Multiple imputation of incomplete categorical data using latent class analysis

Sociological Methodology (Impact Factor: 3). 04/2008; 38(1). DOI: 10.1111/j.1467-9531.2008.00202.x

ABSTRACT We propose using latent class analysis as an alternative to log-linear analysis for the multiple imputation of incomplete categorical data. Similar to log-linear models, latent class models can be used to describe complex association structures between the variables used in the imputation model. However, unlike log-linear models, latent class models can be used to build large imputation models containing more than a few categorical variables. To obtain imputations reflecting uncertainty about the unknown model parameters, we use a nonparametric bootstrap procedure as an alternative to the more common full Bayesian approach. The proposed multiple imputation method, which is implemented in Latent GOLD software for latent class analysis, is illustrated with two examples. In a simulated data example, we compare the new method to well-established methods such as maximum likelihood estimation with incomplete data and multiple imputation using a saturated log-linear model. This example shows that the proposed method yields unbiased parameter estimates and standard errors. The second example concerns an application using a typical social sciences data set. It contains 79 variables that are all included in the imputation model. The proposed method is especially useful for such large data sets because standard methods for dealing with missing data in categorical variables break down when the number of variables is so large.

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    ABSTRACT: The thesis develops nonparametric Bayesian models to handle incomplete categorical variables in data sets with high dimension using the framework of multiple imputation. It presents methods for ignorable missing data in cross-sectional studies, and potentially non-ignorable missing data in panel studies with refreshment samples. The �first contribution is a fully Bayesian, joint modeling approach of multiple imputation for categorical data based on Dirichlet process mixtures of multinomial distributions. The approach automatically models complex dependencies while being computationally expedient. I illustrate repeated sampling properties of the approach using simulated data. This approach o�ffers better performance than default chained equations methods, which are often used in such settings. I apply the methodology to impute missing background data in the 2007 Trends in International Mathematics and Science Study. For the second contribution, I extend the nonparametric Bayesian imputation engine to consider a mix of potentially non-ignorable attrition and ignorable item nonresponse in multiple wave panel studies. Ignoring the attrition in models for panel data can result in biased inference if the reason for attrition is systematic and related to the missing values. Panel data alone cannot estimate the attrition effect without untestable assumptions about the missing data mechanism. Refreshment samples off�er an extra data source that can be utilized to estimate the attrition eff�ect while reducing reliance on strong assumptions of the missing data mechanism. I consider two novel Bayesian approaches to handle the attrition and item nonresponse simultaneously under multiple imputation in a two wave panel with one refreshment sample when the variables involved are categorical and high dimensional. First, I present a semi-parametric selection model that includes an additive nonignorable attrition model with main eff�ects of all variables, including demographic variables and outcome measures in wave 1 and wave 2. The survey variables are modeled jointly using Bayesian mixture of multinomial distributions. I develop the posterior computation algorithms for the semi-parametric selection model under different prior choices for the regression coeffi�cients in the attrition model. Second, I propose two Bayesian pattern mixture models for this scenario that use latent classes to model the dependency among the variables and the attrition. I develop a dependent Bayesian latent pattern mixture model for which variables are modeled via latent classes and attrition is treated as a covariate in the class allocation weights. And, I develop a joint Bayesian latent pattern mixture model, for which attrition and variables are modeled jointly via latent classes. I show via simulation studies that the pattern mixture models can recover true parameter estimates, even when inferences based on the panel alone are biased from attrition. I apply both the selection and pattern mixture models to data from the 2007-2008 Associated Press/Yahoo News election panel study.
    07/2012, Degree: PhD, Supervisor: Jerome P Reiter
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    ABSTRACT: Latent class analysis (LCA) has been found to have important applications in social and behavioural sciences for modelling categorical response variables, and non-response is typical when collecting data. In this study, the non-response mainly included ‘contingency questions’ and real ‘missing data’. The primary objective of this study was to evaluate the effects of some potential factors on model selection indices in LCA with non-response data. We simulated missing data with contingency question and evaluated the accuracy rates of eight information criteria for selecting the correct models. The results showed that the main factors are latent class proportions, conditional probabilities, sample size, the number of items, the missing data rate and the contingency data rate. Interactions of the conditional probabilities with class proportions, sample size and the number of items are also significant. From our simulation results, the impact of missing data and contingency questions can be amended by increasing the sample size or the number of items.
    Journal of Statistical Computation and Simulation 06/2012; DOI:10.1080/00949655.2012.698621 · 0.71 Impact Factor
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    ABSTRACT: In this paper we propose a latent class based multiple imputation approach for analyzing missing categorical covariate data in a highly stratified data model. In this approach, we impute the missing data assuming a latent class imputation model and we use likelihood methods to analyze the imputed data. Via extensive simulations, we study its statistical properties and make comparisons with complete case analysis, multiple imputation, saturated log-linear multiple imputation and the Expectation–Maximization approach under seven missing data mechanisms (including missing completely at random, missing at random and not missing at random). These methods are compared with respect to bias, asymptotic standard error, type I error, and 95% coverage probabilities of parameter estimates. Simulations show that, under many missingness scenarios, latent class multiple imputation performs favorably when jointly considering these criteria. A data example from a matched case–control study of the association between multiple myeloma and polymorphisms of the Inter-Leukin 6 genes is considered.
    Journal of Statistical Planning and Inference 11/2010; 140(11):3252–3262. DOI:10.1016/j.jspi.2010.04.020 · 0.60 Impact Factor

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