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

This is a sel -a chi ed e sion o an o iginal a icle. This e sion may di e om he o iginal in pagina ion and ypog aphic de ails. Au ho (s): Ti le: Yea : Ve sion: Copy igh : Righ s: Righ s u l: Please ci e he o iginal e sion: CC BY 4.0 h ps://c ea i ecommons.o g/licenses/by/4.0/ A mul ig oup andom-in e cep c oss-lagged panel model o Finnish seconda y school s uden s in ame o si ua ed expec ancy- alue heo y © 2024 The Au ho s. Published by Else ie Inc. Published e sion Rau elde , Diana; S einbe g, Olga; Vilja an a, Jaana; Poikkeus, Anna-Maija; Vasalampi, Ka i Rau elde , D., S einbe g, O., Vilja an a, J., Poikkeus, A.-M., & Vasalampi, K. (2024). A mul ig oup andom-in e cep c oss-lagged panel model o Finnish seconda y school s uden s in ame o si ua ed expec ancy- alue heo y. Lea ning and Indi idual Di e ences, 116, A icle 102555. h ps://doi.o g/10.1016/j.lindi .2024.102555 2024 A mul ig oup andom-in e cep c oss-lagged panel model o Finnish seconda y school s uden s in ame o si ua ed expec ancy- alue heo y ☆ Diana Rau elde a,* , Olga S einbe g a , Jaana Vilja an a b , Anna-Maija Poikkeus c , Ka i Vasalampi c,d a Uni e si y o G ei swald, Depa men o de elopmen al psychology and educa ional psychology, F anz-Meh ing-S aße 47, 17487 G ei swald, Ge many b Uni e si y o Eas e n Finland, School o Educa ional Sciences and Psychology, P.O.Box 111, Joensuu FI-80101, Finland c Uni e si y o Jy ¨ askyl¨ a, Depa men o Teache Educa ion, Al a Aallon ka u 9, FI-40014 Uni e si y o Jy ¨ askyl¨ a, Finland d Uni e si y o Jy ¨ askyl¨ a, Depa men o Psychology, Ma ilanniemi 6, FI-40014 Uni e si y o Jy ¨ askyl¨ a, Finland ARTICLE INFO Keywo ds: Academic sel -concep Task alue Gene al uppe seconda y educa ion Voca ional educa ion Si ua ed expec ancy- alue heo y ABSTRACT The aim o his s udy is o examine bo h wi hin-pe son and be ween-pe son associa ions o academic sel -concep and ask alues in li e acy and ma hema ics o iden i y he mos p omising mo i a ional cons uc o p e en mo i a ional decline du ing school ansi ions. The sample included 3636 s uden s (a e age age a he s a : 15.73 yea s, SD: 0.32 yea s) ollowed up h ee imes om lowe seconda y school (T1) o he hi d yea (T3) o uppe seconda y educa ion, ei he in oca ional o academic acks. Mul i-g oup andom in e cep c oss-lagged panel models de ec ed se e al spillo e (c oss-lagged) e ec s be ween sel -concep and ask alues in ma he- ma ics bu no in li e acy. The e we e also ma ginal bu signi ican di e ences be ween s uden s om di e en educa ional acks in bo h subjec s. O e all, u ili y alue and academic sel -concep in ma hema ics we e ound o be he mos p omising mo i a ional cons uc s in changing mo i a ional belie s, hus p esen ing impo an s a ing poin s in mo i a ional in e en ions. Educa ional ele ance and implica ions s a emen : This s udy highligh s ha spillo e e ec s a e mo e p onounced in ma hs han in li e acy, emphasising he need o ailo ed in e en ions in ma hema ics educa ion. Mo eo e , he po en ial dis up ion in s uden s' mo i a ional belie s du ing school ansi ions sugges s he impo ance o ensu ing con inui y in suppo o help mi iga e he impac o hese ansi ions. While ou esul s indica e limi ed ca yo e e ec s, i is possible ha school ansi ions a e expe ienced as b eaks in mo i a ional de elopmen . The ole o u ili y alue in exhibi ing spillo e e ec s o e school ansi ions in bo h ma hs and li e acy sugges s he signi icance o emphasising he p ac ical ele ance o academic subjec s o sus ain s uden s' mo i a ion. Addi ionally, ecognising he supe io ole o academic sel -concep in ma hs in spillo e e ec s on ask alues unde sco es he impo ance o nu u ing s uden s' con idence and belie s in hei own ma hema ical abili ies. 1. In oduc ion Expec ancy- alue heo y (EVT; Eccles e al., 1983) and i s ecen expansion, si ua ional EVT (SEVT; Eccles & Wig ield, 2020, 2023), highligh he ole o s uden s' ask alues and success expec ancies o academic achie emen o u u e ca ee choices. The main p oposi ion o EVT is ha se ing a high alue o a ask (e.g. achie emen in an aca- demic domain) and expec ing o be success ul in ha a ea con ibu e o s uden s' mo i a ion and in es men o mo e e o in mas e ing he equi ed skills (Eccles & Wig ield, 2002; Wig ield & Eccles, 2000). Wi h he shi om EVT o SEVT, he si ua ional cha ac e o mo i a ional componen s has ecei ed special a en ion, accompanied by ques ions abou in a- and in e -indi idual he e ogenei y, s a e– ai ela ions and speci ic lea ning en i onmen s (e.g. di e en school se ings) in he de elopmen o success expec ancies and ask alues (see Moelle e al., 2022). ☆ All au ho s sha e he esea ch in e es in mo i a ional de elopmen p ocesses du ing he school yea s, and hey a e pa icula ly in e es ed in in a- and in e - indi idual di e ences. * Co esponding au ho a : Uni e si y o G ei swald, Ge many, Depa men o School Educa ion, E ns -Lohmeye -Pla z 3, 17487 G ei swald, Ge many. E-mail add esses: [email p o ec ed] (D. Rau elde ), [email p o ec ed] (O. S einbe g), [email p o ec ed] (J. Vilja an a), [email p o ec ed] (A.-M. Poikkeus), [email p o ec ed] (K. Vasalampi). Con en s lis s a ailable a ScienceDi ec Lea ning and Indi idual Di e ences jou nal homepage: www.else ie .com/loca e/lindi h ps://doi.o g/10.1016/j.lindi .2024.102555 Recei ed 16 Augus 2023; Recei ed in e ised o m 27 Augus 2024; Accep ed 6 Sep embe 2024 Lea ning and Indi idual Die ences 116 (2024) 102555 A ailable online 13 Sep embe 2024 1041-6080/© 2024 The Au ho s. Published by Else ie Inc. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ ). Mo e speci ically, Eccles and Wig ield (2023) and Moelle e al. (2022) aised he ques ion o he possible s a e and ai sha es o he indi idual componen s o success expec ancies and ask alues in spe- ci ic si ua ions (o e ime) and, hus, o he na u e o hese componen s pe se. The p esen s udy add esses hese exac ques ions o deepen ou unde s anding o he na u e and p ocessuali y o success expec ancies and ask alues and he possible unde lying ai and s a e dynamics. I is impo an o disen angle hese componen s, especially wi h he aim o posi i ely in luencing hem in a ious educa ional se ings (e.g. classes in di e en school o ms). Acco dingly, he cu en s udy has wo main objec i es. The i s aim is o in es iga e he si ua ed na u e o he de elopmen o success expec a ions (i.e. academic sel -concep ) and ask alues by explo ing he pe iod o school ansi ion om comp e- hensi e school o ei he gene al uppe seconda y school (academic ack) o o oca ional school ( oca ional ack) in Finland (g ades 9, 10 and 12) in di e en domains (li e acy and ma hema ics). The second aim is o speci y possible ai and s a e componen s, as only a ew exis ing SEVT s udies (e.g. Benden & Laue mann, 2023; Moelle e al., 2022) ha e di e en ia ed be ween wi hin-pe son luc ua ions ( empo al de ia ions) and be ween-pe son di e ences (s able ai ac o s) in he de elopmen o success expec ancies and ask alues o e ime. O e all, he pu pose o his s udy is o iden i y he mos e ec i e mo i a ional cons uc o changing mo i a ional belie s and p e en ing mo i a ional declines. 1.1. The de elopmen o success expec ancies and ask alues Acco ding o EVT (Eccles e al., 1983; Wig ield & Eccles, 2000), a s uden 's expec ancies o success in a ask and he subjec i e alue o ha ask cons i u e he basis o he s uden 's mo i a ional belie s. The e a e ou ypes o ask alues: (a) a ainmen alue, encompassing he pe sonal meaning o he s uden o accomplishing a ask; (b) in insic alue, depic ing he pleasu e and in e es expe ienced in unde aking and comple ing a ask; (c) u ili y alue, cap u ing he meaning ulness o a ask o one's own u u e; and (d) cos alue, which includes he pe cei ed nega i e consequences o accomplishing a ask, such as nega i e emo ions o s alling o he ac i i ies. In he cu en s udy, we explo e only he ask alues wi h posi i e conno a ions (1–3). Acco ding o Bong and Skaal ik (2003), Eccles and Wig ield (2020) and Ma sh e al. (2019), expec ancy belie s a e concep ually ela ed o s uden s' academic sel -concep . Addi ionally, p e ious s udies ha e shown some o e lap be ween i ems on expec a ions o success and ac- ademic sel -concep , as hey o en load on a single ac o (see Eccles & Wig ield, 2023), which sugges s ha hese cons uc s a e no always empi ically dis inguishable (see Laza ides e al., 2020). In he cu en s udy, we ely on measu es o s uden s' academic sel -concep , wi h he aim o u he deciphe ing he p opo ion o s able ai s (i.e. academic sel -concep ) and s a es wi h espec o he de elopmen o mo i a ional belie s. In acco dance wi h Sha elson e al.'s (1976) mul idimensional model (Sch¨ one e al., 2003), academic sel -concep is a componen o gene al sel -concep ha depic s an indi idual's ideas abou hei own s udy- ela ed abili ies, ai s and school ac i i ies. Eccles and Wig ield (2020) desc ibed his as an indi idual's mo e s able sel -belie s, while success expec ancies a e mo e ask- and ime-speci ic. S udies ha e indica ed ha , in adolescence, ask alues in key school subjec s can in luence u he academic pa hways e en mo e han aca- demic pe o mance (see Guo e al., 2018). The ela ionship be ween s uden s' expec ancy o success and hei ask alue belie s is a key mechanism o mo i a ional cong uence, as p oposed by Eccles e al. While he o iginal SEVT did no explici ly include c oss-lagged pa hs be ween expec ancy and alues, i sugges ed ha such bidi ec ional in luences we e possible (see Benden & Laue mann, 2023; Eccles, 2005, 2009; Wig ield e al., 1997). S uden s o en alue asks in which hey excel due o he in insic ewa d o compe ence, and con e sely, hey may de alue asks in which success seems unlikely o p o ec hei sel - wo h (see Benden & Laue mann, 2023; Eccles, 2009; Ha e , 1990; Wig ield & Eccles, 2020). Simila ly, aluing a ask can inc ease engagemen and imp o e skills and u u e success expec a ions (Eccles, 2005, 2009). Educa ion esea che s ha e ocused on c oss-lagged ex- pec ancy- alue associa ions o iden i y which mo i a ional cons uc s can signi ican ly in luence o he mo i a ional belie s and, he e o e, should be p io i ised in in e en ions aimed a p e en ing d ops in ac- ademic mo i a ion (Ma sh e al., 2005; Rosenzweig e al., 2022). Benden and Laue mann (2023) s a ed ha ‘Eccles (2005) poin ed ou ha analyses o he c oss-lagged links be ween s uden s’ expec ancy and ask alues mus ca e ully conside (a) which ime lags and (b) which ypes o assessmen s a e bes sui ed o cap u e such links (see also Do mann & G i in, 2015)' (p. 2). Some de elopmen al p ocesses un old o e yea s, while o he s occu du ing sho e pe iods (Benden & Laue mann, 2023; Gaspa d e al., 2020). Mos e idence has come om long- e m s udies ha showed signi ican e ec s o expec ancy on ask alues, bu ewe indings ha e been on ecip ocal e ec s (e.g. A ens e al., 2019; Chung & Kim, 2022; G igg e al., 2018; Lee & Seo, 2021; Ma sh e al., 2005; T au wein e al., 2012; Vilja an a e al., 2014; Vinni- Laakso e al., 2019; Wig ield e al., 2016). Sho e - e m s udies ha e p esen ed mixed esul s due o a ying ime lags and mo i a ional assessmen ypes (Beyme e al., 2022; Moelle e al., 2022; Pe ez e al., 2019). The esul s we e pa ly di e en o di e en subjec s. Fo example, in he s udy by A ens e al. (2019), which conside ed ma hs, li e acy and English as a o eign language in a sample o Ge man s uden s o ma hs and o eign languages, almos all unidi ec ional pa hs om academic sel -concep o in insic alue we e ound o be signi ican o e i e wa es (bu no ice e sa). Howe e , o li e acy, i was he o he way a ound; almos e e y pa h om in insic alue o academic sel -concep was ound o be signi ican (bu no ice e sa). In con as , he asso- cia ions be ween academic sel -concep and a ainmen alue we e ound o be ecip ocal o all h ee subjec s and o e all i e wa es. The s udy by Vinni-Laakso e al. (2019) o Finnish elemen a y school s u- den s could no de ec any signi ican c oss-lagged pa h be ween aca- demic sel -concep and in insic alue o cos om 1s g ade o 2nd g ade in science. In addi ion, he s udy by T au wein e al. (2012) ocused on ma hs and English as a o eign language and ound ha some alue componen s (i.e. u ili y alue and cos ) we e mo e closely ela ed o expec ancy belie s han wi h o he alue ace s. In hei ecen a icle, Eccles and Wig ield (2023) aised he ques ion o how ask alues accumula e and whe he he e migh be a mo e s able la en ac o ( ai ): ‘Second and e en mo e impo an ly, we ha e begun o hink mo e speci ically abou he na u e o STV i sel . Fo example, do he subcomponen s agg ega e addi i ely o o m a mo e s able la en STV o each op ion, o do he subcomponen s agg ega e in a ying ways o o m mo e uns able STVs o each op ion depending on wha any op ion is being con as ed wi h a any gi en poin in ime?’ (p. 10). The cu en s udy akes up his idea by in es iga ing possible ai p o- po ions (be ween le els) and wi hin-pe son di e ences using a andom- in e cep c oss-lagged panel model (RI-CLPM). In doing so, we ollow Moelle e al. (2022), who, ollowing dynamical sys ems heo y, aised he ques ion o ‘how si ua ed expe iences o expec a ions and alues may ela e o ai -like mo i a ional disposi ions’. Howe e , mos exis ing esea ch is based on adi ional CLPM on s uden s' expec ancy- alue belie s o e ime and does no accoun o bo h wi hin- and be ween-pe son a iabili y (e.g. A ens e al., 2019; Chung & Kim, 2022; Vinni-Laakso e al., 2019), which can lead o subs an ially biased es ima es o c oss-lagged associa ions (Be y & Willoughby, 2017; Hamake e al., 2015). To ou knowledge, only wo s udies ha e di e en ia ed be ween wi hin- and be ween-pe son a i- abili y in academic sel -concep and ask alues (Benden & Laue mann, 2023; Moelle e al., 2022). Benden and Laue mann (2023) examined using RI-CLPM wi hin-pe son a ia ions in he connec ions be ween s uden s' cou se-speci ic (summa i e) o week-speci ic (si ua ed) ex- pec ancies and ask alues in ga eway ma hs cou ses o s uden s s udying ma hs, physics o ma hs eache educa ion. The indings D. Rau elde e al. Lea ning and Indi idual Die ences 116 (2024) 102555 2 showed ha du ing a semes e , he e was an inc easing wi hin-pe son alignmen be ween s uden s' cou se-speci ic expec ed success and in insic/u ili y alues (bu no cos ), acco ding o RI-CLPMs. Unidi- ec ional spillo e —o c oss-lagged—e ec s om expec ancy o in insic/u ili y alues we e associa ed wi h his alignmen . The s udy by Moelle e al. (2022) in es iga ed using a mul ile el CLPM whe he ask alues, cos and success expec ancies, measu ed in a lea ning si - ua ion ( ime poin ) du ing a weekly uni e si y lec u e, p edic ed each o he and hemsel es in he subsequen si ua ion ( +1; 27 min la e ). They could no iden i y any signi ican c oss-lagged e ec s om one si ua ion o he nex in any o he measu ed si ua ed expec ancy- alue componen s. As bo h s udies we e based on a sample o uni e si y s u- den s, i was di icul o d aw conclusions abou adolescen s uden s and he school con ex . O e all, while p e ious esea ch has consis en ly indica ed a posi i e associa ion be ween ask mo i a ion and academic sel -concep , which s eng hens wi h age (Jacobs e al., 2002; Vinni-Laakso e al., 2019; Wig ield e al., 1997), he e is no clea e idence o how s uden s' aca- demic sel -concep and ask alues de elop and associa e wi h one ano he o e he span om middle o la e adolescence and du ing school ansi ions and o how wi hin-pe son luc ua ions ( empo al de ia ions) can be sepa a ed om s able be ween-pe son di e ences (s able ai ac o s). The p esen s udy aims o shed ligh on hese associa ions by conside ing ee measu emen wa es (g ades 9, 10 and 12), wo do- mains (ma h and li e acy), a ious school ypes be o e and a e he ansi ion and bo h wi hin- and be ween-pe son di e ences. 1.2. The ole o school ype An impo an gap in he exis ing li e a u e on he de elopmen al dynamics be ween he sel -concep o abili y and ask alues is he scan in o ma ion on he e ec o mode a ing con ex ual ac o s. SEVT (Eccles & Wig ield, 2020, 2023) inco po a es he key p oposi ion in s age- –en i onmen i heo y ha emphasises he ole o he con ex . The e is e idence o a high likelihood o a nega i e impac o school ansi ions on adolescen s uden s' mo i a ional belie s (Eccles e al., 1993; Rose- nzweig e al., 2019). To ou knowledge, no s udies ha e ocused on school ansi ion in middle adolescence ( om lowe seconda y o u he educa ion) and he di e ences among s uden s a ending oca- ional and academic acks. The examina ion o he mo i a ional de elopmen o s uden s a ending di e en school ypes is o key in- e es in he p esen s udy. In Finland, basic educa ion (g ades 1 o 9) does no in ol e selec ion, acking o s eaming (An ikainen & Luukkainen, 2008). A e 9 h g ade, s uden s apply ei he o gene al uppe seconda y school (3-yea academic ack, p o iding he basis o u he educa ion a uni e si ies/ poly echnics) o oca ional educa ion ( oca ional ack, a e which adolescen s p oceed wi h wo k li e). A pe son-o ien a ed subg oup analysis conduc ed app oxima ely a decade ago (Vilja an a e al., 2009) sugges ed ha s uden s who aim o a oca ional ack a e mo e likely o belong o p o iles cha ac e ised as ‘p ac ical skills and language–mo i- a ed’ o ‘p ac ical skills–mo i a ed’, while hose who aim o an aca- demic ack a e mo e likely o belong o p o iles cha ac e ised as ‘mul i- mo i a ed’ o ‘ma hs and science–mo i a ed’. Based on SEVT, s uden s' mo i a ional belie s a e o med du ing hei school ca ee s, so s uden s who a end gene al uppe seconda y schools and oca ional schools may di e in hei mo i a ional belie s p io o he school ansi ion. How- e e , his assump ion has no ye been in es iga ed. Fu he mo e, o in e es is he in e play o di e en dimensions o SEVT in he cou se o he h ee yea s o seconda y educa ion, consid- e ing di e en school acks a e he 9 h g ade. I is possible ha o s uden s in oca ional schools, mo e signi ican c oss-lagged pa hways om u ili y alue o he o he componen s can be iden i ied, since in- s uc ion is speci ically gea ed o u u e p o essions (Finnish Na ional Agency o Educa ion, 2018). One could also assume ha he associa ions be ween he cons uc s o gene al uppe seconda y school s uden s show he same pa e ns a T1 (g ade 9) and T2 (g ade 10), as well as be ween T2 (g ade 10) and T3 (g ade 12), since he lea ning en i on- men and ins uc ional design do no di e much. In u n, o s uden s om oca ional schools, di e ences can be assumed be ween T1 and T2 in compa ison o T2 and T3. 1.3. The cu en s udy The pu pose o his s udy is o add ess in a- and in e indi idual he e ogenei y, s a e– ai ela ions and speci ic lea ning en i onmen s (e.g. di e en school and class oom se ings) in he de elopmen o academic sel -concep and ask alues (c . Moelle e al., 2022). In de ail, i empi ically examines he de elopmen o academic sel -concep and h ee ask alues in wo subjec s (li e acy and ma hema ics), di e en g ades (g ades 9, 10 and 12) and di e en school ypes (join comp e- hensi e schools in g ade 9, gene al uppe seconda y schools s. oca- ional schools in g ades 10 and 12), conside ing bo h he wi hin-pe son a ia ions ( empo al a iances) and he s able be ween-pe son di e - ences (s able ai ac o s). T adi ional c oss-lagged panel models used in p e ious s udies (e.g. A ens e al., 2019; Chung & Kim, 2022) we e no able o di e en ia e be ween he be ween-pe son and he wi hin-pe son e ec s (Be y & Willoughby, 2017; Hamake e al., 2015; Mund & Nes le , 2019). The e o e, i is unclea wha kinds o e ec s (wi hin- pe son o be ween-pe son) hese panels ac ually explo ed. I has ecen ly been a gued ha be ween-pe son associa ions may only ( ully) con e ge wi h wi hin-pe son associa ions unde speci ic ci cums ances (e.g. in e ms o he p esence, magni ude and sign o de ec ed e ec s) and ha in es iga ing bo h ypes o associa ions may p o ide illumi- na ing bu concep ually dis inc insigh s (e.g. Fishe e al., 2018; Hamake e al., 2015; see K yshko e al., 2022; Mu ayama e al., 2017; O h e al., 2021) To o e come he sho comings o he adi ional CLPM, we use he longi udinal andom in e cep c oss-lagged panel model (RI-CLPM) app oach o explo e bo h he wi hin-pe son and be ween-pe son e ec s and ind answe s o he ollowing esea ch ques ions (RQs) and hypo heses (Hs): (RQ1a) A e di e ences be ween indi idual s uden s' academic sel - concep s in li e acy and ma hema ics associa ed wi h di e ences in hei ask alues (be ween-pe son le el)? (H1a) The e a e be ween-pe son associa ions be ween success ex- pec ancies and ask alues. Fo example, i is expec ed ha s uden s wi h highe sco es in academic sel -concep s may also ha e highe sco es in ask alues. (RQ1b) A e di e ences be ween he ask alues o indi idual s u- den s in li e acy and ma hema ics associa ed wi h di e ences in hei o he ask alues (be ween-pe son le el)? (H1b) The e a e be ween-pe son associa ions be ween he di e en ask alues. I is expec ed, o example, ha s uden s wi h highe sco es in a ainmen alue may also ha e highe sco es in in insic alue. The s udy by T au wein e al. (2012) showed ha he alues hemsel es di e in hei na u e; while a ainmen alue and in insic alue de ine ‘in insic’ alues, u ili y alue and cos cons i u e ‘ex insic’ ac o s. (RQ2) To wha ex en a e academic sel -concep and ask alues in li e acy and ma hema ics associa ed wi h each o he a he wi hin- pe son le el o e ime (c oss-lagged associa ions)? (H2) The e a e wi hin-pe son associa ions be ween he di e en componen s o success expec ancies and ask alues. I migh be possible o a pe son o change hei app ecia ion o a pa icula ask o e ime, o example, as hey expe ience success o become mo e deeply in ol ed in he opic. (RQ3) A e indi iduals' de ia ions om hei expec ed sco es in all ou a iables (academic sel -concep and he h ee ask alues) likely o ca y o e om one measu emen wa e o he nex (au o eg essi e associa ions)? (H3) The e a e ca yo e e ec s on s uden s' academic sel -concep and ask alues o e ime, such as an indi idual's changes in academic sel -concep ha ing a cumula i e e ec on hei academic sel -concep D. Rau elde e al. Lea ning and Indi idual Die ences 116 (2024) 102555 3 de elopmen . In o he wo ds, s uden s who ha e sco ed abo e (o below) hei a e age sco es also end o ha e sco es abo e (o below) hei a e age a he subsequen ime poin . Whe he g oup di e ences be ween s uden s a ending gene al uppe seconda y educa ion o oca ional educa ion exis in lagged eg ession coe icien s can be hough o as mode a ion o in e ac ion e ec s, which can be in es iga ed by a mul iple-g oup e sion o he RI- CLPM, as sugges ed by Mulde and Hamake (2021). 2. Me hods 2.1. T anspa ency and openness In his sec ion, we indica e how he da a we e collec ed and he schools ec ui ed, as well as all da a exclusions (i any) and all measu es in he s udy. We ollowed JARS (Kazak, 2018). All da a, analysis codes, and esea ch ma e ials a e a ailable upon eques . The da a we e ana- lysed using Mplus 8.8 (Mu h´ en & Mu h´ en, 1998–2015). The cu en s udy design and analyses we e no p e egis e ed on any speci ic pla o m. 2.2. Sample and p ocedu e The sample (N =3636; M age a he ou se =15.73 yea s, SD =0.32 yea s; 54.5 % emale; n oca ional =1669; n uppe =1967) was d awn om he comp ehensi e longi udinal X1 ( emo ed o e iew pu poses) s udy and i s ex ension, X2 ( emo ed o e iew pu poses). In he X1 s udy, app oxima ely 2000 s uden s we e ollowed om kinde ga en o he end o lowe seconda y school (g ade 9). In X2, he pa icipan s and hei classma es (N =3636) we e ollowed du ing uppe seconda y educa ion. The pa icipa ing s uden s came om ou municipali ies ( wo medium-sized, one big and one u al) in di e en pa s o Finland. A he s a o he p esen s udy (9 h g ade; inal yea o comp ehensi e school), he s uden s a ended 34 lowe seconda y schools. A e he ansi ion ( om lowe seconda y school o uppe seconda y educa ion), he s uden s a ended 72 di e en uppe seconda y educa ion in- s i u ions (36 gene al uppe seconda y schools and 36 oca ional schools). The E hical Commi ee o he Uni e si y o X3 ( emo ed o e iew pu poses) app o ed he s udy and he esea ch design in 2006 and 2018. Be o e collec ing da a a he lowe seconda y schools, w i en consen was collec ed om pa en s o gua dians. In uppe seconda y educa ion, he pa icipa ing s uden s con i med hei olun a y pa icipa ion in he s udy. Class oom-adminis e ed ques ionnai es we e used o da a collec ion on no mal school days by ained esea ch assis an s o eache s du ing h ee wa es: sp ing 2016 (Time 1, T1, 9 h g ade o lowe seconda y school), sp ing 2017 (Time 2, T2, he i s yea o uppe seconda y educa ion), and sp ing 2019 (Time 3, T3, he inal yea o uppe seconda y educa ion). In Finland, school ansi ion akes place a e he 9 h g ade. Acco ding o Finnish educa ional s a is ics (O icial S a is ics o Finland, 2021), 54 % o Finnish s uden s con inue s udying in gene al uppe seconda y schools and 40 % choose oca ional schools, while o he op ions a e a e. The no ma i e ime o comple e uppe seconda y educa ion las s h ee yea s. 2.2.1. Academic sel -concep To assess s uden s' academic sel -concep , scales de eloped by Eccles and Wig ield (1995) and Spina h and S einmay (2008) we e used. The scale used o assess academic sel -concep in ma hema ics consis s o wo ques ions (‘How good a e you a ma hema ics?’ and ‘How good a e you a ma hema ics compa ed o o he s uden s in you g oup?’). Fo each measu emen poin , a composi e sco e was calcula ed as he mean o he i ems measu ing he cons uc . The C onbach eliabili y co- e icien s we e good o bo h he whole sample and he subsamples ( α = 0.87 o 0.92). The scale used o assess s uden s' academic sel -concep in li e acy consis s o wo ques ions (‘How good a e you in you mo he ongue?’ and ‘How good a e you in you mo he ongue compa ed o o he s uden s in you g oup?’). Fo each measu emen poin , a com- posi e sco e was calcula ed by compu ing he mean o he i ems. The scale showed good eliabili y o bo h he whole sample and he sub- samples ( α =0.80 o 0.89). The s uden s esponded using a i e-poin Like scale (1 =‘poo /no e y good’ o 5 =‘ e y good’). 2.2.2. Task alues Based on an adap ed e sion o he scale de eloped by Eccles e al. (1983), he h ee ask alues (i.e. a ainmen , in insic and u ili y alue) we e assessed wi h wo i ems o each dimension o ask alue. The i ems we e as ollows: a ainmen alues in ma hema ics and li e acy (e. g. ‘How impo an is i o you ha you do well in ma hema ics/li e - acy?’ and ‘How impo an is i o you o ge good g ades in ma he- ma ics/li e acy?’), in insic alues in ma hema ics and li e acy (e.g. ‘How much do you like ma hema ics/li e acy in school?’ and ‘How eadily do you do ma hema ics/li e acy?’) and u ili y alues in ma he- ma ics and li e acy (e.g. ‘How use ul wi h ega d o you u u e plans do you conside ma hema ics/li e acy?’ and ‘How use ul a e he ollowing school subjec s in you daily li e?’). The s uden s esponded using a i e- poin Like scale (1 =‘no a all…’ o 5 =‘ e y… much/ eadily/ impo an /use ul’). A composi e sco e was calcula ed sepa a ely o he a ainmen , in insic and u ili y alues o each measu emen poin as he mean o he i ems measu ing he cons uc s. The eliabili y o each measu emen poin o bo h he whole sample and he wo subsamples was accep able o a ainmen alues (li e acy: α =0.81 o 0.94; ma hema ics: α =0.88 o 0.91), in insic alues (li e acy: α =0.79 o 0.85; ma hema ics: α =0.88 o 0.90) and u ili y alues (li e acy: α = 0.74 o 86; ma hema ics: α =0.67 o 0.81). 2.3. S a is ical analysis All s a is ical analyses we e conduc ed wi h Mplus 8.8 using he obus maximum likelihood (MLR) es ima o wi h obus s anda d e - o s, which is conside ed obus o nonno mali y (Mu h´ en & Mu h´ en, 1998–2015). Ini ially, desc ip i e s a is ics we e calcula ed and mea- su emen in a iance o all SEVT cons uc s was es ed o e h ee s eps o check whe he he magni udes o he i em ac o loadings and in- e cep s we e consis en o e ime (con igu al, me ic and scala mea- su emen in a iance). Measu emen in a iance was app o ed when applying equali y cons ain s o he i em ac o loadings and in e cep s did no subs an ially de e io a e model i in e ms o change in Compa a i e Fi Index (ΔCFI =dec ease o ≤0.010) and Roo Mean Squa e E o o App oxima ion (ΔRMSEA =inc ease o ≤0.015; Chen, 2007). To examine longi udinal associa ions om T1 o T2 and om T2 o T3, we conduc ed mul iple-g oup andom-in e cep c oss-lagged panel models (RI-CLPM). Bo h he da a and s udy ma e ial a e no a ailable in any open sou ce bu can be accessed by con ac ing he au ho s. 2.4. Mul iple-g oup andom-in e cep c oss-lagged panel model Two c oss-lagged panel models we e i ed o assess he ex en o which academic sel -concep and ask alues ( o ma hema ics and li - e acy, sepa a ely) p edic ed each o he a each ime poin . An au o e- g essi e c oss-lagged panel model can iden i y po en ial causal associa ions be ween a iables o e ime, con olling o he au o e- g essi e in luence o each a iable o e ime (Kenny, 1975). Howe e , he adi ional au o eg essi e c oss-lagged panel model app oach has been c i icised o no adequa ely conside ing wi hin- and be ween- pe son associa ions (Be y & Willoughby, 2017; Hamake e al., 2015; Mund & Nes le , 2019). We conduc ed RI-CLPM, which allowed us o conside bo h he dynamic changes wi hin an indi idual (wi hin-pe son p ocess) and he s able di e ences be ween indi iduals (s able be ween- pe son di e ences) by including andom in e cep s, leading o mo e accu a e es ima ions o changes o e ime (Hamake e al., 2015). In D. Rau elde e al. Lea ning and Indi idual Die ences 116 (2024) 102555 4 doing so, each cons uc was spli in o a cons an be ween-s uden componen and a a iable wi hin-s uden componen . The alues ha ep esen how much he a iables in luence one ano he wi hin s uden s a e hus unde s ood as c oss-lagged e ec s (see Fig. 1). Fou o e a ching andom in e cep ac o s—one o each measu - e—we e inco po a ed o e lec pe sis en ai -like di e ences ac oss s uden s in academic sel -concep , a ainmen alue, in insic alue and u ili y alue. The ou andom in e cep ac o s showed he ai cha - ac e is ics o ask alues and academic sel -concep s ac oss ime. Wi h all ac o loadings limi ed o 1, he h ee obse ed sco es o each ime poin se ed as indica o s o each andom in e cep . Reg essing each obse ed sco e on i s own la en ac o allowed us o iden i y wi hin- s uden a iabili y. The la en a iables we e hen u ilised o speci y wi hin- ime associa ions, au o eg essi e pa hs and c oss-lagged pa hs (i. e. one o each cons uc o each o he h ee measu emen wa es). The ex en o which wi hin-pe son de ia ions om p edic ed sco es in one a iable migh p edic la e wi hin-pe son de ia ions om expec ed sco es in he same a iable (i.e. ca yo e e ec s) was shown by he au o eg essi e e ec s. The c oss-lagged e ec s, which e ealed he ex en o which a wi hin-pe son de ia ion om he expec ed sco e in one a iable could p edic a subsequen change in he wi hin-pe son de ia ion om he expec ed sco e in he o he a iable, and ice e sa (i.e. spillo e e ec s), while con olling o au o eg essi e e ec s, e e ed o he po en ial ecip ocal associa ions be ween he ou a i- ables wi hin indi iduals o e ime (see K yshko e al., 2022). The wi hin- pe son and be ween-pe son la en ac o s uc u es we e able o accoun o all a ia ions in he obse ed measu es, since he e o a iances o he obse ed sco es we e es ic ed o ze o. To es whe he he e we e subs an ial di e ences in he lagged eg ession coe icien s be ween s uden s om gene al uppe seconda y schools and s uden s om oca ional schools, a mul iple-g oup app oach was ollowed. This app oach enables he de ec ion o g oup di e ences in lagged eg ession coe icien s as mode a ion o in e ac ion e ec s (Mulde & Hamake , 2021). Mo e p ecisely, a mul iple-g oup RI- CLPM wi h no cons ain s ac oss he g oups is compa ed o a model in which he lagged eg ession coe icien s a e cons ained o be iden ical ac oss he g oups. Using he chi-squa e di e ence es , i can be iden- i ied whe he (some o ) he lagged coe icien s di e ac oss he g oups (Mulde & Hamake , 2021). Howe e , because he in e p e a ion o di e ences simply based on signi ican s. non-signi ican chi-squa e di e ences om he uncons ained model is highly inaccu a e, since i only es s i he e a e di e ences in he comple e models bu no in single pa hs, we addi ionally conduc ed he Wald es o each pa h be ween bo h g oups. To indica e he model i o each s uc u al equa ion model, he ollowing pa ame e s we e conside ed (e.g. Hu & Ben le , 1999; Wes e al., 2012): in addi ion o he χ 2 s a is ic, which is sensi i e o sample size (Kline, 2016), we used he compa a i e i index (CFI), he oo mean squa e e o o app oxima ion (RMSEA) and he s anda dized oo mean squa e esidual (SRMR). 2.5. Missing da a Ini ially, s uden s wi h missing alues on he school o m a iable we e excluded om he s udy (n =674). In o he wo ds, he e we e no missing alues on school o m (0 %). Fu he mo e, Mplus excluded missing cases o all a iables (n =26). In he emaining cases (n = 3636), he pe cen age o missing da a (i em le el) a ied be ween 13.3 % (e.g. u ili y alue a T2) and 55.5 % (e.g. u ili y alue in li e acy a T3), which esul ed om n =1998 incomple e cases. The mos p omi- nen missing da a pa e n esul ed om hose s uden s who did no pa icipa e in all h ee wa es o da a collec ion. Tha is, he T2 sample consis ed o pa icipan s o he X1 s udy and hei new classma es; he e o e, he sample size a T2 was la ge han a T1. Mo eo e , we ocused on s uden s who en e ed ei he oca ional o gene al uppe seconda y schools a e comp ehensi e school; hus, app oxima ely 6 % o s uden s who made some o he choice we e excluded om he s udy. No all s uden s comple ed uppe seconda y educa ion, wi h some Fig. 1. A g aphical Rep esen a ion o a bi a ia e, h ee-wa e Random In e cep C oss-Lagged Panel Model (RI-CLPM). No e. Adap ed om “A C i ique o he C oss-Lagged Panel Model,” by E. L. Hamake , R. M. Kuipe , & R. P. P. P. G asman, 2015, Psychological Me hods, 20(1), pp. 102–116 (h ps://doi.o g/10.1037/a0038889). Copy igh 2015 by he Ame ican Psychological Associa ion. D. Rau elde e al. Lea ning and Indi idual Die ences 116 (2024) 102555 5 d opping ou o school be ween T2 and T3. Due o he pa ly missing alues, we ollowed he ecommenda ion o handling missing alues wi h he ull in o ma ion maximum likelihood (FIML) app oach. FIML is well equipped o add essing e en la ge amoun s o missing da a (>50 %) wi h minimal bias (Ende s & Bandalos, 2001; Newsom, 2018). As his app oach is based on he missing a andom assump ion, Li le's missing comple ely a andom (MCAR) es was conduc ed o con i m he MCAR condi ion o he li e acy i ems ( χ 2 (78) =98.40; p >.05) and he ma hs i ems ( χ 2 (78) =74.07; p >.05). P e ious esea ch has e ealed ha FIML ends o yield unbiased pa ame e es ima es when he ype o missingness is ei he MCAR o MAR (Ende s & Bandalos, 2001). 3. Resul s 3.1. Desc ip i e s a is ics The bi a ia e co ela ions, means (Ms) and s anda d de ia ions (SDs) o he s udy a iables a e shown in Table A1 and Table A2 o he Ap- pendix. The esul s o he measu emen in a iance es ing a e shown in Table A3 o he Appendix. Full scala in a iance o e g oups and wa es is gi en o he li e acy model and pa ial scala in a iance o e g oups and wa es is gi en o he ma hs model. 3.2. Mul iple-g oup andom-in e cep c oss-lagged panel model 3.2.1. Li e acy RI-CLPM To es whe he he ecip ocal e ec s be ween academic sel -concep and ask alues in li e acy we e he same o s uden s in gene al uppe seconda y schools e sus s uden s in oca ional schools, a mul iple- g oup analysis was pe o med. Fi s , a mul iple-g oup RI-CLPM o li - e acy wi hou cons ain s ac oss he g oups was compu ed. The model i was good ( χ 2 (12) =12.35, p >.05; CFI =1.00, RMSEA =0.00 (0.00–0.02); SRMR =0.01). Subsequen ly, a model in which lagged pa ame e s a e in a ian ac oss g oups was un, which also showed accep able i indices ( χ 2 (44) =50.44, p >.05; CFI =1.00, RMSEA = 0.01 (0.00–0.02); SRMR =0.02). The chi-squa e di e ence es o hese wo nes ed models yielded Δ χ 2(32) =38.09 (p >.05), which implied ha imposing he cons ain s was enable, wi h he lagged e ec s o s uden s om di e en school ypes appea ing o be he same (Mulde & Hamake , 2021). Howe e , using he Wald es o compa e each pa h in he model be ween he wo g oups subsequen ly, we could iden i y he ollowing ou pa hs in he model ha should allow o eedom be ween bo h g oups (calcula ing he e ec size wi h Cohen's d): he au o e- g essi e pa h om sel -concep a T1 o sel -concep a T2 ( χ 2 (1) =9.64, p =.002; d =0.04), he au o eg essi e pa h om sel -concep a T2 o sel -concep a T3 ( χ 2 (1) =4.34, p =.037; d =0.50), he c oss-lagged pa h om in e es alue a T1 o u ili y alue a T2 ( χ 2 (1) =3.94, p = .047; d =0.31) and he au o eg essi e pa h om u ili y alue a T2 o u ili y alue a T3 ( χ 2 (1) =7.07, p =.008; d =0.62). Acco dingly, we allowed hese ou pa hs o be eely es ima ed in he inal cons ained model, which showed a good model i ( χ 2 (40) =49.90, p >.05; CFI = 1.00, RMSEA =0.01 (0.00–0.02); SRMR =0.02). 3.2.1.1. Be ween-pe son associa ions ( es ing Hypo heses H1a and H1b). All be ween-pe son associa ions be ween all ou a iables we e posi- i ely signi ican o bo h s uden s in gene al uppe seconda y schools and s uden s in oca ional schools, ep esen ing s able, be ween-pe son le els o academic sel -concep and all h ee ask alues. This means ha , on a e age, s uden s who had a highe academic sel -concep o e all in li e acy also expe ienced highe le els o all h ee ask alues (and ice e sa) han s uden s who had a lowe academic sel - concep (H1a was con i med). Fu he , on a e age, s uden s who had one ask alue highe in li e acy also had he o he wo alues (and academic sel -concep ) highe han s uden s who had lowe ask alues (H1b was con i med; see Table 1). 3.2.1.2. Wi hin-pe son associa ions ( es ing Hypo heses H2 and H3). Table 1 epo s he ‘s a e-like’ wi hin-pe son associa ions (co ela ions) wi hin a gi en ime poin be ween academic sel -concep and ask alues in li e acy o s uden s om bo h gene al uppe seconda y schools and oca ional schools. Table 2 epo s he wi hin-pe son au o- eg essi e (H3) and c oss- lagged associa ions (H2) be ween academic sel -concep and ask alues in li e acy o s uden s om bo h gene al uppe seconda y and oca ional schools o e ime. Based on es ing H2, he ollowing c oss-lagged e ec s we e ound o be signi ican . S uden s who pe cei ed a highe (lowe ) u ili y alue ( ela i e o hei own means) a each measu emen wa e we e likely o pe cei e an inc ease (dec ease) in in insic alue om T1 (g ade 9) o T2 (g ade 10) as well as an inc ease (dec ease) in a ainmen alue om T1 (g ade 9) o T2 (g ade 10) and om T2 (g ade 10) o T3 (g ade 12) in ela ion o hei expec ed sco es. The e was also a posi i e c oss-lagged e ec om in insic alue o academic sel -concep and a ainmen alue om he i s o he las yea o uppe seconda y school, indica ing ha s uden s who pe cei ed highe (lowe ) in insic alue in ela ion o hei expec ed sco es we e likely o pe cei e a subsequen inc ease (dec ease) in hei academic sel -concep and a ainmen alue in ela- ion o hei expec ed sco es. In u n, s uden s wi h highe (lowe ) ac- ademic sel -concep a T2 (g ade 10) we e likely o epo highe (lowe ) in insic alue om T2 (g ade 10) o T3 (g ade 12). The esul s pa ially con i med H2. The signi ican au o- eg essi e and (c oss-)lagged asso- cia ions be ween he wi hin-pe son alues o he measu es om he RI- CLPM o li e acy a e shown in Fig. 2. Based on es ing H3, bo h s uden g oups di e ed signi ican ly in he au o eg essi e pa hs o academic sel -concep , which e lec ed he amoun o wi hin-pe son ca yo e e ec , al hough Cohen's d was low Table 1 Be ween-pe son associa ions and wi hin-pe son wi hin- ime associa ions o he cons ained mul ig oup RI-CLPMs in li e acy wi h ou pa hs ee. S uden s om gene al uppe seconda y schools S uden s om oca ional schools us . s d. us . s d. Be ween-pe son associa ions (co a iances/co ela ions be ween he RI ac o s) 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*** Wi hin-pe son wi hin- ime associa ions SC 1 ⬄ AV 1 0.14*** 0.37*** 0.15** 0.43*** SC 1 ⬄ IV 1 0.25*** 0.48*** 0.23*** 0.49*** SC 1 ⬄ UV 1 0.14*** 0.30*** 0.12*0.27** AV 1⬄ IV 1 0.25*** 0.47*** 0.24*** 0.49*** AV 1 ⬄ UV 1 0.25*** 0.49*** 0.21*** 0.44*** IV 1 ⬄ UV 1 0.33*** 0.50*** 0.29*** 0.44*** SC 2 ⬄ AV 2 0.11*** 0.34*** 0.17*** 0.39*** SC 2 ⬄ IV 2 0.21*** 0.54*** 0.22*** 0.45*** SC 2 ⬄ UV 2 0.08** 0.23*** 0.15*** 0.33*** AV 2⬄ IV 2 0.31*** 0.63*** 0.41*** 0.72*** AV 2 ⬄ UV 2 0.28*** 0.60*** 0.41*** 0.75*** IV 2 ⬄ UV 2 0.27*** 0.51*** 0.40*** 0.67*** SC 3 ⬄ AV 3 0.16*** 0.40*** 0.12*** 0.27*** SC 3 ⬄ IV 3 0.21*** 0.48*** 0.16*** 0.36*** SC 3 ⬄ UV 3 0.14*** 0.33*** 0.12*** 0.28*** AV 3⬄ IV 3 0.28*** 0.52*** 0.39*** 0.64*** AV 3 ⬄ UV 3 0.28*** 0.56*** 0.32*** 0.55*** IV 3 ⬄ UV 3 0.25*** 0.47*** 0.30*** 0.49*** No e. RI =Random In e cep ac o ; SC =sel -concep ; AV =a ainmen alue; IV =in insic alue; UV =u ili y alue; 1 =Time1; 2 =Time2; 3 =Time3. * p <.05. ** p <.01. *** p <.001. D. Rau elde e al. Lea ning and Indi idual Die ences 116 (2024) 102555 6 (d = − 0.04) be ween T1 and T2 and mode a e be ween T2 and T3 (d = −0.50). While o s uden s om gene al uppe seconda y schools, all au o eg essi e pa hs o academic sel -concep we e signi ican , o s u- den s om oca ional schools, only he au o eg essi e pa h be ween T2 and T3 was s a is ically signi ican . This sugges s ca yo e e ec s and ha indi idual changes in academic sel -concep ha e a cumula i e e - ec on s uden s' academic sel -concep de elopmen . In o he wo ds, s uden s om gene al uppe seconda y schools who sco ed abo e (o below) hei a e age sco es also ended o ha e sco es abo e (o below) hei a e age a he nex ime poin . Fo s uden s om oca ional schools, his e ec was only ound om T2 o T3, when hey changed o oca ional schools. The non-signi ican au o eg essi e pa hs om aca- demic sel -concep be ween T1 and T2 and om u ili y alue be ween T2 and T3 indica ed highe andomness, as a change a he la e ime poin canno be p edic ed by a change a he p e ious ime poin . All au o eg essi e pa hs o a ainmen alue de elopmen we e non- signi ican (con a y o H3), while all au o eg essi e pa hs o in insic alue de elopmen we e signi ican (con i ming H3). Tha is, he e seemed o be mo e lexibili y in he de elopmen o a ainmen alue, while changes in in insic alue con inuously a ec ed changes in i s de elopmen . This may also be explained by he ac ha he p ac ical o ien a ion o eaching a oca ional schools is mo e di e en om eaching a lowe seconda y schools ( han a uppe seconda y schools), and his is mo e likely o lead o a ‘b eak’ in he de elopmen o a ainmen alue. As in insic alue is ancho ed in he s uden s hem- sel es, i may no be as suscep ible o ex e nal changes (e.g. change o school). 3.2.2. Ma hema ics RI-CLPM To es whe he he ecip ocal e ec s be ween academic sel -concep and ask alues in ma hema ics we e he same o s uden s in gene al uppe seconda y schools e sus s uden s in oca ional schools, a mul iple-g oup analysis was pe o med. Fi s , a mul iple-g oup RI-CLPM o ma hema ics wi hou cons ain s ac oss he g oups was compu ed ( χ 2 (12) =22.38, p <.05; CFI =1.00, RMSEA =0.02 (0.01–0.04); SRMR =0.02). Subsequen ly, a model in which lagged pa ame e s a e in a ian ac oss g oups was un ( χ 2 (44) =78.09, p <.05; CFI =1.00, RMSEA =0.02 (0.01–0.03); SRMR =0.03). The chi-squa e di e ence es o hese wo nes ed models yielded Δ χ 2(32) =55.71 (p <.05), which implied ha he lagged e ec s o academic sel -concep and ask alues in ma hema ics o s uden s om gene al uppe seconda y schools e sus s uden s in oca ional schools appea ed no o be he same (Mulde & Hamake , 2021). Howe e , using he Wald es compa ing each pa h in he model be ween he wo g oups subse- quen ly, we could iden i y only h ee pa hs in he model, in which bo h g oups signi ican ly di e ed (calcula ing he e ec size wi h Cohen's d): he au o eg essi e pa h om sel -concep a T1 o sel -concep a T2 ( χ 2 (1) =18.65, p <.001; d =0.83), he au o eg essi e pa h om sel - concep a T2 o sel -concep a T3 ( χ 2 (1) =5.37, p =.021; d =1.37) and he c oss-lagged pa h om a ainmen alue a T1 o sel -concep a T2 ( χ 2 (1) =6.12, p =.013; d =2.33). Acco dingly, we allowed hese h ee pa hs o be eely es ima ed in he inal cons ained model, which Table 2 Es ima es o he cons ained RI-CLPM in li e acy wi h ou pa hs hold ee be ween g oups. Uns anda dized es ima es equally cons ained ac oss bo h g oups S anda dized es ima es o s uden s in gene al uppe seconda y schools S anda dized es ima es o s uden s in oca ional schools B SE B p ßSE ßpßSE ßp Cohen's d SC 1 → SC 2*GU 0.21 0.09 <. 05 0.24 0.10 <0.05 – – – 0.04 SC 1 → SC 2*VO 0.21 0.16 >0.05 – – – 0.19 0.15 >0.05 SC 2 → SC 3*GU 0.38 0.10 <0.001 0.32 0.09 <0.001 – – – 0.50 SC 2 → SC 3*VO 0.43 0.10 <0.001 – – – 0.42 0.09 <0.001 AV 1 → AV 2 0.07 0.09 >0.05 0.06 0.09 >0.05 0.05 0.07 >0.05 AV 2 → AV 3 0.14 0.08 >0.05 0.12 0.07 >0.05 0.13 0.07 >0.05 IV 1 → IV 2 0.21 0.08 <0.01 0.21 0.08 <0.01 0.20 0.08 <0.01 IV 2 → IV 3 0.32 0.09 <0.001 0.31 0.08 <0.001 0.30 0.08 <0.001 UV 1 → UV 2 0.16 0.06 <0.05 0.18 0.07 <0.01 0.17 0.07 <0.01 UV 2 → UV 3*GU 0.17 0.08 <0.05 0.16 0.08 <0.05 – – – UV 2 → UV 3*VO 0.13 0.04 >0.05 – – – 0.13 0.11 >0.05 0.62 SC 1 → AV 2 0.01 0.08 >0.05 0.01 0.07 >0.05 0.01 0.06 >0.05 SC 1 → IV 2 0.16 0.09 >0.05 0.12 0.07 >0.05 0.11 0.07 >0.05 SC 1 → UV 2 0.06 0.08 >0.05 0.05 0.07 >0.05 0.05 0.06 >0.05 SC 2 → AV 3 0.07 0.08 >0.05 0.05 0.06 >0.05 0.05 0.06 >0.05 SC 2 → IV 3 0.22 0.09 <0.05 0.14 0.06 <0.05 0.15 0.06 <0.05 SC 2 → UV 3 0.16 0.09 >0.05 0.11 0.07 >0.05 0.12 0.07 >0.05 AV 1 → SC 2 −0.07 0.07 >0.05 −0.08 0.08 >0.05 −0.06 0.06 >0.05 AV 1 → IV 2 0.04 0.06 >0.05 0.00 0.07 >0.05 0.00 0.06 >0.05 AV 1 → UV 2 0.06 0.08 >0.05 0.05 0.07 >0.05 0.04 0.06 >0.05 AV 2 → SC 3 −0.03 0.06 >0.05 −0.03 0.06 >0.05 −0.03 0.07 >0.05 AV 2 → IV 3 0.00 0.09 >0.05 −0.00 0.07 >0.05 −0.00 0.07 >0.05 AV 2 → UV 3 0.13 0.09 >0.05 0.11 0.08 >0.05 0.11 0.08 >0.05 IV 1 → SC 2 0.08 0.05 >0.05 0.13 0.08 >0.05 0.11 0.07 >0.05 IV 1 → AV 2 0.04 0.06 >0.05 0.04 0.07 >0.05 0.04 0.07 >0.05 IV 1 → UV 2 *GU 0.02 0.06 >0.05 0.02 0.07 >0.05 – – >0.05 0.31 IV 1 → UV 2 *VO 0.00 0.07 >0.05 – – – 0.00 0.08 >0.05 IV 2 → SC 3 0.12 0.06 <0.05 0.15 0.07 <0.05 0.16 0.07 <0.05 IV 2 → AV 3 0.14 0.07 <0.05 0.15 0.07 <0.05 0.14 0.07 <0.05 IV 2 → UV 3 0.03 0.08 >0.05 0.04 0.08 >0.05 0.03 0.08 >0.05 UV 1 → SC 2 0.03 0.05 >0.05 0.05 0.07 >0.05 0.05 0.06 >0.05 UV 1 → AV 2 0.16 0.05 <0.01 0.18 0.06 <0.01 0.17 0.06 <0.01 UV 1 → IV 2 0.14 0.06 <0.05 0.13 0.06 <0.05 0.13 0.06 <0.05 UV 2 → SC 3 0.02 0.05 >0.05 0.02 0.06 >0.05 0.02 0.06 >0.05 UV 2 → AV 3 0.19 0.06 <0.01 0.18 0.06 <0.01 0.18 0.06 <0.01 UV 2 → IV 3 0.12 0.07 >0.05 0.10 0.06 >0.05 0.11 0.06 >0.05 No e. SC =sel -concep ; AV =a ainmen alue; IV =in insic alue; UV =u ili y alue; 1 =Time1; 2 =Time2; 3 =Time3; GU =gene al uppe seconda y schools; VO = oca ional schools; numbe s in bold =signi ican p <.05; B =uns anda dized alues; ß =s anda dized alues. * Pa h hold ee be ween bo h g oups based on esul s o he Wald es . D. Rau elde e al. Lea ning and Indi idual Die ences 116 (2024) 102555 7 showed a good model i ( χ 2 (41) =69.63, p <.05; CFI =1.00, RMSEA = 0.02 (0.01–0.03); SRMR =0.03). 3.2.2.1. Be ween-pe son associa ions ( es ing Hypo heses H1a and H1b). Fo s uden s om gene al uppe seconda y schools, all be ween-pe son associa ions be ween all ou andom in e cep a iables we e posi i ely signi ican , ep esen ing s able be ween-pe son le els o academic sel - concep and all h ee ask alues. This means ha , on a e age, s u- den s om gene al uppe seconda y schools who had a highe academic sel -concep o e all in ma hs also expe ienced highe le els o all h ee ask alues (and ice e sa) han s uden s who had a lowe academic sel -concep (con i ming H1a). Fu he , on a e age, s uden s who had one ask alue highe in ma hs also had he o he wo alues (and aca- demic sel -concep ) highe compa ed o s uden s who had lowe ask alues (see Table 3) (con i ming H1b). Fo s uden s om oca ional schools, only h ee associa ions we e posi i ely signi ican (pa ially con i ming H1a and H1b): hose be ween academic sel -concep and a ainmen alue (H1a), academic sel - Fig. 2. Th ee-wa e cons ained Mul ig oup Random In e cep C oss-Lagged Panel Model (RI-CLPM) o Li e acy wi h ou lagged pa hs hold ee be ween bo h g oups. No e. Signi ican uns anda dized associa ions (p <.05) o he lagged pa hs om he cons ained RI-CLPM o li e acy among s uden s om uppe seconda y schools and oca ional schools. The s anda dized esul s a e epo ed in Table 1 and Table 2. The igu e displays only he signi ican au o- eg essi e and (c oss-)lagged associa ions be ween he wi hin-pe son alues o he measu es o e ime and he be ween-pe son associa ions be ween he andom in e cep ac o s o he measu es as well as he wi hin-pe son associa ions wi hin ime; non-signi ican associa ions we e excluded o igu e cla i y excep pa hs, in which bo h g oups signi ican ly di e ; RI =Random In e cep (RIs we e eely es ima ed be ween g oups); colo ed lines: pa hs hold ee be ween bo h g oups (blue lines: s uden s om gene al uppe seconda y schools; o ange lines: s uden s om oca ional schools); do ed pa hs =no -signi ican . (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he web e sion o his a icle.) D. Rau elde e al. Lea ning and Indi idual Die ences 116 (2024) 102555 8 causal o de ing. 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