On the Relevance of Assumptions Associated with Classical Factor Analytic Approaches†

Daniel Kasper,Ali Ünlü

doi:10.3389/fpsyg.2013.00109

Abstract

A personal trait, for example a person’s cognitive ability, represents a theoretical concept postulated to explain behavior. Interesting constructs are latent, that is, they cannot be observed. Latent variable modeling constitutes a methodology to deal with hypothetical constructs. Constructs are modeled as random variables and become components of a statistical model. As random variables, they possess a probability distribution in the population of reference. In applications, this distribution is typically assumed to be the normal distribution. The normality assumption may be reasonable in many cases, but there are situations where it cannot be justified. For example, this is true for criterion-referenced tests or for background characteristics of students in large scale assessment studies. Nevertheless, the normal procedures in combination with the classical factor analytic methods are frequently pursued, despite the effects of violating this “implicit” assumption are not clear in general. In a simulation study, we investigate whether classical factor analytic approaches can be instrumental in estimating the factorial structure and properties of the population distribution of a latent personal trait from educational test data, when violations of classical assumptions as the aforementioned are present. The results indicate that having a latent non-normal distribution clearly affects the estimation of the distribution of the factor scores and properties thereof. Thus, when the population distribution of a personal trait is assumed to be non-symmetric, we recommend avoiding those factor analytic approaches for estimation of a person’s factor score, even though the number of extracted factors and the estimated loading matrix may not be strongly affected. An application to the Progress in International Reading Literacy Study (PIRLS) is given. Comments on possible implications for the Programme for International Student Assessment (PISA) complete the presentation.

Highlights

Educational research is concerned with the study of processes of learning and teaching
There are a number of latent variable models that may be used to analyze the factorial structure of a test – for generalized latent variable modeling covering a plethora of models as special cases of a much broader framework, see Bartholomew et al
This paper focuses on classical factor analytic approaches, and it examines how accurately different methods of classical factor analysis can estimate the factorial structure of test data, if assumptions associated with the classical approaches are not satisfied

Summary

Introduction

Educational research is concerned with the study of processes of learning and teaching. The investigated processes are not observable, and to unveil these, manifest human behavior in test situations is recorded. . .] is a routine procedure for the investigation of one or more empirically definable personality traits” (translated by the authors), and to satisfy a minimum of quality criteria, a test is required to be objective, reliable, and valid. In this paper we deal with factor analytic methods for assessing construct validity of a test, in the sense of its factorial validity (e.g., Cronbach and Meehl, 1955; Lienert and Raatz, 1998). There are a number of latent variable models that may be used to analyze the factorial structure of a test – for generalized latent variable modeling covering a plethora of models as special cases of a much broader framework, see Bartholomew et al

Methods

Results

Conclusion