A multigroup random-intercept cross-lagged panel model for Finnish secondary school students in frame of situated expectancy-value theory

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ A multigroup random-intercept cross-lagged panel model for Finnish secondary school students in frame of situated expectancy-value theory © 2024 The Authors. Published by Elsevier Inc. Published version Raufelder, Diana; Steinberg, Olga; Viljaranta, Jaana; Poikkeus, Anna-Maija; Vasalampi, Kati Raufelder, D., Steinberg, O., Viljaranta, J., Poikkeus, A.-M., & Vasalampi, K. (2024). A multigroup random-intercept cross-lagged panel model for Finnish secondary school students in frame of situated expectancy-value theory. Learning and Individual Differences, 116, Article 102555. https://doi.org/10.1016/j.lindif.2024.102555 2024 A multigroup random-intercept cross-lagged panel model for Finnish secondary school students in frame of situated expectancy-value theory ☆ Diana Raufelder a,* , Olga Steinberg a , Jaana Viljaranta b , Anna-Maija Poikkeus c , Kati Vasalampi c,d a University of Greifswald, Department of developmental psychology and educational psychology, Franz-Mehring-Straße 47, 17487 Greifswald, Germany b University of Eastern Finland, School of Educational Sciences and Psychology, P.O.Box 111, Joensuu FI-80101, Finland c University of Jyv¨ askyl¨ a, Department of Teacher Education, Alvar Aallon katu 9, FI-40014 University of Jyv¨ askyl¨ a, Finland d University of Jyv¨ askyl¨ a, Department of Psychology, Mattilanniemi 6, FI-40014 University of Jyv¨ askyl¨ a, Finland ARTICLE INFO Keywords: Academic self-concept Task value General upper secondary education Vocational education Situated expectancy-value theory ABSTRACT The aim of this study is to examine both within-person and between-person associations of academic self-concept and task values in literacy and mathematics to identify the most promising motivational construct to prevent motivational decline during school transitions. The sample included 3636 students (average age at the start: 15.73 years, SD: 0.32 years) followed up three times from lower secondary school (T1) to the third year (T3) of upper secondary education, either in vocational or academic tracks. Multi-group random intercept cross-lagged panel models detected several spillover (cross-lagged) effects between self-concept and task values in mathematics but not in literacy. There were also marginal but significant differences between students from different educational tracks in both subjects. Overall, utility value and academic self-concept in mathematics were found to be the most promising motivational constructs in changing motivational beliefs, thus presenting important starting points in motivational interventions. Educational relevance and implications statement: This study highlights that spillover effects are more pronounced in maths than in literacy, emphasising the need for tailored interventions in mathematics education. Moreover, the potential disruption in students' motivational beliefs during school transitions suggests the importance of ensuring continuity in support to help mitigate the impact of these transitions. While our results indicate limited carryover effects, it is possible that school transitions are experienced as breaks in motivational development. The role of utility value in exhibiting spillover effects over school transitions in both maths and literacy suggests the significance of emphasising the practical relevance of academic subjects to sustain students' motivation. Additionally, recognising the superior role of academic self-concept in maths in spillover effects on task values underscores the importance of nurturing students' confidence and beliefs in their own mathematical abilities. 1. Introduction Expectancy-value theory (EVT; Eccles et al., 1983) and its recent expansion, situational EVT (SEVT; Eccles & Wigfield, 2020, 2023), highlight the role of students' task values and success expectancies for academic achievement or future career choices. The main proposition of EVT is that setting a high value for a task (e.g. achievement in an academic domain) and expecting to be successful in that area contribute to students' motivation and investment of more effort in mastering the required skills (Eccles & Wigfield, 2002; Wigfield & Eccles, 2000). With the shift from EVT to SEVT, the situational character of motivational components has received special attention, accompanied by questions about intraand inter-individual heterogeneity, state–trait relations and specific learning environments (e.g. different school settings) in the development of success expectancies and task values (see Moeller et al., 2022). ☆ All authors share the research interest in motivational development processes during the school years, and they are particularly interested in intraand interindividual differences. * Corresponding author at: University of Greifswald, Germany, Department of School Education, Ernst-Lohmeyer-Platz 3, 17487 Greifswald, Germany. E-mail addresses: [email protected] (D. Raufelder), [email protected] (O. Steinberg), [email protected] (J. Viljaranta), [email protected] (A.-M. Poikkeus), [email protected] (K. Vasalampi). Contents lists available at ScienceDirect Learning and Individual Differences journal homepage: www.elsevier.com/locate/lindif https://doi.org/10.1016/j.lindif.2024.102555 Received 16 August 2023; Received in revised form 27 August 2024; Accepted 6 September 2024 Learning and Individual Dierences 116 (2024) 102555 Available online 13 September 2024 1041-6080/© 2024 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). More specifically, Eccles and Wigfield (2023) and Moeller et al. (2022) raised the question of the possible state and trait shares of the individual components of success expectancies and task values in specific situations (over time) and, thus, of the nature of these components per se. The present study addresses these exact questions to deepen our understanding of the nature and processuality of success expectancies and task values and the possible underlying trait and state dynamics. It is important to disentangle these components, especially with the aim of positively influencing them in various educational settings (e.g. classes in different school forms). Accordingly, the current study has two main objectives. The first aim is to investigate the situated nature of the development of success expectations (i.e. academic self-concept) and task values by exploring the period of school transition from comprehensive school to either general upper secondary school (academic track) or to vocational school (vocational track) in Finland (grades 9, 10 and 12) in different domains (literacy and mathematics). The second aim is to specify possible trait and state components, as only a few existing SEVT studies (e.g. Benden & Lauermann, 2023; Moeller et al., 2022) have differentiated between within-person fluctuations (temporal deviations) and between-person differences (stable trait factors) in the development of success expectancies and task values over time. Overall, the purpose of this study is to identify the most effective motivational construct for changing motivational beliefs and preventing motivational declines. 1.1. The development of success expectancies and task values According to EVT (Eccles et al., 1983; Wigfield & Eccles, 2000), a student's expectancies of success in a task and the subjective value of that task constitute the basis of the student's motivational beliefs. There are four types of task values: (a) attainment value, encompassing the personal meaning to the student of accomplishing a task; (b) intrinsic value, depicting the pleasure and interest experienced in undertaking and completing a task; (c) utility value, capturing the meaningfulness of a task for one's own future; and (d) cost value, which includes the perceived negative consequences of accomplishing a task, such as negative emotions or stalling other activities. In the current study, we explore only the task values with positive connotations (1–3). According to Bong and Skaalvik (2003), Eccles and Wigfield (2020) and Marsh et al. (2019), expectancy beliefs are conceptually related to students' academic self-concept. Additionally, previous studies have shown some overlap between items on expectations of success and academic self-concept, as they often load on a single factor (see Eccles & Wigfield, 2023), which suggests that these constructs are not always empirically distinguishable (see Lazarides et al., 2020). In the current study, we rely on measures of students' academic self-concept, with the aim of further deciphering the proportion of stable traits (i.e. academic self-concept) and states with respect to the development of motivational beliefs. In accordance with Shavelson et al.'s (1976) multidimensional model (Sch¨ one et al., 2003), academic self-concept is a component of general self-concept that depicts an individual's ideas about their own study-related abilities, traits and school activities. Eccles and Wigfield (2020) described this as an individual's more stable self-beliefs, while success expectancies are more taskand time-specific. Studies have indicated that, in adolescence, task values in key school subjects can influence further academic pathways even more than academic performance (see Guo et al., 2018). The relationship between students' expectancy of success and their task value beliefs is a key mechanism for motivational congruence, as proposed by Eccles et al. While the original SEVT did not explicitly include cross-lagged paths between expectancy and values, it suggested that such bidirectional influences were possible (see Benden & Lauermann, 2023; Eccles, 2005, 2009; Wigfield et al., 1997). Students often value tasks in which they excel due to the intrinsic reward of competence, and conversely, they may devalue tasks in which success seems unlikely to protect their selfworth (see Benden & Lauermann, 2023; Eccles, 2009; Harter, 1990; Wigfield & Eccles, 2020). Similarly, valuing a task can increase engagement and improve skills and future success expectations (Eccles, 2005, 2009). Education researchers have focused on cross-lagged expectancy-value associations to identify which motivational constructs can significantly influence other motivational beliefs and, therefore, should be prioritised in interventions aimed at preventing drops in academic motivation (Marsh et al., 2005; Rosenzweig et al., 2022). Benden and Lauermann (2023) stated that ‘Eccles (2005) pointed out that analyses of the cross-lagged links between students’ expectancy and task values must carefully consider (a) which time lags and (b) which types of assessments are best suited to capture such links (see also Dormann & Griffin, 2015)' (p. 2). Some developmental processes unfold over years, while others occur during shorter periods (Benden & Lauermann, 2023; Gaspard et al., 2020). Most evidence has come from long-term studies that showed significant effects of expectancy on task values, but fewer findings have been on reciprocal effects (e.g. Arens et al., 2019; Chung & Kim, 2022; Grigg et al., 2018; Lee & Seo, 2021; Marsh et al., 2005; Trautwein et al., 2012; Viljaranta et al., 2014; VinniLaakso et al., 2019; Wigfield et al., 2016). Shorter-term studies have presented mixed results due to varying time lags and motivational assessment types (Beymer et al., 2022; Moeller et al., 2022; Perez et al., 2019). The results were partly different for different subjects. For example, in the study by Arens et al. (2019), which considered maths, literacy and English as a foreign language in a sample of German students of maths and foreign languages, almost all unidirectional paths from academic self-concept to intrinsic value were found to be significant over five waves (but not vice versa). However, for literacy, it was the other way around; almost every path from intrinsic value to academic self-concept was found to be significant (but not vice versa). In contrast, the associations between academic self-concept and attainment value were found to be reciprocal for all three subjects and over all five waves. The study by Vinni-Laakso et al. (2019) of Finnish elementary school students could not detect any significant cross-lagged path between academic self-concept and intrinsic value or cost from 1st grade to 2nd grade in science. In addition, the study by Trautwein et al. (2012) focused on maths and English as a foreign language and found that some value components (i.e. utility value and cost) were more closely related to expectancy beliefs than with other value facets. In their recent article, Eccles and Wigfield (2023) raised the question of how task values accumulate and whether there might be a more stable latent factor (trait): ‘Second and even more importantly, we have begun to think more specifically about the nature of STV itself. For example, do the subcomponents aggregate additively to form a more stable latent STV for each option, or do the subcomponents aggregate in varying ways to form more unstable STVs for each option depending on what any option is being contrasted with at any given point in time?’ (p. 10). The current study takes up this idea by investigating possible trait proportions (between levels) and within-person differences using a randomintercept cross-lagged panel model (RI-CLPM). In doing so, we follow Moeller et al. (2022), who, following dynamical systems theory, raised the question of ‘how situated experiences of expectations and values may relate to trait-like motivational dispositions’. However, most existing research is based on traditional CLPM on students' expectancy-value beliefs over time and does not account for both withinand between-person variability (e.g. Arens et al., 2019; Chung & Kim, 2022; Vinni-Laakso et al., 2019), which can lead to substantially biased estimates of cross-lagged associations (Berry & Willoughby, 2017; Hamaker et al., 2015). To our knowledge, only two studies have differentiated between withinand between-person variability in academic self-concept and task values (Benden & Lauermann, 2023; Moeller et al., 2022). Benden and Lauermann (2023) examined using RI-CLPM within-person variations in the connections between students' course-specific (summative) or week-specific (situated) expectancies and task values in gateway maths courses for students studying maths, physics or maths teacher education. The findings D. Raufelder et al. Learning and Individual Dierences 116 (2024) 102555 2 showed that during a semester, there was an increasing within-person alignment between students' course-specific expected success and intrinsic/utility values (but not cost), according to RI-CLPMs. Unidirectional spillover—or cross-lagged—effects from expectancy to intrinsic/utility values were associated with this alignment. The study by Moeller et al. (2022) investigated using a multilevel CLPM whether task values, cost and success expectancies, measured in a learning situation (time point t) during a weekly university lecture, predicted each other and themselves in the subsequent situation (t +1; 27 min later). They could not identify any significant cross-lagged effects from one situation to the next in any of the measured situated expectancy-value components. As both studies were based on a sample of university students, it was difficult to draw conclusions about adolescent students and the school context. Overall, while previous research has consistently indicated a positive association between task motivation and academic self-concept, which strengthens with age (Jacobs et al., 2002; Vinni-Laakso et al., 2019; Wigfield et al., 1997), there is no clear evidence of how students' academic self-concept and task values develop and associate with one another over the span from middle to late adolescence and during school transitions and of how within-person fluctuations (temporal deviations) can be separated from stable between-person differences (stable trait factors). The present study aims to shed light on these associations by considering tree measurement waves (grades 9, 10 and 12), two domains (math and literacy), various school types before and after the transition and both withinand between-person differences. 1.2. The role of school type An important gap in the existing literature on the developmental dynamics between the self-concept of ability and task values is the scant information on the effect of moderating contextual factors. SEVT (Eccles & Wigfield, 2020, 2023) incorporates the key proposition in stage- –environment fit theory that emphasises the role of the context. There is evidence of a high likelihood of a negative impact of school transitions on adolescent students' motivational beliefs (Eccles et al., 1993; Rosenzweig et al., 2019). To our knowledge, no studies have focused on school transition in middle adolescence (from lower secondary to further education) and the differences among students attending vocational and academic tracks. The examination of the motivational development of students attending different school types is of key interest in the present study. In Finland, basic education (grades 1 to 9) does not involve selection, tracking or streaming (Antikainen & Luukkainen, 2008). After 9th grade, students apply either for general upper secondary school (3-year academic track, providing the basis for further education at universities/ polytechnics) or vocational education (vocational track, after which adolescents proceed with work life). A person-orientated subgroup analysis conducted approximately a decade ago (Viljaranta et al., 2009) suggested that students who aim for a vocational track are more likely to belong to profiles characterised as ‘practical skills and language–motivated’ or ‘practical skills–motivated’, while those who aim for an academic track are more likely to belong to profiles characterised as ‘multimotivated’ or ‘maths and science–motivated’. Based on SEVT, students' motivational beliefs are formed during their school careers, so students who attend general upper secondary schools and vocational schools may differ in their motivational beliefs prior to the school transition. However, this assumption has not yet been investigated. Furthermore, of interest is the interplay of different dimensions of SEVT in the course of the three years of secondary education, considering different school tracks after the 9th grade. It is possible that for students in vocational schools, more significant cross-lagged pathways from utility value to the other components can be identified, since instruction is specifically geared to future professions (Finnish National Agency of Education, 2018). One could also assume that the associations between the constructs for general upper secondary school students show the same patterns at T1 (grade 9) and T2 (grade 10), as well as between T2 (grade 10) and T3 (grade 12), since the learning environment and instructional design do not differ much. In turn, for students from vocational schools, differences can be assumed between T1 and T2 in comparison to T2 and T3. 1.3. The current study The purpose of this study is to address intraand interindividual heterogeneity, state–trait relations and specific learning environments (e.g. different school and classroom settings) in the development of academic self-concept and task values (cf. Moeller et al., 2022). In detail, it empirically examines the development of academic self-concept and three task values in two subjects (literacy and mathematics), different grades (grades 9, 10 and 12) and different school types (joint comprehensive schools in grade 9, general upper secondary schools vs. vocational schools in grades 10 and 12), considering both the within-person variations (temporal variances) and the stable between-person differences (stable trait factors). Traditional cross-lagged panel models used in previous studies (e.g. Arens et al., 2019; Chung & Kim, 2022) were not able to differentiate between the between-person and the within-person effects (Berry & Willoughby, 2017; Hamaker et al., 2015; Mund & Nestler, 2019). Therefore, it is unclear what kinds of effects (withinperson or between-person) these panels actually explored. It has recently been argued that between-person associations may only (fully) converge with within-person associations under specific circumstances (e.g. in terms of the presence, magnitude and sign of detected effects) and that investigating both types of associations may provide illuminating but conceptually distinct insights (e.g. Fisher et al., 2018; Hamaker et al., 2015; see Kryshko et al., 2022; Murayama et al., 2017; Orth et al., 2021) To overcome the shortcomings of the traditional CLPM, we use the longitudinal random intercept cross-lagged panel model (RI-CLPM) approach to explore both the within-person and between-person effects and find answers to the following research questions (RQs) and hypotheses (Hs): (RQ1a) Are differences between individual students' academic selfconcepts in literacy and mathematics associated with differences in their task values (between-person level)? (H1a) There are between-person associations between success expectancies and task values. For example, it is expected that students with higher scores in academic self-concepts may also have higher scores in task values. (RQ1b) Are differences between the task values of individual students in literacy and mathematics associated with differences in their other task values (between-person level)? (H1b) There are between-person associations between the different task values. It is expected, for example, that students with higher scores in attainment value may also have higher scores in intrinsic value. The study by Trautwein et al. (2012) showed that the values themselves differ in their nature; while attainment value and intrinsic value define ‘intrinsic’ values, utility value and cost constitute ‘extrinsic’ factors. (RQ2) To what extent are academic self-concept and task values in literacy and mathematics associated with each other at the withinperson level over time (cross-lagged associations)? (H2) There are within-person associations between the different components of success expectancies and task values. It might be possible for a person to change their appreciation of a particular task over time, for example, as they experience success or become more deeply involved in the topic. (RQ3) Are individuals' deviations from their expected scores in all four variables (academic self-concept and the three task values) likely to carry over from one measurement wave to the next (autoregressive associations)? (H3) There are carryover effects on students' academic self-concept and task values over time, such as an individual's changes in academic self-concept having a cumulative effect on their academic self-concept D. Raufelder et al. Learning and Individual Dierences 116 (2024) 102555 3 development. In other words, students who have scored above (or below) their average scores also tend to have scores above (or below) their average at the subsequent time point. Whether group differences between students attending general upper secondary education or vocational education exist in lagged regression coefficients can be thought of as moderation or interaction effects, which can be investigated by a multiple-group version of the RICLPM, as suggested by Mulder and Hamaker (2021). 2. Methods 2.1. Transparency and openness In this section, we indicate how the data were collected and the schools recruited, as well as all data exclusions (if any) and all measures in the study. We followed JARS (Kazak, 2018). All data, analysis codes, and research materials are available upon request. The data were analysed using Mplus 8.8 (Muth´ en & Muth´ en, 1998–2015). The current study design and analyses were not preregistered on any specific platform. 2.2. Sample and procedure The sample (N =3636; M age at the outset =15.73 years, SD =0.32 years; 54.5 % female; n vocational =1669; n upper =1967) was drawn from the comprehensive longitudinal X1 (removed for review purposes) study and its extension, X2 (removed for review purposes). In the X1 study, approximately 2000 students were followed from kindergarten to the end of lower secondary school (grade 9). In X2, the participants and their classmates (N =3636) were followed during upper secondary education. The participating students came from four municipalities (two medium-sized, one big and one rural) in different parts of Finland. At the start of the present study (9th grade; final year of comprehensive school), the students attended 34 lower secondary schools. After the transition (from lower secondary school to upper secondary education), the students attended 72 different upper secondary education institutions (36 general upper secondary schools and 36 vocational schools). The Ethical Committee of the University of X3 (removed for review purposes) approved the study and the research design in 2006 and 2018. Before collecting data at the lower secondary schools, written consent was collected from parents or guardians. In upper secondary education, the participating students confirmed their voluntary participation in the study. Classroom-administered questionnaires were used for data collection on normal school days by trained research assistants or teachers during three waves: spring 2016 (Time 1, T1, 9th grade of lower secondary school), spring 2017 (Time 2, T2, the first year of upper secondary education), and spring 2019 (Time 3, T3, the final year of upper secondary education). In Finland, school transition takes place after the 9th grade. According to Finnish educational statistics (Official Statistics of Finland, 2021), 54 % of Finnish students continue studying in general upper secondary schools and 40 % choose vocational schools, while other options are rare. The normative time to complete upper secondary education lasts three years. 2.2.1. Academic self-concept To assess students' academic self-concept, scales developed by Eccles and Wigfield (1995) and Spinath and Steinmayr (2008) were used. The scale used to assess academic self-concept in mathematics consists of two questions (‘How good are you at mathematics?’ and ‘How good are you at mathematics compared to other students in your group?’). For each measurement point, a composite score was calculated as the mean of the items measuring the construct. The Cronbach reliability coefficients were good for both the whole sample and the subsamples ( α = 0.87 to 0.92). The scale used to assess students' academic self-concept in literacy consists of two questions (‘How good are you in your mother tongue?’ and ‘How good are you in your mother tongue compared to other students in your group?’). For each measurement point, a composite score was calculated by computing the mean of the items. The scale showed good reliability for both the whole sample and the subsamples ( α =0.80 to 0.89). The students responded using a five-point Likert scale (1 =‘poor/not very good’ to 5 =‘very good’). 2.2.2. Task values Based on an adapted version of the scale developed by Eccles et al. (1983), the three task values (i.e. attainment, intrinsic and utility value) were assessed with two items for each dimension of task value. The items were as follows: attainment values in mathematics and literacy (e. g. ‘How important is it for you that you do well in mathematics/literacy?’ and ‘How important is it for you to get good grades in mathematics/literacy?’), intrinsic values in mathematics and literacy (e.g. ‘How much do you like mathematics/literacy in school?’ and ‘How readily do you do mathematics/literacy?’) and utility values in mathematics and literacy (e.g. ‘How useful with regard to your future plans do you consider mathematics/literacy?’ and ‘How useful are the following school subjects in your daily life?’). The students responded using a fivepoint Likert scale (1 =‘not at all…’ to 5 =‘very… much/readily/ important/useful’). A composite score was calculated separately for the attainment, intrinsic and utility values for each measurement point as the mean of the items measuring the constructs. The reliability of each measurement point for both the whole sample and the two subsamples was acceptable for attainment values (literacy: α =0.81 to 0.94; mathematics: α =0.88 to 0.91), intrinsic values (literacy: α =0.79 to 0.85; mathematics: α =0.88 to 0.90) and utility values (literacy: α = 0.74 to 86; mathematics: α =0.67 to 0.81). 2.3. Statistical analysis All statistical analyses were conducted with Mplus 8.8 using the robust maximum likelihood (MLR) estimator with robust standard errors, which is considered robust to nonnormality (Muth´ en & Muth´ en, 1998–2015). Initially, descriptive statistics were calculated and measurement invariance for all SEVT constructs was tested over three steps to check whether the magnitudes of the item factor loadings and intercepts were consistent over time (configural, metric and scalar measurement invariance). Measurement invariance was approved when applying equality constraints to the item factor loadings and intercepts did not substantially deteriorate model fit in terms of change in Comparative Fit Index (ΔCFI =decrease of ≤0.010) and Root Mean Square Error of Approximation (ΔRMSEA =increase of ≤0.015; Chen, 2007). To examine longitudinal associations from T1 to T2 and from T2 to T3, we conducted multiple-group random-intercept cross-lagged panel models (RI-CLPM). Both the data and study material are not available in any open source but can be accessed by contacting the authors. 2.4. Multiple-group random-intercept cross-lagged panel model Two cross-lagged panel models were fitted to assess the extent to which academic self-concept and task values (for mathematics and literacy, separately) predicted each other at each time point. An autoregressive cross-lagged panel model can identify potential causal associations between variables over time, controlling for the autoregressive influence of each variable over time (Kenny, 1975). However, the traditional autoregressive cross-lagged panel model approach has been criticised for not adequately considering withinand betweenperson associations (Berry & Willoughby, 2017; Hamaker et al., 2015; Mund & Nestler, 2019). We conducted RI-CLPM, which allowed us to consider both the dynamic changes within an individual (within-person process) and the stable differences between individuals (stable betweenperson differences) by including random intercepts, leading to more accurate estimations of changes over time (Hamaker et al., 2015). In D. Raufelder et al. Learning and Individual Dierences 116 (2024) 102555 4 doing so, each construct was split into a constant between-student component and a variable within-student component. The values that represent how much the variables influence one another within students are thus understood as cross-lagged effects (see Fig. 1). Four overarching random intercept factors—one for each measure—were incorporated to reflect persistent trait-like differences across students in academic self-concept, attainment value, intrinsic value and utility value. The four random intercept factors showed the trait characteristics of task values and academic self-concepts across time. With all factor loadings limited to 1, the three observed scores for each time point served as indicators of each random intercept. Regressing each observed score on its own latent factor allowed us to identify withinstudent variability. The latent variables were then utilised to specify within-time associations, autoregressive paths and cross-lagged paths (i. e. one for each construct for each of the three measurement waves). The extent to which within-person deviations from predicted scores in one variable might predict later within-person deviations from expected scores in the same variable (i.e. carryover effects) was shown by the autoregressive effects. The cross-lagged effects, which revealed the extent to which a within-person deviation from the expected score in one variable could predict a subsequent change in the within-person deviation from the expected score in the other variable, and vice versa (i.e. spillover effects), while controlling for autoregressive effects, referred to the potential reciprocal associations between the four variables within individuals over time (see Kryshko et al., 2022). The withinperson and between-person latent factor structures were able to account for all variations in the observed measures, since the error variances of the observed scores were restricted to zero. To test whether there were substantial differences in the lagged regression coefficients between students from general upper secondary schools and students from vocational schools, a multiple-group approach was followed. This approach enables the detection of group differences in lagged regression coefficients as moderation or interaction effects (Mulder & Hamaker, 2021). More precisely, a multiple-group RICLPM with no constraints across the groups is compared to a model in which the lagged regression coefficients are constrained to be identical across the groups. Using the chi-square difference test, it can be identified whether (some of) the lagged coefficients differ across the groups (Mulder & Hamaker, 2021). However, because the interpretation of differences simply based on significant vs. non-significant chi-square differences from the unconstrained model is highly inaccurate, since it only tests if there are differences in the complete models but not in single paths, we additionally conducted the Wald test for each path between both groups. To indicate the model fit of each structural equation model, the following parameters were considered (e.g. Hu & Bentler, 1999; West et al., 2012): in addition to the χ 2 statistic, which is sensitive to sample size (Kline, 2016), we used the comparative fit index (CFI), the root mean square error of approximation (RMSEA) and the standardized root mean square residual (SRMR). 2.5. Missing data Initially, students with missing values on the school form variable were excluded from the study (n =674). In other words, there were no missing values on school form (0 %). Furthermore, Mplus excluded missing cases for all variables (n =26). In the remaining cases (n = 3636), the percentage of missing data (item level) varied between 13.3 % (e.g. utility value at T2) and 55.5 % (e.g. utility value in literacy at T3), which resulted from n =1998 incomplete cases. The most prominent missing data pattern resulted from those students who did not participate in all three waves of data collection. That is, the T2 sample consisted of participants of the X1 study and their new classmates; therefore, the sample size at T2 was larger than at T1. Moreover, we focused on students who entered either vocational or general upper secondary schools after comprehensive school; thus, approximately 6 % of students who made some other choice were excluded from the study. Not all students completed upper secondary education, with some Fig. 1. A graphical Representation of a bivariate, three-wave Random Intercept Cross-Lagged Panel Model (RI-CLPM). Note. Adapted from “A Critique of the Cross-Lagged Panel Model,” by E. L. Hamaker, R. M. Kuiper, & R. P. P. P. Grasman, 2015, Psychological Methods, 20(1), pp. 102–116 (https://doi.org/10.1037/a0038889). Copyright 2015 by the American Psychological Association. D. Raufelder et al. Learning and Individual Dierences 116 (2024) 102555 5 dropping out of school between T2 and T3. Due to the partly missing values, we followed the recommendation of handling missing values with the full information maximum likelihood (FIML) approach. FIML is well equipped for addressing even large amounts of missing data (>50 %) with minimal bias (Enders & Bandalos, 2001; Newsom, 2018). As this approach is based on the missing at random assumption, Little's missing completely at random (MCAR) test was conducted to confirm the MCAR condition for the literacy items ( χ 2 (78) =98.40; p >.05) and the maths items ( χ 2 (78) =74.07; p >.05). Previous research has revealed that FIML tends to yield unbiased parameter estimates when the type of missingness is either MCAR or MAR (Enders & Bandalos, 2001). 3. Results 3.1. Descriptive statistics The bivariate correlations, means (Ms) and standard deviations (SDs) of the study variables are shown in Table A1 and Table A2 of the Appendix. The results of the measurement invariance testing are shown in Table A3 of the Appendix. Full scalar invariance over groups and waves is given for the literacy model and partial scalar invariance over groups and waves is given for the maths model. 3.2. Multiple-group random-intercept cross-lagged panel model 3.2.1. Literacy RI-CLPM To test whether the reciprocal effects between academic self-concept and task values in literacy were the same for students in general upper secondary schools versus students in vocational schools, a multiplegroup analysis was performed. First, a multiple-group RI-CLPM for literacy without constraints across the groups was computed. The model fit was good ( χ 2 (12) =12.35, p >.05; CFI =1.00, RMSEA =0.00 (0.00–0.02); SRMR =0.01). Subsequently, a model in which lagged parameters are invariant across groups was run, which also showed acceptable fit indices ( χ 2 (44) =50.44, p >.05; CFI =1.00, RMSEA = 0.01 (0.00–0.02); SRMR =0.02). The chi-square difference test of these two nested models yielded Δ χ 2(32) =38.09 (p >.05), which implied that imposing the constraints was tenable, with the lagged effects for students from different school types appearing to be the same (Mulder & Hamaker, 2021). However, using the Wald test to compare each path in the model between the two groups subsequently, we could identify the following four paths in the model that should allow for freedom between both groups (calculating the effect size with Cohen's d): the autoregressive path from self-concept at T1 to self-concept at T2 ( χ 2 (1) =9.64, p =.002; d =0.04), the autoregressive path from self-concept at T2 to self-concept at T3 ( χ 2 (1) =4.34, p =.037; d =0.50), the cross-lagged path from interest value at T1 to utility value at T2 ( χ 2 (1) =3.94, p = .047; d =0.31) and the autoregressive path from utility value at T2 to utility value at T3 ( χ 2 (1) =7.07, p =.008; d =0.62). Accordingly, we allowed these four paths to be freely estimated in the final constrained model, which showed a good model fit ( χ 2 (40) =49.90, p >.05; CFI = 1.00, RMSEA =0.01 (0.00–0.02); SRMR =0.02). 3.2.1.1. Between-person associations (testing Hypotheses H1a and H1b). All between-person associations between all four variables were positively significant for both students in general upper secondary schools and students in vocational schools, representing stable, between-person levels of academic self-concept and all three task values. This means that, on average, students who had a higher academic self-concept overall in literacy also experienced higher levels of all three task values (and vice versa) than students who had a lower academic selfconcept (H1a was confirmed). Further, on average, students who had one task value higher in literacy also had the other two values (and academic self-concept) higher than students who had lower task values (H1b was confirmed; see Table 1). 3.2.1.2. Within-person associations (testing Hypotheses H2 and H3). Table 1 reports the ‘state-like’ within-person associations (correlations) within a given time point between academic self-concept and task values in literacy for students from both general upper secondary schools and vocational schools. Table 2 reports the within-person auto-regressive (H3) and crosslagged associations (H2) between academic self-concept and task values in literacy for students from both general upper secondary and vocational schools over time. Based on testing H2, the following cross-lagged effects were found to be significant. Students who perceived a higher (lower) utility value (relative to their own means) at each measurement wave were likely to perceive an increase (decrease) in intrinsic value from T1 (grade 9) to T2 (grade 10) as well as an increase (decrease) in attainment value from T1 (grade 9) to T2 (grade 10) and from T2 (grade 10) to T3 (grade 12) in relation to their expected scores. There was also a positive cross-lagged effect from intrinsic value to academic self-concept and attainment value from the first to the last year of upper secondary school, indicating that students who perceived higher (lower) intrinsic value in relation to their expected scores were likely to perceive a subsequent increase (decrease) in their academic self-concept and attainment value in relation to their expected scores. In turn, students with higher (lower) academic self-concept at T2 (grade 10) were likely to report higher (lower) intrinsic value from T2 (grade 10) to T3 (grade 12). The results partially confirmed H2. The significant auto-regressive and (cross-)lagged associations between the within-person values of the measures from the RICLPM for literacy are shown in Fig. 2. Based on testing H3, both student groups differed significantly in the autoregressive paths of academic self-concept, which reflected the amount of within-person carryover effect, although Cohen's d was low Table 1 Between-person associations and within-person within-time associations of the constrained multigroup RI-CLPMs in literacy with four paths free. Students from general upper secondary schools Students from vocational schools r ust. r std. r ust. r std. Between-person associations (covariances/correlations between the RI factors) RI-SC ⬄ RI-AV 0.17*** 0.82*** 0.15** 0.66*** RI-SC ⬄ RI-IV 0.14** 0.64*** 0.12*0.72*** RI-SC ⬄ RI-UV 0.12** 0.52*** 0.11*0.50*** RI-AV ⬄ RI-IV 0.16** 0.72*** 0.23*** 0.88*** RI-AV ⬄RI-UV 0.15*** 0.63*** 0.24*** 0.72*** RI-IV ⬄ RI-UV 0.14*0.55*** 0.18** 0.70*** Within-person within-time associations SC t1 ⬄ AV t1 0.14*** 0.37*** 0.15** 0.43*** SC t1 ⬄ IV t1 0.25*** 0.48*** 0.23*** 0.49*** SC t1 ⬄ UV t1 0.14*** 0.30*** 0.12*0.27** AV t1⬄ IV t1 0.25*** 0.47*** 0.24*** 0.49*** AV t1 ⬄ UV t1 0.25*** 0.49*** 0.21*** 0.44*** IV t1 ⬄ UV t1 0.33*** 0.50*** 0.29*** 0.44*** SC t2 ⬄ AV t2 0.11*** 0.34*** 0.17*** 0.39*** SC t2 ⬄ IV t2 0.21*** 0.54*** 0.22*** 0.45*** SC t2 ⬄ UV t2 0.08** 0.23*** 0.15*** 0.33*** AV t2⬄ IV t2 0.31*** 0.63*** 0.41*** 0.72*** AV t2 ⬄ UV t2 0.28*** 0.60*** 0.41*** 0.75*** IV t2 ⬄ UV t2 0.27*** 0.51*** 0.40*** 0.67*** SC t3 ⬄ AV t3 0.16*** 0.40*** 0.12*** 0.27*** SC t3 ⬄ IV t3 0.21*** 0.48*** 0.16*** 0.36*** SC t3 ⬄ UV t3 0.14*** 0.33*** 0.12*** 0.28*** AV t3⬄ IV t3 0.28*** 0.52*** 0.39*** 0.64*** AV t3 ⬄ UV t3 0.28*** 0.56*** 0.32*** 0.55*** IV t3 ⬄ UV t3 0.25*** 0.47*** 0.30*** 0.49*** Note. RI =Random Intercept factor; SC =self-concept; AV =attainment value; IV =intrinsic value; UV =utility value; t1 =Time1; t2 =Time2; t3 =Time3. * p <.05. ** p <.01. *** p <.001. D. Raufelder et al. Learning and Individual Dierences 116 (2024) 102555 6 (d = − 0.04) between T1 and T2 and moderate between T2 and T3 (d = −0.50). While for students from general upper secondary schools, all autoregressive paths of academic self-concept were significant, for students from vocational schools, only the autoregressive path between T2 and T3 was statistically significant. This suggests carryover effects and that individual changes in academic self-concept have a cumulative effect on students' academic self-concept development. In other words, students from general upper secondary schools who scored above (or below) their average scores also tended to have scores above (or below) their average at the next time point. For students from vocational schools, this effect was only found from T2 to T3, when they changed to vocational schools. The non-significant autoregressive paths from academic self-concept between T1 and T2 and from utility value between T2 and T3 indicated higher randomness, as a change at the latter time point cannot be predicted by a change at the previous time point. All autoregressive paths of attainment value development were nonsignificant (contrary to H3), while all autoregressive paths of intrinsic value development were significant (confirming H3). That is, there seemed to be more flexibility in the development of attainment value, while changes in intrinsic value continuously affected changes in its development. This may also be explained by the fact that the practical orientation of teaching at vocational schools is more different from teaching at lower secondary schools (than at upper secondary schools), and this is more likely to lead to a ‘break’ in the development of attainment value. As intrinsic value is anchored in the students themselves, it may not be as susceptible to external changes (e.g. change of school). 3.2.2. Mathematics RI-CLPM To test whether the reciprocal effects between academic self-concept and task values in mathematics were the same for students in general upper secondary schools versus students in vocational schools, a multiple-group analysis was performed. First, a multiple-group RI-CLPM for mathematics without constraints across the groups was computed ( χ 2 (12) =22.38, p <.05; CFI =1.00, RMSEA =0.02 (0.01–0.04); SRMR =0.02). Subsequently, a model in which lagged parameters are invariant across groups was run ( χ 2 (44) =78.09, p <.05; CFI =1.00, RMSEA =0.02 (0.01–0.03); SRMR =0.03). The chi-square difference test of these two nested models yielded Δ χ 2(32) =55.71 (p <.05), which implied that the lagged effects of academic self-concept and task values in mathematics for students from general upper secondary schools versus students in vocational schools appeared not to be the same (Mulder & Hamaker, 2021). However, using the Wald test comparing each path in the model between the two groups subsequently, we could identify only three paths in the model, in which both groups significantly differed (calculating the effect size with Cohen's d): the autoregressive path from self-concept at T1 to self-concept at T2 ( χ 2 (1) =18.65, p <.001; d =0.83), the autoregressive path from selfconcept at T2 to self-concept at T3 ( χ 2 (1) =5.37, p =.021; d =1.37) and the cross-lagged path from attainment value at T1 to self-concept at T2 ( χ 2 (1) =6.12, p =.013; d =2.33). Accordingly, we allowed these three paths to be freely estimated in the final constrained model, which Table 2 Estimates for the constrained RI-CLPM in literacy with four paths hold free between groups. Unstandardized estimates equally constrained across both groups Standardized estimates for students in general upper secondary schools Standardized estimates for students in vocational schools B SE B p ßSE ßpßSE ßp Cohen's d SC t1 → SC t2*GU 0.21 0.09 <. 05 0.24 0.10 <0.05 – – – 0.04 SC t1 → SC t2*VO 0.21 0.16 >0.05 – – – 0.19 0.15 >0.05 SC t2 → SC t3*GU 0.38 0.10 <0.001 0.32 0.09 <0.001 – – – 0.50 SC t2 → SC t3*VO 0.43 0.10 <0.001 – – – 0.42 0.09 <0.001 AV t1 → AV t2 0.07 0.09 >0.05 0.06 0.09 >0.05 0.05 0.07 >0.05 AV t2 → AV t3 0.14 0.08 >0.05 0.12 0.07 >0.05 0.13 0.07 >0.05 IV t1 → IV t2 0.21 0.08 <0.01 0.21 0.08 <0.01 0.20 0.08 <0.01 IV t2 → IV t3 0.32 0.09 <0.001 0.31 0.08 <0.001 0.30 0.08 <0.001 UV t1 → UV t2 0.16 0.06 <0.05 0.18 0.07 <0.01 0.17 0.07 <0.01 UV t2 → UV t3*GU 0.17 0.08 <0.05 0.16 0.08 <0.05 – – – UV t2 → UV t3*VO 0.13 0.04 >0.05 – – – 0.13 0.11 >0.05 0.62 SC t1 → AV t2 0.01 0.08 >0.05 0.01 0.07 >0.05 0.01 0.06 >0.05 SC t1 → IV t2 0.16 0.09 >0.05 0.12 0.07 >0.05 0.11 0.07 >0.05 SC t1 → UV t2 0.06 0.08 >0.05 0.05 0.07 >0.05 0.05 0.06 >0.05 SC t2 → AV t3 0.07 0.08 >0.05 0.05 0.06 >0.05 0.05 0.06 >0.05 SC t2 → IV t3 0.22 0.09 <0.05 0.14 0.06 <0.05 0.15 0.06 <0.05 SC t2 → UV t3 0.16 0.09 >0.05 0.11 0.07 >0.05 0.12 0.07 >0.05 AV t1 → SC t2 −0.07 0.07 >0.05 −0.08 0.08 >0.05 −0.06 0.06 >0.05 AV t1 → IV t2 0.04 0.06 >0.05 0.00 0.07 >0.05 0.00 0.06 >0.05 AV t1 → UV t2 0.06 0.08 >0.05 0.05 0.07 >0.05 0.04 0.06 >0.05 AV t2 → SC t3 −0.03 0.06 >0.05 −0.03 0.06 >0.05 −0.03 0.07 >0.05 AV t2 → IV t3 0.00 0.09 >0.05 −0.00 0.07 >0.05 −0.00 0.07 >0.05 AV t2 → UV t3 0.13 0.09 >0.05 0.11 0.08 >0.05 0.11 0.08 >0.05 IV t1 → SC t2 0.08 0.05 >0.05 0.13 0.08 >0.05 0.11 0.07 >0.05 IV t1 → AV t2 0.04 0.06 >0.05 0.04 0.07 >0.05 0.04 0.07 >0.05 IV t1 → UV t2 *GU 0.02 0.06 >0.05 0.02 0.07 >0.05 – – >0.05 0.31 IV t1 → UV t2 *VO 0.00 0.07 >0.05 – – – 0.00 0.08 >0.05 IV t2 → SC t3 0.12 0.06 <0.05 0.15 0.07 <0.05 0.16 0.07 <0.05 IV t2 → AV t3 0.14 0.07 <0.05 0.15 0.07 <0.05 0.14 0.07 <0.05 IV t2 → UV t3 0.03 0.08 >0.05 0.04 0.08 >0.05 0.03 0.08 >0.05 UV t1 → SC t2 0.03 0.05 >0.05 0.05 0.07 >0.05 0.05 0.06 >0.05 UV t1 → AV t2 0.16 0.05 <0.01 0.18 0.06 <0.01 0.17 0.06 <0.01 UV t1 → IV t2 0.14 0.06 <0.05 0.13 0.06 <0.05 0.13 0.06 <0.05 UV t2 → SC t3 0.02 0.05 >0.05 0.02 0.06 >0.05 0.02 0.06 >0.05 UV t2 → AV t3 0.19 0.06 <0.01 0.18 0.06 <0.01 0.18 0.06 <0.01 UV t2 → IV t3 0.12 0.07 >0.05 0.10 0.06 >0.05 0.11 0.06 >0.05 Note. SC =self-concept; AV =attainment value; IV =intrinsic value; UV =utility value; t1 =Time1; t2 =Time2; t3 =Time3; GU =general upper secondary schools; VO =vocational schools; numbers in bold =significant p <.05; B =unstandardized values; ß =standardized values. * Path hold free between both groups based on results of the Wald test. D. Raufelder et al. Learning and Individual Dierences 116 (2024) 102555 7 showed a good model fit ( χ 2 (41) =69.63, p <.05; CFI =1.00, RMSEA = 0.02 (0.01–0.03); SRMR =0.03). 3.2.2.1. Between-person associations (testing Hypotheses H1a and H1b). For students from general upper secondary schools, all between-person associations between all four random intercept variables were positively significant, representing stable between-person levels of academic selfconcept and all three task values. This means that, on average, students from general upper secondary schools who had a higher academic self-concept overall in maths also experienced higher levels of all three task values (and vice versa) than students who had a lower academic self-concept (confirming H1a). Further, on average, students who had one task value higher in maths also had the other two values (and academic self-concept) higher compared to students who had lower task values (see Table 3) (confirming H1b). For students from vocational schools, only three associations were positively significant (partially confirming H1a and H1b): those between academic self-concept and attainment value (H1a), academic selfFig. 2. Three-wave constrained Multigroup Random Intercept Cross-Lagged Panel Model (RI-CLPM) for Literacy with four lagged paths hold free between both groups. Note. Significant unstandardized associations (p <.05) for the lagged paths from the constrained RI-CLPM for literacy among students from upper secondary schools and vocational schools. The standardized results are reported in Table 1 and Table 2. The figure displays only the significant auto-regressive and (cross-)lagged associations between the within-person values of the measures over time and the between-person associations between the random intercept factors of the measures as well as the within-person associations within time; non-significant associations were excluded for figure clarity except paths, in which both groups significantly differ; RI =Random Intercept (RIs were freely estimated between groups); colored lines: paths hold free between both groups (blue lines: students from general upper secondary schools; orange lines: students from vocational schools); dotted paths =not-significant. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) D. Raufelder et al. Learning and Individual Dierences 116 (2024) 102555 8 causal ordering. Child Development, 76, 397–416. https://doi.org/10.1111/j.14678624.2005.00853.x Moeller, J., Viljaranta, J., Tolvanen, A., Kracke, B., & Dietrich, J. (2022). Introducing the DYNAMICS framework of moment-to-moment development in achievement motivation. Learning and Instruction, 81. https://doi.org/10.1016/j. learninstruc.2022.101653 Mulder, J. D., & Hamaker, E. L. (2021). Three extensions of the random intercept crosslagged panel model. Structural Equation Modeling: A Multidisciplinary Journal, 28(4), 638–648. https://doi.org/10.1080/10705511.2020.1784738 Mund, M., Johnson, M. D., & Nestler, S. (2021). Changes in size and interpretation of parameter estimates in within-person models in the presence of time-invariant and time-varying covariates. Frontiers in Psychology, 12, Article 666928. https://doi.org/ 10.3389/fpsyg.2021.666928 Mund, M., & Nestler, S. (2019). Beyond the cross-lagged panel model: Next-generation statistical tools for analyzing interdependencies across the life course. Advances in Life Course Research, 41, Article 100249. Murayama, K., Goetz, T., Malmberg, L.-E., Pekrun, R., Tanaka, A., & Martin, A. J. (2017). Within-person analysis in educational psychology: Importance and illustrations. In D. W. Putwain, & K. Smart (Eds.), British Journal of Educational Psychology monograph series II: Psychological aspects of education – Current trends: The role of competence beliefs in teaching and learning. Wiley. Muth´ en, L. K., & Muth´ en, B. O. (1998–2015). Mplus user’s guide (7th ed.). Muth´ en & Muth´ en. Newsom, J. T. (2018). Missing data and missing data estimation in SEM. Psy, 523(62), 3. Official Statistics of Finland (OSF). (2021). Entrance to education. Statistics Finland. htt p://www.stat.fi/til/khak/index_en.html. Orth, U., Clark, D. A., Donnellan, M. B., & Robins, R. W. (2021). Testing prospective effects in longitudinal research: Comparing seven competing cross-lagged models. Journal of Personality and Social Psychology, 120(4), 1013–1034. https://doi.org/ 10.1037/pspp0000358 Parrisius, C., Gaspard, H., Zitzmann, S., Trautwein, U., & Nagengast, B. (2022). The “situative nature” of competence and value beliefs and the predictive power of autonomy support: A multilevel investigation of repeated observations. Journal of Educational Psychology, 114(4), 791–814. https://doi.org/10.1037/edu0000680 Perez, T., Dai, T., Kaplan, A., Cromley, J. G., Brooks, W. D., White, A. C., … Balsai, M. J. (2019). Interrelations among expectancies, task values, and perceived costs in undergraduate biology achievement. Learning and Individual Differences, 72, 26–38. https://doi.org/10.1016/j.lindif.2019.04.001 Rosenzweig, E., Wigfield, A., & Eccles, J. (2019). Expectancy-value theory and its relevance for student motivation and learning. In K. Renninger, & S. Hidi (Eds.), The Cambridge handbook of motivation and learning (pp. 617–644). Cambridge University Press. Rosenzweig, E. Q., Wigfield, A., & Eccles, J. S. (2022). Beyond utility value interventions: The why, when, and how for next steps in expectancy-value intervention research. Educational Psychologist, 57(1), 11–30. https://doi.org/10.1080/ 00461520.2021.1984242 Sainio, P. J., Eklund, K., Ahonen, T., & Kiuru, N. (2019). The role of learning difficulties in adolescents’ academic emotions and academic achievement. Journal of Learning Disabilities, 52(4), 287–298. https://doi.org/10.1177/0022219419841567 Schmitt, S. A., Geldhof, G. J., Purpura, D. J., Duncan, R. J., & McClelland, M. M. (2017). Examining the relations between executive function, math, and literacy during the transition to kindergarten: A multi-analytic approach. Journal of Educational Psychology, 109(8), 1120–1140. https://doi.org/10.1037/edu0000193 Sch¨ one, C., Dickhaeuser, O., Spinath, B., & Stiensmeier-Pelster, J. (2003). Das F¨ ahigkeitsselbstkonzept und seine Erfassung. In J. Stiensmeier-Pelster, & F. Rheinberg (Eds.), Diagnostik von motivation und Selbstkonzept. Tests und trends [diagnostic of motivation and self-concept] (pp. 3–14). Hogrefe. Sewasew, D., Schroeders, U., Schiefer, I. M., Weirich, S., & Artelt, C. (2018). Development of sex differences in math achievement, self-concept, and interest from grade 5 to 7. Contemporary Educational Psychology, 54, 55–65. https://doi.org/ 10.1016/j.cedpsych.2018.05.003 Shavelson, R. J., Hubner, J. J., & Stanton, G. C. (1976). Self-concept: Validation of construct interpretations. Review of Educational Research, 46, 407–441. https://doi. org/10.2307/1,170,010 Spinath, B., & Steinmayr, R. (2008). Longitudinal analysis of intrinsic motivation and competence beliefs: Is there a relation over time? Child Development, 79(5), 1555–1569. https://doi.org/10.1111/j.1467-8624.2008.01205.x Trautwein, U., Marsh, H. W., Nagengast, B., Lüdtke, O., Nagy, G., & Jonkmann, K. (2012). Probing for the multiplicative term in modern expectancy-value theory: A latent interaction modeling study. Journal of Educational Psychology, 104, 763–777. https://doi.org/10.1037/a0027470 Viljaranta, J., Nurmi, J.-E., Aunola, K., & Salmela-Aro, K. (2009). The role of task values in adolescents’ educational tracks: A person-oriented approach. Journal of Research on Adolescence, 19, 786–798. https://doi.org/10.1111/j.1532-7795.2009.00619.x Viljaranta, A., Tolvanen, A., Aunola, K., & Nurmi, J.-E. (2014). The developmental dynamics between interest, self-concept of ability, and academic performance. Scandinavian Journal of Educational Research, 58(6), 734–756. https://doi.org/ 10.1080/00313831.2014.904419 Vinni-Laakso, J., Guo, J., Juuti, K., Loukomies, A., Lavonen, J., & Salmela-Aro, K. (2019). The relations of science task values, self-concept of ability, and STEM aspirations among Finnish students from first to second grade. Frontiers in Psychology, 10, 1449. https://doi.org/10.3389/fpsyg.2019.01449 West, S. G., Taylor, A. B., & Wu, W. (2012). Model fit and model selection in structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp. 209–231). Guilford Press. Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of achievement motivation. Contemporary Educational Psychology, 25, 68–81. https://doi.org/10.1006/ ceps.1999.1015 Wigfield, A., & Eccles, J. S. (2020). 35 years of research on students’ subjective task values and motivation: A look back and a look forward. In A. Elliot (Ed.), 7. Advances in motivation science (pp. 161–198). Elsevier. https://doi.org/10.1016/bs. adms.2019.05.002. Wigfield, A., Eccles, J. S., Yoon, K. S., Harold, R. D., Arbreton, A. J., Freedman-Doan, C., & Blumenfeld, P. C. (1997). Change in children’s competence beliefs and subjective task values across the elementary school years: A 3-year study. Journal of Educational Psychology, 89(451–469). https://doi.org/10.1037/0022-0663.89.3.451 Wigfield, A., Tonks, S., & Klauda, S. L. (2016). Expectancy-value theory. In K. R. Wentzel, & D. B. Miele (Eds.), Handbook of motivation at school (pp. 55–74). Routledge. D. Raufelder et al. Learning and Individual Dierences 116 (2024) 102555 15