The determinacy of the regression factor score predictor based on continuous parameter estimates from categorical variables

ABSTRACT

The estimation of population parameters of the continuous common factor model from categorical observed variables is meanwhile regularly performed. It is shown that the formula for the calculation of the determinacy of the regression factor score predictor from the estimated model parameters has to be adapted under these conditions. A method for the calculation of this determinacy from the model parameters of the continuous population factor model based on categorical variables is proposed and evaluated by means of simulated population data. It turns out that using the uncorrected formula can lead to serious overestimation of determinacy for categorical variables.

KEYWORDS:

• Categorical variables
• Determinacy
• Factor score predictor

MATHEMATICS SUBJECT CLASSIFICATION:

• 62H25

Notes

1 Factor score determinacy means that the scores of the common and error factors are not completely determinate as long as none of the error variances vanishes and the number of observed variables is finite (Schönemann, 1971). Thus, different degrees of determinacy occur depending on the size of the error variances and the number of variables.