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Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients,…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
We consider a finite mixture of regressions (FMR) model for high-dimensional inhomogeneous data where the number of covariates may be much larger than sample size. We propose an l1-penalized maximum likelihood estimator in an appropriate…
We propose a random-effects approach to missing values for generalized linear mixed model (GLMM) analysis. The method converts a GLMM with missing covariates to another GLMM without missing covariates. The standard GLMM analysis tools for…
Linear mixed models with large imbalanced crossed random effects structures pose severe computational problems for maximum likelihood estimation and for Bayesian analysis. The costs can grow as fast as $N^{3/2}$ when there are N…
Trial-based cost-effectiveness analyses (CEAs) are an important source of evidence in the assessment of health interventions. In these studies, cost and effectiveness outcomes are commonly measured at multiple time points, but some…
Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction…
Linear mixed effects models are highly flexible in handling a broad range of data types and are therefore widely used in applications. A key part in the analysis of data is model selection, which often aims to choose a parsimonious model…
We consider linear mixed models in which the observations are grouped. A L1-penalization on the fixed effects coefficients of the log-likelihood obtained by considering the random effects as missing values is proposed. A multicycle ECM…
Large language models (LLMs) are often ensembled together to improve overall reliability and robustness, but in practice models are strongly correlated. This raises a fundamental question: which models should be selected when forming an LLM…
Majority voting over multiple LLM attempts improves mathematical reasoning, but correlated errors limit the effective sample size. A natural fix is to assign different reasoning strategies to different voters. The approach, Diverse Prompt…
The rapid development of large language models (LLMs) has not only provided numerous opportunities but also presented significant challenges. This becomes particularly evident when LLMs inadvertently generate harmful or toxic content,…
We consider a linear mixed-effects model with a clustered structure, where the parameters are estimated using maximum likelihood (ML) based on possibly unbalanced data. Inference with this model is typically done based on asymptotic theory,…
Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…
Power analyses are an important aspect of experimental design, because they help determine how experiments are implemented in practice. It is common to specify a desired level of power and compute the sample size necessary to obtain that…
Large Language Models (LLMs) have transformed artificial intelligence by excelling in complex natural language processing tasks. Their ability to generate human-like text has opened new possibilities for market research, particularly in…
Beta regression models are a suitable choice for continuous response variables on the unity interval. Random effects add further flexibility to the models and accommodate data structures such as hierarchical, repeated measures and…
Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Oftentimes, the number of observations is small, and it is thus important to…
A statistical model is a mathematical representation of an often simplified or idealised data-generating process. In this paper, we focus on a particular type of statistical model, called linear mixed models (LMMs), that is widely used in…
As scaled language models (LMs) approach human-level reasoning capabilities, self-improvement emerges as a solution to synthesizing high-quality data corpus. While previous research has identified model collapse as a risk in…