Treffer: When and how to use set-exploratory structural equation modelling to test structural models: A tutorial using the R package lavaan.
Title:
When and how to use set-exploratory structural equation modelling to test structural models: A tutorial using the R package lavaan.
Authors:
Marsh H; Institute of Positive Psychology and Education, Australian Catholic University, Sydney, New South Wales, Australia.; Department of Education, University of Oxford, Oxford, UK., Alamer A; Department of English, King Faisal University, Hofuf, Saudi Arabia.; The University of New South Wales (UNSW), Sydney, Australia.
Source:
The British journal of mathematical and statistical psychology [Br J Math Stat Psychol] 2024 Nov; Vol. 77 (3), pp. 459-476. Date of Electronic Publication: 2024 Feb 15.
Publication Type:
Journal Article; Research Support, Non-U.S. Gov't
Language:
English
Journal Info:
Publisher: Wiley-Blackwell Country of Publication: England NLM ID: 0004047 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 2044-8317 (Electronic) Linking ISSN: 00071102 NLM ISO Abbreviation: Br J Math Stat Psychol Subsets: MEDLINE
Imprint Name(s):
Publication: <2012-> : Chichester : Wiley-Blackwell
Original Publication: London : British Psychological Society
Original Publication: London : British Psychological Society
MeSH Terms:
References:
Alamer, A. (2021a). Construct validation of self‐determination theory in second language scale: The bifactor exploratory structural equation modeling approach. Frontiers in Psychology, 12, 732016. https://doi.org/10.3389/fpsyg.2021.732016.
Alamer, A. (2021b). Grit and language learning: Construct validation of L2‐grit scale and its relation to later vocabulary knowledge. Educational Psychology, 41, 544–562. https://doi.org/10.1080/01443410.2020.1867076.
Alamer, A. (2022). Exploratory structural equation modeling (ESEM) and bifactor ESEM for construct validation purposes: Guidelines and applied example. Research Methods in Applied Linguistics, 1, 100005. https://doi.org/10.1016/j.rmal.2022.100005.
Alamer, A., & Al Khateeb, A. (2023). Effects of using the WhatsApp application on language learners motivation: A controlled investigation using structural equation modelling. Computer Assisted Language Learning, 36, 149–175. https://doi.org/10.1080/09588221.2021.1903042.
Alamer, A., Al Khateeb, A., & Jeno, L. (2023). Using WhatsApp increases L2 students' self‐motivation and achievement, and decreases learning anxiety: A self‐determination theory approach. Journal of Computer Assisted Learning, 39, 417–431. https://doi.org/10.1111/jcal.12753.
Alamer, A., & Alrabai, F. (2023). The causal relationship between learner motivation and language achievement: New dynamic perspective. Applied Linguistics, 44, 148–168. https://doi.org/10.1093/applin/amac035.
Alamer, A., & Marsh, H. (2022). Exploratory structural equation modeling in second language research: An applied example using the dualistic model of passion. Studies in Second Language Acquisition, 44, 1477–1500. https://doi.org/10.1017/S0272263121000863.
Alamer, A., Morin, J. S. A., Alrabai, F., & Alharfi, A. (2023). Introducing the basic psychological needs frustration in second language scale (BPNF‐L2): Examining its factor structure and effect on L2 motivation and achievement. Acta Psychologica, 240, 104021. https://doi.org/10.1016/j.actpsy.2023.104021.
Asparouhov, T., & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 16, 397–438. https://doi.org/10.1080/10705510903008204.
Brosseau‐Liard, P. E., & Savalei, V. (2014). Adjusting incremental fit indices for nonnormality. Multivariate Behavioral Research, 49(5), 460–470. https://doi.org/10.1080/00273171.2014.933697.
Brosseau‐Liard, P. E., Savalei, V., & Li, L. (2012). An investigation of the sample performance of two nonnormality corrections for RMSEA. Multivariate Behavioral Research, 47(6), 904–930. https://doi.org/10.1080/00273171.2012.715252.
Dörnyei, Z., & Ryan, S. (2015). The psychology of the language learner revisited. Routledge.
Dörnyei, Z., & Ushioda, E. (2021). Teaching and researching motivation. Routledge.
Duckworth, A., Peterson, C., Matthews, M., & Kelly, D. (2007). Grit: Perseverance and passion for long‐term goals. Journal of Personality and Social Psychology, 92, 1087–1101. https://doi.org/10.1037/0022‐3514.92.6.1087.
Elahi Shrivan, M., & Alamer, A. (2022). Modeling the interplay of EFL learners' basic psychological needs, grit and L2 achievement. Journal of Multilingual and Multicultural Development, 1–17. https://doi.org/10.1080/01434632.2022.2075002.
Faraci, P., Bottaro, R., Nasonte, G., Valenti, G. D., & Craparo, G. (2023). A new short version of Internet Gaming Disorder‐20 (IGD‐20): An exploratory structural equation modeling. Clinical Neuropsychiatry, 20(3), 205–218.
Gegenfurtner, A. (2022). Bifactor exploratory structural equation modeling: A meta‐analytic review of model fit. Frontiers in Psychology, 13, 1037111. https://doi.org/10.3389/fpsyg.2022.1037111.
Guay, F., Morin, A. J. S., Litalien, D., Valois, P., & Vallerand, R. J. (2015). Application of exploratory structural equation modeling to evaluate the academic motivation scale. Journal of Experimental Education, 83, 51–82. https://doi.org/10.1080/00220973.2013.876231.
Horwood, M., Marsh, H. W., Parker, P. D., Riley, P., Guo, J., & Dicke, T. (2021). Burning passion, burning out: The passionate school principal, burnout, job satisfaction, and extending the dualistic model of passion. Journal of Educational Psychology, 113, 1668–1688. https://doi.org/10.1037/edu0000664.
Hu, L.‐T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1–55. https://doi.org/10.1080/10705519909540118.
Kruk, M., Pawlak, M., Shirvan, M. E., & Soleimanzadeh, S. (2023). Revisiting boredom in practical English language classes via exploratory structural equation modeling. Research Methods in Applied Linguistics, 2, 100038. https://doi.org/10.1016/j.rmal.2022.100038.
Liu, E., Wang, J., & Bai, S. (2022). Validation of L2 grit among Chinese EFL high school students and its enduring effect on achievements: A bifactor model approach. Frontiers in Psychology, 13, 971495. https://doi.org/10.3389/fpsyg.2022.971495.
Lounsbury, J. W., Saudargas, R. A., & Gibson, L. W. (2004). An investigation of personality traits in relation to intention to withdraw from college. Journal of College Student Development, 45(5), 517–534.
Mai, Y., Zhang, Z., & Wen, Z. (2018). Comparing Exploratory Structural Equation Modeling and Existing Approaches for Multiple Regression with Latent Variables. Structural Equation Modeling: A Multidisciplinary Journal, 25(5), 737–749. https://doi.org/10.1080/10705511.2018.1444993.
Marsh, H., Guo, J., Dicke, T., Parker, P. D., & Craven, R. G. (2020). Confirmatory factor analysis (CFA), exploratory structural equation modeling (ESEM), and set‐ESEM: Optimal balance between goodness of fit and parsimony. Multivariate Behavioral Research, 55, 102–119. https://doi.org/10.1080/00273171.2019.1602503.
Marsh, H., & Hau, K. (1996). Assessing goodness of fit: Is parsimony always desirable? Journal of Experimental Education, 64, 364–390. https://doi.org/10.1080/00220973.1996.10806604.
Marsh, H., Morin, A. J., Parker, P., & Kaur, G. (2014). Exploratory structural equation modeling: An integration of the best features of exploratory and confirmatory factor analysis. Annual Review of Clinical Psychology, 10, 85–110.
Marsh, H., Muthén, B., Asparouhov, T., Lüdtke, O., Robitzsch, A., Morin, A., & Trautwein, U. (2009). Exploratory structural equation modeling, integrating CFA and EFA: Application to students’ evaluations of university teaching. Structural Equation Modeling: A Multidisciplinary Journal, 16(3), 439–476. https://doi.org/10.1080/10705510903008220.
Morin, A. J. (2023). Exploratory structural equation modeling. In R. Hoyle (Ed.), Handbook of structural equation modeling (2nd ed.). Guilford.
Morin, A. J., Marsh, H., & Nagengast, B. (2013). Exploratory structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed., pp. 395–436). Information Age Publishing.
Noels, K. (2023). Self‐determination theory and language learning. In The Oxford handbook of self‐determination theory (pp. 619–637). Oxford University Press.
Ostrowska, S., O'Neill, R., Westbrook, C., Sowton, C., White, N. M., Dimond‐Bayir, S., Lansford, L., Pathare, E., & Pathare, G. (2021). Unlock. Cambridge University Press. https://www.cambridge.org/gb/cambridgeenglish/catalog/skills/unlock.
Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48, 1–36. https://doi.org/10.18637/jss.v048.i02.
Ryan, R., & Deci, E. (2017). Self‐determination theory: Basic psychological needs in motivation, development, and wellness. Guilford Publications.
Shao, K., Elahi Shirvan, M., & Alamer, A. (2022). How accurate is your correlation? Different methods derive different results and different interpretations. Frontiers in Psychology, 13, 901412. https://doi.org/10.3389/fpsyg.2022.901412.
Spearman, C. (1904). General intelligence’ objectively determined and measured. American. Journal of Psychology, 5, 201–293.
Swami, V., Maïano, C., & Morin, A. J. (2023). A guide to exploratory structural equation modeling (ESEM) and bifactor‐ESEM in body image research. Body Image, 47, 101641. https://doi.org/10.1016/j.bodyim.2023.101641.
Tabachnick, B. G., & Fidell, L. S. (2023). Using multivariate statistics (7th ed.). Pearson Education.
Thurstone, L. L. (1935). The vectors of the mind. University of Chicago Press.
Thurstone, L. L. (1947). Multiple factor analysis. University of Chicago Press.
Vallerand, R. (2015). The psychology of passion: A dualistic model. Oxford University Press.
Van Zyl, L. E., & ten Klooster, P. M. (2022). Exploratory structural equation modeling: Practical guidelines and tutorial with a convenient online tool for Mplus. Frontiers in Psychiatry, 12, 2397. https://doi.org/10.3389/fpsyt.2021.795672.
Woodrow, L. (2006). A model of adaptive language learning. Modern Language Journal, 90, 297–319.
Yuan, K.‐H., & Bentler, P. M. (2000). 5. Three likelihood‐based methods for mean and covariance structure analysis with nonnormal missing data. Sociological Methodology, 30(1), 165–200. https://doi.org/10.1111/0081‐1750.00078.
Alamer, A. (2021b). Grit and language learning: Construct validation of L2‐grit scale and its relation to later vocabulary knowledge. Educational Psychology, 41, 544–562. https://doi.org/10.1080/01443410.2020.1867076.
Alamer, A. (2022). Exploratory structural equation modeling (ESEM) and bifactor ESEM for construct validation purposes: Guidelines and applied example. Research Methods in Applied Linguistics, 1, 100005. https://doi.org/10.1016/j.rmal.2022.100005.
Alamer, A., & Al Khateeb, A. (2023). Effects of using the WhatsApp application on language learners motivation: A controlled investigation using structural equation modelling. Computer Assisted Language Learning, 36, 149–175. https://doi.org/10.1080/09588221.2021.1903042.
Alamer, A., Al Khateeb, A., & Jeno, L. (2023). Using WhatsApp increases L2 students' self‐motivation and achievement, and decreases learning anxiety: A self‐determination theory approach. Journal of Computer Assisted Learning, 39, 417–431. https://doi.org/10.1111/jcal.12753.
Alamer, A., & Alrabai, F. (2023). The causal relationship between learner motivation and language achievement: New dynamic perspective. Applied Linguistics, 44, 148–168. https://doi.org/10.1093/applin/amac035.
Alamer, A., & Marsh, H. (2022). Exploratory structural equation modeling in second language research: An applied example using the dualistic model of passion. Studies in Second Language Acquisition, 44, 1477–1500. https://doi.org/10.1017/S0272263121000863.
Alamer, A., Morin, J. S. A., Alrabai, F., & Alharfi, A. (2023). Introducing the basic psychological needs frustration in second language scale (BPNF‐L2): Examining its factor structure and effect on L2 motivation and achievement. Acta Psychologica, 240, 104021. https://doi.org/10.1016/j.actpsy.2023.104021.
Asparouhov, T., & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 16, 397–438. https://doi.org/10.1080/10705510903008204.
Brosseau‐Liard, P. E., & Savalei, V. (2014). Adjusting incremental fit indices for nonnormality. Multivariate Behavioral Research, 49(5), 460–470. https://doi.org/10.1080/00273171.2014.933697.
Brosseau‐Liard, P. E., Savalei, V., & Li, L. (2012). An investigation of the sample performance of two nonnormality corrections for RMSEA. Multivariate Behavioral Research, 47(6), 904–930. https://doi.org/10.1080/00273171.2012.715252.
Dörnyei, Z., & Ryan, S. (2015). The psychology of the language learner revisited. Routledge.
Dörnyei, Z., & Ushioda, E. (2021). Teaching and researching motivation. Routledge.
Duckworth, A., Peterson, C., Matthews, M., & Kelly, D. (2007). Grit: Perseverance and passion for long‐term goals. Journal of Personality and Social Psychology, 92, 1087–1101. https://doi.org/10.1037/0022‐3514.92.6.1087.
Elahi Shrivan, M., & Alamer, A. (2022). Modeling the interplay of EFL learners' basic psychological needs, grit and L2 achievement. Journal of Multilingual and Multicultural Development, 1–17. https://doi.org/10.1080/01434632.2022.2075002.
Faraci, P., Bottaro, R., Nasonte, G., Valenti, G. D., & Craparo, G. (2023). A new short version of Internet Gaming Disorder‐20 (IGD‐20): An exploratory structural equation modeling. Clinical Neuropsychiatry, 20(3), 205–218.
Gegenfurtner, A. (2022). Bifactor exploratory structural equation modeling: A meta‐analytic review of model fit. Frontiers in Psychology, 13, 1037111. https://doi.org/10.3389/fpsyg.2022.1037111.
Guay, F., Morin, A. J. S., Litalien, D., Valois, P., & Vallerand, R. J. (2015). Application of exploratory structural equation modeling to evaluate the academic motivation scale. Journal of Experimental Education, 83, 51–82. https://doi.org/10.1080/00220973.2013.876231.
Horwood, M., Marsh, H. W., Parker, P. D., Riley, P., Guo, J., & Dicke, T. (2021). Burning passion, burning out: The passionate school principal, burnout, job satisfaction, and extending the dualistic model of passion. Journal of Educational Psychology, 113, 1668–1688. https://doi.org/10.1037/edu0000664.
Hu, L.‐T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1–55. https://doi.org/10.1080/10705519909540118.
Kruk, M., Pawlak, M., Shirvan, M. E., & Soleimanzadeh, S. (2023). Revisiting boredom in practical English language classes via exploratory structural equation modeling. Research Methods in Applied Linguistics, 2, 100038. https://doi.org/10.1016/j.rmal.2022.100038.
Liu, E., Wang, J., & Bai, S. (2022). Validation of L2 grit among Chinese EFL high school students and its enduring effect on achievements: A bifactor model approach. Frontiers in Psychology, 13, 971495. https://doi.org/10.3389/fpsyg.2022.971495.
Lounsbury, J. W., Saudargas, R. A., & Gibson, L. W. (2004). An investigation of personality traits in relation to intention to withdraw from college. Journal of College Student Development, 45(5), 517–534.
Mai, Y., Zhang, Z., & Wen, Z. (2018). Comparing Exploratory Structural Equation Modeling and Existing Approaches for Multiple Regression with Latent Variables. Structural Equation Modeling: A Multidisciplinary Journal, 25(5), 737–749. https://doi.org/10.1080/10705511.2018.1444993.
Marsh, H., Guo, J., Dicke, T., Parker, P. D., & Craven, R. G. (2020). Confirmatory factor analysis (CFA), exploratory structural equation modeling (ESEM), and set‐ESEM: Optimal balance between goodness of fit and parsimony. Multivariate Behavioral Research, 55, 102–119. https://doi.org/10.1080/00273171.2019.1602503.
Marsh, H., & Hau, K. (1996). Assessing goodness of fit: Is parsimony always desirable? Journal of Experimental Education, 64, 364–390. https://doi.org/10.1080/00220973.1996.10806604.
Marsh, H., Morin, A. J., Parker, P., & Kaur, G. (2014). Exploratory structural equation modeling: An integration of the best features of exploratory and confirmatory factor analysis. Annual Review of Clinical Psychology, 10, 85–110.
Marsh, H., Muthén, B., Asparouhov, T., Lüdtke, O., Robitzsch, A., Morin, A., & Trautwein, U. (2009). Exploratory structural equation modeling, integrating CFA and EFA: Application to students’ evaluations of university teaching. Structural Equation Modeling: A Multidisciplinary Journal, 16(3), 439–476. https://doi.org/10.1080/10705510903008220.
Morin, A. J. (2023). Exploratory structural equation modeling. In R. Hoyle (Ed.), Handbook of structural equation modeling (2nd ed.). Guilford.
Morin, A. J., Marsh, H., & Nagengast, B. (2013). Exploratory structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (2nd ed., pp. 395–436). Information Age Publishing.
Noels, K. (2023). Self‐determination theory and language learning. In The Oxford handbook of self‐determination theory (pp. 619–637). Oxford University Press.
Ostrowska, S., O'Neill, R., Westbrook, C., Sowton, C., White, N. M., Dimond‐Bayir, S., Lansford, L., Pathare, E., & Pathare, G. (2021). Unlock. Cambridge University Press. https://www.cambridge.org/gb/cambridgeenglish/catalog/skills/unlock.
Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48, 1–36. https://doi.org/10.18637/jss.v048.i02.
Ryan, R., & Deci, E. (2017). Self‐determination theory: Basic psychological needs in motivation, development, and wellness. Guilford Publications.
Shao, K., Elahi Shirvan, M., & Alamer, A. (2022). How accurate is your correlation? Different methods derive different results and different interpretations. Frontiers in Psychology, 13, 901412. https://doi.org/10.3389/fpsyg.2022.901412.
Spearman, C. (1904). General intelligence’ objectively determined and measured. American. Journal of Psychology, 5, 201–293.
Swami, V., Maïano, C., & Morin, A. J. (2023). A guide to exploratory structural equation modeling (ESEM) and bifactor‐ESEM in body image research. Body Image, 47, 101641. https://doi.org/10.1016/j.bodyim.2023.101641.
Tabachnick, B. G., & Fidell, L. S. (2023). Using multivariate statistics (7th ed.). Pearson Education.
Thurstone, L. L. (1935). The vectors of the mind. University of Chicago Press.
Thurstone, L. L. (1947). Multiple factor analysis. University of Chicago Press.
Vallerand, R. (2015). The psychology of passion: A dualistic model. Oxford University Press.
Van Zyl, L. E., & ten Klooster, P. M. (2022). Exploratory structural equation modeling: Practical guidelines and tutorial with a convenient online tool for Mplus. Frontiers in Psychiatry, 12, 2397. https://doi.org/10.3389/fpsyt.2021.795672.
Woodrow, L. (2006). A model of adaptive language learning. Modern Language Journal, 90, 297–319.
Yuan, K.‐H., & Bentler, P. M. (2000). 5. Three likelihood‐based methods for mean and covariance structure analysis with nonnormal missing data. Sociological Methodology, 30(1), 165–200. https://doi.org/10.1111/0081‐1750.00078.
Grant Information:
5538 Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University
Contributed Indexing:
Keywords: basic psychological needs; confirmatory factor analysis (CFA); exploratory structural equation modelling (ESEM); motivation; set‐exploratory structural equation modelling (set‐ESEM); structural equation modelling (SEM)
Entry Date(s):
Date Created: 20240216 Date Completed: 20241008 Latest Revision: 20250702
Update Code:
20250703
DOI:
10.1111/bmsp.12336
PMID:
38361388
Database:
MEDLINE
Weitere Informationen
Exploratory structural equation modelling (ESEM) is an alternative to the well-known method of confirmatory factor analysis (CFA). ESEM is mainly used to assess the quality of measurement models of common factors but can be efficiently extended to test structural models. However, ESEM may not be the best option in some model specifications, especially when structural models are involved, because the full flexibility of ESEM could result in technical difficulties in model estimation. Thus, set-ESEM was developed to accommodate the balance between full-ESEM and CFA. In the present paper, we show examples where set-ESEM should be used rather than full-ESEM. Rather than relying on a simulation study, we provide two applied examples using real data that are included in the OSF repository. Additionally, we provide the code needed to run set-ESEM in the free R package lavaan to make the paper practical. Set-ESEM structural models outperform their CFA-based counterparts in terms of goodness of fit and realistic factor correlation, and hence path coefficients in the two empirical examples. In several instances, effects that were non-significant (i.e., attenuated) in the CFA-based structural model become larger and significant in the set-ESEM structural model, suggesting that set-ESEM models may generate more accurate model parameters and, hence, lower Type II error rate.
(© 2024 The Authors. British Journal of Mathematical and Statistical Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.)
Authors declare that there are no conflicts of interest.