Approaches for structural investigations of binary data using confirmatory factor models

Schweizer, Karl; Reiss, Siegbert; Troche, Stefan (2018). Approaches for structural investigations of binary data using confirmatory factor models. International Journal of Statistics and Probability, 7(6), pp. 68-80. Canadian Center of Science and Education CCSE 10.5539/ijsp.v7n6p68

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An investigation of the suitability of threshold-based and threshold-free approaches for structural investigations of binary data is reported. Both approaches implicitly establish a relationship between binary data following the binomial distribution on one hand and continuous random variables assuming a normal distribution on the other hand. In two simulation studies we investigated: whether the fit results confirm the establishment of such a relationship, whether the differences between correct and incorrect models are retained and to what degree the sample size influences the results. Both approaches proved to establish the relationship. Using the threshold-free approach it was achieved by customary ML estimation whereas robust ML estimation was necessary in the threshold-based approach. Discrimination between correct and incorrect models was observed for both approaches. Larger CFI differences were found for the threshold-free approach than for the threshold-based approach. Dependency on sample size characterized the threshold-based approach but not the threshold-free approach. The threshold-based approach tended to perform better in large sample sizes, while the threshold-free approach performed better in smaller sample sizes.

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