Spatial small area smoothing models for handling survey data with nonresponse

Spatial smoothing models play an important role in the field of small area estimation. In the context of complex survey designs, the use of design weights is indispensable in the estimation process. Recently, efforts have been made in these spatial smoothing models, in order to obtain reliable estimates of the spatial trend. However, the concept of missing data remains a prevalent problem in the context of spatial trend estimation as estimates are potentially subject to bias. In this paper, we focus on spatial health surveys where the available information consists of a binary response and its associated design weight. Furthermore, we investigate the impact of nonresponse as missing data on a range of spatial models for different missingness mechanisms and different degrees of missingness by means of an extensive simulation study. The computations were performed in R, using INLA and other existing packages. The results show that weight adjustment to correct for missingness has a beneficial effect on the bias in the missing at random setting for all models. Furthermore, we estimate the geographical distribution of perceived health at the district level based on the Belgian Health Interview Survey (2001). Copyright © 2017 John Wiley & Sons, Ltd.

[1]  William J. Browne,et al.  Bayesian and likelihood-based methods in multilevel modeling 1 A comparison of Bayesian and likelihood-based methods for fitting multilevel models , 2006 .

[2]  L. Waller,et al.  Applied Spatial Statistics for Public Health Data: Waller/Applied Spatial Statistics , 2004 .

[3]  Andrew B. Lawson,et al.  Statistical Methods in Spatial Epidemiology: Lawson/Statistical Methods in Spatial Epidemiology , 2006 .

[4]  Danny Pfeffermann,et al.  New important developments in small area estimation , 2013, 1302.4907.

[5]  S. Rosenbaum,et al.  Food Taxation in the United Kingdom, France, Germany, and the United States , 1908 .

[6]  Jon Wakefield,et al.  The use of sampling weights in Bayesian hierarchical models for small area estimation. , 2014, Spatial and spatio-temporal epidemiology.

[8]  D. Horvitz,et al.  A Generalization of Sampling Without Replacement from a Finite Universe , 1952 .

[9]  Nathaniel Schenker,et al.  Combining Information From Two Surveys to Estimate County-Level Prevalence Rates of Cancer Risk Factors and Screening , 2007 .

[10]  R. Little,et al.  Inference for the Population Total from Probability-Proportional-to-Size Samples Based on Predictions from a Penalized Spline Nonparametric Model , 2003 .

[11]  A B Lawson,et al.  Comparing INLA and OpenBUGS for hierarchical Poisson modeling in disease mapping. , 2015, Spatial and spatio-temporal epidemiology.

[12]  Yajuan Si,et al.  Bayesian Nonparametric Weighted Sampling Inference , 2013, 1309.1799.

[13]  H. Rue,et al.  Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations , 2009 .

[14]  Danny Pfeffermann,et al.  Comment: Struggles with Survey Weighting and Regression Modeling , 2007 .

[15]  J. N. K. Rao,et al.  Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective Appraisal , 2011, 1108.2356.

[16]  Jon Wakefield,et al.  A comparison of spatial smoothing methods for small area estimation with sampling weights. , 2014, Spatial statistics.

[17]  R. Little,et al.  Bayesian penalized spline model-based inference for finite population proportion in unequal probability sampling. , 2010, Survey methodology.

[18]  María Dolores Ugarte,et al.  Spline smoothing in small area trend estimation and forecasting , 2009, Comput. Stat. Data Anal..

[19]  R. Fay,et al.  Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data , 1979 .

[20]  R. Royall.  On finite population sampling theory under certain linear regression models , 1970 .

[21]  R. Little,et al.  Penalized Spline Model-Based Estimation of the Finite Populations Total from Probability-Proportional-to-Size Samples , 2003 .

[22]  Tihomir Asparouhov,et al.  General Multi-Level Modeling with Sampling Weights , 2006 .

[23]  J. Besag,et al.  Bayesian image restoration, with two applications in spatial statistics , 1991 .

[24]  B. Efron,et al.  Data Analysis Using Stein's Estimator and its Generalizations , 1975 .

[25]  Andrew Gelman,et al.  Struggles with survey weighting and regression modeling , 2007, 0710.5005.

[26]  Isabel Molina,et al.  Small Area Estimation: Rao/Small Area Estimation , 2005 .

[27]  A. Gelman.  Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[28]  R. Little.  Comment: Struggles with Survey Weighting and Regression Modeling , 2007, 0710.5013.

[29]  Hukum Chandra,et al.  Small area estimation using a nonparametric model-based direct estimator , 2010, Comput. Stat. Data Anal..

[30]  N Hens,et al.  Model-based inference for small area estimation with sampling weights. , 2016, Spatial statistics.

[31]  Peter Congdon,et al.  Estimating Small Area Diabetes Prevalence in the US Using the Behavioral Risk Factor Surveillance System , 2010, Journal of Data Science.