摘要 :
In medical literature, researchers suggested various statistical procedures to estimate the parameters in claim count or frequency model. In the recent years, the Poisson regression model has been widely used particularly. However...
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In medical literature, researchers suggested various statistical procedures to estimate the parameters in claim count or frequency model. In the recent years, the Poisson regression model has been widely used particularly. However, it is also recognized that the count or frequency data in medical practice often display over-dispersion, i.e., a situation where the variance of the response variable exceeds the mean. Inappropriate imposition of the Poisson may underestimate the standart errors and overstate the significance of the regression parameters, and consequently, giving misleading inference about the regression parameters. This article suggests the Negative Binomial (NB) and Conway-Maxwell-Poisson (COM-Poisson) regression models as an alternatives for handling overdispersion. All mentioned regression models are applied to simulation data and dataset of hospitalization number of people with schizophrenia, the results are compared.
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Fisheries discard data are often characterized by a smooth distribution of positive amounts of per-set discard but with an extremely large number of zero observations. This discontinuity is difficult to fit with a standard distrib...
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Fisheries discard data are often characterized by a smooth distribution of positive amounts of per-set discard but with an extremely large number of zero observations. This discontinuity is difficult to fit with a standard distribution. One approach is to model per-set discard with a mixture of two distributions, with one component representing the zero observations and the other representing the observations of positive discard. In this paper, we describe such a mixture model that is suitable when the discard observations have been rounded to integer amounts. In particular, when ''rounded'' zeros (representing small amounts of discard) and ''true'' zeros (representing no discard) are indistinguishable in the data, the mixture model can be used to estimate the proportion of either. We fit this model to tuna discard data collected by observers aboard the U.S. tuna purse-seine fleet in the eastern tropical Pacific Ocean during the years 1989-92. We use the model to estimate discard per set, allowing the model parameters to depend upon fishing strategy and geographic location, and we estimate mean discard per set fisherywide.
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Likelihood ratio, Wald and Score test statistics were derived for the three discrete distributions, namely Poisson, truncated Poisson and negative binomial, which are widely used in count regression models. These three tests were ...
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Likelihood ratio, Wald and Score test statistics were derived for the three discrete distributions, namely Poisson, truncated Poisson and negative binomial, which are widely used in count regression models. These three tests were compared through simulation for the entire three - distributions with respect to type-I and type-II error rates and we arrived that likelihood ratio test is better as compared to other two tests.
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The assumption that is usually made when modeling count data is that the response variable, which is the count, is correctly reported. Some counts might be over- or under-reported. We derive the Generalized PoissonPoisson mixture ...
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The assumption that is usually made when modeling count data is that the response variable, which is the count, is correctly reported. Some counts might be over- or under-reported. We derive the Generalized PoissonPoisson mixture regression (GPPMR) model that can handle accurate, underreported and overreported counts. The parameters in the model will be estimated via the maximum likelihood method. We apply the GPPMR model to a real-life data set.
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The zero-inflated Poisson regression (ZIP) in many situations is appropriate for analyzing multilevel correlated count data with excess zeros. In this paper, a score test for assessing ZIP regression against Poisson regression in ...
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The zero-inflated Poisson regression (ZIP) in many situations is appropriate for analyzing multilevel correlated count data with excess zeros. In this paper, a score test for assessing ZIP regression against Poisson regression in multilevel count data with excess zeros is developed. The sampling distribution and power of the score statistic test is evaluated using a simulation study. The results show that under a wide range of conditions, the score statistic performs satisfactorily. Finally, the use of the score test is illustrated on DMFT index data of children 7-8 years old.
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A local maximum likelihood estimator based on Poisson regression is presented as well as its bias, variance and asymptotic distribution. This semiparametric estimator is intended to be an alternative to the Poisson, negative binom...
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A local maximum likelihood estimator based on Poisson regression is presented as well as its bias, variance and asymptotic distribution. This semiparametric estimator is intended to be an alternative to the Poisson, negative binomial and zero-inflated Poisson regression models that does not depend on regularity conditions and model specification accuracy. Some simulation results are presented. The use of the local maximum likelihood procedure is illustrated on one example from the literature. This procedure is found to perform well.
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This paper deals with an empirical study of generalized linear model (GLM) for count data. In particular, Poisson regression model which is also known as generalized linear model for Poisson error structure has been widely used in...
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This paper deals with an empirical study of generalized linear model (GLM) for count data. In particular, Poisson regression model which is also known as generalized linear model for Poisson error structure has been widely used in recent years; it is also used in modeling of count and frequency data. Quasi Poisson model was employ for handling over and under dispersion which the data was found to be over dispersed and another way of handling over dispersion is negative binomial regression model. In this study, the two regression model were compare using the Akaike information criterion (AIC), the model with minimum AIC shows the best which implies the Poisson regression model.
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The Poisson regression model (PRM) is employed in modelling the relationship between a count variable (y) and one or more explanatory variables. The parameters of PRM are popularly estimated using the Poisson maximum likelihood es...
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The Poisson regression model (PRM) is employed in modelling the relationship between a count variable (y) and one or more explanatory variables. The parameters of PRM are popularly estimated using the Poisson maximum likelihood estimator (PMLE). There is a tendency that the explanatory variables grow together, which results in the problem of multicollinearity. The variance of the PMLE becomes inflated in the presence of multicollinearity. The Poisson ridge regression (PRRE) and Liu estimator (PLE) have been suggested as an alternative to the PMLE. However, in this study, we propose a new estimator to estimate the regression coefficients for the PRM when multicollinearity is a challenge. We perform a simulation study under different specifications to assess the performance of the new estimator and the existing ones. The performance was evaluated using the scalar mean square error criterion and the mean squared error prediction error. The aircraft damage data was adopted for the application study and the estimators' performance judged by the SMSE and the mean squared prediction error. The theoretical comparison shows that the proposed estimator outperforms other estimators. This is further supported by the simulation study and the application result.
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Ordinary Least Squares (OLS), Poisson, Negative Binomial, and Quasi-Poisson Regression methods were assessed for testing the statistical significance of a trend by performing 10,000 simulations. The Poisson method should be used w...
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Ordinary Least Squares (OLS), Poisson, Negative Binomial, and Quasi-Poisson Regression methods were assessed for testing the statistical significance of a trend by performing 10,000 simulations. The Poisson method should be used when data follow a Poisson distribution. The other methods should be used when data follow a normal distribution.
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摘要 :
A local maximum likelihood estimator based on Poisson regression is presented as well as its bias, variance and asymptotic distribution. This semiparametric estimator is intended to be an alternative to the Poisson, negative binom...
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A local maximum likelihood estimator based on Poisson regression is presented as well as its bias, variance and asymptotic distribution. This semiparametric estimator is intended to be an alternative to the Poisson, negative binomial and zero-inflated Poisson regression models that does not depend on regularity conditions and model specification accuracy. Some simulation results are presented. The use of the local maximum likelihood procedure is illustrated on one example from the literature. This procedure is found to perform well.
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