# Principal Component Factor Analysis

5-1968

Report

## Degree Name

Master of Science (MS)

## Department

Mathematics and Statistics

Jolliff

Jolliff

## Abstract

Factor analysis came into being around 1900 in the field f psychology to explain theories of human ability. Several methods of factor analysis exist; but according to Harman (1967) principal component factor analysis is unique in the mathematical sense, therefore, quite often the preferred method. The centroid method is computationally easier, and it gives close approximations to the principal component method on some data sets. An example of this is shown in Appendixes B and F by comparison.

Factor analysis is being used in many fields. A few of the fields are sociology, meteorology, political science, medicine, geography, business, economics, ecology, soil science, and geology. The following are three specific examples.

In meteorology, White (1958) found that factor analysis could reduce considerably the number of variables in his study of sea-level pressure forecasting. In this study, there were 42 original variables. With 5, 10, and 20 underlying variables, White was able to account for 75.51, 90.70, and 97.37 per cent of the original variance, respectively.

In ecology, Orloci (1966) found that factor analysis could be used to reduce the number of variables in his study of vegetation on Newborough Warren, Anglesey. In this study, there were 101 original variables. With three underlying variables, Orloci was able to account for 43.98 per cent of the original variance.

In the study by White names were not given for the new variables that were found; whereas in the study by Orloci, meaningful names were obtained for the first three factors. Just because a factor accounts for a large portion of the variance does not imply that meaningful names may be readily applied to these factors.

In soil science, Lombard (1965) found that factor analysis could be used in his study of citrus irrigations to reduce the number of variables from 12 to 3. These three underlying variables accounted for 99.5 per cent of the variance. Meaningful names were obtained for the three underlying variables. If meaningful names cannot be obtained for the roots or new variables, then factor analysis is not of much value as a statistical tool.

Many different programs have been written to perform factor analysis. A few of the existing programs are those by Cooley and Lohnes (1962), Horst (1965), Hurst (n.d., d), in the System/360 Scientific Subroutine Package (1968), and Veldman (1967).

This report contains program write-ups and listings for three computer programs, one for principal component factor analysis, one for factor analysis transformation, and another for the centroid method factor analysis.

The Principal Component Factor Analysis program will handle up to 50 variables. The Factor Analysis Transformation program will handle up to 50 variables and 15 factors. The Centroid Method Factor Analysis program will handle up to 60 variables. These programs will all run on a 65K byte IBM 360/44 with FORTRAN IV. A card reader, card punch, printer, and one disk or tape are needed.

## Share

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#### DOI

https://doi.org/10.26076/f0f7-39a9