Factor Analysis is a general name denoting a class of procedures primarily used for data reduction and summarization. In research, researchers extensively correlate a large number of variables and reduce them to a manageable level. They examine and represent the relationships among sets of many interrelated variables in terms of a few underlying factors. There are basically 2 approaches to Factor Analysis:
Exploratory Factor Analysis (EFA) seeks to uncover the underlying structure of a relatively large set of variables. The researcher assumes that any indicator may associate with any factor. This is the most common form of factor analysis. There is no prior theory and one uses factor loadings to intuit the factor structure of the data.
Confirmatory Factor Analysis (CFA) checks if the number of factors and loadings of indicator variables align with pre-established theory. Researchers select variables based on theory and use factor analysis to confirm if they load as predicted.
The basic difference between Exploratory Factor Analysis and CFA is that in CFA, a researcher’s a priori assumption is that each factor (the number and labels of which may be specified a priori) is associated with a specified subset of indicator variables. The major limitation behind Exploratory Factor Analysis is its simplicity. Hence, the researcher will not get a reliable inference. Therefore, researchers use Exploratory Factor Analysis less frequently compared to Confirmatory Factor Analysis.
Researchers use the following techniques in both approaches—Exploratory Factor Analysis and CFA:
Researchers use the Principal Component Technique in Exploratory Factor Analysis, where they consider the total variance in the data. They set the diagonal of the correlation matrix to unities and bring the full variance into the factor matrix. Researchers recommend the technique when their primary concern is determining the minimum number of factors that will account for the maximum variance in the data for use in subsequent multivariate analysis.
Researchers use several techniques, in addition to the Principal Component Technique, in Exploratory Factor Analysis and Confirmatory Factor Analysis, and these techniques are complex. They also call these techniques Extraction Methods. These techniques are as follows:
Image factoring: This technique in Exploratory Factor Analysis is based on the correlation matrix of predicted or dependent variables rather than actual variables. In this, we predict each variable from the others by using multiple regressions.
Maximum likelihood factoring(MLF): This technique in Exploratory Factor Analysis is based on a linear combination of variables to form factors, where the parameter estimates are such that they are most likely to have resulted in the observed correlation matrix, by using Maximum Likelihood Estimation (MLE) methods and assuming multivariate normality. Researchers weight correlations by each variable’s uniqueness. Here, uniqueness refers to the difference between the variability of a variable and its communality. MLF generates a chi-square goodness-of-fit test. The researcher can increase the number of factors one at a time until they obtain a satisfactory goodness-of-fit.
Alpha factoring maximizes the reliability of factors in Exploratory Factor Analysis, assuming that researchers randomly sample the variables from a very large set of variables. Unlike other methods, this method does not assume sampled cases and fixed variables.
Unweighted least squares (ULS) factoring: This technique in Exploratory Factor Analysis is based upon minimizing the sum of squared differences between the observed and estimated correlation matrices, without counting the diagonal.
Generalized least squares (GLS) factoring: This technique in Exploratory Factor Analysis is based on adjusting ULS by measuring the correlations, which are inversely proportional to their uniqueness (more unique variables weight less). Like MLF, GLS also generates a chi-square goodness-of-fit test. The researcher can increase the number of factors one at a time until a satisfactory goodness-of-fit is obtained.
The major disadvantage of using these techniques in Exploratory Factor Analysis is that they are quiet complex and are not recommended for an inexperienced user. Hence, researchers usually do not use these methods in extraction methods. For help with these techniques, click here.