Factor Analysis of Multi collinear variables in Economics

Factor Analysis is a statistical procedure used to classify the functional form of relationships between several variables and narrow it down to a smaller set of variables. If there are many variables, and they are linearly correlated, factor analysis tries to club highly correlated variables together as a latent variable called factors. The number of factors defining all variables in most cases is less in numbers than the number of variables. Factor analysis is generally useful for linearly combining two or more variables in economic analysis.

Here is an example of factor analysis in R program:

Step I: Prepare Data

Data frame name = my_data_final

Step II: Run Factor Analysis

The analysis above showed when 13 variables were tested for five factors with varimax rotation and 0.1 cutoffs. The cutoff is taking of 0.32 to while printing to define the loadings. Factor analysis is an exploratory process in nature. If adding one more factor adds more to the cumulative variance of the model, it should keep adding. Analysis of eigenvalue also gives a basis for how many factors to use. The general principle factors having more than one eigenvalues are kept.

Step III:  Exploratory Process and Further Processing:

Further information on correlation matrix and loadings is obtained as follows. 

Use print instead of head for detail result.

Step IV: Plotting

Step V: Determining Number of Factors to Use

For this, factor having eigenvalue > 1 is considered as factor to use. Here we use 5 factors based on the eigen value from Scree Plot.