Mixture of linear mixed models using multivariate<i>t</i>distribution

Bai, Xiuqin; Chen, Kun; Yao, Weixin

doi:10.1080/00949655.2015.1036431

Cited by 22 publications

(12 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, we first used the least square method to estimate the parameters of the two-dimensional regression problem and used it as a control. Secondly, the normal data has good explanatory property, that is, the joint probability distribution of the random variable is equal to the product of the edge distribution under the condition of mutual independence [25][26][27]. Based on this feature, we assume that the machine learning model conforms to the multivariate gaussian distribution model, we solve the bivariate gaussian distribution model of the maximum likelihood function, and using the maximum likelihood estimation method of the bivariate gaussian distribution parameters, the discovery gave a big item is about the L2 loss function and the parameters of least squares method calculated the same;…”

Section: Discussionmentioning

confidence: 99%

Model Loss and Distribution Analysis of Regression Problems in Machine Learning

Nan

Zheng

Wang

2019

Proceedings of the 2019 11th International Conference on Machine Learning and Computing

View full text Add to dashboard Cite

The machine learning regression model is based on the assumption of normal distribution. In this paper, we mainly study the probability distribution of the machine learning model and the effect of the convergence values of different loss functions on the probability distribution model. Based on the idea of robust regression and the assumption of homogeneous variance of the model, we solved the statistical solution of two-dimensional regression problem by using least square method. The maximum likelihood estimation parameters of the probabilistic model are obtained by using the maximum likelihood estimation method. In order to compare the solving parameters of the two methods, the convergence values of L1 loss function and L2 loss function are used for the regression verification. Through the mathematical and statistical rigorous derivation, obtained two important conclusions; First, under the condition that the data satisfies normal distribution and is based on the assumption of homogeneous variance, the probability model conforms to the multivariate gaussian distribution. Secondly, the model satisfying the multi-gaussian distribution has little influence on the parameter estimation under the condition of the large number theorem, that is, the multi-gaussian distribution model has good tolerance to the loss function.

show abstract

Section: Discussionmentioning

confidence: 99%

Model Loss and Distribution Analysis of Regression Problems in Machine Learning

Nan

Zheng

Wang

2019

Proceedings of the 2019 11th International Conference on Machine Learning and Computing

View full text Add to dashboard Cite

show abstract

“…Motivated by the procedures for robust estimation using the t-distribution outlined in Bai, Chen, and Yao (2016), Lange, Little, and Taylor (1989), Pinheiro, Liu, and Wu (2001), we recast the joint distributional assumption for EPD as…”

Section: Model Set Upmentioning

confidence: 99%

A robustness evaluation of Bayesian tests for longitudinal data

Arnroth

Ahmad

2021

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

Linear mixed models are standard models to analyze repeated measures or longitudinal data under the assumption of normality for random components in the model. Although the mixed models are often used in both frequentist and Bayesian inference, their evaluation from robustness perspective has not received as much attention in Bayesian inference as in frequentist. The aim of this study is to evaluate Bayesian tests in mixed models for their robustness to normality. We use a general class of exponential power distributions, EPD, and particularly focus on testing fixed effects in longitudinal models. The EPD class contains both light and heavy tailed distributions, with normality as a special case. Further, we consider a new paradigm of Bayesian testing decision theory where the hypotheses are formulated as a mixture model, with subsequent testing based on the posterior distribution of the mixture weights. It is shown that the EPD class provides a flexible alternative to normality assumption, particularly in the presence of outliers. Real data applications are also demonstrated.

show abstract

“…Several researchers have extended the single-term modelling framework (8) by decoupling the scalings of the random effects and the measurement error terms. See, for example, Rosa et al (2004), Aralleno-Valle et al (2007), Jara et al (2008), Meza et al (2012), Choudhary et al (2014) and Bai et al (2016). Lu and Zhang (2014) extended the approach to include nonignorable drop-out.…”

Section: Non-gaussian Models For Real-valued Repeated Measurement Datamentioning

confidence: 99%

Linear Mixed Effects Models for Non-Gaussian Continuous Repeated Measurement Data

Asar

Bolin

Diggle

et al. 2020

Journal of the Royal Statistical Society Series C: Applied Statistics

View full text Add to dashboard Cite

We consider the analysis of continuous repeated measurement outcomes that are collected longitudinally. A standard framework for analysing data of this kind is a linear Gaussian mixed effects model within which the outcome variable can be decomposed into fixed effects, time invariant and time-varying random effects, and measurement noise. We develop methodology that, for the first time, allows any combination of these stochastic components to be non-Gaussian, using multivariate normal variance-mean mixtures. To meet the computational challenges that are presented by large data sets, i.e. in the current context, data sets with many subjects and/or many repeated measurements per subject, we propose a novel implementation of maximum likelihood estimation using a computationally efficient subsampling-based stochastic gradient algorithm. We obtain standard error estimates by inverting the observed Fisher information matrix and obtain the predictive distributions for the random effects in both filtering (conditioning on past and current data) and smoothing (conditioning on all data) contexts. To implement these procedures, we introduce an R package: ngme. We reanalyse two data sets, from cystic fibrosis and nephrology research, that were previously analysed by using Gaussian linear mixed effects models.

show abstract

Mixture of linear mixed models using multivariatetdistribution

Cited by 22 publications

References 26 publications

Model Loss and Distribution Analysis of Regression Problems in Machine Learning

Model Loss and Distribution Analysis of Regression Problems in Machine Learning

A robustness evaluation of Bayesian tests for longitudinal data

Linear Mixed Effects Models for Non-Gaussian Continuous Repeated Measurement Data

Contact Info

Product

Resources

About