共查询到20条相似文献，搜索用时 15 毫秒
1.
Overdispersion is a common phenomenon in Poisson modeling, and the negative binomial (NB) model is frequently used to account for overdispersion. Testing approaches (Wald test, likelihood ratio test (LRT), and score test) for overdispersion in the Poisson regression versus the NB model are available. Because the generalized Poisson (GP) model is similar to the NB model, we consider the former as an alternate model for overdispersed count data. The score test has an advantage over the LRT and the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis. This paper proposes a score test for overdispersion based on the GP model and compares the power of the test with the LRT and Wald tests. A simulation study indicates the score test based on asymptotic standard Normal distribution is more appropriate in practical application for higher empirical power, however, it underestimates the nominal significance level, especially in small sample situations, and examples illustrate the results of comparing the candidate tests between the Poisson and GP models. A bootstrap test is also proposed to adjust the underestimation of nominal level in the score statistic when the sample size is small. The simulation study indicates the bootstrap test has significance level closer to nominal size and has uniformly greater power than the score test based on asymptotic standard Normal distribution. From a practical perspective, we suggest that, if the score test gives even a weak indication that the Poisson model is inappropriate, say at the 0.10 significance level, we advise the more accurate bootstrap procedure as a better test for comparing whether the GP model is more appropriate than Poisson model. Finally, the Vuong test is illustrated to choose between GP and NB2 models for the same dataset. 相似文献
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Count data often show a higher incidence of zero counts than would be expected if the data were Poisson distributed. Zero-inflated Poisson regression models are a useful class of models for such data, but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the Poisson distribution. We therefore provide a score test for testing zero-inflated Poisson regression models against zero-inflated negative binomial alternatives. 相似文献
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zmen 《Biometrical journal. Biometrische Zeitschrift》2000,42(3):303-314
This paper reviews the generalized Poisson regression model, the restricted generalized Poisson regression model and the mixed Poisson regression (negative binomial regression and Poisson inverse Gaussian regression) models which can be used for regression analysis of counts. The aim of this study is to demonstrate the quasi likelihood/moment method, which is used for estimation of the parameters of mixed Poisson regression models, also applicable to obtain the estimates of the parameters of the generalized Poisson regression and the restricted generalized Poisson regression models. Besides, at the end of this study an application related to this method for zoological data is given. 相似文献
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Ridout, Hinde, and Demétrio (2001, Biometrics 57, 219-223) derived a score test for testing a zero-inflated Poisson (ZIP) regression model against zero-inflated negative binomial (ZINB) alternatives. They mentioned that the score test using the normal approximation might underestimate the nominal significance level possibly for small sample cases. To remedy this problem, a parametric bootstrap method is proposed. It is shown that the bootstrap method keeps the significance level close to the nominal one and has greater power uniformly than the existing normal approximation for testing the hypothesis. 相似文献
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Shieh G 《Biometrics》2000,56(4):1192-1196
A direct extension of the approach described in Self, Mauritsen, and Ohara (1992, Biometrics 48, 31-39) for power and sample size calculations in generalized linear models is presented. The major feature of the proposed approach is that the modification accommodates both a finite and an infinite number of covariate configurations. Furthermore, for the approximation of the noncentrality of the noncentral chi-square distribution for the likelihood ratio statistic, a simplification is provided that not only reduces substantial computation but also maintains the accuracy. Simulation studies are conducted to assess the accuracy for various model configurations and covariate distributions. 相似文献
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Several analysis of the geographic variation of mortality rates in space have been proposed in the literature. Poisson models allowing the incorporation of random effects to model extra‐variability are widely used. The typical modelling approach uses normal random effects to accommodate local spatial autocorrelation. When spatial autocorrelation is absent but overdispersion persists, a discrete mixture model is an alternative approach. However, a technique for identifying regions which have significant high or low risk in any given area has not been developed yet when using the discrete mixture model. Taking into account the importance that this information provides to the epidemiologists to formulate hypothesis related to the potential risk factors affecting the population, different procedures for obtaining confidence intervals for relative risks are derived in this paper. These methods are the standard information‐based method and other four, all based on bootstrap techniques, namely the asymptotic‐bootstrap, the percentile‐bootstrap, the BC‐bootstrap and the modified information‐based method. All of them are compared empirically by their application to mortality data due to cardiovascular diseases in women from Navarra, Spain, during the period 1988–1994. In the small area example considered here, we find that the information‐based method is sensible at estimating standard errors of the component means in the discrete mixture model but it is not appropriate for providing standard errors of the estimated relative risks and hence, for constructing confidence intervals for the relative risk associated to each region. Therefore, the bootstrap‐based methods are recommended for this matter. More specifically, the BC method seems to provide better coverage probabilities in the case studied, according to a small scale simulation study that has been carried out using a scenario as encountered in the analysis of the real data. 相似文献
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On the equivalence of case-crossover and time series methods in environmental epidemiology 总被引：2，自引：0，他引：2
The case-crossover design was introduced in epidemiology 15 years ago as a method for studying the effects of a risk factor on a health event using only cases. The idea is to compare a case's exposure immediately prior to or during the case-defining event with that same person's exposure at otherwise similar "reference" times. An alternative approach to the analysis of daily exposure and case-only data is time series analysis. Here, log-linear regression models express the expected total number of events on each day as a function of the exposure level and potential confounding variables. In time series analyses of air pollution, smooth functions of time and weather are the main confounders. Time series and case-crossover methods are often viewed as competing methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for overdispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics. 相似文献
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We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. They have slight differences in many situations, but their zero-inflated distributions, with masses at zero, means and variances fixed, can differ more. These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated. 相似文献
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Summary In many applications of two-component mixture models for discrete data such as zero-inflated models, it is often of interest to conduct inferences for the mixing weights. Score tests derived from the marginal model that allows for negative mixing weights have been particularly useful for this purpose. But the existing testing procedures often rely on restrictive assumptions such as the constancy of the mixing weights and typically ignore the structural constraints of the marginal model. In this article, we develop a score test of homogeneity that overcomes the limitations of existing procedures. The technique is based on a decomposition of the mixing weights into terms that have an obvious statistical interpretation. We exploit this decomposition to lay the foundation of the test. Simulation results show that the proposed covariate-adjusted test statistic can greatly improve the efficiency over test statistics based on constant mixing weights. A real-life example in dental caries research is used to illustrate the methodology. 相似文献
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The purpose of this article is to draw attention to the possible need for inclusion of interaction effects between regions and age groups in mapping studies. We propose a simple model for including such an interaction in order to develop a test for its significance. The assumption of an absence of such interaction effects is a helpful simplifying one. The measure of relative risk related to a particular region becomes easily and neatly summarized. Indeed, such a test seems warranted because it is anticipated that the simple model, which ignores such interaction, as is in common use, may at times be adequate. The test proposed is a score test and hence only requires fitting the simpler model. We illustrate our approaches using mortality data from British Columbia, Canada, over the 5-year period 1985-1989. For this data, the interaction effect between age groups and regions is quite large and significant. 相似文献
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Izabela R. C. Oliveira Geert Molenberghs Clarice G. B. Demétrio Carlos T. S. Dias Suely R. Giolo Marcela C. Andrade 《Biometrical journal. Biometrische Zeitschrift》2016,58(4):852-867
The intraclass correlation is commonly used with clustered data. It is often estimated based on fitting a model to hierarchical data and it leads, in turn, to several concepts such as reliability, heritability, inter‐rater agreement, etc. For data where linear models can be used, such measures can be defined as ratios of variance components. Matters are more difficult for non‐Gaussian outcomes. The focus here is on count and time‐to‐event outcomes where so‐called combined models are used, extending generalized linear mixed models, to describe the data. These models combine normal and gamma random effects to allow for both correlation due to data hierarchies as well as for overdispersion. Furthermore, because the models admit closed‐form expressions for the means, variances, higher moments, and even the joint marginal distribution, it is demonstrated that closed forms of intraclass correlations exist. The proposed methodology is illustrated using data from agricultural and livestock studies. 相似文献
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Summary
We consider a functional linear Cox regression model for characterizing the association between time‐to‐event data and a set of functional and scalar predictors. The functional linear Cox regression model incorporates a functional principal component analysis for modeling the functional predictors and a high‐dimensional Cox regression model to characterize the joint effects of both functional and scalar predictors on the time‐to‐event data. We develop an algorithm to calculate the maximum approximate partial likelihood estimates of unknown finite and infinite dimensional parameters. We also systematically investigate the rate of convergence of the maximum approximate partial likelihood estimates and a score test statistic for testing the nullity of the slope function associated with the functional predictors. We demonstrate our estimation and testing procedures by using simulations and the analysis of the Alzheimer's Disease Neuroimaging Initiative (ADNI) data. Our real data analyses show that high‐dimensional hippocampus surface data may be an important marker for predicting time to conversion to Alzheimer's disease. Data used in the preparation of this article were obtained from the ADNI database ( adni.loni.usc.edu ). 相似文献15.
A note on a test for Poisson overdispersion 总被引：3，自引：0，他引：3
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Overdispersed count data are very common in ecology. The negative binomial model has been used widely to represent such data. Ecological data often vary considerably, and traditional approaches are likely to be inefficient or incorrect due to underestimation of uncertainty and poor predictive power. We propose a new statistical model to account for excessive overdisperson. It is the combination of two negative binomial models, where the first determines the number of clusters and the second the number of individuals in each cluster. Simulations show that this model often performs better than the negative binomial model. This model also fitted catch and effort data for southern bluefin tuna better than other models according to AIC. A model that explicitly and properly accounts for overdispersion should contribute to robust management and conservation for wildlife and plants. 相似文献
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David C. Heilbron 《Biometrical journal. Biometrische Zeitschrift》1994,36(5):531-547
On occasion, generalized linear models for counts based on Poisson or overdispersed count distributions may encounter lack of fit due to disproportionately large frequencies of zeros. Three alternative types of regression models that utilize all the information and explicitly account for excess zeros are examined and given general formulations. A simple mechanism for added zeros is assumed that directly motivates one type of model, here called the added-zero type, particular forms of which have been proposed independently by D. LAMBERT (1992) and in unpublished work by the author. An original regression formulation (the zero-altered model) is presented as a reduced form of the two-part model for count data, which is also discussed. It is suggested that two-part models be used to aid in development of an added-zero model when the latter is thought to be appropriate. 相似文献
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Radiologists' interpretation on screening mammograms is measured by accuracy indices such as sensitivity and specificity. The hypothesis that radiologists' interpretation on screening mammograms is constant across time can be tested by measuring overdispersion. However, small sample sizes are problematic for the accuracy of asymptotic approaches. In this article, we propose an exact conditional distribution for testing overdispersion of the binomial assumption that is assumed for the accuracy indices. An exact p -value can be defined from the developed distribution. We also describe an algorithm for computing this exact test. This proposed method is applied to data from a study in reading screening mammograms in a population of US radiologists (Beam et al., 2003). The exact method is compared analytically with a currently available method based on large sample approximations. 相似文献
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Qi-Guang Chen 《Biometrical journal. Biometrische Zeitschrift》1988,30(3):351-358
The Poisson regression model for the analysis of life table and follow-up data with covariates is presented. An example is presented to show how this technique can be used to construct a parsimonious model which describes a set of survival data. All parameters in the model, the hazard and survival functions are estimated by maximum likelihood. 相似文献