Abstract

Co-author: Serena Arima (Sapienza Università di Roma)

We focus on mixed effects with data subject to PRAM . An instance of this is a small area model.  We assume that categorical covariates have been perturbed by Post Randomization,
whereas the level identifier is not perturbed. We also assume that a continuous response is available,  and consider a nested linear regression model:
$$
y_{ij}= X_{ij}^{\beta +v_{i}+e_{ij},     j=1,...,n_{i}; \,\,i=1,...,m
$$
where
$v_{i}\iid N(0,\sigma}{2})$ (model error);$e{i}\iid
N(\mu,\sigma^{2}_{e})$ (design error).

We resort to a measurement error model and define a unit-level small area model accounting for measurement error  in   discrete covariates.
PRAM is defined in terms of  a transition matrix $P$ modeling the changes in categories; we consider both the case of known $P$, and the case when  $P$ is
unknown and is estimated from the data.

A small simulation study is conducted to assess the effectiveness of the proposed Bayesian measurement error model in estimating the model
parameters and to investigate the protection provided by PRAM in this context.