scholarly journals Modelling Mixed Types of Outcomes in Additive Genetic Models

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Wagner Hugo Bonat
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Model Simulation ◽  
Asymptotic Properties ◽  
Passer Domesticus ◽  
Statistical Modelling ◽  
Data Set ◽  
Linear Predictor ◽  
Genetic Components ◽  
Mixed Types

Abstract: We present a general statistical modelling framework for handling multivariate mixed types of outcomes in the context of quantitative genetic analysis. The models are based on the multivariate covariance generalized linear models, where the matrix linear predictor is composed of an identity matrix combined with a relatedness matrix defined by a pedigree, representing the environmental and genetic components, respectively. We also propose a new index of heritability for non-Gaussian data. A case study on house sparrow (Passer domesticus) population with continuous, binomial and count outcomes is employed to motivate the new model. Simulation of multivariate marginal models is not trivial, thus we adapt the NORTA (Normal to anything) algorithm for simulation of multivariate covariance generalized linear models in the context of genetic data analysis. A simulation study is presented to assess the asymptotic properties of the estimating function estimators for the correlation between outcomes and the new heritability index parameters. The data set and R code are available in the supplementary material.

scholarly journals Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 123
Author(s):  
María Jaenada ◽  
Leandro Pardo
Keyword(s):  
Generalized Linear Models ◽  
Influence Function ◽  
Regression Models ◽  
Linear Models ◽  
Asymptotic Properties ◽  
Significant Loss ◽  
Superior Performance ◽  
Test Statistics ◽  
Linear Regression Models ◽  
Type Test

Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests.

Models of the Fish Yield from Lakes: Does the Random Component Matter?

1991 ◽  
Vol 48 (4) ◽  
pp. 619-622 ◽  
Author(s):  
Chris D. Bajdik ◽  
David C. Schneider
Keyword(s):  
Generalized Linear Models ◽  
Random Error ◽  
Linear Models ◽  
Parameter Estimates ◽  
Random Component ◽  
Lake Area ◽  
Data Set ◽  
Fish Yield ◽  
Pearson Residuals ◽  
Distributional Assumptions

Generalized linear models were used to investigate the sensitivity of paramater estimates to choice of the random error assumption in models of fisheries data. We examined models of fish yield from lakes as a function of (i) Ryder's morphoedaphic index, (ii) lake area, lake depth, and concentration of dissolved solids, and (iii) fishing effort. Models were fit using a normal, log-normal, gamma, or Poisson distribution to generate the random error. Plots of standardized Pearson residuals and standardized deviance residuals were used to evaluate the distributional assumptions. For each data set, observations were found to be consistent with several distributions; however, some distributions were shown to be clearly inappropriate. Inappropriate distributional assumptions produced substantially different parameter estimates. Generalized linear models allow a variety of distributional assumptions to be incorporated in a model, and thereby let us study their effects.

scholarly journals COMPARAÇÃO DE TÉCNICAS ESTATÍSTICAS PARA ANALISAR A RELAÇÃO ENTRE DOENÇAS RESPIRATÓRIAS E CONCENTRAÇÕES DE POLUENTES ATMOSFÉRICOS

2013 ◽  
Vol 35 (1) ◽  
pp. 98
Author(s):  
Angela Radünz Lazzari
Keyword(s):  
Logistic Regression ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Generalized Linear Models ◽  
Respiratory Diseases ◽  
Linear Models ◽  
Ordinal Logistic Regression ◽  
Atmospheric Pollutants ◽  
Meteorological Variables ◽  
Data Set

Air pollution is a risk factor for the population health. Its harmful effects on the population are observed even when the atmospheric pollutants are within the parameters set out in specific legislation, and they develop mainly through respiratory diseases. The aim of this study was to analyze the relationship between the concentrations of air pollutants and the incidence of respiratory diseases in the city of Porto Alegre, in 2005 and 2006. Applied multiple linear regression analysis, ordinal logistic regression and generalized linear models were used in the work. The results show good adjustment by the three techniques. The ordinal logistic regression detected only positive influence of air temperature and relative humidity in hospitalizations for respiratory diseases. Multiple linear regression related negatively hospitalizations with meteorological variables and positively with the particulate matter (PM10). The generalized linear model detected negative influence of meteorological variables and positive of pollutants, tropospheric ozone (O3) and PM10 in hospitalizations. Comparing the three statistical techniques to analyze the same data set, it can be concluded that all of them had a model with good fit to the data, but the technique of generalized linear models showed higher sensitivity in capturing the influence of pollutants, except in ordinal logistic regression and multiple linear regression.

scholarly journals Estimation of breeding values for mean and dispersion, their variance and correlation using double hierarchical generalized linear models

2012 ◽  
Vol 94 (6) ◽  
pp. 307-317 ◽  
Author(s):  
M. FELLEKI ◽  
D. LEE ◽  
Y. LEE ◽  
A. R. GILMOUR ◽  
L. RÖNNEGÅRD
Keyword(s):  
Random Effects ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Estimation Algorithm ◽  
Least Square ◽  
Residual Variance ◽  
Hierarchical Generalized Linear Models ◽  
Genetic Components ◽  
The Difference ◽  
Variance Component Estimates

SummaryThe possibility of breeding for uniform individuals by selecting animals expressing a small response to environment has been studied extensively in animal breeding. Bayesian methods for fitting models with genetic components in the residual variance have been developed for this purpose, but have limitations due to the computational demands. We use the hierarchical (h)-likelihood from the theory of double hierarchical generalized linear models (DHGLM) to derive an estimation algorithm that is computationally feasible for large datasets. Random effects for both the mean and residual variance parts of the model are estimated together with their variance/covariance components. An important feature of the algorithm is that it can fit a correlation between the random effects for mean and variance. An h-likelihood estimator is implemented in the R software and an iterative reweighted least square (IRWLS) approximation of the h-likelihood is implemented using ASReml. The difference in variance component estimates between the two implementations is investigated, as well as the potential bias of the methods, using simulations. IRWLS gives the same results as h-likelihood in simple cases with no severe indication of bias. For more complex cases, only IRWLS could be used, and bias did appear. The IRWLS is applied on the pig litter size data previously analysed by Sorensen & Waagepetersen (2003) using Bayesian methodology. The estimates we obtained by using IRWLS are similar to theirs, with the estimated correlation between the random genetic effects being −0·52 for IRWLS and −0·62 in Sorensen & Waagepetersen (2003).

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