Here is a SAS program code for the Factor Analysis function. Please leave me a comment if you need Factor Analysis results interpretation, I might interpret the results for you, for free :-)
Factor analysis is a data reduction technique. It is used to simplify complex and diverse relationships that exist among a set of observed variables by uncovering common factors. It provides an insight into the underlying structure of the data. The common factor models express each observable variable in terms of unobservable common factors that link together the seemingly unrelated variables.
The purpose of a factor analysis is to develop a new set of uncorrelated variables, called underlying factors, or common factors, with the hope that these new variables will give a better understanding of the data being analyzed. These new variables can then be used in future analyses of the data.
SAS software has a procedure "PROC FACTOR" for performing Factor Analysis. The procedure can also create a new set of data that contains the values of the factor scores. This new dataset can be used for later data analysis.
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Run the SAS program for Factor Analysis in the following example and explain the results such as how to choose the appropriate number of common factors and report the communalities. The Factor Pattern in the SAS output contains the values of the factor loadings. They are used for solving the factor equations to get the factor scores.
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dm log 'clear';
dm output 'clear';
options nodate;
data FA;
input ID X1 X2 X3 X4 X5 X6 X7 X8 ;
datalines;
1 6 7 2 5 8 7 8 8
2 9 10 5 8 10 9 9 10
3 7 8 3 6 9 8 9 7
4 5 6 8 5 6 5 9 2
5 6 8 8 8 4 4 9 5
6 7 7 7 6 8 7 10 5
7 9 9 8 8 8 8 8 8
8 9 9 9 8 9 9 8 8
9 9 9 7 8 8 8 8 5
10 4 7 10 2 10 10 7 10
11 4 7 10 0 10 8 3 9
12 4 7 10 4 10 10 7 8
13 6 9 8 10 5 4 9 4
14 8 9 8 9 6 3 5 1
15 4 8 8 7 5 4 10 2
16 6 9 6 7 8 9 8 9
17 8 7 7 7 9 5 8 6
18 6 8 8 4 8 8 6 4
19 6 7 8 4 7 8 5 4
20 4 8 7 8 8 9 10 5
;
PROC factor DATA=FA METHOD=Principal scree;
VAR X1--X8;
TITLE'Factor Analysis';
TITLE2'Scree Plot of Eigenvalues';
RUN;
PROC factor DATA=FA METHOD=Principal nfactors=3 score OUT=scores;
VAR X1--X8;
TITLE2'Computing the Values of the First Three Factor Scores';
RUN;
PROC PRINT DATA=scores;
VAR ID factor1 factor2 factor3;
TITLE2 'Displaying the Values of the First Three Factor Scores';
run;
quit;
*****
2 Comments:
I am new in PCA and factor analysis? How do you interpret the results from the above example? How do you use it?
Thanks
September 23, 2008 8:14 AM
Have you run the SAS code above already?
The Common Factor Analysis is more or less the same as the Principal Component Analysis. Both are similar since they reduce the original variables into fewer composite variables. The distinction of the two lies on the purpose the obtained composite variables serve.
In common factor analysis, a small number of factors are extracted to account for the inter-correlations among the observed variables--to identify the latent dimensions that explain why the variables are correlated with each other. In principal component analysis, the objective is to account for the maximum portion of the variance present in the original set of variables with a minimum number of composite variables called principal components.
September 23, 2008 11:41 AM
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