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With the arrival of the R packages nlme and lme4, linear mixed models (LMMs) have come to be widely used in experimentally-driven areas like psychology, linguistics, and cognitive science. This tutorial provides a practical introduction to…
This paper introduces the R package slm which stands for Stationary Linear Models. The package contains a set of statistical procedures for linear regression in the general context where the error process is strictly stationary with short…
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…
In clinical trials, studies often present longitudinal data or clustered data. These studies are commonly analyzed using linear mixed models (LMMs), usually considering Gaussian assumptions for random effect and error terms. Recently,…
While distributed parameter estimation has been extensively studied in the literature, little has been achieved in terms of robust analysis and tuning methods in the presence of disturbances. However, disturbances such as measurement noise…
Many real-life data sets can be analyzed using Linear Mixed Models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters…
The analysis of longitudinal data gives the chance to observe how unit behaviors change over time, but it also poses a series of issues. These have been the focus of an extensive literature in the context of linear and generalized linear…
Linear mixed-effects model (LMM) is a cornerstone of longitudinal data analysis, but is limited to adeptly make heterogeneous analyses predictable under both group-specific fixed effects and subject-specific random effects. To address this…
Nonlinear mixed effects modeling is a powerful tool when analyzing data from several entities in an experiment. In this paper, we present NLMEModeling, a package for mixed effects modeling in Wolfram Mathematica. NLMEModeling supports mixed…
Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if…
Additive smooth models, such as Generalized additive models (GAMs) of location, scale, and shape (GAMLSS), are a popular choice for modeling experimental data. However, software available to fit such models is usually not tailored…
We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error…
This paper discusses minimum distance estimation method in the linear regression model with dependent errors which are strongly mixing. The regression parameters are estimated through the minimum distance estimation method, and asymptotic…
Datasets that exhibit non-Gaussian characteristics are common in many fields, while the current modeling framework and available software for non-Gaussian models is limited. We introduce Linear Latent Non-Gaussian Models (LLnGMs), a unified…
In this note, we reconsider Cohen's effect size measure $f^2$ under linear mixed models and demonstrate its application by employing an artificially generated data set. It is shown how $f^2$ can be computed with the statistical software…
We take a new look at parameter estimation for Gaussian Mixture Models (GMMs). In particular, we propose using \emph{Riemannian manifold optimization} as a powerful counterpart to Expectation Maximization (EM). An out-of-the-box invocation…
The loss function used to train a neural network is strongly connected to its output layer from a statistical point of view. This technical report analyzes common activation functions for a neural network output layer, like linear, sigmoid,…
Under a partially linear models we study a family of robust estimates for the regression parameter and the regression function when some of the predictor variables take values on a Riemannian manifold. We obtain the consistency and the…
In this work, we propose an efficient implementation of mixtures of experts distributional regression models which exploits robust estimation by using stochastic first-order optimization techniques with adaptive learning rate schedulers. We…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…