Composite scores

## Overview

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An example of a simple, first-order factor structure; which would justify the calculation of three composite scores based on 12 items

In statistics, and particularly psychometrics, composite scores are calculated from data in multiple variables (or items e.g., from a survey or questionnaire) 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/or reliability analysis.

Higher-order composite scores (such as global or total scores) may also be appropriate when multi-item factors are correlated and theoretically related (e.g., combining physical self-concept and academic self-concept into overall self-concept).

## Methods

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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

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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.

In SPSS syntax:

1. Use COMPUTE NEWVARNAME = mean.3(var1, var2, var3, var4, var5) 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.

In jamovi:

1. Create a variable (var_N_missing) which counts the number of missing items using the formula: IFMISS(var1, 1, 0) + IFMISS(var2, 1, 0) + IFMISS (var3, 1, 0) + IFMISS (var4, 1, 0) + IFMISS (var5, 1, 0). By using this code, if a case is missing any of the five variables, the IFMISS() function returns a value of 1. If a case does not have any missing data, the function returns a value of 0. The five IFMISS() functions are added together to give a count of the number of missing values across the five variables.
2. Use this formula to compute the composite score: IF(var_N_missing <= 2, MEAN(var1, var2, var3, var4, var5, ignore_missing=1)). This formula calculates the mean of the 5 variables, allowing for up to 2 missing values. If there are more than 2 missing values, the composite score will be a missing value.
3. Explanation: The IF function checks if the number of missing values across all the five variables is less than or equal to 2. If true, the code calculates the mean of the five variables. If the IF function is false (i.e., more than 2 missing values), the code does not calculate the mean and returns a missing value. The MEAN function also has an argument called “ignore_missing” set to 1. This allows the function to ignore missing values while calculating the mean.

## See also

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* Composite scores in SPSS (Tutorial)
* Reliability and validity (Tutorial)
* Missing data