Multivariate Covariance Generalized Linear Models

Bonat, Wagner Hugo; Jørgensen, Bent

doi:10.1111/rssc.12145

Cited by 59 publications

(93 citation statements)

References 69 publications

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“…We shall now introduce the quasi-likelihood estimation using terminology and results from Jørgensen and Knudsen (2004); Holst and Jørgensen (2015); Bonat and Jørgensen (2016). The quasi-likelihood approach adopted in this paper combines the quasi-score and Pearson estimating functions to estimation of regression and dispersion parameters, respectively.…”

Section: Quasi-likelihood Estimationmentioning

confidence: 99%

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Flexible Tweedie regression models for continuous data

Bonat

Kokonendji

2017

Journal of Statistical Computation and Simulation

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Tweedie regression models provide a flexible family of distributions to deal with non-negative highly right-skewed data as well as symmetric and heavy tailed data and can handle continuous data with probability mass at zero. The estimation and inference of Tweedie regression models based on the maximum likelihood method are challenged by the presence of an infinity sum in the probability function and non-trivial restrictions on the power parameter space. In this paper, we propose two approaches for fitting Tweedie regression models, namely, quasi-and pseudo-likelihood. We discuss the asymptotic properties of the two approaches and perform simulation studies to compare our methods with the maximum likelihood method. In particular, we show that the quasilikelihood method provides asymptotically efficient estimation for regression parameters. The computational implementation of the alternative methods is faster and easier than the orthodox maximum likelihood, relying on a simple Newton scoring algorithm. Simulation studies showed that the quasi-and pseudo-likelihood approaches present estimates, standard errors and coverage rates similar to the maximum likelihood method. Furthermore, the secondmoment assumptions required by the quasi-and pseudo-likelihood methods enables us to extend the Tweedie regression models to the class of quasiTweedie regression models in the Wedderburn's style. Moreover, it allows to eliminate the non-trivial restriction on the power parameter space, and thus provides a flexible regression model to deal with continuous data. We provide R implementation and illustrate the application of Tweedie regression models using three data sets.

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Section: Quasi-likelihood Estimationmentioning

confidence: 99%

“…In a similar way, the entry (j, k) of the Q × Q variability matrix for U q β is given by (2004); Bonat and Jørgensen (2016), the Pearson estimating function for the dispersion parameters has the following form,…”

Section: Quasi-likelihood Estimationmentioning

confidence: 99%

Flexible Tweedie regression models for continuous data

Bonat

Kokonendji

2017

Journal of Statistical Computation and Simulation

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“…, R. Similarly, let Σ b be the R × R correlation matrix between outcomes. The McGLMs (Bonat and Jørgensen 2016) are defined by…”

Section: Multivariate Covariance Generalized Linear Modelsmentioning

confidence: 99%

“…The mcglm package (Bonat 2018) for R (R Core Team 2017) provides functions to fit and analyze multivariate covariance generalized linear models (McGLMs; Bonat and Jørgensen 2016). The package is designed to take full advantage of the modular specification of the models using a glm style interface.…”

Section: Introductionmentioning

confidence: 99%

“…McGLMs are fitted by means of quasi-likelihood and Pearson estimating functions, based on second-moment assumptions, and implemented in an efficient Newton scoring algorithm (Bonat and Jørgensen 2016;Jørgensen and Knudsen 2004). The mean structure for each response variable is specified in the orthodox way by means of a link function and a linear predictor.…”

Section: Introductionmentioning

confidence: 99%

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Multiple Response Variables Regression Models in R: The mcglm Package

Bonat¹

2018

J. Stat. Soft.

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This article describes the R package mcglm implemented for fitting multivariate covariance generalized linear models (McGLMs). McGLMs provide a general statistical modeling framework for normal and non-normal multivariate data analysis, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link function and a matrix linear predictor involving known symmetric matrices. The models take non-normality into account in the conventional way by means of a variance function, and the mean structure is modeled by means of a link function and a linear predictor. The models are fitted using an estimating function approach based on second-moment assumptions. This provides a unified approach to a wide variety of different types of response variables and covariance structures, including multivariate extensions of repeated measures, time series, longitudinal, genetic, spatial and spatio-temporal structures. The mcglm package allows a flexible specification of the mean and covariance structures, and explicitly deals with multivariate response variables, through a user friendly formula interface similar to the ordinary glm function. Illustrations in this article cover a wide range of applications from the traditional one response variable Gaussian mixed models to multivariate spatial models for areal data using the multivariate Tweedie distribution. Additional features, such as robust and bias-corrected standard errors for regression parameters, residual analysis, measures of goodness-of-fit and model selection using the score information criterion are discussed through six worked examples. The mcglm package is a full R implementation based on the Matrix package which provides efficient access to BLAS (basic linear algebra subroutines), Lapack (dense matrix), TAUCS (sparse matrix) and UMFPACK (sparse matrix) routines for efficient linear algebra in R.

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Quantile modeling through multivariate log‐normal/independent linear regression models with application to newborn data

2021

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In this article, we propose and study the class of multivariate log‐normal/independent distributions and linear regression models based on this class. The class of multivariate log‐normal/independent distributions is very attractive for robust statistical modeling because it includes several heavy‐tailed distributions suitable for modeling correlated multivariate positive data that are skewed and possibly heavy‐tailed. Besides, expectation‐maximization (EM)‐type algorithms can be easily implemented for maximum likelihood estimation. We model the relationship between quantiles of the response variables and a set of explanatory variables, compute the maximum likelihood estimates of parameters through EM‐type algorithms, and evaluate the model fitting based on Mahalanobis‐type distances. The satisfactory performance of the quantile estimation is verified by simulation studies. An application to newborn data is presented and discussed.

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Multivariate Covariance Generalized Linear Models

Cited by 59 publications

References 69 publications

Flexible Tweedie regression models for continuous data

Flexible Tweedie regression models for continuous data

Multiple Response Variables Regression Models in R: The mcglm Package

Quantile modeling through multivariate log‐normal/independent linear regression models with application to newborn data

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