maroce

This m-file deals with the iterated principal factor method (principal axis factoring) thru the complete data matrix, the latent root criterion, iteration convergence criterion, and uses the varimax factor rotation. It works with an iterative solution for communalities and factor loadings. At iteration i, the communalities from the preceding iteration are placed on the diagonal of R, and the resulting R is denoted Ri. The eigenanalysis is performed on Ri and the new communality of variables are estimated. Iterations continue until the maximum change in the communality estimates is less than the convergence criteriun (default 0.001), number of iterations reached are given; it also gives the residual matrix, which results of the difference between the original correlation and the correlation structure for the factor model.

Some of the purposes for which Factor Analysis can be used are (1) that the number of variables for further research can be minimized while also maximizing the amount of information in the analysis (the smaller set can be used as operational representatives of the constructs underlying the complete set of variables), (2) can be used to search data for possible qualitative and quantitative distinctions and particularly useful when the sheer amount of available data exceeds comprehensibility, and (3) if the domain of data can be hypothesized to have certain qualitative and quantitative distinctions, then this hypothesis can be tested by factor analysis.

According to Rencher (2002), there are four approaches to estimation of the loadings and communalities: (1) Principal Component Method; (2) Principal Factor Method; (3) Iterated Principal Factor Method, and (4) Maximum Likelihood Method. The two most popular methods of parameter estimation are the principal component and the maximum likelihood method. The solution from either method can be rotated in order to simplify the interpretation of factors. It is always prudent to try more than one method of solution.

Input:
X - Data matrix. Size n-data x p-variables.
d - Convergence criterion (default = 0.001).

Outputs:
Complete Factor Analysis Results such as:
- Table of the Extraction of Components.
- Table of Iterated Unrotated Principal Factor Analysis.
- Proportion of Total (standardized) Sample Variance.
- Table of Cumulative Proportion of Total (standardized) Sample Variance.
Optionally:
- Table of Iterated Varimax Rotated Principal Factor Analysis.
- Pair-wise Iterated Unrotated Factor Score Plots.
- Pair-wise Iterated Varimax Rotated Factor Score Plots.
- Object labels.
- Residual Matrix.