8,879 research outputs found
A Poisson Mixed Model with Nonnormal Random Effect Distribution
We propose in this paper a random intercept Poisson model in which the random
effect distribution is assumed to follow a generalized log-gamma (GLG)
distribution. We derive the first two moments for the marginal distribution as
well as the intraclass correlation. Even though numerical integration methods
are in general required for deriving the marginal models, we obtain the
multivariate negative binomial model for a particular parameter setting of the
hierarchical model. An iterative process is derived for obtaining the maximum
likelihood estimates for the parameters in the multivariate negative binomial
model. Residual analysis are proposed and two applications with real data are
given for illustration.Comment: Submitted in the Computational Statistics & Data Analysis journa
New Flexible Regression Models Generated by Gamma Random Variables with Censored Data
We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models
A flexible regression model for count data
Poisson regression is a popular tool for modeling count data and is applied
in a vast array of applications from the social to the physical sciences and
beyond. Real data, however, are often over- or under-dispersed and, thus, not
conducive to Poisson regression. We propose a regression model based on the
Conway--Maxwell-Poisson (COM-Poisson) distribution to address this problem. The
COM-Poisson regression generalizes the well-known Poisson and logistic
regression models, and is suitable for fitting count data with a wide range of
dispersion levels. With a GLM approach that takes advantage of exponential
family properties, we discuss model estimation, inference, diagnostics, and
interpretation, and present a test for determining the need for a COM-Poisson
regression over a standard Poisson regression. We compare the COM-Poisson to
several alternatives and illustrate its advantages and usefulness using three
data sets with varying dispersion.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS306 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Overlooked Potential of Generalized Linear Models in Astronomy-III: Bayesian Negative Binomial Regression and Globular Cluster Populations
In this paper, the third in a series illustrating the power of generalized
linear models (GLMs) for the astronomical community, we elucidate the potential
of the class of GLMs which handles count data. The size of a galaxy's globular
cluster population is a prolonged puzzle in the astronomical
literature. It falls in the category of count data analysis, yet it is usually
modelled as if it were a continuous response variable. We have developed a
Bayesian negative binomial regression model to study the connection between
and the following galaxy properties: central black hole mass,
dynamical bulge mass, bulge velocity dispersion, and absolute visual magnitude.
The methodology introduced herein naturally accounts for heteroscedasticity,
intrinsic scatter, errors in measurements in both axes (either discrete or
continuous), and allows modelling the population of globular clusters on their
natural scale as a non-negative integer variable. Prediction intervals of 99%
around the trend for expected comfortably envelope the data,
notably including the Milky Way, which has hitherto been considered a
problematic outlier. Finally, we demonstrate how random intercept models can
incorporate information of each particular galaxy morphological type. Bayesian
variable selection methodology allows for automatically identifying galaxy
types with different productions of GCs, suggesting that on average S0 galaxies
have a GC population 35% smaller than other types with similar brightness.Comment: 14 pages, 12 figures. Accepted for publication in MNRA
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