Exploratory Factor Analysis

Exploratory factor analysis is a statistical technique that is used to reduce data to a smaller set of summary variables and to explore the underlying theoretical structure of the phenomena. It identifies the structure of the relationship between the variable and the respondent.  You can perform exploratory factor analysis using two methods:

• R-type factor analysis: You can perform exploratory factor analysis using two methods:
• Q-type factor analysis: When factors are calculated from the individual respondent, then it said to be Q-type factor analysis.

Driving factor:

There are two methods for driving factor, these two methods are as follows:

1. Principle component factor analysis method: This method drives the minimum number of factors and explains the maximum portion of variance in the original variable.
2. Common factor analysis: Researchers use this method when they do not know the nature of the factor they need to extract and the common error variance.

Selection of Factors to Extract: Researchers use theory as the first criterion to determine how many factors to extract.  From theory, we know that the number of factors extracted does make sense. Researchers most often use the Eigenvalue criterion to determine the number of factors to extract. Researchers also use the value of the percentage and variance explained method for exploratory factor analysis.  Therefore, researchers conduct reliability analysis to check the homogeneity between variables.

Orthogonal rotation:

In this method, researchers maintain the axes at 90 degrees, so the factors remain uncorrelated with each other.  In orthogonal rotation, the following three methods are available based on the rotation:

A. QUARTIMAX: Researchers simplify the rows so that the variables load on a single factor.

B. VARIMAX: Researchers simplify the columns of the factor matrix to clearly associate the factor extracts and ensure separation among the variables.

C. EQUIMAX: The combination of the above two methods. This method simplifies row and column at a single time.

Criteria for Practical and Statistical Significance of Factor Loadings: Factor loading can be classified based on their magnitude:

Greater than + .30 — minimum consideration level
+ .40 — more important
+ .50 — practically significant

Power and significance level: The researcher can determine the statistical power and significance level. For instance, researchers need a sample of 100 to achieve a factor loading of .55 with a power of .80.

Factor analysis and SPSS: Researchers can perform factor analysis in SPSS by clicking on ‘Analysis’ from the menu and selecting ‘Factor’ from the Data Reduction option.

Assumptions:

1. Variables used should be metric. Researchers can also consider dummy variables, but only in special cases.
2. Sample size: Sample size should be more than 200.  Researchers may consider a sample size of 5 observations per variable in some cases.
3. Homogeneous sample: A sample should be homogenous.  Violation of this assumption increases the sample size as the number of variables increases.  Researchers conduct reliability analysis to check the homogeneity between variables.
4. In exploratory factor analysis, multivariate normality is not required.
5. Correlation: At least 0.30 correlations are required between the research variables.
6. There should be no outliers in the data.

Related Pages:

• Factor Analysis
• Confirmatory Factor Analysis