Prime Factor Loadings
This report provides a specially sorted presentation of the factor loadings. Like the standard report of factor loadings, the rows represent the variables and the columns represent the factors. In this case, however, each variable is associated with the factor for which it has the largest loading as an absolute value. The variables having factor 1 as the prime factor are listed first, in descending order of the loading with factor 1. Then the variables having factor 2 as the prime factor are listed, continuing on until all the variables are listed. It is possible that not all factors will appear in the Prime Factor column, but all the variables will be listed once and only once with all their factor loadings.
The following is an example of a Prime Factor Loadings report.
| Variable | Prime Factor | Factor 1 | Factor 2 | Factor 3 |
|---|---|---|---|---|
| income | Factor 1 | .8229 | -1.1675E-02 | .1353 |
| revenue | Factor 1 | .8171 | .4475 | 2.3336E-02 |
| single | Factor 1 | -.7705 | .4332 | .1554 |
| age | Factor 1 | .7348 | -4.5584E-02 | 1.0212E-02 |
| cust_years | Factor 2 | .5158 | .6284 | .1577 |
| purchases | Factor 2 | .5433 | -.5505 | -.254 |
| female | Factor 3 | -4.1177E-02 | .3366 | -.9349 |
Prime Factor Variables
The Prime Factor Variables report is closely related to the Prime Factor Loadings report. It associates variables with their prime factors and possibly other factors if a threshold percent or loading value is specified. It provides a simple presentation, without numbers, of the relationships between factors and the variables that contribute to them.
If a threshold percent of 1.0 is used, only prime factor relationships are reported. A threshold percentage of less than 1.0 indicates that if the loading for a particular factor is equal to or above this percentage of the loading for the variable's prime factor, then an association is made between the variable and this factor as well. When the variable is associated with a factor other than its prime factor, the variable name is given in parentheses. A threshold loading value may alternately be used to determine the associations between variables and factors. In this case, it is possible that a variable may not appear in the report, depending on the threshold value and the loading values. However, if the option to reverse signs was enabled, positive values may actually represent inverse relationships between factors and original variables. Deselecting this option in a second run and examining factor loading results will provide the true nature (directions) of relationships among variables and factors.
The following is an example of a Prime Factor Variables report.
| Factor 1 | Factor 2 | Factor 3 |
|---|---|---|
| income | cust_years | female |
| revenue | purchases | * |
| single | * | * |
| age | * | * |
| (purchases) | * | * |
Prime Factor Variables with Loadings
The Prime Factor Variables with Loadings is functionally the same as the Prime Factor Variables report except that the actual loading values determining the associations between the variables and factors are also given. The magnitude of the loading gives some idea of the relative strength of the relationship and the sign indicates whether or not it is an inverse relationship. A negative sign indicates an inverse relationship in the values (i.e., a negative correlation).
The following is an example of a Prime Factor Variables with Loadings report.
| Factor | Variable | Loading |
|---|---|---|
| Factor 1 | income | .8229 |
| Factor 1 | revenue | .8171 |
| Factor 1 | single | -.7705 |
| Factor 1 | age | .7348 |
| Factor 1 | (purchases) | .5433 |
| Factor 2 | cust_years | .6284 |
| Factor 2 | purchases | -.5505 |
| Factor 3 | female | -.9349 |
Missing Data
Null values for columns in a Factor analysis can adversely affect results. Teradata recommends using the listwise deletion option when building the SSCP matrix with the Build Matrix function. This ensures that any row for which one of the columns is null will be left out of the matrix computations completely. Additionally, the Recode transformation function can be used to build a new column, substituting a fixed known value for null.