Hot deck imputation is a method for handling missing data in which each missing value is replaced with an observed response from a “similar” unit. Despite being used extensively in practice, the theory is not as well developed as that of other imputation methods. We have found that no consensus exists as to the best way to apply the hot deck and obtain inferences from the completed data set. Here we review different forms of the hot deck and existing research on its statistical properties. We describe applications of the hot deck currently in use, including the U.S. Census Bureau’s hot deck for the Current Population Survey (CPS). We also provide an extended example of variations of the hot deck applied to the third National Health and Nutrition Examination Survey (NHANES III). Some potential areas for future research are highlighted.

/pdf/a-review-of-hot-deck-imputation-for-survey-non-response-i9se16l20w.pdf

A Review of Hot Deck Imputation for Survey Non-response.

(2008). Introduction to Variance Estimation. Journal of the American Statistical Association: Vol. 103, No. 483, pp. 1324-1325.

Introduction to Variance Estimation

BACKGROUND Depression is more common in obese than non-obese individuals, especially in women, but the causal relationship between obesity and depression is complex and uncertain. Previous studies have used genetic variants associated with BMI to provide evidence that higher body mass index (BMI) causes depression, but have not tested whether this relationship is driven by the metabolic consequences of BMI nor for differences between men and women. METHODS We performed a Mendelian randomization study using 48 791 individuals with depression and 291 995 controls in the UK Biobank, to test for causal effects of higher BMI on depression (defined using self-report and Hospital Episode data). We used two genetic instruments, both representing higher BMI, but one with and one without its adverse metabolic consequences, in an attempt to 'uncouple' the psychological component of obesity from the metabolic consequences. We further tested causal relationships in men and women separately, and using subsets of BMI variants from known physiological pathways. RESULTS Higher BMI was strongly associated with higher odds of depression, especially in women. Mendelian randomization provided evidence that higher BMI partly causes depression. Using a 73-variant BMI genetic risk score, a genetically determined one standard deviation (1 SD) higher BMI (4.9 kg/m2) was associated with higher odds of depression in all individuals [odds ratio (OR): 1.18, 95% confidence interval (CI): 1.09, 1.28, P = 0.00007) and women only (OR: 1.24, 95% CI: 1.11, 1.39, P = 0.0001). Meta-analysis with 45 591 depression cases and 97 647 controls from the Psychiatric Genomics Consortium (PGC) strengthened the statistical confidence of the findings in all individuals. Similar effect size estimates were obtained using different Mendelian randomization methods, although not all reached P < 0.05. Using a metabolically favourable adiposity genetic risk score, and meta-analysing data from the UK biobank and PGC, a genetically determined 1 SD higher BMI (4.9 kg/m2) was associated with higher odds of depression in all individuals (OR: 1.26, 95% CI: 1.06, 1.50], P = 0.010), but with weaker statistical confidence. CONCLUSIONS Higher BMI, with and without its adverse metabolic consequences, is likely to have a causal role in determining the likelihood of an individual developing depression.

Using genetics to understand the causal influence of higher BMI on depression.

Foundations of Statistical Inference

C. H. Albert (cecile.albert@m4x.org) and W. Thuiller, Laboratoire d’Ecologie Alpine, UMR-CNRS 5553, Univ. Joseph Fourier, Bp 53,FR-38041 Grenoble Cedex 9, France. N. G. Yoccoz, Dept of Arctic and Marine Biology, Faculty of Biosciences, Fisheries and Economics,Univ. of Tromso, NO-9037 Tromso, Norway. T. C. Edwards, Jr, U.S. Geological Survey, Utah Cooperative Fish and Wildlife Research Unitand Wildland Resources, Utah State Univ., Logan, UT 84322-5290, USA. C. H. Graham, Dept of Ecology and Evolution, Stony BrookUniv., Stony Brook, NY 11794, USA. N. E. Zimmermann, Land Use Dynamics, Swiss Federal Research Inst. WSL, CH-8903 Birmensdorf,Switzerland.Sampling is a key issue for answering most ecological and evolutionary questions. The importance of developing arigorous sampling design tailored to specific questions has already been discussed in the ecological and sampling literatureand has provided useful tools and recommendations to sample and analyse ecological data. However, sampling issues areoften difficult to overcome in ecological studies due to apparent inconsistencies between theory and practice, oftenleading to the implementation of simplified sampling designs that suffer from unknown biases. Moreover, we believe thatclassical sampling principles which are based on estimation of means and variances are insufficient to fully address manyecological questions that rely on estimating relationships between a response and a set of predictor variables over time andspace. Our objective is thus to highlight the importance of selecting an appropriate sampling space and an appropriatesampling design. We also emphasize the importance of using prior knowledge of the study system to estimate models orcomplex parameters and thus better understand ecological patterns and processes generating these patterns. Using a semi-virtual simulation study as an illustration we reveal how the selection of the space (e.g. geographic, climatic), in whichthe sampling is designed, influences the patterns that can be ultimately detected. We also demonstrate the inefficiency ofcommon sampling designs to reveal response curves between ecological variables and climatic gradients. Further, we showthat response-surface methodology, which has rarely been used in ecology, is much more efficient than more traditionalmethods. Finally, we discuss the use of prior knowledge, simulation studies and model-based designs in definingappropriate sampling designs. We conclude by a call for development of methods to unbiasedly estimate nonlinearecologically relevant parameters, in order to make inferences while fulfilling requirements of both sampling theory andfield work logistics.

/pdf/sampling-in-ecology-and-evolution-bridging-the-gap-between-39l6yd10k3.pdf

Sampling in ecology and evolution – bridging the gap between theory and practice

There are two different empirical likelihood approaches for complex sampling designs: the “pseudo-empirical likelihood ” introduced by Chen and Sitter (1999) and the “unequal probability empirical likelihood ” approach proposed by Berger and Torres (2014, 2016). Both approaches are described and reviewed critically. We do not pretend to give an exhaustive account of all the applications of empirical likelihood in survey sampling. This paper is an extended version of Berger (2018b).

Empirical likelihood approaches in survey sampling

Survey data are often collected with unequal probabilities from a stratified population. We propose an empirical likelihood approach for sample data selected with unequal probabilities. We show that the empirical likelihood ratio statistic follows a chi-squared distribution asymptotically. The approach proposed does not rely on variance estimates, re-sampling or joint-inclusion probabilities, even when the parameter of interest is not linear. Standard confidence intervals based on variance estimates may give poor coverages, when normality does not hold. This can be the case with skewed data and outlying values. This paper contains the main results of Oguz-Alper & Berger (2016a,c) published by Oxford University Press. Oguz-Alper & Berger’s (2016a) empirical likelihood confidence interval has good coverages, even when the sampling distribution of the point estimator is not normal.

An empirical likelihood approach for complex sampling

There are two different empirical likelihood approaches for complex sampling designs: “pseudoempirical likelihood” and “unequal probability empirical likelihood”. Both approaches are described and reviewed critically. The key difference is the fact that the self‐normalization property of the pseudoempirical likelihood approach is limited to unidimensional parameters. This property holds for multidimensional parameters, with the unequal probability empirical likelihood approach. This manuscript is a brief description of the key empirical likelihood approaches for complex sampling. This is not an exhaustive account of all the applications of empirical likelihood in survey sampling.

/pdf/empirical-likelihood-approaches-under-complex-sampling-16jf9tbyel.pdf

Empirical likelihood approaches under complex sampling designs

When two surveys carried out separately in the same population have common variables, it might be desirable to adjust each survey’s weights so that they give equal estimates for the common variables. This problem has been studied extensively and has often been referred to as ‘alignment’ or ‘numerical consistency’. We develop a design-based empirical likelihood approach for alignment and estimation of complex parameters defined by estimating equations. We focus on a general case when a single set of adjusted weights, which can be applied to both common and non-common variables, is produced for each survey. The main contribution of the paper is to show that the empirical log-likelihood ratio statistic is pivotal in presence of alignment constraints. This pivotal statistic can be used to test hypotheses and derive confidence regions. Hence, the empirical likelihood approach proposed for alignment possesses the self-normalization property, under a design-based approach. The proposed approach accommodates large sampling fractions, stratification and population level auxiliary information. It is particularly well suited for inference about small domains, when data are skewed. It includes implicit adjustments when the samples considerably differ in size. The confidence regions are constructed without the need for variance estimates, joint-inclusion probabilities, linearisation and re-sampling.

/pdf/empirical-likelihood-approach-for-aligning-information-from-49zwk9ax9z.pdf

Empirical Likelihood Approach for Aligning Information from Multiple Surveys

The Hartley-Rao-Cochran sampling design is an unequal probability sampling design which can be used to select samples from finite populations. We propose to adjust the empirical likelihood approach for the Hartley-Rao-Cochran sampling design. The approach proposed intrinsically incorporates sampling weights, auxiliary information and allows for large sampling fractions. It can be used to construct confidence intervals. In a simulation study, we show that the coverage may be better for the empirical likelihood confidence interval than for standard confidence intervals based on variance estimates. The approach proposed is simple to implement and less computer intensive than bootstrap. The confidence interval proposed does not rely on re-sampling, linearization, variance estimation, design-effects or joint inclusion probabilities.

/pdf/empirical-likelihood-inference-for-the-rao-hartley-cochran-3ymwjzluy1.pdf

Empirical Likelihood Inference for the Rao-Hartley-Cochran Sampling Design.

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