Imaginary latent variables: Empirical testing for detecting deficiency in reflective measures
Yıl 2024,
Cilt: 11 Sayı: 4, 721 - 732, 15.11.2024
Marco Vassallo
Öz
Imaginary latent variables are variables with negative variances and have been used to implement constraints in measurement models. This article aimed to advance this practice and rationalize the imaginary latent variables as a method to detect possible latent deficiencies in measurement models. This rationale is based on the theory of complex numbers used in the measurement process of common factor model–based structural equation modeling. Modeling an imaginary latent variable produces a potential deficiency within its relative reflective measures through a considerable reduction in common variance indicating the most affected indicator(s).
Kaynakça
- Bentler, P.M., & Lee, S.Y. (1983). Covariance structures under polynomial constraints: Applications to correlation and alpha-type structural models. Journal of Educational Statistics, 8, 207–222. https://doi.org/10.2307/1164760
- Bollen, K.A. (1989). Structural equations with latent variables. New York NY, USA: Wiley Press.
- Bollen, K.A., & Diamantopoulos, A. (2015). In defense of causal–formative indicators: A minority report. Psychological Methods. Advance online publication. http://dx.doi.org/10.1037/met0000056
- Bollen, K.A., Lilly, A.G., & Luo, L. (2022). Selecting scaling ındicators in structural equation models (SEMs). Psychological Methods, Advance online publication. http://dx.doi.org/10.1037/met0000530
- Brown, T.A. (2006). Confirmatory factor analysis for applied research. New York NY, USA: The Guilford Press.
- ESS Round 10: European Social Survey. (2022). ESS-10 2020 Documentation Report. Edition 1.0. Bergen, European Social Survey Data Archive, Sikt - Norwegian Agency for Shared Services in Education and Research for ESS ERIC, Norway. https://doi:10.21338/NSD-ESS10-2020
- ESS Round 10: European Social Survey Round 10 Data. (2020). Data file edition 1.2. Sikt - Norwegian Agency for Shared Services in Education and Research, Norway – Data Archive and distributor of ESS data for ESS ERIC, Norway. https://doi:10.21338/NSD-ESS10-2020
- Fabricar, L.R., Wegener, D.T., MacCallum, R.C., & Strahan, E.J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4, 272-299. https://doi.org/10.1037/1082-989X.4.3.272
- Fan, Y., Chen, J., Shirkey, G., John, R., Wu, S.R., Park, H., & Shao, C. (2016). Applications of structural equation modeling (SEM) in ecological studies: An updated review. Ecological Processes, 5(19). https://doi.org/10.1186/s13717-016-0063-3
- Finney, S.J., & DiStefano, C. (2013). Non-normal and categorical data in structural equation modeling. In G.R. Hancock & R.O. Mueller (Eds.), Structural Equation Modeling: A Second Course (2nd ed., pp. 439-492). Greenwich, CT, Information Age Publishing.
- Hair, J.F., Sarstedt, M., Ringle, C.M., & Gudergan, S.P. (2018). Advanced Issues in Partial Least Squares Structural Equation Modeling. Thousand Oaks, CA, USA: Sage.
- Hancock, G.R., Stapleton, L.M., & Arnold-Berkovits, I. (2009). The tenuousness of invariance tests within multi-sample covariance and mean structure models. In T. Teo & M.S. Khine (Eds.), Structural Equation Modeling in Educational Research: Concepts and Applications (pp. 137-174). Rotterdam, Netherlands: Sense Publishers.
- Hu, L., & Bentler, P.M. (1999). Cutoff criteria for fit ındexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling Multidisciplinary Journal, 6, 1–55. https://doi.org/10.1080/10705519909540118
- Jöreskog, K.G. (1966). Testing a simple structure hypothesis in factor analysis. Psychometrika, 31, 165-178. https://doi.org/10.1007/BF02289505
- Jöreskog, K.G., & Goldberger, A.S. (1975). Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of American Statistical Association, 70, 631-639. https://doi.org/10.2307/2285946
- Jöreskog, K.G., & Sörbom, D. (2017). LISREL 9.30 for Windows. [Computer software manual]. Scientific Software Skokie, IL, USA: International Inc.
- Kline, B.R. (2011). Principles and Practice of Structural Equation Modeling, 3rd ed. New York, NY, USA: The Guilford Press.
- Lord, F.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading MA, USA: Addison-Wesley press.
- Muthén, L.K., & Muthén, B.O. (1998-2017). Mplus User’s Guide. Eighth Edition. [Computer software manual]. Los Angeles, CA: Muthén & Muthén.
- R Core Team. (2014). R: A language and environment for statistical computing. [Computer software manual]. http://www.R-project.org/
- Rindskopf, D. (1984). Using phantom and imaginary latent variables to parameterize constraints in linear structural models. Psychometrika, 49, 37 47. https://doi.org/10.1007/BF02294204
- 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/
- Schermelleh-Engel, K., Moosbruger, H., & Müller, H. (2003). Evaluating the fit of structural equation models: Tests of significance and descriptive-of-fit measures. Methods of Psychological Research, 8, 23–74. https://doi.org/10.23668/psycharchives.12784
- Schwartz, S.H. (1992). Universals in the content and structure of values: Theoretical advance and empirical tests in 20 countries. Advances in Experimental Social Psychology, 25, 1-65.
- Schwartz, S.H. (2004). Basic human values: Their content and structure across countries. In A. Tamayo & J. Porto (Eds.). Valores e Trabalho (Values and Work). Brasilia, Brasile: Editora Universidade de Brasilia.
- Schwartz, S.H., Melech, G., Lehman, A., Burgess, S., Harris, M., & Owens, V. (2001). Extending the cross-cultural validity of the theory of basic human values with a different method of measurement. Journal of Cross Cultural Psychology, 32, 519-542. https://doi.org/10.1177/0022022101032005001
- Thurstone, L.L. (1947). Multiple-factor analysis. Chicago, USA: University of Chicago Press.
- Weisstein, E.W. (2023). Argand Diagram. From MathWorld [A Wolfram Web Resource]. https://mathworld.wolfram.com/ArgandDiagram.html
Imaginary latent variables: Empirical testing for detecting deficiency in reflective measures
Yıl 2024,
Cilt: 11 Sayı: 4, 721 - 732, 15.11.2024
Marco Vassallo
Öz
Imaginary latent variables are variables with negative variances and have been used to implement constraints in measurement models. This article aimed to advance this practice and rationalize the imaginary latent variables as a method to detect possible latent deficiencies in measurement models. This rationale is based on the theory of complex numbers used in the measurement process of common factor model–based structural equation modeling. Modeling an imaginary latent variable produces a potential deficiency within its relative reflective measures through a considerable reduction in common variance indicating the most affected indicator(s).
Kaynakça
- Bentler, P.M., & Lee, S.Y. (1983). Covariance structures under polynomial constraints: Applications to correlation and alpha-type structural models. Journal of Educational Statistics, 8, 207–222. https://doi.org/10.2307/1164760
- Bollen, K.A. (1989). Structural equations with latent variables. New York NY, USA: Wiley Press.
- Bollen, K.A., & Diamantopoulos, A. (2015). In defense of causal–formative indicators: A minority report. Psychological Methods. Advance online publication. http://dx.doi.org/10.1037/met0000056
- Bollen, K.A., Lilly, A.G., & Luo, L. (2022). Selecting scaling ındicators in structural equation models (SEMs). Psychological Methods, Advance online publication. http://dx.doi.org/10.1037/met0000530
- Brown, T.A. (2006). Confirmatory factor analysis for applied research. New York NY, USA: The Guilford Press.
- ESS Round 10: European Social Survey. (2022). ESS-10 2020 Documentation Report. Edition 1.0. Bergen, European Social Survey Data Archive, Sikt - Norwegian Agency for Shared Services in Education and Research for ESS ERIC, Norway. https://doi:10.21338/NSD-ESS10-2020
- ESS Round 10: European Social Survey Round 10 Data. (2020). Data file edition 1.2. Sikt - Norwegian Agency for Shared Services in Education and Research, Norway – Data Archive and distributor of ESS data for ESS ERIC, Norway. https://doi:10.21338/NSD-ESS10-2020
- Fabricar, L.R., Wegener, D.T., MacCallum, R.C., & Strahan, E.J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4, 272-299. https://doi.org/10.1037/1082-989X.4.3.272
- Fan, Y., Chen, J., Shirkey, G., John, R., Wu, S.R., Park, H., & Shao, C. (2016). Applications of structural equation modeling (SEM) in ecological studies: An updated review. Ecological Processes, 5(19). https://doi.org/10.1186/s13717-016-0063-3
- Finney, S.J., & DiStefano, C. (2013). Non-normal and categorical data in structural equation modeling. In G.R. Hancock & R.O. Mueller (Eds.), Structural Equation Modeling: A Second Course (2nd ed., pp. 439-492). Greenwich, CT, Information Age Publishing.
- Hair, J.F., Sarstedt, M., Ringle, C.M., & Gudergan, S.P. (2018). Advanced Issues in Partial Least Squares Structural Equation Modeling. Thousand Oaks, CA, USA: Sage.
- Hancock, G.R., Stapleton, L.M., & Arnold-Berkovits, I. (2009). The tenuousness of invariance tests within multi-sample covariance and mean structure models. In T. Teo & M.S. Khine (Eds.), Structural Equation Modeling in Educational Research: Concepts and Applications (pp. 137-174). Rotterdam, Netherlands: Sense Publishers.
- Hu, L., & Bentler, P.M. (1999). Cutoff criteria for fit ındexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling Multidisciplinary Journal, 6, 1–55. https://doi.org/10.1080/10705519909540118
- Jöreskog, K.G. (1966). Testing a simple structure hypothesis in factor analysis. Psychometrika, 31, 165-178. https://doi.org/10.1007/BF02289505
- Jöreskog, K.G., & Goldberger, A.S. (1975). Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of American Statistical Association, 70, 631-639. https://doi.org/10.2307/2285946
- Jöreskog, K.G., & Sörbom, D. (2017). LISREL 9.30 for Windows. [Computer software manual]. Scientific Software Skokie, IL, USA: International Inc.
- Kline, B.R. (2011). Principles and Practice of Structural Equation Modeling, 3rd ed. New York, NY, USA: The Guilford Press.
- Lord, F.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading MA, USA: Addison-Wesley press.
- Muthén, L.K., & Muthén, B.O. (1998-2017). Mplus User’s Guide. Eighth Edition. [Computer software manual]. Los Angeles, CA: Muthén & Muthén.
- R Core Team. (2014). R: A language and environment for statistical computing. [Computer software manual]. http://www.R-project.org/
- Rindskopf, D. (1984). Using phantom and imaginary latent variables to parameterize constraints in linear structural models. Psychometrika, 49, 37 47. https://doi.org/10.1007/BF02294204
- 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/
- Schermelleh-Engel, K., Moosbruger, H., & Müller, H. (2003). Evaluating the fit of structural equation models: Tests of significance and descriptive-of-fit measures. Methods of Psychological Research, 8, 23–74. https://doi.org/10.23668/psycharchives.12784
- Schwartz, S.H. (1992). Universals in the content and structure of values: Theoretical advance and empirical tests in 20 countries. Advances in Experimental Social Psychology, 25, 1-65.
- Schwartz, S.H. (2004). Basic human values: Their content and structure across countries. In A. Tamayo & J. Porto (Eds.). Valores e Trabalho (Values and Work). Brasilia, Brasile: Editora Universidade de Brasilia.
- Schwartz, S.H., Melech, G., Lehman, A., Burgess, S., Harris, M., & Owens, V. (2001). Extending the cross-cultural validity of the theory of basic human values with a different method of measurement. Journal of Cross Cultural Psychology, 32, 519-542. https://doi.org/10.1177/0022022101032005001
- Thurstone, L.L. (1947). Multiple-factor analysis. Chicago, USA: University of Chicago Press.
- Weisstein, E.W. (2023). Argand Diagram. From MathWorld [A Wolfram Web Resource]. https://mathworld.wolfram.com/ArgandDiagram.html