Abstract

A major characteristic of the threshold-free approach to the investigation of the structure of binary data is the step from binary to continuous by computing probabilities instead of estimating thresholds. Another characteristic is the consideration of the shift from the distribution of the binary data to the normal distribution of the latent variables at the level of variances and covariances. Two ways of relating the distributions are considered: standardization and modifying the assumed model of measurement accordingly. Furthermore, there is the consideration of the change in the proportion of true variance. A method for estimating the effect on the completely standardized factor loadings is proposed. In an example the various steps of this threshold-free approach of investigating the structure of binary data are demonstrated. A major advantage of this approach is the avoidance of estimating thresholds that requires especially large samples.

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