An Empirical Comparison of Multiple Imputation Methods for Categorical Data

Multiple imputation is a common approach for dealing with missing values in statistical databases. The imputer fills in missing values with draws from predictive models estimated from the observed data, resulting in multiple, completed versions of the database. Researchers have developed a variety of default routines to implement multiple imputation; however, there has been limited research comparing the performance of these methods, particularly for categorical data. We use simulation studies to compare repeated sampling properties of three default multiple imputation methods for categorical data, including chained equations using generalized linear models, chained equations using classification and regression trees, and a fully Bayesian joint distribution based on Dirichlet Process mixture models. We base the simulations on categorical data from the American Community Survey. In the circumstances of this study, the results suggest that default chained equations approaches based on generalized linear models are dominated by the default regression tree and Bayesian mixture model approaches. They also suggest competing advantages for the regression tree and Bayesian mixture model approaches, making both reasonable default engines for multiple imputation of categorical data. A supplementary material for this article is available online

Robust bootstrap procedures for the chain-ladder method

Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component one may apply generalized linear models to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive. A popular alternative approach to obtain inference is to use the bootstrap technique. However, the standard procedures are very sensitive to the possible presence of outliers. These atypical observations, deviating from the pattern of the majority of the data, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Even when paired with a robust chain-ladder method, classical bootstrap inference may break down. Therefore, we discuss and implement several robust bootstrap procedures in the claims reserving framework and we investigate and compare their performance on both simulated and real data. We also illustrate their use for obtaining the distribution of one year risk measures

Q-learning: flexible learning about useful utilities

Dynamic treatment regimes are fast becoming an important part of medicine, with the corresponding change in emphasis from treatment of the disease to treatment of the individual patient. Because of the limited number of trials to evaluate personally tailored treatment sequences, inferring optimal treatment regimes from observational data has increased importance. Q-learning is a popular method for estimating the optimal treatment regime, originally in randomized trials but more recently also in observational data. Previous applications of Q-learning have largely been restricted to continuous utility end-points with linear relationships. This paper is the first attempt at both extending the framework to discrete utilities and implementing the modelling of covariates from linear to more flexible modelling using the generalized additive model (GAM) framework. Simulated data results show that the GAM adapted Q-learning typically outperforms Q-learning with linear models and other frequently-used methods based on propensity scores in terms of coverage and bias/MSE. This represents a promising step toward a more fully general Q-learning approach to estimating optimal dynamic treatment regimes

Zero-inflated truncated generalized Pareto distribution for the analysis of radio audience data

Extreme value data with a high clump-at-zero occur in many domains. Moreover, it might happen that the observed data are either truncated below a given threshold and/or might not be reliable enough below that threshold because of the recording devices. These situations occur, in particular, with radio audience data measured using personal meters that record environmental noise every minute, that is then matched to one of the several radio programs. There are therefore genuine zeros for respondents not listening to the radio, but also zeros corresponding to real listeners for whom the match between the recorded noise and the radio program could not be achieved. Since radio audiences are important for radio broadcasters in order, for example, to determine advertisement price policies, possibly according to the type of audience at different time points, it is essential to be able to explain not only the probability of listening to a radio but also the average time spent listening to the radio by means of the characteristics of the listeners. In this paper we propose a generalized linear model for zero-inflated truncated Pareto distribution (ZITPo) that we use to fit audience radio data. Because it is based on the generalized Pareto distribution, the ZITPo model has nice properties such as model invariance to the choice of the threshold and from which a natural residual measure can be derived to assess the model fit to the data. From a general formulation of the most popular models for zero-inflated data, we derive our model by considering successively the truncated case, the generalized Pareto distribution and then the inclusion of covariates to explain the nonzero proportion of listeners and their average listening time. By means of simulations, we study the performance of the maximum likelihood estimator (and derived inference) and use the model to fully analyze the audience data of a radio station in a certain area of Switzerland.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS358 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Generalized Estimating Equations Approach to Model Heterogeneity and Time Dependence in Capture-Recapture Studies

Individual heterogeneity in capture probabilities and time dependence are fundamentally important for estimating the closed animal population parameters in capture-recapture studies. A generalized estimating equations (GEE) approach accounts for linear correlation among capture-recapture occasions, and individual heterogeneity in capture probabilities in a closed population capture-recapture individual heterogeneity and time variation model. The estimated capture probabilities are used to estimate animal population parameters. Two real data sets are used for illustrative purposes. A simulation study is carried out to assess the performance of the GEE estimator. A Quasi-Likelihood Information Criterion (QIC) is applied for the selection of the best fitting model. This approach performs well when the estimated population parameters depend on the individual heterogeneity and the nature of linear correlation among capture-recapture occasions