Nonresponse is a common problem in survey sampling. Appropriate treatment can be challenging, especially when dealing with detailed breakdowns of totals. Often, the nearest neighbor imputation method is used to handle such incomplete multinomial data. In this article, we investigate the nearest neighbor ratio imputation estimator, in which auxiliary variables are used to identify the closest donor and the vector of proportions from the donor is applied to the total of the recipient to implement ratio imputation. To estimate the asymptotic variance, we first treat the nearest neighbor ratio imputation as a special case of predictive matching imputation and apply the linearization method of \cite{yang2020asymptotic}. To account for the non-negligible sampling fractions, parametric and generalized additive models are employed to incorporate the smoothness of the imputation estimator, which results in a valid variance estimator. We apply the proposed method to estimate expenditures detail items based on empirical data from the 2018 collection of the Service Annual Survey, conducted by the United States Census Bureau. Our simulation results demonstrate the validity of our proposed estimators and also confirm that the derived variance estimators have good performance even when the sampling fraction is non-negligible.
Missing data is a common problem in medical research, and is commonly addressed using multiple imputation. Although traditional imputation methods allow for valid statistical inference when data are missing at random (MAR), their implementation is problematic when the presence of missingness depends on unobserved variables, i.e. the data are missing not at random (MNAR). Unfortunately, this MNAR situation is rather common, in observational studies, registries and other sources of real-world data. While several imputation methods have been proposed for addressing individual studies when data ar…
Missingness in categorical data is a common problem in various real applications. Traditional approaches either utilize only the complete observations or impute the missing data by some ad hoc methods rather than the true conditional distribution of the missing data, thus losing or distorting the rich information in the partial observations. In this paper, we propose the Dirichlet Process Mixture of Collapsed Product-Multinomials (DPMCPM) to model the full data jointly and compute the model efficiently. By fitting an infinite mixture of product-multinomial distributions, DPMCPM is applicable f…
Imputation procedures in biomedical fields have turned into statistical practice, since further analyses can be conducted ignoring the former presence of missing values. In particular, non-parametric imputation schemes like the random forest or a combination with the stochastic gradient boosting have shown favorable imputation performance compared to the more traditionally used MICE procedure. However, their effect on valid statistical inference has not been analyzed so far. This paper closes this gap by investigating their validity for inferring mean differences in incompletely observed pairs…
When analyzing incomplete data, is it better to use multiple imputation (MI) or full information maximum likelihood (ML)? In large samples ML is clearly better, but in small samples ML's usefulness has been limited because ML commonly uses normal test statistics and confidence intervals that require large samples. We propose small-sample t-based ML confidence intervals that have good coverage and are shorter than t-based confidence intervals under MI. We also show that ML point estimates are less biased and more efficient than MI point estimates in small samples of bivariate normal data. With …
Multiple imputation (MI) is a technique especially designed for handling missing data in public-use datasets. It allows analysts to perform incomplete-data inference straightforwardly by using several already imputed datasets released by the dataset owners. However, the existing MI tests require either a restrictive assumption on the missing-data mechanism, known as equal odds of missing information (EOMI), or an infinite number of imputations. Some of them also require analysts to have access to restrictive or non-standard computer subroutines. Besides, the existing MI testing procedures cove…
We focus on the problem of generalizing a causal effect estimated on a randomized controlled trial (RCT) to a target population described by a set of covariates from observational data. Available methods such as inverse propensity sampling weighting are not designed to handle missing values, which are however common in both data sources. In addition to coupling the assumptions for causal effect identifiability and for the missing values mechanism and to defining appropriate estimation strategies, one difficulty is to consider the specific structure of the data with two sources and treatment an…
We introduce methods for estimating the spectral density of a random field on a $d$-dimensional lattice from incomplete gridded data. Data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance function. The imputations are convenient computationally, in that circulant embedding and preconditioned conjugate gradient methods can produce imputations in $O(n\log n)$ time and $O(n)$ memory. However, these so-called periodic imputations are motivated mainly by their ability to produce accurace spectral density estimates. In addition, we introduce a parametr…
Missing data are ubiquitous in real world applications and, if not adequately handled, may lead to the loss of information and biased findings in downstream analysis. Particularly, high-dimensional incomplete data with a moderate sample size, such as analysis of multi-omics data, present daunting challenges. Imputation is arguably the most popular method for handling missing data, though existing imputation methods have a number of limitations. Single imputation methods such as matrix completion methods do not adequately account for imputation uncertainty and hence would yield improper statist…
Three-level data structures arising from repeated measures on individuals clustered within larger units are common in health research studies. Missing data are prominent in such studies and are often handled via multiple imputation (MI). Although several MI approaches can be used to account for the three-level structure, including adaptations to single- and two-level approaches, when the substantive analysis model includes interactions or quadratic effects these too need to be accommodated in the imputation model. In such analyses, substantive model compatible (SMC) MI has shown great promise …
We consider the problem of handling missing data with deep latent variable models (DLVMs). First, we present a simple technique to train DLVMs when the training set contains missing-at-random data. Our approach, called MIWAE, is based on the importance-weighted autoencoder (IWAE), and maximises a potentially tight lower bound of the log-likelihood of the observed data. Compared to the original IWAE, our algorithm does not induce any additional computational overhead due to the missing data. We also develop Monte Carlo techniques for single and multiple imputation using a DLVM trained on an inc…
Causal discovery algorithms estimate causal graphs from observational data. This can provide a valuable complement to analyses focussing on the causal relation between individual treatment-outcome pairs. Constraint-based causal discovery algorithms rely on conditional independence testing when building the graph. Until recently, these algorithms have been unable to handle missing values. In this paper, we investigate two alternative solutions: Test-wise deletion and multiple imputation. We establish necessary and sufficient conditions for the recoverability of causal structures under test-wise…
Missing data occur in many types of studies and typically complicate the analysis. Multiple imputation, either using joint modelling or the more flexible fully conditional specification approach, are popular and work well in standard settings. In settings involving non-linear associations or interactions, however, incompatibility of the imputation model with the analysis model is an issue often resulting in bias. Similarly, complex outcomes such as longitudinal or survival outcomes cannot be adequately handled by standard implementations. In this paper, we introduce the R package JointAI, whic…
Partial least squares regression---or PLS---is a multivariate method in which models are estimated using either the SIMPLS or NIPALS algorithm. PLS regression has been extensively used in applied research because of its effectiveness in analysing relationships between an outcome and one or several components. Note that the NIPALS algorithm is able to provide estimates on incomplete data. Selection of the number of components used to build a representative model in PLS regression is an important problem. However, how to deal with missing data when using PLS regression remains a matter of debate…
Using directed acyclic graphs to determine whether multiple imputation or subsample multiple imputation estimates of an exposure-outcome association are unbiased
Analysis of sample survey data often requires adjustments to account for missing data in the outcome variables of principal interest. Standard adjustment methods based on item imputation or on propensity weighting factors rely heavily on the availability of auxiliary variables for both responding and non-responding units. Application of these adjustment methods can be especially challenging in cases for which the auxiliary variables are numerous and are themselves subject to substantial incomplete-data problems. This paper shows how classification and regression trees and forests can overcome …
For multi-source data, blocks of variable information from certain sources are likely missing. Existing methods for handling missing data do not take structures of block-wise missing data into consideration. In this paper, we propose a Multiple Block-wise Imputation (MBI) approach, which incorporates imputations based on both complete and incomplete observations. Specifically, for a given missing pattern group, the imputations in MBI incorporate more samples from groups with fewer observed variables in addition to the group with complete observations. We propose to construct estimating equatio…
Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering algorithm to the resulting altered dataset. Here, we develop clustering methodology through a model-based approach using the marginal density for the observed values, assuming a finite mixture model of multivariate $t$ distributions. We compare our approximate algorithm to the corresponding full expectation-maximization (EM) approach that considers the missing valu…
