Journal of Data Science

Missing data is a common occurrence in various fields, spanning social science, education, economics, and biomedical research. Disregarding missing data in statistical analyses can introduce bias to study outcomes. To mitigate this issue, imputation methods have proven effective in reducing nonresponse bias and generating complete datasets for subsequent analysis of secondary data. The efficacy of imputation methods hinges on the assumptions of the underlying imputation model. While machine learning techniques such as regression trees, random forest, XGBoost, and deep learning have demonstrated robustness against model misspecification, their optimal performance may necessitate fine-tuning under specific conditions. Moreover, imputed values generated by these methods can sometimes deviate unnaturally, falling outside the normal range. To address these challenges, we propose a novel Predictive Mean Matching imputation (PMM) procedure that leverages popular machine learning-based methods. PMM strikes a balance between robustness and the generation of appropriate imputed values. In this paper, we present our innovative PMM approach and conduct a comparative performance analysis through Monte Carlo simulation studies, assessing its effectiveness against other established methods.

Abstract: Missing data are a common problem for researchers working with surveys and other types of questionnaires. Often, respondents do not respond to one or more items, making the conduct of statistical analyses, as well as the calculation of scores difficult. A number of methods have been developed for dealing with missing data, though most of these have focused on continuous variables. It is not clear that these techniques for imputation are appropriate for the categorical items that make up surveys. However, methods of imputation specifically designed for categorical data are either limited in terms of the number of variables they can accommodate, or have not been fully compared with the continuous data approaches used with categorical variables. The goal of the current study was to compare the performance of these explicitly categorical imputation approaches with the more well established continuous method used with categorical item responses. Results of the simulation study based on real data demonstrate that the continuous based imputation approach and a categorical method based on stochastic regression appear to perform well in terms of creating data that match the complete datasets in terms of logistic regression results.

Longitudinal data analysis had been widely developed in the past three decades. Longitudinal data are common in many fields such as public health, medicine, biological and social sciences. Longitudinal data have special nature as the individual may be observed during a long period of time. Hence, missing values are common in longitudinal data. The presence of missing values leads to biased results and complicates the analysis. The missing values have two patterns: intermittent and dropout. The missing data mechanisms are missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). The appropriate analysis relies heavily on the assumed mechanism and pattern. The parametric fractional imputation is developed to handle longitudinal data with intermittent missing pattern. The maximum likelihood estimates are obtained and the Jackkife method is used to obtain the standard errors of the parameters estimates. Finally a simulation study is conducted to validate the proposed approach. Also, the proposed approach is applied to a real data.

Abstract: Latent class analysis (LCA) is a popular method for analyzing multiple categorical outcomes. Given the potential for LCA model assump tions to influence inference, model diagnostics are a particulary important part of LCA. We suggest using the rate of missing information as an addi tional diagnostic tool. The rate of missing information gives an indication of the amount of information missing as a result of observing multiple sur rogates in place of the underlying latent variable of interest and provides a measure of how confident one can be in the model results. Simulation studies and real data examples are presented to explore the usefulness of the proposed measure.

Subsampling the data is used in this paper as a learning method about the influence of the data points for drawing inference on the parameters of a fitted logistic regression model. The alternative, alternative regularized, alternative regularized lasso, and alternative regularized ridge estimators are proposed for the parameter estimation of logistic regression models and are then compared with the maximum likelihood estimators. The proposed alternative regularized estimators are obtained by using a tuning parameter but the proposed alternative estimators are not regularized. The proposed alternative regularized lasso estimators are the averaged standard lasso estimators and the alternative regularized ridge estimators are also the averaged standard ridge estimators over subsets of groups where the number of subsets could be smaller than the number of parameters. The values of the tuning parameters are obtained to make the alternative regularized estimators very close to the maximum likelihood estimators and the process is explained with two real data as well as a simulated study. The alternative and alternative regularized estimators always have the closed form expressions in terms of observations that the maximum likelihood estimators do not have. When the maximum likelihood estimators do not have the closed form expressions, the alternative regularized estimators thus obtained provide the approximate closed form expressions for them.