In this paper, we consider statistical inference for linear regression models when neither the response nor the predictors can be directly observed, but are measured with errors in a multiplicative fashion and distorted as single index models of observable confounding variables. We propose a...

In analyzing correlated data or clustered data with linear or logistic mixed effects model, one commonly assumes that the random effects follow a normal distribution with mean zero. However, this assumption might not be appropriate in many cases. In particular, substantial violation of normality...

An algorithm that computes nonparametric maximum likelihood estimates of a mixing distribution for a logistic regression model containing random intercepts and slopes is proposed. The algorithm identifies mixing distribution support points as the maxima of the gradient function using a direct...

When units belong to a specific group, such as employees nested within companies, the data present a hierarchical structure that can be modeled by using mixed models. In addition to fixed effects, these models estimate the random effects for each group. The problem of assigning values to the...

Mixture model-based methods assuming independence may not be valid for clustering growth trajectories arising from multilevel studies because longitudinal data collected from the same unit are often correlated. A mixture of mixed effects models is considered to capture the correlation using...

Latent class models with crossed subject-specific and test(rater)-specific random effects have been proposed to estimate the diagnostic accuracy (sensitivity and specificity) of a group of binary tests or binary ratings. However, the computation of these models are hindered by their complicated...

Based on a semiparametric Bayesian framework, a joint-quantile regression method is developed for analyzing clustered data, where random effects are included to accommodate the intra-cluster dependence. Instead of posing any parametric distributional assumptions on the random errors, the...

The generalized linear mixed models (GLMMs) for clustered data are studied when covariates are measured with error. The most conventional measurement error models are based on either linear mixed models (LMMs) or GLMMs. Even without the measurement error, the frequentist analysis of LMM, and...

Joint models for longitudinal and time-to-event data have recently attracted a lot of attention in statistics and biostatistics. Even though these models enjoy a wide range of applications in many different statistical fields, they have not yet found their rightful place in the toolbox of modern...

In a register-assisted census, the main information about the population is obtained from population registers. Additionally, a sample is drawn to allow for the estimation of population counts for variables that are not included in the registers. Typically, registers suffer from over and...