# Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models with Local Dependence

arXiv: https://arxiv.org/abs/1410.0438 · HTML: https://mlsanity.com/paper/1410.0438/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2014.

## Built on by (most cited first, 10 of 10)

- [Handling Missing Data via Max-Entropy Regularized Graph Autoencoder](https://mlsanity.com/paper/2211.16771/) (2022)
- [Are deep learning models superior for missing data imputation in large surveys? Evidence from an empirical comparison](https://mlsanity.com/paper/2103.09316/) (2021)
- [Explainability of Machine Learning Models under Missing Data](https://mlsanity.com/paper/2407.00411/) (2024)
- [Incomplete Graph Learning: A Comprehensive Survey](https://mlsanity.com/paper/2502.12412/) (2025)
- [Principal Component Analysis based frameworks for efficient missing data imputation algorithms](https://mlsanity.com/paper/2205.15150/) (2022)
- [Conditional expectation with regularization for missing data imputation](https://mlsanity.com/paper/2302.00911/) (2023)
- [A Generalized Theory of Mixup for Structure-Preserving Synthetic Data](https://mlsanity.com/paper/2503.02645/) (2025)
- [Imputation using training labels and classification via label imputation](https://mlsanity.com/paper/2311.16877/) (2023)
- [Directly Handling Missing Data in Linear Discriminant Analysis for Enhancing Classification Accuracy and Interpretability](https://mlsanity.com/paper/2407.00710/) (2024)
- [Markov Missing Graph: A Graphical Approach for Missing Data Imputation](https://mlsanity.com/paper/2509.03410/) (2025)

## Abstract (arXiv)

We present a nonparametric Bayesian joint model for multivariate continuous and categorical variables, with the intention of developing a flexible engine for multiple imputation of missing values. The model fuses Dirichlet process mixtures of multinomial distributions for categorical variables with Dirichlet process mixtures of multivariate normal distributions for continuous variables. We incorporate dependence between the continuous and categorical variables by (i) modeling the means of the normal distributions as component-specific functions of the categorical variables and (ii) forming distinct mixture components for the categorical and continuous data with probabilities that are linked via a hierarchical model. This structure allows the model to capture complex dependencies between the categorical and continuous data with minimal tuning by the analyst. We apply the model to impute missing values due to item nonresponse in an evaluation of the redesign of the Survey of Income and Program Participation (SIPP). The goal is to compare estimates from a field test with the new design to estimates from selected individuals from a panel collected under the old design. We show that accounting for the missing data changes some conclusions about the comparability of the distributions in the two datasets. We also perform an extensive repeated sampling simulation using similar data from complete cases in an existing SIPP panel, comparing our proposed model to a default application of multiple imputation by chained equations. Imputations based on the proposed model tend to have better repeated sampling properties than the default application of chained equations in this realistic setting.