AUTHOR=Schweizer Karl , Gold Andreas , Krampen Dorothea 

TITLE=Effect of Dichotomization on the Latent Structure of Data

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=7

YEAR=2021

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2021.723258

DOI=10.3389/fams.2021.723258

ISSN=2297-4687

ABSTRACT=<p>We investigated whether dichotomous data showed the same latent structure as the interval-level data from which they originated. Given constancy of dimensionality and factor loadings reflecting the latent structure of data, the focus was on the variance of the latent variable of a confirmatory factor model. This variance was shown to summarize the information provided by the factor loadings. The results of a simulation study did not reveal exact correspondence of the variances of the latent variables derived from interval-level and dichotomous data but shrinkage. Since shrinkage occurred systematically, methods for recovering the original variance were fleshed out and evaluated.</p>