Factor Analysis: Confirmatory

Introduction

Fundamental to the factor analytic model is that some variables of theoretical interest cannot be directly observed; these unobserved variables are termed latent variables, or factors. Although latent variables cannot be directly observed, information related to them can be obtained indirectly by noting their effects on observed variables believed to represent them. The oldest and best-known statistical procedure for investigating relations between sets of observed and latent variables is that of factor analysis. In using this approach to data analyses, researchers examine the covariation among a set of observed variables in order to gather information on the latent constructs (or factors) that underlie them. Because factor analysis is concerned with the extent to which the observed variables are generated by the underlying latent constructs, strength of the regression paths from the factors to the observed variables (i.e. the factor loadings) are of primary interest.

There are two basic types of factor analyses: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). EFA is most appropriately used when the links between the observed variables and their underlying factors are unknown or uncertain. It is considered to be exploratory in the sense that the researcher has no prior knowledge that the observed variables do, indeed, measure the intended factors. In contrast, CFA is appropriately used when the researcher has some knowledge of the underlying latent variable structure. Based on theory and/or empirical research, he or she postulates relations between the observed measures and the underlying factors a priori, and then tests this hypothesized structure statistically. More specifically, the CFA approach examines the extent to which a highly constrained a priori factor structure is consistent with the sample data.

Of the two factor analytic approaches, CFA is by far the more rigorous procedure. Indeed, it enables the researcher to overcome many limitations associated with the EFA model; these are as follows: first, whereas the EFA model assumes that all common factors are either correlated, or that they are uncorrelated, the CFA model makes no such assumptions. Rather, the researcher specifies, a priori, only those factor correlations that are considered to be substantively meaningful. Second, with the EFA model, all observed variables are directly influenced by all common factors. With CFA, each factor influences only those observed variables with which it is purported to be linked. Third, although each observed variable has associated with it a unique factor that comprises random as well as systematic error, the EFA model is incapable of taking this measurement error into account. The CFA model, on the other hand, allows for the quantification of this measurement error. Fourth, whereas in EFA the unique factors are assumed to be uncorrelated, in CFA specified covariation among particular uniquenesses can be tapped. Finally, provided with a malfitting model in [Page 400]EFA, there is no mechanism for identifying which areas of the model are contributing most to the misfit. In CFA, on the other hand, the researcher is guided to a more appropriately specified model via indices of misfit provided by the statistical program.

Given the a priori knowledge of a factor structure and the testing of this factor structure based on the analysis of covariance structures, CFA belongs to a class of methodology known as structural equation modelling (SEM). The term structural equation modelling conveys two important notions: (a) that structural relations can be modelled pictorially to enable a clearer conceptualization of the theory under study, and (b) that the causal processes under study are represented by a series of structural (i.e. regression) equations. The hypothesized model can then be tested statistically in a simultaneous analysis of the entire system of variables to determine the extent to which it is consistent with the data. If goodness-of-fit is adequate, the model argues for the plausibility of postulated relations among variables; if it is inadequate, the tenability of such relations is rejected.

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