends, or walking to school. Some examples of physical activity are running, brisk walking, rollerblading, biking, dancing, skateboarding, swimming, soccer, basketball, football, and surfing" and then asked: "Over the course of the week (past 7 days), how many days were you physically active for a total of at least 60 minutes per day?" and "Over the course of a typical or usual week, how many days are you physically active for a total of at least 60 minutes per day?" Response options ranged from 0 to 7 days. The two items were averaged to estimate a weekly MVPA score. In previous work, this method to create MVPA scores was significantly correlated (r = 0.40, p < 0.001) with accelerometer data, had an interclass correlation of 0.77 (Prochaska et al., 2001) and was supported for use among children and adolescents. (Biddle et al., 2011;Cm & Crocker, 2008;Hardie Murphy et al., 2015) As the original items were available in English, the aforementioned translation procedures were also used to translate the English MVPA items into French.

Data Analyses
Descriptive Statistics. Data were summarized to describe the participants at study inception and all other time points. Means and ranges were computed to describe the age of participants. The median was calculated to describe the typical number of days reported for participating in at least 60 minutes of MVPA. Average scores and standard deviations for PA motives were also calculated using the average of all subscale items.
Factor Structure of the MPAM-R. The hypothesized correlated five-factor structure of the MPAM-R was tested using confirmatory factor analysis (CFA) at each assessment (i.e., 15 independent CFAs were computed). To address the issue of missing data, the computation was estimated with full information maximum likelihood (FIML) estimation to adjust the likelihood function so that each case contributes information on the variables that are observed. Then, the appropriateness of the model specification was verified in a second computation by using robust estimation of the errors (i.e. the Huber/White/ Sandwich estimator). Each of the 30 items were set to load onto their corresponding factor as identified by Ryan et al. (Ryan et al., 1997) As the chi-square statistic has a tendency to reject the null hypothesis when the sample is large, model fit was evaluated with approximate methods. Specifically, model fit was considered acceptable when a Root Mean Square Error of Approximation (RMSEA) < 0.08, a Comparative Fit Index (CFI) ≥ 0.90, and a Tucker-Lewis Index (TLI) ≥ 0.90 were obtained at each assessment. (Norman & Streiner, 2008) If acceptable model fit was not achieved at least at one assessment, standardized loadings, modification indices, standardized residuals, squared multiple correlations, and covariances between items were scrutinized to determine if lack of acceptable model fit was due to a problematic item or a function of the hypothesized factor structure. Items that cross-loaded on factors not identified by the original authors of the MPAM-R, (Ryan et al., 1997) were dropped from subsequent re-specified models until acceptable model fit was achieved at each assessment. In every re-specified model, only one item at a time was dropped in the computation of the 15 CFAs corresponding to each assessment (e.g., item 8 was identified as cross-loading after the first estimation of CFAs, then it was dropped from the next iteration of CFAs). Once an item was dropped it was not brought back to subsequent computations of CFAs. To confirm construct validity for the French version of the MPAM-R, a subsequent CFA with all assessments was conducted with the truncated version of the MPAM-R separate for French and for English speaking participants.
Score Reliability. To create the variables used for the main analysis in this study, five PA motives scores were calculated at each assessment using the mean of items retained for each of the motives (i.e., enjoyment, competence, social, fitness, appearance) in the final and reduced CFA model. Cronbach's alpha was calculated using all 30 items from the MPAM-R and using retained items from the reduced CFA (both analyses were completed once with the full sample, once with the sample of French-speaking participants, and once with the sample of English-speaking participants). This was completed to assess score reliability on the originally hypothesized variables as well as the variables informed from the reduced CFAs, and to confirm score reliability of the French version of the questionnaire, respectively. Additionally, composite reliability was calculated using the "relicoef" command in Stata (StataCorp, 2017) that is based on Raykov's computation of reliability coefficients. (Raykov, 1997) Invariance. To ensure that the results reflected true change over time and not change in the psychometric structure of MPAM-R scores, the factor structure and measurement invariance over time was examined. (Widaman et al., 2011) Four levels of invariance were estimated with the truncated MPAM-R using maximum likelihood parameter estimates with standard errors and a chi-square test statistic that are robust to nonnormality in Mplus: (Muthén & Muthén, 2019) (1) configural invariance (i.e., no equality constraints), (2) weak invariance (i.e., factor loadings constrained to be equal), (3) strong invariance (i.e., factor loadings and intercepts constrained to be equal), and (4) strict invariance (i.e., factor loadings, intercepts, and errors constrained to be equal). (Widaman et al., 2011) Following Chen's (Chen, 2007) and Cheung's (Cheung & Rensvold, 2002) recommendations, a change of ≤ 0.010 in CFI supplemented by a change of ≤ 0.015 in RMSEA was used as an indicator of invariance at each level.
In addition, to ensure that the MPAM-R scores from French and English-speaking participants could be combined, the four levels of invariance described above were conducted with data from year one to establish language invariance. Language invariance was tested to confirm that the MPAM-R scores held a similar psychometric structure among French and Englishspeaking participants.
Trajectories of PA Motives. Participants provided up to 15 assessments for the current analyses. As such, the slopes and intercepts for each PA motive were estimated with mixed effects regression models using data from all assessments. Both linear and quadratic fixed and random effects for assessment were tested in order to establish the functional form of change in PA motives. The quadratic term was retained for further analyses when it was statistically significant at p < 0.05. If the quadratic term was statistically significant, the command "Utest" in Stata was run to identify the inflection point marking when a change in slope direction could be noted. (Lind & Mehlum, 2010) Interactions for sex with time for each PA motive were tested and if they were significant for at least one of the motives, further analyses involving PA motives trajectories were stratified by sex. After deciding on final models, variables representing the slopes and intercepts for each PA motive were generated so that they could be used in the primary analysis.
Trajectories of MVPA. Similar to PA motives, trajectories for MVPA were estimated with mixed effects regression models using all 15 assessments. Linear and quadratic fixed and random effects for each assessment were also examined, and quadratic terms were retained if they were statistically significant at p < 0.05. If the quadratic term was statistically significant, the command "Utest" in Stata was run to identify the inflection point marking when a change in slope direction could be noted. (Lind & Mehlum, 2010) Sex interactions with time were tested and if significant, further analyses involving MVPA trajectories were stratified by sex.
Trajectories of PA Motives and MVPA. To address the main objective of this study, mixed effects regression models were used to examine longitudinal associations between slopes and intercepts of each PA motive and MVPA using all 15 assessments. Variables representing the slopes and intercepts for each PA motive were used as independent variables in the same model (i.e., the effect of one PA motive was adjusted for all other PA motives). Sex interactions were tested and if statistically significant, further analyses of the association between PA motives and MVPA were stratified by sex.
Longitudinal invariance testing was conducted using Mplus 7.4, (Muthén & Muthén, 2019) whereas all other analysis (i.e., CFAs, mixed effects regression models) were estimated using Stata MP 15.1. (StataCorp, 2017) In all mixed effects regression models, the unstructured matrix was used to estimate the covariance matrix, and tests of underlying assumptions for linear mixed effects regressions were conducted for the model depicting the longitudinal associations between PA motives and MVPA. Specifically, a linear relationship between PA motives and MVPA variables were visually inspected using a scatter plot, multivariate normality was examined by plotting residuals against a normal regression line using Q-Q plot, multi collinearity was assessed with the variance inflation factor and a pairwise correlation matrix (highly correlated variables were expected as our model contained variables that represented different aspects of one concept [e.g., fitness motives: intercept, slope, and quadratic terms], and finally homoscedasticity was evaluated by visually inspecting a scatter plot of the residuals and the fitted fixed effects. No assumptions were violated. Statistical significance was evaluated based on the traditional cut point of p < 0.05.

Results
Descriptive Statistics. These analyses were performed on data from 418 boys and 517 girls (Table 1). These participants were included in the final analysis since they participated in at least one assessment of PA motives and self-reported MVPA. At the first assessment (i.e., study inception), participants (n = 608) were on average 10.3 years old (range 9-12) and they reported participating in at least 60 minutes of MVPA on a median of 4.5 days per week. Moreover, boys reported a median of 5 days per week of achieving at least 60 minutes of MVPA, whereas girls reported a median of 4 days per week of achieving at least 60 minutes of MVPA. At each assessment, enjoyment motives received the highest mean score, followed by fitness, competence, social, and appearance motives respectively (Figure 1). Missing data for MVPA were minimal at any one assessment, the average completion rate per assessment was 98.1% (range 93.2-99.8). Missing data for PA motives varied by assessment, with an 84.1% (range 62.9-91.0) average questionnaire completion rate (i.e., responses available on the 30 items in the MPAM-R).
Factor Structure of MPAM-R Scores. The individual CFAs using the original 30 items as recommended by the authors of MPAM-R were unacceptable at each assessment in the full sample. The average RMSEA was 0.085 (range 0.062-0.104; 90% CI 0.082-0.089; p-close < 0.001), the average CFI was 0.87 (range 0.84-0.90), and the average TLI was 0.86 (range 0.83-0.88). After multiple iterations in which one item at a time was dropped from each assessment due to cross-loadings on other factors, the final truncated MPAM-R included 22 items (i.e., the same 8 items were dropped from all assessments; see supplementary Table S1 for more details Median MVPA = median number of average days per week in which study participants engaged in at least 60 minutes of moderate-to-vigorous physical activity Enjoyment = is the mean of items 2, 7, 11, 18, 22, 26 and 29 from the MPAM-R Fitness = is the mean of items 1, 13, 16, 19, and 23 from the MPAM-R Competence = is the mean of items 3,4,8,9,12,14, and 25 from the MPAM-R Social = is the mean of items 6, 15, 21, 28 and 30 from the MPAM-R Appearance = is the mean of items 5, 10, 17, 20, 24, and 27 from the MPAM-R Motives Complete = is the percentage of participants that responded to the 30 items on the MPAM-R Missing all motives = is the percentage of participants that did not respond to any items from the MPAM-R MVPA Complete = is the percentage of participants that responded to measures of MVPA Survey measurements were conducted at 4-month intervals, F = Fall, W = Winter, S = Spring, Assessments 1-3 are during year 1, assessments 4-6 are during year 2, assessments 7-9 are during year 3, assessments 10-12 are during year 4, and assessments 13-15 are during year 5 motives (see supplemental Table S1 for final retained items per subscale). Score Reliability. Alphas across all assessments for the original MPAM-R scale with all 30 items ranged between 0.76 and 0.95 for the full sample, between 0.78 and 0.95 for Frenchspeaking participants, and between 0.69 and 0.96 for Englishspeaking participants (see supplemental Table S3 for    was 0.88 (range 0.82-0.93), for competence motives was 0.92 (range 0.87-0.95), for appearance motives was 0.92 (range 0.-88-0.94), and for social motives was 0.86 (range 0.77-0.94). Measurement Invariance. Invariance over time was tested with the truncated MPAM-R; though, due to computational limitations (i.e., convergence issues related to model complexity with 15 assessments and 75 latent variables) only mid-year measurements (i.e., winter assessment, chosen because participants were expected to be stable in their behaviour for the past few weeks) over the 5 years were used (one assessment per year). Results of the longitudinal invariance testing of the truncated MPAM-R suggest that the factor structure met the conditions for strong invariance (i.e., factor loadings and item intercepts constrained) ( Table 2). (Chen, 2007) Strict invariance testing (i.e., factor loadings, item intercepts, and errors restrained) led to a change > 0.010 in CFI and 0.015 in RMSEA and was not tenable. As strong invariance is considered the minimum to proceed with testing change over time, (Cheung & Rensvold, 2002) analyses continued to the mixed effects regression models.
Language invariance was completed using data collected in mid-way through the first year of the MATCH study. This assessment was chosen for two primary reasons, 1) it served as the first assessment in the longitudinal invariance, and 2) it contained the largest number of participants from all assessments used in the longitudinal invariance. Table 4 of supplementary tables shows detailed fit statistics for the four levels of group invariance. The four levels of invariance yielded acceptable model fit statistics.
Trajectories of PA Motives. Mixed effects regression models to estimate PA motives trajectories revealed a statistically significant sex interaction for appearance and competence motives. Hence, the trajectories for all PA motives were stratified by sex. For both sexes, mixed effects regression models revealed that four of the PA motives (i.e., fitness, competence, social, and appearance) followed a U-shape trajectory ( Figure  2.), whereas enjoyment motives followed a linear decrease for boys and girls (Table 3). Specifically, for boys, fitness motives decreased from the 1 st to the 12 th assessment (from an average age of 10.3 years to 13.8 years; the inflection point of the curb was at 11.89) and increased thereafter; competence motives decreased from the 1 st to the 9 th assessment (to an average age of 12.8 years; the inflection point of the curb was at 9.18) and increased thereafter; social motives decreased from the 1 st to the 11 th assessment (to an average age of 13.6 years; the inflection point of the curb was 10.88) and increased thereafter; and appearance motives decreased from the 1 st to the 7 th assessment (to an average age of 12.2 years; the inflection point of the curb was at 7.37) and increased thereafter. For girls, fitness motives decreased from the 1 st to the 11 th assessment (from an average age of 10.3 years to 13.5 years; the inflection point of the curb was at 9.87) and increased thereafter; competence motives decreased from the 1 st to the 9 th assessment (to an average age of 12.8 years; the inflection point of the curb was at 8.89) and increased thereafter; social motives decreased from the 1 st to the 11 th assessment (to an average age of 13.5 years; the inflection point of the curb was at 10.66) and increased thereafter; and appearance motives decreased from the 1 st to the 6 th assessment (to an average age of 11.9 years; the inflection point of the curb was at 5.88) and increased thereafter.
Trajectories of MVPA. Mixed effects regression models to estimate MVPA trajectories revealed a statistically significant sex interaction. Hence, all mixed effects regression models were stratified by sex. For both girls and boys, MVPA followed an inverse U-shape peaking at the 7 th assessment (the inflection point of the curb was at 7.88) for girls (mean age in years 12.1; SD 0.6; range 11-14) and at the 9 th assessment (the inflection point of the curb was at 8.97) for boys (mean age in years 12.8; SD 0.7; range 12-15) ( Figure 3).
To facilitate interpretation of the magnitude of the results an estimation of MVPA was computed at the first assessment for an average boy and girl, then the effect of a PA motive was added to the estimation by adding a standard deviation to the mean of that motive. Controlling for all variables in the model, at study inception, an average boy was expected to accumulate an average of 4.5 days of MVPA, whereas an average girl was expected to accumulate an average of 4.2 days of MVPA. For boys, MVPA decreased by 44.5% when one standard deviation was added to fitness motives, increased by 19% when one standard deviation was added to enjoyment motives, and increased by 56.1% when one standard deviation was added to competence motives. For girls, MVPA increased by 10.9% when one standard deviation was added to enjoyment motives, increased by 48.3% when one standard deviation was added to competence motives.

Discussion
In this study, the longitudinal relationship of PA motives with self-report MVPA across 15 time points over a 5-year period spanning late childhood (10-11 years), early adolescence (12-14 years), and middle adolescence (15-16 years) was explored. Based on these findings, there are differences a.Estimated PA Motives for Boys b.Estimated PA Motives for Girls  in how PA motives relate to MVPA by sex and developmental period. Specifically, fitness motives were negatively associated with boys' MVPA levels from late childhood to middle adolescence, both at study inception and longitudinally such that maintaining higher fitness motives were associated with lower MPVA levels across the 5 years. In addition, enjoyment motives were positively associated with MVPA during late childhood for both sexes (i.e., at study inception), and for boys, this positive association was maintained over time such that, holding greater enjoyment motives across the 5 years were associated with higher MVPA levels. Also, competence motives were positively associated with MVPA for both sexes from late childhood to middle adolescence, both at study inception and longitudinally such that, maintaining higher competence motives were associated with greater MVPA levels, though associations were stronger for girls after the 9 th assessment. Furthermore, social and appearance motives for both sexes were not significantly related to MVPA during any examined developmental period. All results were statistically significant at p < 0.05 Table 4. Results of sex-stratified mixed effects regression models estimating the relationship between physical activity motives and moderate-tovigorous physical activity.  (Dishman et al., 2013;F Gillison et al., 2009;Iannotti et al., 2012;Kopcakova et al., 2015) Although the present results are consistent with several studies showing that fitness motives are not related to girls' participation in PA, (Dishman et al., 2013;Iannotti et al., 2012;Kopcakova et al., 2015) they show that for boys, greater fitness motives predict lower initial MVPA and are associated with decreasing MVPA over time. In relation to the latter, boys reporting increasing fitness motives during the study period also reported a large (44%) decrease in the number of days on which they accumulated the recommended amount of MVPA. Stated differently, a one standard deviation increase in boys' fitness motives score was related to two less days of MVPA participation. Whilst causality cannot be inferred, fitness motives are considered extrinsic forms of motivation and do not relate to the maintenance of PA. (Ryan et al., 1997) Considering the negative associations observed herein, strategies previously used to foster fitness motives in previous PA promotion efforts should be used with caution. (Iannotti et al., 2012) It may be that for young adolescents, the inability to truly consider the long-term fitness benefits of a behaviour may be a factor limiting the impact of fitness as a motive for PA. (Iannotti et al., 2012) By demonstrating a negative association with MVPA as early as in 9-10 years old boys, the current findings lend further support that fitness concerns may only serve as determinants of PA in more mature individuals that have developed the cognitive processes required to realize the benefits of engaging in PA for fitness reasons. (Johnson et al., 2009) Therefore, future studies may benefit from investigating how youth are interpreting fitness items, including whether boys and girls interpret these items similarly, to ensure accuracy in how researchers describe their results.
Enjoyment Motives. Others have argued that enjoyment motives should be the initial focus of any physical activity intervention. (Emf & Kriemler, 2016;Lewis et al., 2016) Our results also highlight the need to ensure that PA interventions are enjoyable as holding (at study inception) and maintaining (longitudinally across the 5 years at each assessment) higher enjoyment motives were strongly associated with greater PA levels. These results are corroborated by several other studies. (Dishman et al., 2013;F Gillison et al., 2009;Iannotti et al., 2012;Seghers et al., 2014;Woods et al., 2007) However, previous studies, were unable to discern different patterns by sex in the relationship of enjoyment motives with the maintenance of PA behaviour. The current results suggest that enjoyment motives are positively related to MVPA from age 9-16 years among boys; whereas among girls the positive relationship between enjoyment motives and MVPA was only noted during late childhood (9-10 years). Specifically, holding higher enjoyment motives (one standard deviation) resulted in gaining (20%) almost one complete additional day of achieving MVPA recommendations among boys, whereas it resulted in lower (10%) gain among girls. A possible explanation for this result is that when girls are younger they display greater physical selfperception and as such they report greater enjoyment of PA which then reinforces their desire to participate in further PA. (Labbrozzi et al., 2013) However, as girls transition through puberty they may experience a degradation in their physical self-perception and a reduction in their enjoyment of PA. (Labbrozzi et al., 2013) Differences between the current results and results from other publications (Dishman et al., 2013;   Gillison et al., 2009;Iannotti et al., 2012;Seghers et al., 2014;Woods et al., 2007) may be due to differences in research design (i.e., cross-sectional studies, short longitudinal studies) and different age groups (e.g., ages 7-12 years not encompassing the pubertal transition).
Competence Motives. The present results are in line with other research suggesting a positive association between competence motives and PA. (Dishman et al., 2013;Kopcakova et al., 2015;Seghers et al., 2014) The findings demonstrated that holding (at study inception) and maintaining (longitudinally across the 5 years at each assessment) higher competence motives for boys and girls were associated with higher levels of self-reported PA. Additionally, after the 9 th assessment when girls were aged on average 12.8 years, maintaining higher levels of competence motives were related more strongly to greater self-reported PA. Specifically, a one standard deviation increase in competence motives among boys and girls was related to attaining MVPA recommendations on two additional days, reflecting the importance of promoting participation in PA for competence reasons. A systematic review that examined which factors contributed to drop out from organized sport among children and youth found that low perceptions of competence was one of the key factors influencing drop out. (Crane & Temple, 2015) Furthermore, data from qualitative studies suggests that youth may feel embarrassed to participate in sports in front of their peers if they are not able to show that they are competent in the sport. (F Gillison et al., 2009) It is possible that youth who engage in greater PA are driven by competence motives, and hence, maintain their PA participation. On the other hand, youth who do not hold high competence motives for PA participation are more susceptible to eventual barriers and are at a greater likelihood to discontinue their PA participation. This study hints that fostering competence motives in PA interventions may assist youth in adopting a PA mindset that will support their behaviour for a longer term especially among girls, whom have been observed to drop out of PA much sooner and at a faster rate than boys. (Chung et al., 2012) Social Motives The present results suggest that social motives were not associated with MVPA for both sexes. Previous investigations on this relationship have not been consistent with some showing that greater social motives were related to more PA, (F Gillison et al., 2009;Iannotti et al., 2012) others indicated it was associated to less PA, (Seghers et al., 2014) and some, like this study suggested it was not related to PA. (Dishman et al., 2013;Kopcakova et al., 2015) The current results are similar to the only other longitudinal study that examined the relationship of the five motives with objectively measured PA. (Dishman et al., 2013) A recent systematic review of qualitative studies on barriers and facilitators of PA behaviour in adolescents suggests that friendships have an influence on PA behaviour. (Martins et al., 2015) However, researchers have found that youth tend to be friends with peers that accumulate similar levels of PA. (De La Haye et al., 2011) This might suggest that social motives are not helpful in the initiation of PA behaviour, as children and adolescents choose friends that share certain behaviours, and not because these friends are going to make them start something new. Social motives may therefore not be key elements in the initiation and maintenance of PA.
Appearance Motives. Results from this work show that greater appearance motives were not related to MVPA, for either boys or girls. However, there were sex differences in the trajectories of appearance motives. In this study, both girls and boys identified appearance motives as their least important motives for taking part in PA throughout the study. Still, boys rated appearance motives higher than girls, but after turning 12 years old, the increase in the rating of this motive was more pronounced for girls than for boys. Previous cross-sectional publications have been inconsistent in their findings in relation to how appearance motives may relate to MVPA (F Gillison et al., 2009;Seghers et al., 2014) and a longitudinal study with two measurement points found no association between appearance motives and MVPA. (Dishman et al., 2013) Collectively, this suggests that perceived and experienced social pressures to achieve a specific physique by both girls and boys may not lead to increased PA. (Grogan & Richards, 2002;Niven et al., 2009;Sampasa-Kanyinga et al., 2017) It is therefore recommended that interventions do not foster appearance motives as a means to increase PA.

Strengths and Limitations
The comprehensive long-term and frequent record keeping in the MATCH study is a strength that should be acknowledged. This extensive data collection enabled the use of truncated MPAM-R items that were confirmed to be invariant across time to investigate changes in PA motives and PA from when children were 9-11 years until they were 15-16 years. Some limitations include the self-reporting of MVPA. Although selfreported PA correlates with health outcomes and can be used for providing proxy-level knowledge about behaviours that would be otherwise absent with device-based PA assessment, (R Colley et al., 2019) it may over/under estimate PA. (Pd et al., 2011) These potential errors are nevertheless mitigated by the interest in describing general PA trends made possible with repeated measures, rather than an interest in reporting specific PA levels. (Levin et al., 1999) Furthermore, although extra efforts were taken to recruit a representative sample of youth from New Brunswick, study results may not be generalizable to all children and adolescents. Moreover, computational challenges inhibited the estimation of longitudinal measurement invariance test using all available data from all seasons. As such, despite showing invariance by using mid-year measurements of every academic year, there may be some masked errors that could not be identified. These same computational challenges hindered the inclusion of potential confounding variables such as pubertal maturity and body mass index. Furthermore, the use of a truncated version of the MPAM-R may make other studies less comparable. To avoid having to truncate questionnaires, future studies may benefit from using confirmatory factor analysis techniques that permit cross-loading of items without impacting model fit such as exploratory structural equation modelling. (Marsh et al., 2014) Finally, the statistical methods that were used to answer the primary objective of this study do not permit causal interpretations of the results.

Conclusions/Public Health Implications
With the objective to increase PA in adolescents, fostering motives centred on enjoyment and competence seem to be important intervention targets. Public health messages and interventions should place more importance on these motives to encourage older children and adolescents to adopt physically active lifestyles. It is possible that this in turn will foster such motives, though the reverse associations still warrant investigation. Further, actions aimed at promoting MVPA should avoid promoting fitness motives to get older children and adolescents more active.

Data Availability
The original data analyzed for these analyses are available through a data sharing agreement with the MATCH study research team. More information on this may be obtained from the principal investigator of the MATCH study, Dr. Mathieu Belanger.

Disclosure statement
The authors declare that they have no competing interests.

Funding
The MATCH project is supported by the New Brunswick Health Research Foundation  Authors' contributions PAN conceptualized the objectives of the analysis, designed and conducted statistical analyses, and wrote the manuscript. JG helped with writing the introduction, discussion, and critically reviewed all other content. JB, KG and ID helped with the development of the analysis plan, data interpretation and critically reviewed and edited all other content. CS helped with interpretation of data and critically reviewed all other content. JB helped with writing the introduction and critically reviewed all other content. MB discussed objectives, data analysis plan, contributed to interpreting results and critically reviewed the manuscript. MB is the principal investigator of the MATCH study.

Ethics approval
All participants and their parents provided informed consent and the MATCH study was approved by the Comité d'Éthique de la Recherche du Centre Hospitalier de l'Université de Sherbrooke (11-025-M9).