Abstract
Quantile regression (QR) is a valuable tool for data analysis and multiple imputation (MI) of missing values – especially when standard parametric modelling assumptions are violated. Yet, Monte Carlo simulations that systematically evaluate QR-based MI in a variety of different practically relevant settings are still scarce. In this paper, we evaluate the method regarding the imputation of ordinal data and compare the results with other standard and robust imputation methods. We then apply QR-based MI to an empirical dataset, where we seek to identify risk factors for corporal punishment of children by their fathers. We compare the modelling results with previously published findings based on complete cases. Our Monte Carlo results highlight the advantages of QR-based MI over fully parametric imputation models: QR-based MI yields unbiased statistical inferences across large parts of the conditional distribution, when parametric modelling assumptions, such as normal and homoscedastic error terms, are violated. Regarding risk factors for corporal punishment, our MI results support previously published findings based on complete cases. Our empirical results indicate that the identified “missing at random” processes in the investigated dataset are negligible.
Highlights
Quantile regression (QR) is a valuable tool for data analysis and multiple imputation (MI) of missing values – especially when standard parametric modelling assumptions are violated
We expect QR- and GAMLSS-based MI to yield comparable results. We assume that both approaches will outperform predictive mean matching (PMM) and standard normal model-based MI – especially when quantiles farther away from the center of the distribution of the response are considered: PMM and normal model-based MI create imputations based on predictions for the conditional mean
Results were averaged across all parameter estimates; pmm is predictive mean matching; rq is quantile regression-based MI; gamlss is MI based on generalized additive models for location, scale, and shape; norm is Bayesian linear regression. % Bias above 10% of the true population parameter was considered substantial
Summary
Kristian Kleinke 1, Markus Fritsch 2, Mark Stemmler 3, Jost Reinecke 4, Friedrich Lösel 3,5. [1] Department of Eductation Studies and Psychology, University of Siegen, Siegen, Germany. [2] School of Business, Economics and Information Systems, University of Passau, Passau, Germany. [3] Institute of Psychology, University of Erlangen-Nurnberg, Erlangen, Germany. [4] Faculty of Sociology, University of Bielefeld, Bielefeld, Germany. [5] Institute of Criminology, University of Cambridge, Cambridge, United Kingdom
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