Learning Latent and Hierarchical Structures in Cognitive Diagnosis Models

Investigating risk factors associated with injury severity in highway crashes: A hybrid approach integrating two-step cluster analysis and latent class ordered regression model with covariates

Highway crashes are responsible for a significant number of severe and fatal injuries drawing considerable attention from transportation authorities and safety researchers. This paper aims to investigate the unobserved heterogeneous effects of various risk factors, such as pre-crash circumstances, environmental and road conditions, vehicle-involved information, and driver attributes on injury severities. Our methodology uses a hybrid approach that combines two-step cluster analysis and latent class ordered regression model with covariates. The proposed approach extends traditional latent class model by elucidating potential relationships among predictors, covariates, and outcomes. A cross-sectional crash data covering a period of over five years (2011-2016) was obtained via the Dutch crash registration database for modeling injury severity outcomes. The results reveal substantial and statistically significant differences in injury severity between two latent classes. Moreover, we identify road lighting, time of crash, road surface conditions, weather, and season as covariates influencing class membership prediction. Factors such as high speed, alcohol involvement, frontal collision points, and older driver demographics increase the probability of serious injury and facility across all cases analyzed. Additionally, we observe notable heterogeneity effects between the two classes regarding temporal characteristics, the number and type of vehicles involved, as well as driver gender. Our findings provide specific and valuable insights into injury severity outcomes, which can inform the formulation of targeted safety countermeasures and regulatory strategies for traffic policies and relevant agencies.

Tree-informed Bayesian multi-source domain adaptation: cross-population probabilistic cause-of-death assignment using verbal autopsy

Determining causes of deaths (CODs) occurred outside of civil registration and vital statistics systems is challenging. A technique called verbal autopsy (VA) is widely adopted to gather information on deaths in practice. A VA consists of interviewing relatives of a deceased person about symptoms of the deceased in the period leading to the death, often resulting in multivariate binary responses. While statistical methods have been devised for estimating the cause-specific mortality fractions (CSMFs) for a study population, continued expansion of VA to new populations (or "domains") necessitates approaches that recognize between-domain differences while capitalizing on potential similarities. In this article, we propose such a domain-adaptive method that integrates external between-domain similarity information encoded by a prespecified rooted weighted tree. Given a cause, we use latent class models to characterize the conditional distributions of the responses that may vary by domain. We specify a logistic stick-breaking Gaussian diffusion process prior along the tree for class mixing weights with node-specific spike-and-slab priors to pool information between the domains in a data-driven way. The posterior inference is conducted via a scalable variational Bayes algorithm. Simulation studies show that the domain adaptation enabled by the proposed method improves CSMF estimation and individual COD assignment. We also illustrate and evaluate the method using a validation dataset. The article concludes with a discussion of limitations and future directions.

A two-step estimator for multilevel latent class analysis with covariates

We propose a two-step estimator for multilevel latent class analysis (LCA) with covariates. The measurement model for observed items is estimated in its first step, and in the second step covariates are added in the model, keeping the measurement model parameters fixed. We discuss model identification, and derive an Expectation Maximization algorithm for efficient implementation of the estimator. By means of an extensive simulation study we show that (1) this approach performs similarly to existing stepwise estimators for multilevel LCA but with much reduced computing time, and (2) it yields approximately unbiased parameter estimates with a negligible loss of efficiency compared to the one-step estimator. The proposal is illustrated with a cross-national analysis of predictors of citizenship norms.

A Tensor-EM Method for Large-Scale Latent Class Analysis with Binary Responses

Latent class models are powerful statistical modeling tools widely used in psychological, behavioral, and social sciences. In the modern era of data science, researchers often have access to response data collected from large-scale surveys or assessments, featuring many items (large J) and many subjects (large N). This is in contrary to the traditional regime with fixed J and large N. To analyze such large-scale data, it is important to develop methods that are both computationally efficient and theoretically valid. In terms of computation, the conventional EM algorithm for latent class models tends to have a slow algorithmic convergence rate for large-scale data and may converge to some local optima instead of the maximum likelihood estimator (MLE). Motivated by this, we introduce the tensor decomposition perspective into latent class analysis with binary responses. Methodologically, we propose to use a moment-based tensor power method in the first step and then use the obtained estimates as initialization for the EM algorithm in the second step. Theoretically, we establish the clustering consistency of the MLE in assigning subjects into latent classes when N and J both go to infinity. Simulation studies suggest that the proposed tensor-EM pipeline enjoys both good accuracy and computational efficiency for large-scale data with binary responses. We also apply the proposed method to an educational assessment dataset as an illustration.