If you do not know the number of factors to use, first perform the analysis using the principal components method of extraction, without specifying the number of factors. Then use one of the following methods to determine the number of factors.
Use the percentage of variance (% Var) to determine the amount of variance that the factors explain. Retain the factors that explain an acceptable level of variance. The acceptable level depends on your application. For descriptive purposes, you may need only 80% of the variance explained. However, if you want to perform other analyses on the data, you may want to have at least 90% of the variance explained by the factors.
If you use principal components to extract factors, the variance equals the eigenvalue. You can use the size of the eigenvalue to determine the number of factors. Retain the factors with the largest eigenvalues. For example, using the Kaiser criterion, you use only the factors with eigenvalues that are greater than 1.
The scree plot orders the eigenvalues from largest to smallest. The ideal pattern is a steep curve, followed by a bend, and then a straight line. Use the components in the steep curve before the first point that starts the line trend.
Step 2: Interpret the factors
After you determine the number of factors (step 1), you can repeat the analysis using the maximum likelihood method. Then examine the loading pattern to determine the factor that has the most influence on each variable. Loadings close to -1 or 1 indicate that the factor strongly influences the variable. Loadings close to 0 indicate that the factor has a weak influence on the variable. Some variables may have high loadings on multiple factors.
Unrotated factor loadings are often difficult to interpret. Factor rotation simplifies the loading structure, allowing you to more easily interpret the factor loadings. However, one method of rotation may not work best in all cases. You may want to try different rotations and use the one that produces the most interpretable results. You can also sort the rotated loadings to more clearly assess the loadings within a factor.
Step 3: Check your data for problems
If the first two factors account for most of the variance in the data, you can use the score plot to assess the data structure and detect clusters, outliers, and trends. Groupings of data on the plot may indicate two or more separate distributions in the data. If the data follow a normal distribution and no outliers are present, the points are randomly distributed about the value of 0.
To see the calculated score for each observation, hold your pointer over a data point on the graph. To create score plots for other factors, store the scores and use Graph > Scatterplot.