Empirical analysis of individual response behavior is sometimes
limited due to the lack of explanatory variables at the individual
level. In this paper we put forward a new approach to estimate the
effects of covariates on individual response, where the covariates
are unknown at the individual level but observed at some aggregated
level. This situation may, for example, occur if the response
variable is available at the household level but covariates only at
the zip-code level.
We describe the missing individual covariates by a latent variable
model which matches the sample information at the aggregate level.
Parameter estimates can be obtained using maximum likelihood or a
Bayesian approach. We illustrate the approach estimating the effects
of household characteristics on donating behavior to a Dutch
charity. Donating behavior is observed at the household level, while
the covariates are only observed at the zip-code level