Confirmatory factor analysis (CFA) is a multivariate statistical procedure that is used to test how well the measured variables represent the number of constructs. Confirmatory factor analysis (CFA) and exploratory factor analysis (EFA) are similar techniques, but in exploratory factor analysis (EFA), data is simply explored and provides information about the numbers of factors required to represent the data. In exploratory factor analysis, all measured variables are related to every latent variable. But in confirmatory factor analysis (CFA), researchers can specify the number of factors required in the data and which measured variable is related to which latent variable. Confirmatory factor analysis (CFA) is a tool that is used to confirm or reject the measurement theory.
Terms and concepts in confirmatory factor analysis (CFA):
Theory: In confirmatory factor analysis (CFA), theory is a systematic set of casual relationships that provide the comprehensive explanation of a phenomenon.
Model: In confirmatory factor analysis (CFA), model is a specified set of dependant relationships that can be used to test the theory.
Path analysis: In confirmatory factor analysis (CFA), path analysis is used to test structural equations.
Path diagram: In confirmatory factor analysis (CFA), the path diagram shows the graphical representation of cause and effect relationships of the theory.
Endogenous variable: In confirmatory factor analysis (CFA), endogenous variables are the resulting variables that are a causal relationship.
Exogenous variable: In confirmatory factor analysis (CFA), exogenous variables are the predictor variables.
Confirmatory analysis: In confirmatory factor analysis (CFA), confirmatory analysis is used to test the pre-specified relationship.
Cronbach’s alpha: In confirmatory factor analysis (CFA), Cronbach’s alpha is used to measure the reliability of two or more construct indicators.
Identification: In confirmatory factor analysis (CFA), identification is used to test whether or not there are a sufficient number of equations to solve the unknown coefficient. In confirmatory factor analysis (CFA) identifications are of three types: (1) underidentified, (2) exact identified, and (3) over-identified.
Goodness of fit: In confirmatory factor analysis (CFA), goodness of fit is the degree to which the observed input matrix is predicted by the estimated model.
The following are the procedures involved in confirmatory factor analysis (CFA):
- Defining individual construct: In confirmatory factor analysis (CFA), first we have to define the individual constructs. In confirmatory factor analysis (CFA), the first step involves the procedure that defines constructs theoretically. This involves a pretest to evaluate the construct items, and a confirmatory test of the measurement model that is conducted using confirmatory factor analysis (CFA), etc.
- Developing the overall measurement model theory: In confirmatory factor analysis (CFA), we should consider the concept of unidimensionality between construct error variance and within construct error variance. At least four constructs and three items per constructs should be present in the research.
- Designing a study to produce the empirical results: In confirmatory factor analysis (CFA), the measurement model must be specified. In confirmatory factor analysis (CFA), most commonly, the value of one loading estimate should be one per construct. In confirmatory factor analysis (CFA), two methods are available for identification. The first is rank condition, and the second is order condition.
- Assessing the measurement model validity: In confirmatory factor analysis (CFA), assessing the measurement model validity occurs when the theoretical measurement model is compared with the reality model to see how well the data fits. In confirmatory factor analysis (CFA), to check the measurement model validity, the number of the indicator helps us. For example, in confirmatory factor analysis (CFA), the factor loading latent variable should be greater than 0.7. Chi-square test and other goodness of fit statistics like RMR, GFI, NFI, RMSEA, SIC, BIC, etc., are some key indicators that help in measuring the model validity in confirmatory factor analysis (CFA).
Confirmatory factor analysis (CFA) and statistical software: Usually, statistical software like AMOS, LISREL, EQS and SAS are used for confirmatory factor analysis (CFA). In AMOS, visual paths are manually drawn on the graphic window and analysis is performed. In confirmatory factor analysis (CFA) in LISREL, confirmatory factor analysis (CFA) can be performed graphically as well as from the menu. In SAS, confirmatory factor analysis (CFA) can be performed by using the programming languages.
