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.