To get started, let’s review the syntax and output to produce a factor analysis of the engineering data (example data set 1 in Example data sets). We will use iterated PAF extraction and ask SAS to extract two factors since the items in the data generally represent two scales (please note, in Chapter 3 we will discuss the criteria to determine the number of factors to extract. The syntax to do this is presented below.

proc factor data = engdata  nfactors = 2  method = PRINIT  priors = SMC;
   var EngProbSolv1 EngProbSolv2 EngProbSolv3 EngProbSolv4 
      EngProbSolv5 EngProbSolv6 EngProbSolv7 EngProbSolv8
      INTERESTeng1 INTERESTeng2 INTERESTeng3 INTERESTeng4
      INTERESTeng5 INTERESTeng6;
run;

Since we are at heart lazy programmers who enjoy shortcuts (where appropriate), we are going to take a minute to explain two handy shortcuts for referring to a set of variables that contain the same prefixes: ranges and lists. Variable ranges require the same prefix and a numeric suffix (e.g., var1 var2 var3). You can then refer to a set of variables by the first variable and last variable in the range separated by a dash (e.g., var1-var3). Variable lists require only an identical prefix. The suffix can be numeric or character (e.g., var011 varXYZ varABC). You can then refer to the set by the common prefix followed by a colon (e.g., var :). There is another type of range that uses a double dash (e.g., --) that refers to variables based on position in the data set, but we do not recommend using that because variable order can change and you can get yourself in trouble. If we used a range or a list with the above syntax, this would change our VAR statement to the following:

var EngProbSolv1-EngProbSolv8 INTERESTeng1-INTERESTeng6;
*OR;
var EngProbSolv: INTERESTeng: ;

We will use the list notation to refer to variables throughout the remainder of this book to reduce and simplify the syntax that we present.

The syntax produces a series of results. Of particular interest to us right now are the communalities and the eigenvalues. We present these results, along with some of the related tables, below. Figure 2.1 Initial communality estimates and Figure 2.2 Initial eigenvalues extracted present the initial communalities and eigenvalues extracted. Figure 2.3 Iterative estimates of communalities shows us the iterative estimates of communalities that are produced as SAS attempts to identify stable estimates of the communalities. The final eigenvalues and communalities are presented in Figure 2.4 Final eigenvalue estimates, Figure 2.5 Final eigenvalues extracted, and Figure 2.6 Final communalities extracted. Notice that two different tables are produced to show the final eigenvalues extracted. The first shows the value of all the eigenvalues, and the second shows only the eigenvalues that were extracted.