The quality of a simple sum score
Examples of these complex concepts are variables like the “total time spend at the Media” based on the sum of the time spend on the different media. Concepts with a similar structure are “total household income” and “total expenditure of a household”.
In the case that the complex concept is just the sum score of different measures of simple concepts which may be correlated, the model for this complex concept can be represented by the following model:
In the case that the complex concept is just the sum score of different measures of simple concepts which may be correlated, the model for this complex concept can be represented by the following model:
The model for a complex concept with three indicators all measured with the same method M and with random measurement errors.
Assuming that all variables are standardized, it can be shown that the general equation forYi is:
Yi=qiFi+rimjM+ei´ for i = 1, 2, …, k
Where qi = rivi
The standardized composite score is the standardized weighted sum of all standardized variables :
It has been derived by Anna DeCastellarnau and Willem Saris that the quality of the standardized composite score is equal to
This term is equal the variance of the standardized composite score corrected for measurement error.
The method effect in the composite score is equal to
The method effect in the composite score is equal to
The variance of the unstandardized composite score corrected for measurement error is denoted as
which is equal to
