Domain prediction with grouped income data

One popular small area estimation method for estimating poverty and inequality indicators is the empirical best predictor under the unit‐level nested error regression model with a continuous dependent variable. However, parameter estimation is more challenging when the response variable is grouped due to data confidentiality concerns or concerns about survey response burden. The work in this paper proposes methodology that enables fitting a nested error regression model when the dependent variable is grouped. Model parameters are then used for small area prediction of finite population parameters of interest. Model fitting in the case of a grouped response variable is based on the use of a stochastic expectation–maximization algorithm. Since the stochastic expectation–maximization algorithm relies on the Gaussian assumptions of the unit‐level error terms, adaptive transformations are incorporated for handling departures from normality. The estimation of the mean squared error of the small area parameters is facilitated by a parametric bootstrap that captures the additional uncertainty due to the grouping mechanism and the possible use of adaptive transformations. The empirical properties of the proposed methodology are assessed by using model‐based simulations and its relevance is illustrated by estimating deprivation indicators for municipalities in the Mexican state of Chiapas.