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Effects of ignoring clustered data structures in factor analysis and item response theory

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In research, data for analysis come principally from two sources: directly from the respondents themselves and from interviewers/raters. In the latter case, clustering by interviewer/rater needs to be considered when performing analyses such as factor analysis or item response theory modelling (IRT), although it is usually ignored. We use simulated data to study the consequences of aggregated analysis (i.e., analysis ignoring clustering) on factor analytic estimates (both exploratory factor analysis (EFA) and confirmatory factor analysis (CFA)) and fit indices when the data are clustered.

Occasionally, certain aspects of the hierarchical information on clustering displayed by data are partly known (as in the case of clustering by patient service or treatment site, for example). However, information about the interviewers within each service is likely to be missing. In such cases, it might be better to consider using the available information to improve the quality of factor analytic estimates rather than completely ignoring the hierarchical structure of the data. We study the usefulness of this approach using simulated datasets. We also study the performance of different estimators – maximum likelihood, weighted least squares and Markov chain Monte Carlo – on factor analytic estimates when hierarchical clustering is ignored.

The results show that ignoring clustering in the data leads to serious underestimation of the factor loadings and item thresholds in ordinal IRT treatment of rating data. In addition, fit indices tend to show a poor fit for the candidate structural model. The Markov chain Monte Carlo (MCMC) estimator shows better robustness than the maximum likelihood and weighted least squares approaches. Partial information on clustering helps to correct (and may overcorrect) fit indices, but unfortunately, it does not improve the factor analytic model estimates themselves.

This talk is part of the Cambridge Psychometrics Centre Seminars series.

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