On Modeling Missing Data in Structural Investigations Based on Tetrachoric Correlations With Free and Fixed Factor Loadings

In modeling missing data, the missing data latent variable of the confirmatory factor model accounts for systematic variation associated with missing data so that replacement of what is missing is not required. This study aimed at extending the modeling missing data approach to tetrachoric correlations as input and at exploring the consequences of switching between models with free and fixed factor loadings. In a simulation study, confirmatory factor analysis (CFA) models with and without a missing data latent variable were used for investigating the structure of data with and without missing data. In addition, the numbers of columns of data sets with missing data and the amount of missing data were varied. The root mean square error of approximation (RMSEA) results revealed that an additional missing data latent variable recovered the degree-of-model fit characterizing complete data when tetrachoric correlations served as input while comparative fit index (CFI) results showed overestimation of this degree-of-model fit. Whereas the results for fixed factor loadings were in line with the assumptions of modeling missing data, the other results showed only partial agreement. Therefore, modeling missing data with fixed factor loadings is recommended.

Automated summary

This study extends the modeling missing data approach to tetrachoric correlations and explores the consequences of switching between models with free and fixed factor loadings. Results show that an additional missing data latent variable can recover the degree-of-model fit characterizing complete data when tetrachoric correlations serve as input, but the comparative fit index may overestimate this degree-of-model fit. Therefore, modeling missing data with fixed factor loadings is recommended.