Small area estimation of proportions under area-level compositional mixed models

Abstract

This paper introduces area-level compositional mixed models by applying transformations to a multivariate Fay–Herriot model. Small area estimators of the proportions of the categories of a classification variable are derived from the new model, and the corresponding mean squared errors are estimated by parametric bootstrap. Several simulation experiments designed to analyse the behaviour of the introduced estimators are carried out. An application to real data from the Spanish Labour Force Survey of Galicia (north-west of Spain), in the first quarter of 2017, is given. The target is the estimation of domain proportions of people in the four categories of the variable labour status: under 16 years, employed, unemployed and inactive.

Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model

“…Accordingly, we should apply LMMs in order to exploit this property. Similar to Esteban et al (2020), we therefore choose an approach based on the isometric logratio transformation of the composition. This allows us to treat the nonlinear problem of estimating proportions by means of multivariate LMMs, for which we can apply min-max robust regression.…”

“…Furthermore, the RBP of E(p d,i |u d ) is analytically intractable as it contains nonsolvable integrals of E(p d,i |u d ) with respect to the probability density of u d conditional on y d . Therefore, we adapt the proposal of Esteban et al (2020) to our setting and predict…”

“…In particular, they allow to estimate domain compositions by means of multivariate LMMs. Recently, Esteban et al (2020) used this property within a multivariate Fay-Herriot model (MFH model) to perform SAE of labor force compositions. They extended the applications of the MFH model that Morales (2016, 2021) and Ubaidillah, Notodiputro, Kurnia, and Wayan (2019) suggested to predict domain means, totals, or proportions.…”

A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates

“…Fay and Herriot (1979) proposed the original area-level model, which regresses regional direct estimates of target variables on covariates using cross-sectional data. This model was later extended and applied to multivariate data by Benavent and Morales (2016), Arima et al (2017), Ubaidillah et al (2019), Burgard et al (2021) and Esteban et al (2020). Since analyzing the development of domain characteristics over time is often relevant in empirical studies, generalizations of the area-level model to the temporal context soon appeared.…”

Small area estimation of socioeconomic indicators for sampled and unsampled domains

“…Datta et al (1996) employed a multivariate FH model for obtaining hierarchical Bayes predictors. González-Manteiga et al (2008) considered a multivariate FH model with a common domain random effect for the target vector, Arima et al (2017) and Burgard et al (2020) study multivariate measurement errors FH models, Porter et al (2015), Benavent and Morales (2016), Ubaidillah et al (2019), Esteban et al (2019) and Benavent and Morales (2021) investigate and give further applications of multivariate FH models. Many other authors have studied further variants of the FH model and the multivariate FH model adapted to different setups.…”