Comparación entre modelos de datos multinivel a través de ecuaciones estructurales con estimación bayesiana y pequeñas varianzas a priori en las cargas factoriales cruzadas
Fecha
2020-11-09
Tipo
tesis de maestría
Autores
Fernández Arauz, Andrés Felipe
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Resumen
Debido a las bondades del enfoque Bayesiano para la estimación de modelos de ecuaciones estructurales, en la última década se ha desarrollado un nuevo enfoque con la intención de producir un análisis que refleje de una mejor manera las teorías del investigador y sus creencias a priori. Esto se hace al utilizar sistemáticamente distribuciones a priori informativas para los parámetros que no deberían ser estimados libremente de acuerdo con la teoría del investigador. En el análisis frecuentista tales parámetros son fijados como iguales a cero, pero fueran liberados y debieran ser estimados el modelo presentaría problemas de identificación y de estimación. Mediante el enfoque Bayesiano, por el contrario, se logra la identificación del modelo al impulsar el uso de varianzas a priori muy pequeñas para estos parámetros.
Si bien es reciente la discusión sobre el uso de varianzas pequeñas en las distribuciones a priori de parámetros que usualmente son fijados a ser cero, nada ha sido discutido acerca de las implicaciones de su aplicación en el contexto de ecuaciones estructurales para datos jerárquicos o multinivel. Por tales motivos, la presente investigación aborda esta discusión en el contexto de modelos de ecuaciones estructurales para datos multinivel con estimación Bayesiana al plantear modelos en los que fue liberada la estimación de parámetros en las cargas factoriales cruzadas. Para hacer esto, fueron establecidos tres niveles de información a introducir en la varianza de las cargas factoriales cruzadas: poco informativa, débilmente informativa e informativa.
El estudio de simulación permitió mostrar que, en el nivel inferior (o dentro de grupos) el uso de distribuciones a priori informativas en las cargas factoriales cruzadas mejora la precisión con la que son estimados los parámetros principales. En el nivel superior jerárquico (o entre grupos), a nivel general la estimación Bayesiana con varianzas a priori informativas en las cargas factoriales cruzadas presenta resultados muy superiores a los de las demás condiciones de estimación.
El ajuste global del modelo al comparar el uso de distribuciones a priori débilmente informativas y difusas tiende a ser similar; sin embargo, se refuerza el hecho de que cuando se tienen pocos datos, un pequeño número de grupos y valores bajos del ICC, el uso de distribuciones a priori muy informativas en las cargas factoriales cruzadas sí produce mejores ajustes del modelo global.
Se puede afirmar que, de forma consistente, el uso de distribuciones a priori con varianza pequeña o muy informativa en las cargas factoriales cruzadas produce mejores resultados bajo distintas condiciones de estimación de los modelos de ecuaciones estructurales multinivel, por lo que esta investigación aporta evidencia para que este enfoque pueda ser replicado en otras investigaciones que busquen obtener ganancias en la estimación de modelos de ecuaciones estructurales para datos multinivel con enfoque Bayesiano
In the last decade, the use of very small variance prior of cross-factor loadings has been discussed in the context of estimating confirmatory factor analysis models or structural equations with a Bayesian approach (Muthén, B., & Asparouhov, T , 2012, 2013) Traditionally, researches that relies on confirmatory factor analysis establish cross-factor loadings as equal to zero, meaning that the particular indicator has no relation to the latent factor or construct for which the factor load has been established as exactly equal to zero. However, the indicator variables are rarely perfectly pure construction indicators, especially in the study of social sciences, which implies that significant levels of association with multiple constructs can occur. In fact, in the reflexive logic of factor analysis, latent factors are those that have an influence on the indicators, rather than the other way around. This means that establishing small cross-loads reflects the influence of the factor on the relevant part of the construction of the indicators, rather than the indicators having an impact on the nature of the factor itself. For this reason, this research addresses this discussion in the context of Multilevel Bayesian Structural Equation Models (ML-BSEM) by proposing models in which the estimation of parameters in cross factor loadings will be released. Therefore, it is necessary to examine whether for this type of models the discussion described in the literature is maintained and if there are gains in the goodness of fit of the models by allowing that condition. This will be done by evaluating the possible effects on the parameter estimates, the hypothesis tests associated with them, as well as the tests of goodness of fit of models, which may vary according to the definition of the prior distributions of the cross loadings, from little informative or diffuse to very informative, in the context of estimating Multilevel Bayesian Structural Equation Models. For this, in addition, robustness will be analyzed for different scenarios in which hierarchical models can operate, such as different group sizes at the high level, different sample sizes in the low level groups and different intensities of the intraclass correlation. In general terms, the results show that the goodness of fit when comparing weakly informative priors and diffuse priors distributions for the cross-loadings tends to be similar, especially for large samples and ICC values; However, when there is little data, a small number of groups and low ICC values, the use of very informative prior distributions with small variance priors for the cross loadings does produce better fit.
In the last decade, the use of very small variance prior of cross-factor loadings has been discussed in the context of estimating confirmatory factor analysis models or structural equations with a Bayesian approach (Muthén, B., & Asparouhov, T , 2012, 2013) Traditionally, researches that relies on confirmatory factor analysis establish cross-factor loadings as equal to zero, meaning that the particular indicator has no relation to the latent factor or construct for which the factor load has been established as exactly equal to zero. However, the indicator variables are rarely perfectly pure construction indicators, especially in the study of social sciences, which implies that significant levels of association with multiple constructs can occur. In fact, in the reflexive logic of factor analysis, latent factors are those that have an influence on the indicators, rather than the other way around. This means that establishing small cross-loads reflects the influence of the factor on the relevant part of the construction of the indicators, rather than the indicators having an impact on the nature of the factor itself. For this reason, this research addresses this discussion in the context of Multilevel Bayesian Structural Equation Models (ML-BSEM) by proposing models in which the estimation of parameters in cross factor loadings will be released. Therefore, it is necessary to examine whether for this type of models the discussion described in the literature is maintained and if there are gains in the goodness of fit of the models by allowing that condition. This will be done by evaluating the possible effects on the parameter estimates, the hypothesis tests associated with them, as well as the tests of goodness of fit of models, which may vary according to the definition of the prior distributions of the cross loadings, from little informative or diffuse to very informative, in the context of estimating Multilevel Bayesian Structural Equation Models. For this, in addition, robustness will be analyzed for different scenarios in which hierarchical models can operate, such as different group sizes at the high level, different sample sizes in the low level groups and different intensities of the intraclass correlation. In general terms, the results show that the goodness of fit when comparing weakly informative priors and diffuse priors distributions for the cross-loadings tends to be similar, especially for large samples and ICC values; However, when there is little data, a small number of groups and low ICC values, the use of very informative prior distributions with small variance priors for the cross loadings does produce better fit.
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Palabras clave
Bayesiana, Multinivel, Distribución a priori, Ecuaciones Estructurales, PISA