Does the Constraint of Factor Loadings Impair Model Fit and Accuracy in Parameter Estimation?

Karl Schweizer,Xuezhu Ren,Tengfei Wang,Florian Zeller

doi:10.5539/ijsp.v4n4p40

Abstract

The paper reports on the comparison of models of measurement with constrained and free factor loadings as part of confirmatory factor analysis in a simulation study. The comparison was conducted in order to find out whether constrained factor loadings that cause a reduced degree of adaptability to specificities of data mean a disadvantage in comparison to factor loadings that are freely estimated. Furthermore, the way of conducting the link transformation, the sample size and the number of variables were varied. The simulated data were dichotomous and constructed to conform to one underlying source of responding. The investigation of model fit and accuracy in estimating factor loadings yielded similar results for constrained and free factor loadings in confirmatory factor analysis. Furthermore, there were effects due to the type of link transformation and sample size.

Highlights

The item discriminability is a characteristic of the model of measurement and reflects the relationship between the item and the corresponding latent attribute (Lucke, 2005)
The paper reports on the comparison of models of measurement with constrained and free factor loadings as part of confirmatory factor analysis in a simulation study
Despite the lack of discriminability, the Rasch model and the corresponding one-parameter model have so far played a major role in research and application guided by item-response theory (IRT), while the consideration of the linear logistic test model has been more or less restricted to investigations of specific effects, as for example the effects of the item position, learning and fatigue (Kubinger, 2008)

Summary

Introduction

The item discriminability is a characteristic of the model of measurement and reflects the relationship between the item and the corresponding latent attribute (Lucke, 2005). The second way is due to the opportunity to modify the model of measurement in such a way that a link transformation is conducted (Schweizer, 2013; Schweizer & Reiss, 2014; Schweizer, Ren, & Wang, 2015) In this case probability-based covariances that are known as a pre-stage reached in computing the Phi coefficient (McDonald & Ahlawat, 1974) are recommended as input to confirmatory factor analysis in order to achieve interval scale. Of this manuscript a simulation study is reported It investigates whether constrained discriminability means an impairment of model fit and accuracy in parameter estimation (i.e., factor loadings) as compared to free discriminability if the data are dichotomous and the model is correct. Of potentially moderating factors, the type of the link transformation, the sample size and the number of variables are considered

The Simulation Study

Data Generation and Analysis

The Results of Investigating Model-data Fit

The Results of Investigating Accuracy in Parameter Estimation

Discussion