Research Article
A Bayesian Latent Class Framework for Multiple Imputation of Multivariate Categorical Data Under Ignorable and Non-Ignorable Missingness
Daniel Fundi Murithi*
,
Josephine Njeri Ngure,
Victor Muthama Musau
Issue:
Volume 15, Issue 6, December 2026
Pages:
317-340
Received:
24 September 2026
Accepted:
8 October 2026
Published:
11 November 2026
DOI:
10.11648/j.ajtas.20261506.11
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Abstract: Missing data in multivariate categorical datasets are commonly handled under the Missing at Random (MAR) assumption, although this assumption may be inadequate when nonresponse is associated with unobserved response patterns. This study develops a covariate-dependent Bayesian latent class model for multiple imputation under Missing Not at Random (MNAR), denoted by BLCMMNAR. The model specifies covariate-dependent latent class membership through multinomial logistic regression, while the missingness indicators are modelled as Bernoulli variables with class-specific response probabilities. The response and missingness processes are thereby associated through their shared dependence on latent class membership. Bayesian estimation is implemented using Gibbs sampling, with Pólya–Gamma data augmentation for the class-membership regression coefficients, and missing responses are generated from the posterior predictive distribution. Finite-sample performance was examined through 500 simulation replications under scenarios with no, moderate, and strong covariate effects at primary sample sizes of 500 and 1,000. Multiple-imputation RMSE was additionally examined across sample sizes of 500, 1,000, 1,500, 2,000, and 2,500 to assess its behaviour with increasing sample size. BLCMMNAR was evaluated alongside a baseline Bayesian latent class model without covariates (BLCM0) and a covariate-dependent MAR formulation (BLCMMAR). Across the simulation settings, bias in multiple-imputation estimates was negligible for all three models, while relative RMSE varied by scenario and sample size. BLCMMNAR attained the lowest multiple-imputation RMSE in three of the six primary simulation conditions and recovered the class-specific response probabilities with small bias and RMSE. Recovery of latent class proportions and class-membership coefficients varied across scenarios and sample sizes, and improved point recovery did not uniformly correspond to improved interval calibration. The models were further applied to data from 32,156 women in the 2022 Kenya Demographic and Health Survey (KDHS). All three specifications were fitted with ten latent classes, but their posterior class occupancies differed. The completed-data and imputed-only distributions showed substantial sensitivity to the assumed missingness specification, particularly for skilled antenatal care, skilled delivery, and household decision-making outcomes. BLCM0 and BLCMMAR produced broadly similar imputations for several outcomes, whereas BLCMMNAR produced materially different distributions. Class-specific response probabilities under BLCMMNAR also exhibited substantial heterogeneity across latent classes. These findings demonstrate the importance of accounting for potential nonignorable missingness in Bayesian multiple imputation of multivariate categorical data and provide a framework for assessing the sensitivity of imputations to alternative assumptions about the missingness process.
Abstract: Missing data in multivariate categorical datasets are commonly handled under the Missing at Random (MAR) assumption, although this assumption may be inadequate when nonresponse is associated with unobserved response patterns. This study develops a covariate-dependent Bayesian latent class model for multiple imputation under Missing Not at Random (M...
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