Composite scores

Overview
In statistics, and particularly psychometrics, composite scores are calculated from data in multiple variables in order to form reliable and valid measures of latent, theoretical constructs.

The variables which are combined to form a composite score should be related to one another. This can be tested through factor analysis and reliability analysis.

Higher-order composite scores (such as global or total scores) may also be appropriate when factors themselves are correlated and theoretically related.

Methods
Two common methods for calculating composite scores are:
 * Unit weighted - each item is equally weighted, e.g., X = mean (A, B, C, D)
 * Regression-weighted - each item is weighted according to its factor loading, e.g., X = .5*A + 0.4*B + 0.4*C + 0.3*D

In most situations, you can use either unit-weighted or regression-weighted composite scores. Regression-weighted scores are, technically, more valid. However regression-weighted scores are standardised (to a mean of 0 and SD of 1), so in some situations e.g., comparisons between means of two or more composite scores (e.g., for an RM ANOVA or Mixed ANOVA), unit-weighted scores should be used. But regression-weighted are appropriate for MLR and some ANOVAs, as well as many other types of statistical analysis.

Missing data
When computing composite scores, consider whether some allowance could be made for missing data. If a multi-item scale is internally consistent, then a composite score could be created even when some data are missing. For example, in SPSS syntax, use COMPUTE NEWVARNAME = mean.3(v1, v2, v3, v4, v5) will create a new variable based on the means of v1 to v5 and it will still calculate a mean for a case as long as there at least 3 responses to the 5 items. If there are 2 or less responses, the result will be a missing value for the composite score.