submitted to the Stata Journal
One way in which one can better measure a variable, is to measure it more than once. However, after the different measures have been collected, one needs models that can combine the information from these different measurements. In this article I will introduce three such models: Sheaf coefficients, models with parametrically weighted covariates, and MIMIC models. What these models have in common is that they are models for so called ‘causal indicators’, that is, the observed variables are assumed to influence the underlying latent variable. Typical situations where these models can be useful occur when the observed variables can be thought of as resources adding up to a more general resource. For example, occupation and education of respondents adding up to socioeconomic status, or the amount of exercise and proportion of fruit in a diet adding up to the healthyness of the lifestyle. These models can also be used to scale the categories of a categorical explanatory variable such that the effect of that variable can be summarized by one number.