Comparison of structural equation models with observed and latent variables: an application to the mediating role of disability in the impact of common conditions on perceived health

Abstract

Structural Equation Modeling (SEM) allows to study the simultaneous relationships among chronic conditions and perceived health mediated by disability dimensions. We hypothesized that considering some items as indicator variables of the underlying concept they describe (a latent variable) would provide more accurate estimates and better fit than using observed scores. Methods: Two Complex Disability Mediated Models CDMM-O (with all the variables Observed) and CDMM-L (with some Latent variables) were fitted in an epidemiological sample (n=24,797). SEM was used to estimate total, direct, and indirect effects of conditions on perceived health. Before comparing CDMM-O and CDMM-L in terms of parameter estimates, standard errors and model fit, a Confirmatory Factor Analysis (CFA) was conducted. Results: The CFA presented excellent fit (RMSEA=0.011, CFI=TLI=0.999). A better fit was observed for CDMM-L. Standard errors were lower for CDMM-L, and parameter estimates were more distinct among CDMM-O and CDMM-L than expected. CDMM-O presented inconsistent estimates. Conclusions: A model with latent variables is preferred.. This project aims at comparing two structural equation models, one with observed and the other with latent variables. The models will be fitted in an epidemiological database, and the mediating role of disability in the impact of common conditions on perceived health will be assessed. The latent variables will be defined by means of ordinal indicators. The comparison will be carried out evaluating model fit indices and the size of both model coefficients and standard errors. It is expected that the fit will be better and the standard errors lower for the latent model.