Hypothesis Testing Using Factor Score Regression: A Comparison of Four Methods

Abstract

In this article, an overview is given of four methods to perform factor score regression (FSR), namely regression FSR, Bartlett FSR, the bias avoiding method of Skrondal and Laake, and the bias correcting method of Croon. The bias correcting method is extended to include a reliable standard error. The four methods are compared with each other and with structural equation modeling (SEM) by using analytic calculations and two Monte Carlo simulation studies to examine their finite sample characteristics. Several performance criteria are used, such as the bias using the unstandardized and standardized parameterization, efficiency, mean square error, standard error bias, type I error rate, and power. The results show that the bias correcting method, with the newly developed standard error, is the only suitable alternative for SEM. While it has a higher standard error bias than SEM, it has a comparable bias, efficiency, mean square error, power, and type I error rate.

Keywords: bias; factor score regression; standard error; standardized parameterization; unstandardized parameterization.

Conflict of interest statement

Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figures

Figure 1.

The four scenarios considered.

Figure 2.

The population model.

Figure 3.

Bias. (A) The influence of sample size, coefficients of determination (CD), number of items, and the value of γ on the bias, in interaction with the method. (B) The influence of sample size, coefficient of determination, number of items, and the value of γ on the bias, in interaction with the method, when the data are not normally distributed.

Figure 4.

Bias using the standardized parameterization. (A) The influence of sample size, coefficients of determination (CD), number of items, and the value of γ on the bias using the standardized parameterization, in interaction with the method. (B) The influence of sample size, coefficients of determination (CD), number of items, and the value of γ on the bias using the standardized parameterization, in interaction with the method, in interaction with the method, when the data are not normally distributed.

Figure 5.

Standard error bias. (A) The influence of sample size, coefficients of determination, number of items, and the value of γ on the standard error bias, in interaction with the method. (B) The influence of sample size, coefficients of determination, number of items, and the value of γ on the standard error bias, in interaction with the method, in interaction with the method, when the data are not normally distributed. Note that the scale of the y-axis is not the same as in (A).