Abstract
The paper reports an investigation on whether valid results can be achieved in analyzing the structure of datasets although a large percentage of data is missing without replacement. Two types of confirmatory factor analysis (CFA) models were employed for this purpose: the missing data CFA model with an additional latent variable for representing the missing data and the semi-hierarchical CFA model that also includes the additional latent variable and reflects the hierarchical structure assumed to underlie the data. Whereas, the missing data CFA model assumes that the model is equally valid for all participants, the semi-hierarchical CFA model is implicitly specified differently for subgroups of participants with and without omissions. The comparison of these models with the regular one-factor model in investigating simulated binary data revealed that the modeling of missing data prevented negative effects of missing data on model fit. The investigation of the accuracy in estimating the factor loadings yielded the best results for the semi-hierarchical CFA model. The average estimated factor loadings for items with and without omissions showed the expected equal sizes. But even this model tended to underestimate the expected values.
Highlights
The simulation study served the evaluation of the two described confirmatory factor analysis (CFA) models, the missing data CFA model and the semihierarchical CFA model, for investigating the structure of data generated according to an incomplete design
The deviations from expected value (EV) indicated that overestimation characterized the factor loadings of the one-factor CFA model whereas underestimation was characteristic of the factor loadings of the other models
One major problem with missing data is that we never know what would have been the responses that did not occur in the past and not found their way into the dataset
Summary
The simulation study served the evaluation of the two described CFA models, the missing data CFA model and the semihierarchical CFA model, for investigating the structure of data generated according to an incomplete design. Up to 25% of the entries of regular datasets of structured random data were turned into missing data for this investigation. There was variation of the number of columns showing missing data. The investigation focused on model fit and accuracy in estimating the sizes of factor loadings. The performance of the one-factor CFA model served as comparison level
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