Statistical Consulting Blog

Factor Analysis

Posted May 13, 2009

Factor analysis is a class of procedures that allow the researcher to observe a group of variables that tend to be correlated to each other and identify the underlying dimensions that explain these correlations. In other words, it is a class of procedures that are primarily used for data reduction and data summarization.

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There are many statistical methods that are used to study the relationship between independent variables and dependent variables, but factor analysis is used to understand the patterns of relationships among many dependent variables while simultaneously discovering the nature of the independent variables that affect them.

In the business field, there are large numbers of variables that are correlated and are required to get reduced to a manageable level.

Factor analysis is an interdependence technique because it involves the examination of interdependence relationship. It involves factors that are the underlying dimensions that define the correlations among the set of variables.

In the field of psychology, researchers can utilize factor analysis to understand the psychographic profile of a person by studying his lifestyle statements.

Factor analysis is widely used in the business field. In market research, it can be used in market segmentation in order to identify the underlying variables upon which the consumers are being grouped. It is then used to segment the customers into categories like economically sensitive, convenience sensitive, comfort sensitive, performance sensitive, etc.

There are two approaches of factor analysis. One of the approaches is common factor analysis. This, as the name suggests, involves the estimation of the factors based only on the common variance. On the other hand, in principal component factor analysis, the total variance of the data is considered.

There are certain statistics that are associated.

The Bartlett’s test of sphericity is a test statistic that is used to examine the null hypothesis that is assumed. This says that the variables are uncorrelated in the population.
The correlation matrix is used to show that there exists some correlation between all the pairs of variables that are being included in the analysis.

The Kaiser – Meyer- Olkin (KMO) measures of sampling adequacy is an index that is used to examine the appropriateness of factor analysis. Therefore, the researcher should keep in mind that if the value of this index is between 0.5 and 1, then it is appropriate. And if the values are below 0.5, then factor analysis is an inappropriate technique for that study.

Factor loadings in factor analysis are nothing but the simple correlation between the variables and the factors under study.

A matrix in factor analysis consists of the loadings of all the variables on all the factors being extracted.

The scores in factor analysis are the combined scores estimated for each respondent on the derived factors. As in all analysis, the first task is to formulate the problem. The next task is to construct the correlation matrix. Then, the researcher determines the method or an approach of the factor analysis. After determining the approach of factor analysis, the researcher determines the number of factors. The next task is to rotate the factors and interpret them by either calculating the scores or selecting the surrogate variables in factor analysis. After this, the researcher determines the model being fit.

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