Statistical Consulting Blog

Exploratory Factor Analysis

Posted April 1, 2009

Factor Analysis is a general name denoting a class of procedures primarily used for data reduction and summarization. In research, there are a large number of variables which are extensively correlated and must be reduced to a manageable level. Relationships among sets of many interrelated variables are examined and represented 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 has a priori assumption that any indicator may be associated 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) seeks to determine if the number of factors and the loadings of measured (indicator) variables on them conform to what is expected on the basis of pre-established theory. Indicator variables are selected on the basis of prior theory, and factor analysis is used to see if they loaded, as predicted, on the expected number of factors.

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, Exploratory Factor Analysis is used less as compared to Confirmatory Factor Analysis.

The following techniques are used in both the approaches—both Exploratory Factor Analysis and CFA:

· Principal Component Technique: This technique is used in Exploratory Factor Analysis, where the total variance in the data is considered. The diagonal of the correlation matrix consists of unities, and full variance is brought into the factor matrix. Principal technique is recommended when the primary concern is to determine the minimum number of factors that will account for maximum variance in the data for use in subsequent multivariate analysis.

There are some techniques, in addition to Principal Component Technique, that are used in Exploratory factor analysis and Confirmatory factor analysis and that are complex. These techniques are also called 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. Correlations are weighted 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 a satisfactory goodness-of-fit is obtained.

· Alpha factoring: This technique in Exploratory Factor Analysis is based on the maximization of the reliability of factors, assuming that the variables are randomly sampled 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, these methods are usually not used in extraction methods. For help with these techniques, click here.

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