Small area estimation for semicontinuous data

Abstract

Survey data often contain measurements for variables that are semicontinuous in nature, i.e. they either take a single fixed value (we assume this is zero) or they have a continuous, often skewed, distribution on the positive real line. Standard methods for small area estimation (SAE) based on the use of linearmixed models can be inefficient for such variables. We discuss SAE techniques for semicontinuous variables under a two part random effects model that allows for the presence of excess zeros as well as the skewed nature of the nonzero values of the response variable. In particular, we first model the excess zeros via a generalized linear mixed model fitted to the probability of a nonzero, i.e. strictly positive, value being observed, and then model the response, given that it is strictly positive, using a linear mixed model fitted on the logarithmic scale. Empirical results suggest that the proposed method leads to efficient small area estimates for semicontinuous data of this type. We also propose a parametric bootstrap method to estimate the MSE of the proposed small area estimator. These bootstrap estimates of the MSE are compared to the true MSE in a simulation study. Disciplines Engineering | Science and Technology Studies AbstractSurvey data often contain measurements for variables that are semicontinuous in nature,i.e. they either take a single fixed value (we assume this is zero) or they have a continuous, often skewed, distribution on the positive real line. Standard methods for small area estimation (SAE) based on the use of linear mixed models can be inefficient for such variables. We discuss SAE techniques for semicontinuous variables under a two part random effects model that allows for the presence of excess zeros as well as the skewed nature of the non-zero values of the response variable. In particular, we first model the excess zeros via a generalized linear mixed model fitted to the probability of a non-zero, i.e. strictly positive, value being observed, and then model the response, given that it is strictly positive, using a linear mixed model fitted on the logarithmic scale.Empirical results suggest that the proposed method leads to efficient small area estimates for semicontinuous data of this type. We also propose a parametric bootstrap method to estimate the MSE of the proposed small area estimator. These bootstrap estimates of the MSE are compared to the true MSE in a simulation study.

Localised Estimates of Dynamics of Multi‐dimensional Disadvantage: An Application of the Small Area Estimation Technique Using Australian Survey and Census Data

“…However, the existing small area estimation methods for zero‐inflated data are mostly developed for continuous data; see, for example, (Chandra & Sud, ; Chandra & Chambers, ; ; Dreassi et al , ; Dreassi & Rocco, ) and the references therein. To the best of our knowledge, suitable methodology for the area‐level small area estimation approach for zero‐inflated count data is yet to be developed (Lambert, ; Lee et al , ; Chandra & Chambers, ). Recently, Torabi () described small area estimation for zero‐inflated count data under the area‐level model using a Bayesian framework.…”

Empirical Bayes small area prediction under a zero‐inflated lognormal model with correlated random area effects

“…Existing approaches to small area estimation for zero-inflated skewed data include Dreassi et al (2014) and Chandra and Chambers (2016). Dreassi et al (2014) develop a zero-inflated gamma model and apply the zero-inflated model to estimate grape wine production in small areas in Italy.…”

Small Area Estimation on Zero-Inflated Data Using Frequentist and Bayesian Approach

“…This prior information is called the prior distribution. Then, the sample is drawn from the population and the prior distribution is updated with the sample information so that it will be a distribution that is called posterior distribution (Casella & Berger, 2002). Some types of wellknown prior distributions are, according to Gelman et al (2014), informative prior that consisting of conjugate and nonconjugate prior, noninformative prior that consisting of proper and improper prior, and weakly informative prior.…”

“…SAE with an indirect estimation which is based on a model (model-based), by utilizing data from the national survey and the addition of auxiliary variables, is an alternative to that problem. Those auxiliary variables may be other variables that are related to the variable of concern (Suhartini et al, 2016;Asfar & Sadik, 2016). The variable of concern can be called the target variable.…”