Factor Analysis

Factors are linear combinations between different variables. Factor analysis is a concept that is not openly observed but requires an arbitrary load of other input variables. It is a method of correlation which is used for finding as well as describing the underlying factors that determine data values for a wide range of variables. In addition, factor analysis is a method in statistical econometrics that describes the variability between pragmatic correlated variable(s) in terms of a probably slight number of un-observed correlated variable(s), knows as factor. In simple words, factor analysis is a statistical method for the identification of underlying factors that are measured by a great number of observed variables.

Thus, factor analysis method is a study of the correlation matrix of the observed variable(s). The factor is the WA (weighted average) of the original variable. Usually data interpretation is the goal or aim of factor analysis for identifying each factor which is representing a specific theoretical factor. Hence, the central theme of factor analysis is to condense the number of variable(s); therefore, it could be said that shaping the right number of factors is one of the most elusive task(s) in factor analysis.

Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy

The suitability of data for factor analysis could be examined through KMO test; in other words, sampling adequacy can be investigated through this particular test which ranges from 0 to 1. The decision criteria for this test is depends on its range; if value lies between 0.6 and 1 suggesting the suitability of factor analysis and adequacy of sapling and if value is less than 0.6 then rejection is recommended. 

Bartlett Test

This test had been developed by Bartlett in 1950- testing the null hypothesis of homogeneity of correlation coefficient matrix. For instance, the coefficients of correlation are tending to zero. According, this test is used for testing the hypothesis- no correlation amid factors. In addition, it tests either the correlation of matrix is an identity matrix or not, if the yes then it provides signal about the inappropriateness of factor analysis. The decision in this test is based upon the significance value, if it is less that 0.05 means significant otherwise insignificant.

Eigen Value

The eigenvalue of a particular factor refers to the measure of variance of all factors described through that factor. In other words, the Eigenvalue is the amount of variance described by a factor. It is the sum of the columns of the square load of a factor. The Eigen value is also called the characteristic root.  A rule of thumb, if value is one or greater than 1 it explained variance, if the case is opposite (<1) then the factor must be removed. 

Varimax Rotation

The most common technique of orthogonal rotation is Varimax rotation. Orthogonal rotation intends to curtail the complexity of element/items by increasing both, the large loadings more larger and slight loads slighter in individual element. In other words, varimax is used in component analysis to determine relationship between variable and its component, it refers to varimax due to the reason that it maximizes the sum of variances of squared loadings. If factor landing is less than 0.5 then the factor must be eliminated.