Confirmatory Factor Analysis

Research in the social and behavioral sciences often focuses on the measurement of unobservable, theoretical constructs such as ability, anxiety, depression, intelligence, and motivation. Constructs are identified by directly observable, manifest variables generally referred to as indicator variables (note that indicator, observed, and manifest variables are often used interchangeably). Indicator variables can take many forms, including individual items or one or more composite scores constructed across multiple items. Many indicators are available for measuring a construct, and each may differ in how reliably it measures the construct. The choice of which indicator to use is based largely on availability. Traditional statistical techniques using single indicator measurement, such as regression analysis and path analysis, assume the indicator variable to be an error-free measure of the particular construct of interest. Such an assumption can lead to erroneous results.

Measurement error can be accounted for by the use of multiple indicators of each construct, thus creating a latent variable. This process is generally conducted in the framework of factor analysis, a multivariate statistical technique developed in the early to mid-1900s primarily for identifying and/or validating theoretical constructs. The general factor analysis model can be implemented in an exploratory or confirmatory framework. The exploratory framework, referred to as exploratory factor analysis (EFA), seeks to explain the relationships among the indicator variables through a given number of previously undefined latent variables. In contrast, the confirmatory framework, referred to as confirmatory factor analysis (CFA), uses latent variables to reproduce and test previously defined relationships between the indicator variables. The methods differ in their underlying purpose. Whereas EFA is a data-driven approach, CFA is a hypothesis driven approach requiring theoretically and/or empirically based insight into the relationships among the indicator variables. This insight is essential for establishing a starting point-for the specification of a model to be tested. What follows is a more detailed, theoretical discussion of the CFA model, the process of implementing the CFA model, and the manner and settings in which the CFA model is most commonly implemented.