Herramientas de modelado

academic achievement. However, further research is needed to support the pre-sented fi ndings. As has been mentioned above, the construct of SWB was not oper-ationalized satisfyingly. To be able to draw conclusions which are more content-re-lated, future studies should consider a greater number of facets of SWB to satisfy the complexity of the construct and should analyze students’ SWB by means of well-validated instruments. Furthermore, it would be desirable to investigate the reciprocal relation between SWB and academic achievement on basis of at least three points of measurement and shorter time lags between each of them. This would enable researchers to distinguish stable variability between persons from within person variance (Hamaker et al., 2015).

Moreover, future studies should examine eff ects of additional variables. In this regard, variables like socioeconomic status and ethnic heritage should be includ-ed to control for pre-existing diff erences in achievement. The role of variables like self-concept, interest and divergent thinking that possibly mediate the relation be-tween SWB and academic achievement should be investigated, as well. Because we found evidence that – especially – higher scores in MC were associated with high-er scores of sevhigh-eral aspects of SWB on a lathigh-er time, it would be inthigh-eresting to inves-tigate a possible mediation through self-concept in mathematics on this relation.

Furthermore, recent fi ndings suggest that the association between positive emo-tions and academic achievement might be mediated through motivation (Mega, Ronconi, & De Beni, 2014). Therefore, it would be interesting to investigate if these results apply on other facets of well-being as well. Another desideratum in this context might be to investigate infl uences of variables on higher hierarchical lev-els on students’ SWB or academic achievement. For example, the role of compo-sitional eff ects of classes or the big-fi sh-little-pond-eff ect (Marsh, & Parker, 1984), which explains diff erences in academic self-concepts could be related to SWB of students. Big-fi sh-little-pond-eff ects are a result of academic achievement groupage which is very prominent in Germany (Köller, 2004). Additionally, teachers’ SWB

should also be investigated more deeply, because teachers’ SWB might have an in-fl uence on quality of teacher-student relationships, which, in turn, could inin-fl uence the emotional-motivational characteristics of students. In order to study such re-search questions that require consideration of variables on the class (or the school) level, multi-level models should be specifi ed to determine, for example, cross-lev-el eff ects.

After a replication of the results, also implications for educational practice are possible. Due to the importance of students’ SWB (e.g., satisfaction with school) for academic achievement, it would be thinkable to emphasize its relevance in train-ing programs for teachers or to involve it in university curricula of teacher stu-dents. Furthermore, the infl uence of mathematical competence on SWB has to be investigated more deeply to derive implications for educational practice: If, for ex-ample, self-concept would mediate the relation between mathematical competence and well-being, intervention programs might be developed in order to strengthen mathematical self-concept of students, which also may have positive infl uences on their SWB.

Acknowledgements

This paper uses data from the National Educational Panel Study (NEPS): Starting Cohort Grade 5, doi:10.5157/NEPS:SC3:8.0.1. From 2008 to 2013, NEPS data was collected as part of the Framework Program for the Promotion of Empirical Educational Research funded by the German Federal Ministry of Education and Research (BMBF). As of 2014, NEPS is carried out by the Leibniz Institute for Educational Trajectories (LIfBi) at the University of Bamberg in cooperation with a nationwide network.

References

Baumert, J., Maaz, K., Stanat, P., & Watermann, R. (2009). Schulkomposition oder Institution – was zählt? Schulstrukturen und die Entstehung schulformspezifi scher Entwicklungsverläufe. Die Deutsche Schule, 101, 33–46.

Berger, C., Alcalay, L., Torretti, A., & Milicic, N. (2011). Socio-emotional well-being and academic achievement: Evidence from a multilevel approach. Psicologia: Refl exão e Crítica, 24, 344–351.

Bird, J. M., & Markle, R. S. (2012). Subjective well-being in school environments:

Promoting positive youth development through evidence-based assessment and in-tervention. American Journal of Orthopsychiatry, 82, 61–66.

Blossfeld, H.-P. & Roßbach, H.-G. (Eds.). (2019). Education as a lifelong process:

The German National Educational Panel Study (NEPS) (2nd ed.). Wiesbaden, Germany: VS.

Blossfeld, H.-P., Roßbach, H.-G. & Maurice, J. von (Eds.). (2011). Education as a life-long process. The German National Educational Panel Study (NEPS). Wiesbaden, Germany: VS.

Bollen, K. A. (1989). A new incremental fi t index for general structural equation mod-els. Sociological Methods & Research, 17(3), 303–316.

Bradburn, N. M. (1969). The structure of psychological well-being. Chicago: Aldine.

Brosseau-Liard, P. E., Savalei, V., & Li, L. (2012). An investigation of the sample perfor-mance of two nonnormality corrections for RMSEA. Multivariate behavioral re-search, 47, 904–930.

Bücker, S., Nuraydin, S., Simonsmeier, B. A., Schneider, M., & Luhmann, M. (2018).

Subjective well-being and academic achievement: A meta-analysis. Journal of Research in Personality, 74, 83–94.

Casas, F., & González-Carrasco, M. (2019). Subjective well-being decreasing with age:

New research on children over 8. Child Development, 90, 375–394.

Chang, L., McBride-Chang, C., Stewart, S. M., & Au, E. (2003). Life satisfaction, self-concept, and family relations in Chinese adolescents and children. International Journal of Behavioral Development, 27, 182–189.

Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fi t indexes for testing measurement invariance. Structural Equation Modeling, 9, 233–255.

Crede, J., Wirthwein, L., McElvany, N., & Steinmayr, R. (2015). Adolescents’ academ-ic achievement and life satisfaction: The role of parents’ education. Frontiers in Psychology, 6, 1–8.

Czerwenka, K., Nölle, K., Pause, G., Schlotthaus, W., Schmidt, H. J., & Tesslo, J. (1990).

Schülerurteile über die Schule: Bericht über eine internationale Untersuchung.

Frankfurt am Main, Germany: Lang.

Dicke, T., Marsh, H. W., Parker, P. D., Pekrun, R., Guo, J., & Televantou, I. (2018).

Eff ects of school-average achievement on individual self-concept and achievement:

Unmasking phantom eff ects masquerading as true compositional eff ects. Journal of Educational Psychology, 110, 1112–1126.

Diedrich, J., Schiepe-Tiska, A., Ziernwald, L., Tupac-Yupanqui, A., McElvany, N., ...

(2019). Lesebezogene Schülermerkmale in PISA 2018: Motivation, Leseverhalten, Selbstkonzept und Lesestrategiewissen. In K. Reiss, M. Weis, E. Klieme, & O.

Köller (Eds.)., PISA 2018. Grundbildung im internationalen Vergleich (pp. 81–

109). Münster, Germany: Waxmann.

Diener, E. (1984). Subjective well-being. Psychological Bulletin, 95, 542–575.

Diener, E., & Emmons, R. A. (1984). The independence of positive and negative aff ect.

Journal of personality and social psychology, 47(5), 1105–1117.

Diener, E., Inglehart, R., & Tay, L. (2013). Theory and validity of life satisfaction scales.

Social Indicators Research, 112, 497–527.

Diener, E., Suh, E. M., Lucas, R. R., & Smith, H. L. (1999). Subjective well-being: three decades of progress. Psychological Bulletin, 125, 276–302.

Dweck, C. S. (1986). Motivational processes aff ecting learning. American Psychologist, 41, 1040–1048.

Eid, M., & Larsen, R. J. (2008). The Science of subjective well-being. New York, NY:

Guilford Press.

Eide, E. R., Showalter, M. H., & Goldhaber, D. D. (2010). The relation between chil-dren’s health and academic achievement. Children and Youth Services Review, 32, 231–238.

Farmer, H. S., & Vispoel, W. P. (1990). Attributions of female and male adolescents for real-life failure experiences. Journal of Experimental Education, 58, 127–140.

Fend, H., Knörzer, W., Nagl, W., Specht, W., & Väth-Szusdziara, R. (1976). Sozialisa-tionseff ekte der Schule. Weinheim, Germany: Beltz.

Fincham, F. D., Hokoda, A., & Sanders, R. (1989). Learned helplessness, test anxiety, and academic achievement: A longitudinal analysis. Child Development, 60, 1461–

1474.

Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden-and-build theory of positive emotions. American Psychologist, 56, 218–

226.

Gehrer, K., Zimmermann, S., Artelt, C., & Weinert, S. (2012). The assessment of read-ing competence (includread-ing sample items for grade 5 and 9): Scientifi c Use File 2012, Version 1.0.0. Bamberg: University of Bamberg, National Educational Panel Study (NEPS).

Gilman, R., & Huebner, E. S. (2006). Characteristics of adolescents who report very high life satisfaction. Journal of Youth and Adolescence, 35, 311–319.

Gumora, G., & Arsenio, W. F. (2002). Emotionality, emotion regulation, and school per-formance in middle school children. Journal of School Psychology, 40, 395–413.

Gysin, S. H. (2017). Subjektives Wohlbefi nden von Schülerinnen und Schülern.

Weinheim, Germany: Beltz Juventa.

Haecker, H., & Werres, W.(1983). Schule und Unterricht im Urteil der Schüler: Bericht einer Schülerbefragung in der Sekundarstufe I. Frankfurt am Main, Germany:

Lang.

Hamaker, E. L., Kuiper, R. M., & Grasman, R. P. P. P. (2015). A critique of the cross-lagged panel model. Psychological Methods, 20(1), 102–116.

Hascher, T. (2007). Exploring students’ well-being by taking a variety of looks in the classroom. Hellenic Journal of Psychology, 4, 331–349.

Hascher, T. (2008). Quantitative and qualitative research approaches to assess student well-being. International Journal of Educational Research, 47, 84–96.

Hascher, T., & Hagenauer, G. (2011). Wohlbefi nden und Emotionen in der Schule als zentrale Elemente des Schulerfolgs unter der Perspektive geschlechtsspezifi scher Ungleichheiten. In A. Hadjar (Eds.), Geschlechtsspezifi sche Bildungsungleichheiten (pp. 285–308). Wiesbaden, Germany: VS.

Hascher, T., & Winkler-Ebner, C. (2010). Gesundheit und Bildung von Kindern und Jugendlichen. In P. Paulus (Ed.), Bildungsförderung durch Gesundheit.

Bestandsaufnahme und Perspektiven für eine gute gesunde Schule (pp. 31–56).

Weinheim, Germany: Juventa.

Heff ner, A. L., & Antaramian, S. P. (2016). The role of life satisfaction in predicting stu-dent engagement and achievement. Journal of Happiness, 17, 1681–1701.

Herman, K. C., Lambert, S. F., Reinke, W. M., & Ialongo, N. S. (2008). Low academic competence in fi rst grade as a risk factor for depressive cognitions and symptoms in middle school. Journal of Counseling Psychology, 55, 400–410.

Huebner, E. S. (1991). Correlates of life satisfaction in children. School Psychology Quarterly, 6, 103–111.

Huebner, E. S., & Alderman, G. L. (1993). Convergent and discriminant validation of a children’s life satisfaction scale: Its relationship to self and teacher-reported psy-chological problems and school functioning. Social Indicators Research, 30, 71–

82.

Jerusalem, M., & Schwarzer, R. (1993). Dimensionen der Hilfl osigkeit. In G. Westhoff (Ed.), Handbuch psychosozialer Meßinstrumente: Ein Kompendium für epide-miologische und klinische Forschung zu chhronischer Krankheit (pp. 402–404).

Göttingen, Germany: Hogrefe.

Jöreskog, K. G., & Sörbom, D. (1982). Recent developments in structural equation mod-eling. Journal of marketing research, 19(4), 404–416.

Köller, O. (2004). Konsequenzen von Leistungsgruppierungen [Consequences of achievement groupage]. Münster, Gemany: Waxmann.

Lavy, V., & Sand, E. (2012). The friends factor: How students’ social networks aff ect their academic achievement and well-being? Camridge, MA: National Bureau of Economic Research.

Linnenbrink, E. A., & Pintrich, P. R. (2002). Achievement goal theory and aff ect: An asymmetrical bidirectional model. Educational Psychologist, 37, 69–78.

Marsh, H. W., & Parker, J. W. (1984). Determinants of student self-concept: Is it better to be a relatively large fi sh in a small pond even if you don’t learn to swim as well?

Journal of personality and social psychology, 47(1), 213–231.

Mega, C., Ronconi, L., & De Beni, R. (2014). What makes a good student? How emo-tions, self-regulated learning, and motivation contribute to academic achievement.

Journal of Educational Psychology, 106, 121–131.

Möller, J., Pohlmann, B., Köller, O., & Marsh, H. W. (2009). A meta-analytic path anal-ysis of the internal/external frame of reference model of academic achievement and academic self-concept. Review of Educational Research, 79, 1129–1167.

Morris, S. B., & DeShon, R. P. (2002). Combining eff ect size estimates in meta-analysis with repeated measures and independent-groups designs. Psychological methods, 7(1), 105–125.

Neumann, I., Duchhardt, C., Grüßing, M., Heinze, A., Knopp, E., & Ehmke, T. (2013).

Modeling and assessing Mathematical competence over the lifespan. Journal for Educational Research Online, 5(2), 80–109.

Ng, Z. J., Huebner, S. E., & Hills, K. J. (2015). Life satisfaction and academic perfor-mance in early adolescents: Evidence for reciprocal association. Journal of school psychology, 53, 479–491.

Opdenakker, M. C., & Van Damme, J. (2000). Eff ects of schools, teaching staff and classes on achievement and well-being in secondary education: Similarities and diff erences between school outcomes. School eff ectiveness and school improve-ment, 11, 165–196.

OECD – Organisation for Economic Cooperation Development. (2017). PISA 2015.

Results (Volume III): Students’ Well-Being. Paris, France: OECD.

Palsdottir, A., Asgeirsdottir, B. B., & Sigfusdottir, I. D. (2012). Gender diff erence in wellbeing during school lessons among 10–12-year-old children: The importance of school subjects and student-teacher relationships. Scandinavian Journal of Public Health, 40, 605–613.

Petrescu, M. (2013). Marketing research using single-item indicators in structural equa-tion models. Journal of Marketing Analytics, 1(2), 99–117.

Pietarinen, J., Soini, T., & Pyhältö, K. (2014) Students’ emotional and cognitive engage-ment as the determinants of well-being and achieveengage-ment in school. International Journal of Educational Research, 67, 40–51.

Proctor, C., Linley, P. A., & Maltby, J. (2010). Very happy youths: Benefi ts of very high life satisfaction among adolescents. Social Indicators Research, 98, 519–532.

Putnick, D. L., & Bornstein, M. H. (2016). Measurement invariance conventions and reporting: The state of the art and future directions for psychological research.

Developmental review, 41, 71–90.

R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Retrived from http://

www.R-project.org/.

Richter, M., & Hurrelmann, K. (Eds.). (2009). Gesundheitliche Ungleichheit: Grund

-lagen, Probleme, Konzepte (2nd ed.). Wiesbaden, Germany: VS.

Rohlfs, C. (2011). Bildungseinstellungen. Schule und formale Bildung aus der Perspektive von Schülerinnen und Schülern. Wiesbaden, Germany: VS.

Rosseel Y (2012). “lavaan: An R Package for Structural Equation Modeling.” Journal of Statistical Software, 48(2), 1–36. http://www.jstatsoft.org/v48/i02/.

Russell, J. A., & Carroll, J. M. (1999). On the bipolarity of positive and negative aff ect.

Psychological bulletin, 125(1), 3–30.

Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of in-trinsic motivation, social development, and well-being. American Psychologist, 55, 68–78.

Ryan, R. M., & Deci, E. L. (2001). On happiness and human potentials: a review of re-search on hedonic and eudaimonic well-being. Annual Review of Psychology, 52, 141–166.

Samdal, O., Wold, B., & Bronis, M. (1999). Relationship between Students’ Perceptions of School Environment, Their Satisfaction with School and Perceived Academic

Achievement: An International Study. School Eff ectiveness and School Improvement, 10, 296–320.

Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399–419). Thousands Oaks, CA: Sage.

Scharl, A., Fischer, L., Gnambs, T., & Rohm, T. (2017). NEPS Technical Report for Reading–Scaling Results of Starting Cohort 3 for Grade 9.

Schimmack, U. (2008). Structure of subjective well-being. In M. Eid & R. J. Larsen (Eds.), The science of subjective well-being (pp. 97–123). New York, NY: Guilford Press.

Seligman, M. E. (1972). Learned helplessness. Annual review of medicine, 23, 407–412.

Seligman, M. E. (2011). Flourish: A visionary new understanding of happiness and well-being. New York, NY: Free Press.

Seligman, M. E., Ernst, R. M., Gillham, J., Reivich, K., & Linkins, M. (2009). Positive education: Positive psychology and classroom interventions. Oxford Review of Education, 35, 293–311.

Sigfúsdóttir, I. D., Kristjánsson, A. L., & Allegrante, J. P. (2007). Health behaviour and academic achievement in Icelandic school children. Health Education Research, 22, 70–80.

Sparfeldt, J. R., Buch, S. R., Schwarz, F., Jachmann, J., & Rost, D. H. (2009). “Rechnen ist langweilig” – Langeweile in Mathematik bei Grundschülern. Psychologie in Erziehung und Unterricht, 56, 16–26.

Steinmayr, R., Crede, J., McElvany, N., & Wirthwein, L. (2016). Subjective wellbeing, test anxiety, academic achievement: Testing for reciprocal eff ects. Frontiers in Psychology, 6, 1–13.

Suldo, S. M., Riley, K. N., & Shaff ner, E. J. (2006). Academic correlates of children and adolescents’ life satisfaction. School Psychology International, 27, 567–582.

Suldo, S. M., & Shaff er, E. J. (2008). Looking beyond psychopathology: The dual factor model of mental health in youth. School Psychology Review, 37, 52–68.

Suldo, S. M., Shaff er, E. J., & Riley, K. N. (2008). A social-cognitive-behavioral mo-del of academic predictors of adolescents’ life satisfaction. School Psychology Quarterly, 23, 56–69.

Urhahne, D., & Zhu, M. (2015). Accuracy of teachers’ judgments of students’ subjective well-being. Learning and Individual Diff erences, 43, 226–232.

van Petegem, K., Aelterman, A., Rossell, Y., & Creemers, B. (2006). Student perception as moderator for student well-being. Social Indicators Research, 83, 447–463.

Verkuyten, M., & Thijs, J. (2002). School satisfaction of elementary school children:

the role of performance, peer relations, ethnicity, and gender. Social Indicators Research, 59, 203–228.

Véronneau, M. H., & Dishion, T. J. (2012). Middle school friendships and aca-demic achievement in early adolescence: A longitudinal analysis. Journal Early Adolescence, 31, 99–124.

Widaman, K. F., & Reise, S. P. (1997). Exploring the measurement invariance of psy-chological instruments: Applications in the substance use domain. In K. J. Bryant, M. Windle & S. G. West (Eds.), The science of prevention: Methodological advan-ces from alcohol and substance abuse research (pp. 281–324). Washington, DC:

American Psychological Association.

Wilson, W. R. (1967). Correlates of avowed happiness. Psychological bulletin, 67, 294–

306.

WHO – World Health Organization. (2014). Basic documents: Forty-eighth edition.

Geneva, Switzerland: World Health Organization.

Zajacova, A., Lynch, S. M., & Espenshade, T. J. (2005). Self-effi cacy, stress, and aca-demic success in college. Research in Higher Education, 46, 677–706.

Appendix

Appendix A

Table A1: Means, standard deviations and skewness for the variables used in the analyses of the present study

Grade 5^a Grade 7 Grade 9

Variable M (SD) Skewness M (SD) Skewness M (SD) Skewness

DA - 1.44 (4.09) 10.79 1.36 (2.52) 3.95

SH - 4.25 (0.78) -0.94 4.14 (0.80) -0.77

SL 8.89 (1.51) -3.14 8.39 (1.43)^a -1.62 ^a 8.13 (1.66)^a -1.73^a SS 8.06 (2.25) -1.59 7.10 (2.31)^a -1.00 ^a 6.94 (2.26)^a -0.97^a

HG - 1.77 (0.69) 0.87 1.80 (0.69) 0.68

HM - 1.68 (0.71) 0.96 1.74 (0.75) 0.85

MC 0.24 (1.14) 0.00 0.89 (1.22) -0.01 0.15 (1.20) 0.20

RC 0.24 (1.23) 0.17 0.84 (1.37) 0.20 0.10 (1.13) 0.20

Notes. n = 4180. DA = Days of absence from school, SH = Self-estimated health, SL = Satisfaction with life, SS = Satisfaction with school, HG = Helplessness German, HM = Helplessness Math, MC = Mathematical competence, RC = Reading competence. Values for MC and RC are WLEs.

an = 2902 students.

Table A2: Means, standard deviations and skewness for the variables used in the analyses of the present study separately for both sexes MaleaFemaleb Grade 5 cGrade 7Grade 9Grade 5 dGrade 7Grade 9 VariableM (SD)SkewnessM (SD)SkewnessM (SD)SkewnessM (SD)SkewnessM (SD)SkewnessM (SD)Skewness DA-1.63 (4.96)10.571.33 (2.70)4.51-1.24 (2.94)6.591.39 (2.34)3.05 SH-4.26 (0.78)-1.024.22 (0.79)-0.90-4.25 (0.77)-0.874.06 (0.79)-0.67 SL8.83 (1.54)-3.088.37 (1.48)c-1.85c8.19 (1.73)c-1.87c8.94 (1.48)-3.218.41 (1.39)d-1.33d8.08 (1.58)d-1.56d SS7.90 (2.36)-1.466.95 (2.38)c-0.94c6.88 (2.33)c-0.92c8.22 (2.12)-1.737.25 (2.23)d-1.06d7.01 (2.19)d-1.03d HG-1.86 (0.72)0.711.90 (0.73)0.56-1.68 (0.65)1.041.70 (0.64)0.77 HM-1.60 (0.69)1.071.64 (0.72)1.00-1.75 (0.71)0.871.84 (0.77)0.71 MC0.37 (1.14)1.211.06 (1.27)-0.020.29 (1.25)0.160.11 (1.12)-0.020.73 (1.14)-0.100.00 (1.12)0.17 RC0.17 (1.27)0.160.69 (1.39)0.230.01 (1.17)0.260.32 (1.19)0.210.98 (1.32)0.210.21 (1.06)0.20 Notes. DA = Days of absence from school, SH = Self-estimated health, SL = Satisfaction with life, SS = Satisfaction with school, HG = Helplessness German, HM = Help- lessness Math, MC = Mathematical competence, RC = Reading competence. Values for MC and RC are weighted likelihood estimates. an = 2109, bn = 2071, cn = 1461, dn = 1441.

Table A3: Means and standard deviations for the variables used in the analyses of the present study separately for diff erent types of school HauptschuleaRealschulebGymnasiumc Grade 5dGrade 7Grade 9Grade 5eGrade 7Grade 9Grade 5fGrade 7Grade 9 VariableM (SD)SKM (SD)SKM (SD)SKM (SD)SKM (SD)SKM (SD)SKM (SD)SKM (SD)SKM (SD)SK DA-2.93 (8.67)6.311.84 (3.21)3.77-1.58 (3.86)6.641.53 (2.92)4.42-1.01 (2.33)5.141.21 (2.23)3.51 SH-4.25 (0.85)-1.034.11 (0.80)-0.46-4.22 (0.77)-0.854.08 (0.80)-0.78-4.29 (0.77)-1.014.17 (0.79)-0.83 SL8.48 (1.89)-2.318.23 (1.68)d-1.21d8.15 (1.84)d-1.64d8.63 (1.91)-2.728.34 (1.42)e-1.428.03 (1.75)e-1.559.08 (1.15)-3.248.44 (1.38)f-1.80f8.17 (1.57)f-1.84f SS7.33 (2.84)-1.026.76 (2.64)d-0.79d7.02 (2.38)d-0.91d7.68 (2.54)-1.296.82 (2.44)e-0.906.78 (2.28)e-0.908.37 (1.91)-1.807.29 (2.16)f-1.06 f7.00 (2.22)f-1.03f HG-2.03 (0.81)0.461.89 (0.76)0.66-1.85 (0.73)0.731.83 (0.69)0.62-1.65 (0.64)1.051.73 (0.68)0.85 HM-1.96 (0.84)0.531.89 (0.84)0.73-1.78 (0.75)0.791.71 (0.72)0.81-1.58 (0.66)1.171.69 (0.73)0.91 MC-1.17 (0.91)0.19-0.64 (0.97)0.09-1.09 (0.91)0.44-0.21 (0.84)-0.000.41 (0.97)0.19-0.34 (0.93)0.290.73 (0.96)0.291.42 (1.02)0.170.67 (1.06)0.19 RC-1.11 (0.98)0.51-0.62 (1.10)0.14-1.04 (0.83)0.32-0.15 (1.04)0.370.30 (1.12)0.36-0.26 (0.90)0.380.69 (1.08)0.371.30 (1.23)0.260.55 (1.03)0.18 Notes. n = 4180. DA = Days of absence from school, SH = Self-estimated health, SL = Satisfaction with life, SS = Satisfaction with school, HG = Helplessness German, HM = Helplessness Math, MC = Mathematical competence, RC = Reading competence, SK = Skewness. Values for MC and RC are weighted likelihood estimates. an = 583, bn = 1176, cn = 2431, dn = 363, en = 789, fn = 1750.

Appendix B Table B1: Correlations between all variables included in the present study 1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20. 1. DA t2 2. DA t3 .13*** 3. SH t2-.22***-.08*** 4. SH t3-.11***-.15*** .40*** 5. SL t1-.07***-.03 .16*** .13*** 6. SL t2-.11**-.08** .45*** .26*** .30*** 7. SL t3-.07**-.11*** .27*** .43*** .20*** .40*** 8. SS t1-.06**-.06** .13*** .11*** .57*** .25*** .15*** 9. SS t2-.11***-.09*** .27*** .17*** .19*** .50*** .27*** .29*** 10. SS t3-.08***-.12*** .19*** .25*** .11*** .25*** .52*** .16*** .38*** 11. HG t2 .06** .09***-.13***-.09***-.15***-.27***-.13***-.21***-.36***-.21*** 12. HG t3 .04 .06**-.08***-.06**-.08***-.14***-.12***-.16***-.22***-.26*** .37*** 13. HM t2 .10*** .08***-.12***-.08***-.13***-.21***-.15***-.17***-.32***-.22*** .34*** .13*** 14. HM t3 .05* .12***-.09***-.11***-.04-.13***-.16***-.09***-.21***-.30*** .08*** .16*** .38*** 15. MC t1-.12***-.12*** .02-.00 .06** .00 -.00 .11*** .14*** .10***-.13***-.08***-.25***-.21*** 16. MC t2-.10***-.11*** .05*** .03 .07*** .03 .02 .11*** .13*** .14***-.17***-.06***-.28***-.22*** .73*** 17. MC t3-.10***-.13*** .05** .02 .06** .01 -.00 .10*** .14*** .16***-.15***-.07***-.28***-.27*** .70*** .73*** 18. RC t1-.10***-.07***-.00-.05* .07*** -.01-.05* .11*** .13*** .07***-.23***-.17***-.16***-.07*** .62*** .56*** .55*** 19. RC t2-.09***-.09*** .03-.02 .11*** .06** .02 .11*** .19*** .14***-.27***-.16***-.19***-.11*** .54*** .61*** .57*** .61*** 20. RC t3-.07***-.08*** .01-.02 .06** .01-.02 .12*** .17*** .12***-.25***-.21***-.20***-.14*** .53*** .53*** .60*** .61*** .63*** 21. Gen- der-.04** .01-.01-.10*** .04.01**-.03 .07*** .07*** .03-.13***-.15*** .10*** .13***-.12***-.14***-.12*** .06*** .10*** .10*** Notes. DA = Days of absence from school, SH = Self-estimated health, SL = Satisfaction with life, SS = Satisfaction with school, HG = Helplessness German, HM = Help- lessness Math, MC = Mathematical competence, RC = Reading competence, t1 = measurement in grade 5, t2 = measurement in grade 7, t3 = measurement in grade 9. *p < .05. **p < .01. ***p < .001.

Appendix C

In the following you can see the intraclass correlation coeffi cients (ICC) for the var-iables we used in our analyses. Sample sizes diff ered depending on the number of measurement time points used in the respective analysis. Therefore, ICCs are dis-played once for variables included in the analysis over three points of measurement (see Table C1) and once for the variables included in the analyses over two points of measurement (see Table C2). As can be seen from the tables the ICC values of the variables mathematical competence and reading comprehension are very high.

This is not a surprising fi nding because the cluster variable contains schools from diff erent types of school and those should vary highly on academic achievement.

Table C1: ICC values of variables included in the analysis over t₁ to t₃

t₁ t₂ t₃

Satisfaction with life .04 .05 .03

Satisfaction with school .06 .03 .03

Mathematical competence .41 .41 .38

Reading comprehension .31 .31 .33

Table C2: ICC values of variables included in the analyses over t₂ to t₃

t₂ t₃

Days of absence from school .03 .02

Self-estimated health .03 .02

Helplessness German .07 .03

Helplessness Math .06 .05

Mathematical competence .41 .38

Reading comprehension .32 .33

Appendix D

Measurement invariance of the helplessness scale had to be tested between dif-ferent points of measurement, as well as between sexes and types of school.

Therefore, we started by testing measurement invariance between diff erent occa-sions. More precisely, we fi rst checked measurement invariance between points of measurement considering all individuals and afterwards by focusing on diff erent groups of gender and type of school (see Table D1). Subsequently, we tested mea-surement invariance between diff erent sexes and types of school for single points of measurement (see Table D2). Confi gural invariance over points of measurement was achieved through excluding items 4 (“When my teacher calls me surprising-ly in German I cannot answer even the simplest questions”) and 5 (“No matter if I try to do my homework in German, I always make many mistakes”) of the subscale helplessness German and 1 (“No matter how much I try in Math, my grades won’t get better”) and 2 (“It’s not worth practicing mathematics for a class test, I will be bad again”) of the subscale helplessness Math. Tables D1 and D2 show that – ac-cording to ΔCFI – metric invariance could be assumed for the helplessness scale.

Table D1: Examination of measurement invariance of the helplessness scale over points of measurement Modelχ2DfpCFI/TLIRMSEA/SRMRComparisonΔCFIΔχ2Δdfp(Δχ2) Overall: 1. confi gural 216.6642<.001.989/0.982.039/.025 2. metric237.8946<.001.987/0.982.039/.0272 vs. 1.00221.234<.001 3. scalar295.9052<.001.984/0.980.041/.0283 vs. 2.00362.636<.001 4. residual302.4458<.001.983/0.981.040/.0284 vs. 2.00464.2312<.001 Gender = malea: 1. confi gural 114.6842<.001.990/0.984.036/.025 2. metric129.8246<.001.989/0.984.037/.0282 vs. 1.00115.044<.01 3. scalar160.8052<.001.985/0.981.040/.0293 vs. 2.00433.876<.001 4. residual162.3158<.001.985/0.983.038/.0284 vs. 2.00432.6812<.01 Gender = femaleb: 1. confi gural 147.2742<.001.987/0.979.042/.027 2. metric155.0946<.001.986/0.980.041/.0292 vs. 1.0018.024.091 3. scalar187.6052<.001.983/0.978.042/.0313 vs. 2.00334.086<.001 4. residual193.5658<.001.982/0.979.041/.0324 vs. 2.00438.7512<.001 Type of school = “Hauptschule”c: 1. confi gural 85.7142<.001.978/0.966.056/.039 2. metric92.9346<.001.977/0.967.055/.0412 vs. 1.0017.054.134 3. scalar108.8752<.001.973/0.965.057/.0473 vs. 2.00416.526<.05 4. residual118.1558<.001.969/0.965.057/.0464 vs. 2.00825.0912<.05 Type of school = “Realschule”d: 1. confi gural 105.2142<.001.985/0.977.044/.029 2. metric111.6046<.001.985/0.978.043/.0302 vs. 1.0006.594.159 3. scalar127.4052<.001.983/0.978.043/.0303 vs. 2.00216.016<.05 4. residual144.9658<.001.979/0.976.045/.0314 vs. 2.00632.8312<.01 Type of school = “Gymnasium”e: 1. confi gural 134.4542<.001.990/0.984.036/.025 2. metric156.6146<.001.988/0.982.038/.0292 vs. 1.00221.764<.001 3. scalar258.2852<.001.978/0.972.048/.0383 vs. 2.010113.146<.001 4. residual263.6558<.001.976/0.973.047/.0394 vs. 2.01297.6912<.001 Notes. N = 4180. χ2 = Chi-Square, df = degrees of freedom. CFI = Comparative Fit Index. TLI = Tucker-Lewis index. RMSEA = Root mean square error of approximation. SRMR = Standardized root mean square residual. p(Δχ2)-values are calculated based on the Satorra-Bentler scaled chi-square diff erence test (Satorra & Bentler, 1994). an = 2109, bn = 2071, cn = 583, dn = 1166, en = 2431.

Table D2: Examination of measurement invariance of the helplessness scale over gender and types of school on single occasions Modelχ2DfpCFI/TLIRMSEA/SRMRComparisonΔCFIΔχ2Δdfp(Δχ2) Over gender on t2: 1. confi gural 121.0116<.001.985/0.971.070/.030 2. metric134.7620<.001.984/0.976.064/.0322 vs. 1.0018.194.085 3. scalar277.8626<.001.967/0.962.081/.0593 vs. 2.017171.496<.001 4. residual286.9532<.001.963/0.965.077/.0604 vs. 2.021147.2112<.001 Over gender on t3: 1. confi gural 68.5916<.001.993/0.987.048/.023 2. metric76.0420<.001.993/0.989.044/.0262 vs. 1.0007.484.112 3. scalar224.5326<.001.975/0.971.071/.0643 vs. 2.018172.346<.001 4. residual229.7932<.001.972/0.974.068/.0654 vs. 2.021143.0712<.001 Over types of school on t2: 1. confi gural 111.1624<.001.987/0.976.063/.029 2. metric127.4532<.001.986/0.981.056/.0312 vs. 1.00113.468.097 3. scalar289.9544<.001.968/0.967.074/.0743 vs. 2.018200.5912<.001 4. residual383.4256<.001.952/0.962.080/.0774 vs. 2.034251.4724<.001 Over types of school on t3: 1. confi gural 73.2624<.001.993/0.988.047/.023 2. metric87.5132<.001.993/0.990.043/.0272 vs. 1.00013.598.093 3. scalar161.5744<.001.986/0.985.051/.0403 vs. 2.00782.9512<.001 4. residual175.9756<.001.983/0.986.049/.0444 vs. 2.01078.4524<.001 Notes. N = 4180. χ2 = Chi-Square, df = degrees of freedom. CFI = Comparative Fit Index. TLI = Tucker-Lewis index. RMSEA = Root mean square error of approximation. SRMR = Standardized root mean square residual. p(Δχ2)-values are calculated based on the Satorra-Bentler scaled chi-square diff erence test (Satorra & Bentler, 1994).

Similar to the procedure described above, measurement invariance of the satisfac-tion scale had to be tested between diff erent points of measurement, as well as between sexes and types of school. Therefore, we started by testing measurement invariance between diff erent occasions. More precisely, we fi rst checked measure-ment invariance between points of measuremeasure-ment considering all individuals and

Similar to the procedure described above, measurement invariance of the satisfac-tion scale had to be tested between diff erent points of measurement, as well as between sexes and types of school. Therefore, we started by testing measurement invariance between diff erent occasions. More precisely, we fi rst checked measure-ment invariance between points of measuremeasure-ment considering all individuals and

In document Propuesta de un procedimiento para la captura de requisitos no funcionales en el diseno de redes en los proyectos de software. (página 34-38)