Empirical best prediction under area-level Poisson mixed models

Boubeta, Miguel; Lombardía, María José; Morales, Domingo

doi:10.1007/s11749-015-0469-8

Cited by 45 publications

(34 citation statements)

References 19 publications

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“…Simplifications to the expressions of these approximations, using arguments similar to those of Prasad & Rao (1990), can be achieved using estimates of θ obtained with the method of Simulated Moments (Jiang, 1998a). We refer the interested reader to Jiang (2003), Jiang (2007) for a summary of the extensions of this approach to the general case and to Boubeta et al (2016) for an illustration in a Mixed Poisson setting, since we will not be providing further treatment of these procedures in this manuscript, because of the scarcity of the implementations of the method of Simulated Moments as an inferential procedure for the parameters in GLMM, which makes the use of the approximations to the MSEP hardly widespread.…”

Section: Estimation Of Msep Via Approximationsmentioning

confidence: 99%

Bootstrap estimation of uncertainty in prediction for generalized linear mixed models

Flores-Agreda

Cantoni

2019

Computational Statistics & Data Analysis

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In this article, we focus on the estimation of the Mean Squared Error for the Predictors (MSEP) of Random Effects (RE) in Generalized Linear Mixed Models (GLMM) by means of non-parametric bootstrap methods. In the frequentist paradigm, the MSEP is used as a measure of the uncertainty in prediction and has been shown to be affected by the estimation of the model parameters. In the particular case of linear mixed models (LMM), two solutions are provided to practitioners: on one hand, secondorder correct approximations which yield estimators of this quantity and, on the other hand, several Parametric Bootstrap algorithms. We propose a non-parametric bootstrap scheme, consisting of an adaptation of the Random Weighted Laplace Bootstrap (RWLB) that can be used in the entire class of GLMM. On a first stage, the RWLB is used to generate bootstrap replicates of the parameters while, on a second stage, simulation is used to generate bootstrap samples of standardized RE. We conduct a first simulation study in the framework of Gaussian LMM to contrast the quality of our approach with respect to: (i) analytical estimators of MSEP based on approximations, (ii) Conditional Variances obtained with a Bayesian representation and (iii) other bootstrap schemes, on the grounds of their relative bias, relative efficiency and the coverage ratios of resulting prediction intervals. A second simulation study serves the purpose to illustrate the use and benefits of our proposal against other feasible alternatives in a pure, Non-Gaussian, GLMM setting.

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Section: Estimation Of Msep Via Approximationsmentioning

confidence: 99%

Bootstrap estimation of uncertainty in prediction for generalized linear mixed models

Flores-Agreda

Cantoni

2019

Computational Statistics & Data Analysis

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“…Some important areal level models are available, but they are generally unsuitable for our problem. For example, the Fay–Herriot model (Fay and Herriot, ), and most of its extended versions like generalized linear models (Boubeta et al ., ), including those with spatial correlations or geographical interactions (Jiang and Lahiri, ; Molina et al ., ) or with Bayesian settings (You and Rao (), Rao and Molina () and Datta and Ghosh (), chapter 9) all require direct survey estimates at the small areas of interest.…”

Section: Problem Identification and Reviewmentioning

confidence: 99%

A Bayesian Spatial Categorical Model for Prediction to Overlapping Geographical Areas in Sample Surveys

Bakar

Biddle

Kokic

et al. 2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary Motivated by the Australian National University poll, we consider a situation where survey data have been collected from respondents for several categorical variables and a primary geographic classification, e.g. postcode. Here, a common and important problem is to obtain estimates for a second target geography that overlaps with the primary geography but has not been collected from the respondents. We examine this problem when areal level census information is available for both geographic classifications. Such a situation is challenging from a small area estimation perspective for several reasons: there is a misalignment between the census and survey information as well as the geographical classifications; the geographic areas are potentially small and so prediction can be difficult because of the sparse or spatially missing data issue; and there is the possibility of non‐stationary spatial dependence. To address these problems we develop a Bayesian model using latent processes, underpinned by a non‐stationary spatial basis that combines Moran's I and multiresolution basis functions with a small but representative set of knots. The study results based on simulated data demonstrate that the model can be highly effective and gives more accurate estimates for areas defined by the target geography than several existing models. The model also performs well for the Australian National University poll data to predict on a second geographic classification: statistical area level 2.

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“…. Note that (4) differs from the empirical predictor Boubeta et al (2016) in that it includes rather than predicts observed y-values. Clearly, when sample sizes are small relative to population sizes there will be very little difference between these two predictors.…”

Section: Small Area Estimation For Discrete Datamentioning

confidence: 99%

Small area prediction of counts under a non-stationary spatial model

2017

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There is a growing need for current and reliable counts at small area level. The empirical predictor under a generalized linear mixed model (GLMM) is often used for small area estimation (SAE) of such counts. However, the fixed effect parameters of a GLMM are spatially invariant and do not account for the presence of spatial nonstationarity in the population of interest. A geographically weighted regression extension of the GLMM is developed, extending this model to allow for spatial nonstationarity, and SAE based on this spatially nonstationary model (NSGLMM) is described. The empirical predictor for small area counts (NSEP) under an area level NSGLMM is proposed. Analytic and bootstrap approaches to estimating the mean squared error of the NSEP are also developed, and a parametric approach to testing for spatial nonstationarity is described. The approach is illustrated by applying it to a study of poverty mapping using socio- economic survey data from India

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Empirical best prediction under area-level Poisson mixed models

Cited by 45 publications

References 19 publications

Bootstrap estimation of uncertainty in prediction for generalized linear mixed models

Bootstrap estimation of uncertainty in prediction for generalized linear mixed models

A Bayesian Spatial Categorical Model for Prediction to Overlapping Geographical Areas in Sample Surveys

Small area prediction of counts under a non-stationary spatial model

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