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Robust confirmatory factor analysis based on the forward search algorithm

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Abstract

A key concept of the forward search algorithm in confirmatory factor analysis is ordering of the data on the basis of observational residuals. These residuals are computed under the proposed model and measure the discrepancy between the observed and predicted response for each unit of the sample. Regression-type factor scores are used to estimate model predictions. Informative forward plots are created for indexing influential observations and to show the dynamics of the estimates throughout the search. The detailed influence of each observation on the model parameters and fit indices is analyzed and a robust model inference is achieved. Real and simulated data sets with known contamination schemes are used to demonstrate the performance of the forward search algorithm.

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Notes

  1. CFI stands for comparative fit index. Similar to TLI, it compares the proposed model with the baseline model.

  2. These changes cannot be seen in the plots of Fig. 3.

  3. A linear regression of \(\widehat{\beta }_1\) on a constant and basic set size was used.

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Acknowledgments

The research was supported by the Slovenian Research agency. The author would like to thank Prof. Matjaž Omladič for tireless assistance and support during the conduct of this research and the preparation of this paper. Special thanks also go to the anonymous reviewers. Their comments and suggestions led to significant improvements to the initial manuscript.

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  1. Institute of Mathematics, Physics and Mechanics, Jadranska ulica 19, 1000 , Ljubljana, Slovenia

    Aleš Toman

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  1. Aleš Toman
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Correspondence to Aleš Toman.

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Toman, A. Robust confirmatory factor analysis based on the forward search algorithm. Stat Papers 55, 233–252 (2014). https://doi.org/10.1007/s00362-013-0525-y

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