FACTOR INVARIANCE IN LONGITUDINAL STUDIES: MEASURING THE SAME CONSTRUCT ACROSS TIME
Keywords:
factor invariance, measurement invariance, repeated measures, confirmatory factor analysis
Abstract
When researchers are conducting studies that require repeated measures, it is not uncommon for them to assume that the particular instrument is equally going to assess the latent construct of interest no matter how many times the instrument (test) is administered. In other words, it is not in question whether the properties of the test are likely to change or not. However, measurement invariance is not something that the instrument possesses by default. Measurement invariance has to be tested. The aim of this paper was to provide an insight into testing factorial invariance by performing the confirmatory factor analysis on a set of longitudinal data. The first part of this paper is theoretical and describes different forms of invariance. The second part offers a concrete example and a step-by-step guide on how to perform confirmatory factor analysis for repeated measurements to test the invariance using statistical software R.
References
Brown, T. A. (2015). Confirmatory factor analysis for applied research. New York: Guilford
Carmines, E. G., & McIver, J. D. (1981). Analyzing models with unobserved variables: Analysis of covariance structures. U G. W. Bohinstedt & E. F. Borgatta (Eds.), Social measurement: Current issues (pp. 65 - 115). Sage.
Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling, 14(3), 464–504. https://doi.org/10.1207/s15328007sem0902_5
Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling, 9(2), 233–255.
Chungkham, H. S., Ingre, M., Karasek, R., Westerlund, H., & Theorell, T. (2013). Factor Structure and Longitudinal Measurement Invariance of the Demand Control Support Model: An Evidence from the Swedish Longitudinal Occupational Survey of Health (SLOSH). PLoS ONE 8(8): e70541. https://doi.org/10.1371/journal.pone.0070541
Hirschfeld, G. & von Brachel, R. (2014). Improving Multiple-Group confirmatory factor analysis in R – A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19(7), 1-12. Available online: http://pareonline.net/getvn.asp?v=19&n=7
Hu, L., & Bentler, P., M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55. https://doi.org/10.1080/10705519909540118
Jovanović, V., Gavrilov-Jerković, V., Žuljević, D. i Brdarić, D. (2014). Psihometrijska evaluacija Skale depresivnosti, anksioznosti i stresa – 21 (DAS–21) na uzorku studenata u Srbiji. Psihologija, 47, 93–112. https://doi.org/10.2298/PSI1401093J
Kenny, D. A., Kaniskan, B., & McCoach, D. B. (2014). The Performance of RMSEA in Models With Small Degrees of Freedom. Sociological Methods & Research, 44(3), 486–507. https://doi.org/10.1177/0049124114543236
Kline, R. B. (2010). Principles and practice of structural equation modeling. Guilford.
Lovibond, S. H., Lovibond, P. F. (1995). Manual for the Depression Anxiety Stress Scales (2nd ed.). Psychology Foundation of Australia.
Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58(4), 525–543. https://doi.org/10.1007/bf02294825
Milfont, T. L., & Fischer, R. (2010). Testing measurement invariance across groups: Applications in cross-cultural research. International Journal of Psychological Research, 3(1), 111-130. https://doi.org/10.21500/20112084.857
Newsom, J. T. (2015). Longitudinal Structural Equation Modeling: A Comprehensive Introduction. Routledge.
Raykov, T., & Amemiya, Y. (2008). Testing Time-Invariance of Variable Specificity in Repeated Measure Designs Using Structural Equation Modeling. Structural Equation Modeling: A Multidisciplinary Journal, 15(3), 449–461. https://doi.org/10.1080/10705510802154315
Raykov, T. & Marcoulides, G. A. (2006). A First Course in Structural Equation Modeling (2nd edition). Mahwah, NJ: Lawrence Erlbaum. https://doi.org/10.4324/9780203930687
Rosseel, Y. (2017). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. URL: http://www.jstatsoft.org/v48/i02/.
RStudio Team (2017). RStudio: Integrated Development for R. RStudio, Inc., Boston, MA. URL: http://www.rstudio.com/.
Vandenberg, R. J., & Lance, C. E. (2000). A Review and Synthesis of the Measurement Invariance Literature: Suggestions, Practices, and Recommendations for Organizational Research. Organizational Research Methods, 3(1), 4–70. https://doi.org/10.1177/109442810031002
Widaman, K. F., Ferrer, E., & Conger, R. D. (2010). Factorial Invariance Within Longitudinal Structural Equation Models: Measuring the Same Construct Across Time. Child Development Perspectives, 4(1), 10–18. https://doi.org/10.1111/j.1750-8606.2009.00110.x
Widaman, K. F., & Reise, S. P. (1997). Exploring the measurement invariance of psychological instruments: Applications in the substance use domain. The Science of Prevention: Methodological Advances from Alcohol and Substance Abuse Research, 281–324. https://doi.org/10.1037/10222-009
Carmines, E. G., & McIver, J. D. (1981). Analyzing models with unobserved variables: Analysis of covariance structures. U G. W. Bohinstedt & E. F. Borgatta (Eds.), Social measurement: Current issues (pp. 65 - 115). Sage.
Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling, 14(3), 464–504. https://doi.org/10.1207/s15328007sem0902_5
Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling, 9(2), 233–255.
Chungkham, H. S., Ingre, M., Karasek, R., Westerlund, H., & Theorell, T. (2013). Factor Structure and Longitudinal Measurement Invariance of the Demand Control Support Model: An Evidence from the Swedish Longitudinal Occupational Survey of Health (SLOSH). PLoS ONE 8(8): e70541. https://doi.org/10.1371/journal.pone.0070541
Hirschfeld, G. & von Brachel, R. (2014). Improving Multiple-Group confirmatory factor analysis in R – A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19(7), 1-12. Available online: http://pareonline.net/getvn.asp?v=19&n=7
Hu, L., & Bentler, P., M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55. https://doi.org/10.1080/10705519909540118
Jovanović, V., Gavrilov-Jerković, V., Žuljević, D. i Brdarić, D. (2014). Psihometrijska evaluacija Skale depresivnosti, anksioznosti i stresa – 21 (DAS–21) na uzorku studenata u Srbiji. Psihologija, 47, 93–112. https://doi.org/10.2298/PSI1401093J
Kenny, D. A., Kaniskan, B., & McCoach, D. B. (2014). The Performance of RMSEA in Models With Small Degrees of Freedom. Sociological Methods & Research, 44(3), 486–507. https://doi.org/10.1177/0049124114543236
Kline, R. B. (2010). Principles and practice of structural equation modeling. Guilford.
Lovibond, S. H., Lovibond, P. F. (1995). Manual for the Depression Anxiety Stress Scales (2nd ed.). Psychology Foundation of Australia.
Meredith, W. (1993). Measurement invariance, factor analysis and factorial invariance. Psychometrika, 58(4), 525–543. https://doi.org/10.1007/bf02294825
Milfont, T. L., & Fischer, R. (2010). Testing measurement invariance across groups: Applications in cross-cultural research. International Journal of Psychological Research, 3(1), 111-130. https://doi.org/10.21500/20112084.857
Newsom, J. T. (2015). Longitudinal Structural Equation Modeling: A Comprehensive Introduction. Routledge.
Raykov, T., & Amemiya, Y. (2008). Testing Time-Invariance of Variable Specificity in Repeated Measure Designs Using Structural Equation Modeling. Structural Equation Modeling: A Multidisciplinary Journal, 15(3), 449–461. https://doi.org/10.1080/10705510802154315
Raykov, T. & Marcoulides, G. A. (2006). A First Course in Structural Equation Modeling (2nd edition). Mahwah, NJ: Lawrence Erlbaum. https://doi.org/10.4324/9780203930687
Rosseel, Y. (2017). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. URL: http://www.jstatsoft.org/v48/i02/.
RStudio Team (2017). RStudio: Integrated Development for R. RStudio, Inc., Boston, MA. URL: http://www.rstudio.com/.
Vandenberg, R. J., & Lance, C. E. (2000). A Review and Synthesis of the Measurement Invariance Literature: Suggestions, Practices, and Recommendations for Organizational Research. Organizational Research Methods, 3(1), 4–70. https://doi.org/10.1177/109442810031002
Widaman, K. F., Ferrer, E., & Conger, R. D. (2010). Factorial Invariance Within Longitudinal Structural Equation Models: Measuring the Same Construct Across Time. Child Development Perspectives, 4(1), 10–18. https://doi.org/10.1111/j.1750-8606.2009.00110.x
Widaman, K. F., & Reise, S. P. (1997). Exploring the measurement invariance of psychological instruments: Applications in the substance use domain. The Science of Prevention: Methodological Advances from Alcohol and Substance Abuse Research, 281–324. https://doi.org/10.1037/10222-009
Published
2022/03/30
Section
Professional Paper
Autori koji objavljuju u ovom časopisu pristaju na sledeće uslove:
- Autori zadržavaju autorska prava i pružaju časopisu pravo prvog objavljivanja rada i licenciraju ga "Creative Commons Attribution licencom" koja omogućava drugima da dele rad, uz uslov navođenja autorstva i izvornog objavljivanja u ovom časopisu.
- Autori mogu izraditi zasebne, ugovorne aranžmane za neekskluzivnu distribuciju članka objavljenog u časopisu (npr. postavljanje u institucionalni repozitorijum ili objavljivanje u knjizi), uz navođenje da je članak izvorno objavljen u ovom časopisu.
- Autorima je dozvoljeno i podstiču se da postave objavljeni članak onlajn (npr. u institucionalni repozitorijum ili na svoju internet stranicu) pre ili tokom postupka prijave rukopisa, s obzirom da takav postupak može voditi produktivnoj razmeni ideja i ranijoj i većoj citiranosti objavljenog članka (Vidi Efekti otvorenog pristupa).