New important developments in small area estimation

The purpose of this paper is to review and discuss some of the new important developments in small area estimation (SAE) methods. Rao (2003) wrote a very comprehensive book, which covers all the main developments in this topic until that time and so the focus of this review is on new developments in the last 7 years. However, to make the review more self contained, I also repeat shortly some of the older developments. The review covers both design based and model-dependent methods with emphasis on the prediction of the area target quantities and the assessment of the prediction error. The style of the paper is similar to the style of my previous review on SAE published in 2002, explaining the new problems investigated and describing the proposed solutions, but without dwelling on theoretical details, which can be found in the original articles. I am hoping that this paper will be useful both to researchers who like to learn more on the research carried out in SAE and to practitioners who might be interested in the application of the new methods

Estimation of treatment effects in observational studies by recovering the assignment probabilities and the population model

In observational studies the assignment of units to treatments is with unknown probabilities. Consequently, estimation and comparison of treatment effects based on the empirical distributions of the response under the various treatments can be biased since units exposed to one treatment could differ in important but unknown characteristics from units exposed to other treatments. In this article we study the plausibility of analyzing observational data by deriving the parametric distribution of the observed response under a given treatment as a function of the distribution that would be obtained under a strongly ignorable assignment, and the assignment process, which is modeled as a function of the observed data (the response and covariate values). The use of this approach is founded by showing that the sample distribution of the observed responses is identifiable under some general conditions. The goodness of fit of this distribution can be tested by using standard test statistics since it refers to the observed data, but we also develop a new test. The proposed approach allows also testing the assumptions underlying the use of methods that employ instrumental variables, or methods that use propensity scores with a given set of covariates.We assess the performance of the proposed approach and compare it to existing approaches using data collected in the year 2000 by OECD for the Programme for International Student Assessment (PISA). In the present application we compare students’ scores in mathematics between public and private schools in Ireland and conclude, somewhat surprisingly, that the public schools perform better than the private schools. This finding is supported by one of the existing methods as well

Ethics and OR: Operationalising Discourse Ethics

Operational researchers help managers decide what they ought to do and yet this is generally evaluated in terms of efficiency or effectiveness, not ethicality. However, the combination of the tremendous power of global corporations and the financial markets, and the problems the world faces in terms of economic and environmental sustainability, has led to a revival of interest in ethical approaches. This paper explores a relatively recent and innovative process called discourse ethics. This is very different from traditional ethical systems in taking ethical decisions away from individuals or committees and putting them in the hands of the actual people who are involved and affected through processes of debate and deliberation. The paper demonstrates that discourse ethics has strong connections to OR, especially in the areas of soft and critical systems, and that OR can actually contribute to the practical operationalisation of discourse ethics. At the same time, discourse ethics can provide a rigorous discursive framework for “ethics beyond the model"

Bootstrap Approximation to Prediction MSE for State-Space Models with Estimated Parameters

We propose a simple but general bootstrap method for estimating the Prediction Mean Square Error (PMSE) of the state vector predictors when the unknown model parameters are estimated from the observed series. As is well known, substituting the model parameters by the sample estimates in the theoretical PMSE expression that assumes known parameter values results in under-estimation of the true PMSE. Methods proposed in the literature to deal with this problem in state-space modelling are inadequate and may not even be operational when fitting complex models, or when some of the parameters are close to their boundary values. The proposed method consists of generating a large number of series from the model fitted to the original observations, re-estimating the model parameters using the same method as used for the observed series and then estimating separately the component of PMSE resulting from filter uncertainty and the component resulting from parameter uncertainty. Application of the method to a model fitted to sample estimates of employment ratios in the U.S.A. that contains eighteen unknown parameters estimated by a three-step procedure yields accurate results. The procedure is applicable to mixed linear models that can be cast into state-space form. (Updated 6th October 2004

State-space modeling with correlated measurements with application to small area estimation under benchmark constraints

The problem of Small Area Estimation is how to produce reliable estimates of area (domain) characteristics, when the sizes within the areas are too small to warrant the use of traditional direct survey estimates. This problem is commonly tackled by borrowing information from either neighboring areas and/or from previous surveys, using appropriate time series/cross-sectional models. In order to protect against possible model breakdowns and for other reasons, it is often required to benchmark the model dependent estimates to the corresponding direct survey estimates in larger areas, for which the survey estimates are sufficiently accurate. The benchmarking process defines another way of borrowing information across the areas.This article shows how benchmarking can be implemented with the state-space models used by the Bureau of Labor Statistics in the U.S. for the production of the monthly employment and unemployment estimates at the state level. The computation of valid estimators for the variances of the benchmarked estimators requires joint modeling of the direct estimators in several states, which in turn requires the development of a filtering algorithm for state-space models with correlated measurement errors. No such algorithm has been developed so far. The application of the proposed procedure is illustrated using real unemployment series

Imputation and estimation under nonignorable nonresponse for household surveys with missing covariate information

In this paper we develop and apply new methods for handling not missing at random (NMAR) nonresponse. We assume a model for the outcome variable under complete response and a model for the response probability, which is allowed to depend on the outcome and auxiliary variables. The two models define the model holding for the outcomes observed for the responding units, which can be tested. Our methods utilize information on the population totals of some or all of the auxiliary variables in the two models, but we do not require that the auxiliary variables are observed for the nonresponding units. We develop an algorithm for estimating the parameters governing the two models and show how to estimate the distributions of the missing covariates and outcomes, which are then used for imputing the missing values for the nonresponding units and for estimating population means and the variances of the estimators. We also consider several test statistics for testing the model fitted to the observed data and study their performance, thus validating the proposed procedure. The new developments are illustrated using simulated data and a real data set collected as part of the Household Expenditure Survey carried out by the Israel Central Bureau of Statistics in 2005

Small Area Estimation under a Two Part Random Effects Model with Application to Estimation of Literacy in Developing Countries

The UNESCO Institute for Statistics has initiated a programme to collect data on the level of literacy of adults in developing countries. This will involve conducting small-scale surveys in a few countries that will consist of giving interviewees aged 15+ a test to measure their literacy score. One of the main objectives of these surveys is to obtain summary measures of literacy levels in small geographical areas for which only very small samples would be available, thus requiring the use of model based small area estimation methods.Available methods are not suitable, however, for this kind of data due to the mixed distribution of the literacy scores in developing countries. This distribution has a large peak at zero, i.e., a large proportion of adults that are illiterate, and juxtaposed to this peak is an approximately bell-shaped distribution of the non-zero scores measured for the rest of the sample.In this paper we develop a two part three-level model that is suitable for this kind of data and show how to obtain the small area measures and their variances, or compute confidence intervals, based on this model. The proposed method is illustrated using simulated data and data obtained from a similar literacy survey conducted in Cambodia. <br/

Small area estimation under a two-part random effects model with application to estimation of literacy in developing countries

This paper considers situations where the target response value is either zero or an observation from a continuousdistribution. A typical example analyzed in the paper is the assessment of literacy proficiency with the possible outcome being either zero, indicating illiteracy, or a positive score measuring the level of literacy. Our interest is in how to obtain valid estimates of the average response, or the proportion of positive responses in small areas, for which only small samples or no samples are available. As in other small area estimation problems, the small sample sizes in at least some of the sampled areas and/or the existence of nonsampled areas requires the use of model based methods. Available methods, however, are not suitable for this kind of data because of the mixed distribution of the responses, having a large peak at zero,juxtaposed to a continuous distribution for the rest of the responses. We develop, therefore, a suitable two-part random effects model and show how to fit the model and assess its goodness of fit, and how to compute the small area estimators of interest and measure their precision. The proposed method is illustrated using simulated data and data obtained from a literacy survey conducted in Cambodia