Factor Analysis is an exploratory multivariate statistical method used to summarize the information contained in a large set of variables in terms of a smaller set of composite variables, called FACTORS.

Suppose a retail firm has identified 80 different characteristics of retail stores and their services that consumers have mentioned as affecting their patronage choice among stores. The retailer wants to understand how consumers make decisions but can not analyze 80 separate characteristics. He can use Factor Analysis to find out the more general evaluative dimensions of the characteristics.

Each factor is a linear combinations of all the variables included in the model and represents a group of variables that are a facet of this broader evaluative dimension. In other words, it stands for the variables with which it has a high correlation.

For each data set there exists an optimal number of factors. Several commonly used criteria are there to find out the optimal number of factors. These criteria ensure the significance of the factors in explaining the variability of the total information.

Here FEATURE consists of the original variables. Under FACTOR1, FACTOR2 and FACTOR3 the individual coefficients of the variables for the respective factors are given. These coefficients are called factor loadings.

A diagnostic test is also done to check whether the retained factors are sufficient to explain the correlations among the observed variables. An infinite number of solution can be obtained for the fixed optimal number of factors. To simplify the factor structure and to achieve a more meaningful and interpretable unique solution the factors are rotated i.e. the reference axes of the factors are turned around the origin. Orthogonal or Oblique rotations are performed as per the priority.

Once all significant loadings are identified, the analyst attempts to assign some meaning to the factors based on the patterns of the factor loadings. To do this, the significant loading for each factor is examined. In general, the larger the absolute size of the factor loading for a variable, the more important the variable is in interpreting the factor. The sign of the loadings is also considered in labeling the factors.

Here In-store experience, product offerings and Value are the three factors.

The factors are used to explain the correlations among the original variables and thus understand the data structure. It also simplifies the subsequent multivariate analysis.