Statistical Inference for Zero-Inflated Poisson Regression Models with Excess Zeros

2013 ◽  
Vol 367 ◽  
pp. 253-258
Author(s):  
Lin Dai ◽  
Ying Zi Fu
Keyword(s):  
Poisson Regression ◽  
Regression Models ◽  
Test Procedure ◽  
Score Test ◽  
Zero Inflation ◽  
Test Statistic ◽  
Inference Procedure ◽  
Data Set ◽  
Excess Zeros ◽  
Fire Accident

In this paper, we deal with a class of zero-inflated Poisson regression models and propose a score test procedure for assessing whether there exists zero-inflation or not. The sampling distribution and the power of the score test statistic are investigated by a limited simulation study. Furthermore, a Bayesian inference procedure is also presented for comparison. Finally, a data set of fire accident is used to illustrate our methodology and our numerical results show that our approach is useful and appealing for the analysis of count data with zero-inflation.

Common risk difference test and interval estimation of risk difference for stratified bilateral correlated data

2018 ◽  
Vol 28 (8) ◽  
pp. 2418-2438
Author(s):  
Xi Shen ◽  
Chang-Xing Ma ◽  
Kam C Yuen ◽  
Guo-Liang Tian
Keyword(s):  
Data Analysis ◽  
Confidence Interval ◽  
Score Test ◽  
Real Data ◽  
Risk Difference ◽  
Error Rates ◽  
Correlated Data ◽  
Test Statistic ◽  
Data Set ◽  
Intra Class Correlation

Bilateral correlated data are often encountered in medical researches such as ophthalmologic (or otolaryngologic) studies, in which each unit contributes information from paired organs to the data analysis, and the measurements from such paired organs are generally highly correlated. Various statistical methods have been developed to tackle intra-class correlation on bilateral correlated data analysis. In practice, it is very important to adjust the effect of confounder on statistical inferences, since either ignoring the intra-class correlation or confounding effect may lead to biased results. In this article, we propose three approaches for testing common risk difference for stratified bilateral correlated data under the assumption of equal correlation. Five confidence intervals of common difference of two proportions are derived. The performance of the proposed test methods and confidence interval estimations is evaluated by Monte Carlo simulations. The simulation results show that the score test statistic outperforms other statistics in the sense that the former has robust type [Formula: see text] error rates with high powers. The score confidence interval induced from the score test statistic performs satisfactorily in terms of coverage probabilities with reasonable interval widths. A real data set from an otolaryngologic study is used to illustrate the proposed methodologies.

The Effect of Data Aggregation on a Poisson Regression Model of Canadian Migration

1992 ◽  
Vol 24 (10) ◽  
pp. 1381-1391 ◽  
Author(s):  
C G Amrhein ◽  
R Flowerdew
Keyword(s):  
Data Aggregation ◽  
Poisson Regression ◽  
Regression Models ◽  
High Spatial Resolution ◽  
Simulation Experiments ◽  
Data Set ◽  
Migration Data ◽  
Statistics Canada ◽  
Aggregate Population ◽  
Canada Data

A Statistics Canada data set for Canadian migration data at the census division level incorporating information on income tax for 1986 has already been presented. This matrix of 260 × 260 flows was used to calibrate a set of Poisson regression models by utilizing flows for the aggregate population. In this paper, the relatively high spatial resolution is used to test for aggregation effects as the original 260 units are combined to form fewer, synthetic regions with larger areas. A series of simulation experiments are performed with three different aggregation algorithms to create 130, 65, and ultimately 10 (corresponding to the provinces) synthetic regions. Average results from the experiments are compared with the original model. Results are obtained that suggest that, in this case, obvious aggregation effects similar to those observed elsewhere (by Openshaw) are not observed.

Testing modified zeros for Poisson regression models

2018 ◽  
Vol 28 (10-11) ◽  
pp. 3123-3141 ◽  
Author(s):  
Yi Tang ◽  
Wan Tang
Keyword(s):  
Likelihood Ratio ◽  
Poisson Regression ◽  
Regression Models ◽  
Score Test ◽  
Poisson Model ◽  
Real Data ◽  
Likelihood Ratio Tests ◽  
Type I ◽  
Simulation Studies ◽  
Zero Inflated Poisson Models

Excessive zeros are common in practice and may cause overdispersion and invalidate inferences when fitting Poisson regression models. Zero-inflated Poisson regression models may be applied if there are inflated zeros; however, it is desirable to test if there are inflated zeros before such zero-inflated Poisson models are applied. Assuming a constant probability of being a structural zero in a zero-inflated Poisson regression model, the existence of the inflated zeros may be tested by testing whether the constant probability is zero. In such situations, the Wald, score, and likelihood ratio tests can be applied. Without specifying a zero-inflated Poisson model, He et al. recently developed a test by comparing the amount of observed zeros with that expected under the Poisson model. In this paper, we develop a closed form for the test and compare it with the Wald, score, and likelihood ratio tests through simulation studies. The simulation studies show that the test of He et al. is the best in controlling type I errors, while the score test generally has the least power among the tests. The tests are illustrated with two real data examples.

scholarly journals Climate changes and their effects in the public health: use of poisson regression models

2010 ◽  
Vol 30 (2) ◽  
pp. 427-442 ◽  
Author(s):  
Jonas Bodini Alonso ◽  
Jorge Alberto Achcar ◽  
Luiz Koodi Hotta
Keyword(s):  
Poisson Regression ◽  
Regression Models ◽  
Climate Changes ◽  
Random Effect ◽  
Poisson Regression Model ◽  
Air Humidity ◽  
Data Set ◽  
The Public ◽  
Bayesian Paradigm ◽  
Ischemic Diseases

In this paper, we analyze the daily number of hospitalizations in São Paulo City, Brazil, in the period of January 01, 2002 to December 31, 2005. This data set relates to pneumonia, coronary ischemic diseases, diabetes and chronic diseases in different age categories. In order to verify the effect of climate changes the following covariates are considered: atmosphere pressure, air humidity, temperature, year season and also a covariate related to the week day when the hospitalization occurred. The possible effects of the assumed covariates in the number of hospitalization are studied using a Poisson regression model in the presence or not of a random effect which captures the possible correlation among the hospitalization accounting for the different age categories in the same day and the extra-Poisson variability for the longitudinal data. The inferences of interest are obtained using the Bayesian paradigm and MCMC (Markov chain Monte Carlo) methods.

scholarly journals Anticipated help-seeking for cancer symptoms before and after the coronavirus pandemic: results from the Onco-barometer population survey in Spain

2021 ◽  
Author(s):  
Dafina Petrova ◽  
Marina Pollán ◽  
Miguel Rodriguez-Barranco ◽  
Dunia Garrido ◽  
Josep M. Borrás ◽  
...  
Keyword(s):  
Poisson Regression ◽  
Help Seeking ◽  
Regression Models ◽  
Population Survey ◽  
Waiting Times ◽  
Perceived Barriers ◽  
Older Individuals ◽  
Cancer Symptoms ◽  
Before And After ◽  
Diagnostic Delays

Abstract Background The patient interval—the time patients wait before consulting their physician after noticing cancer symptoms—contributes to diagnostic delays. We compared anticipated help-seeking times for cancer symptoms and perceived barriers to help-seeking before and after the coronavirus pandemic. Methods Two waves (pre-Coronavirus: February 2020, N = 3269; and post-Coronavirus: August 2020, N = 1500) of the Spanish Onco-barometer population survey were compared. The international ABC instrument was administered. Pre–post comparisons were performed using multiple logistic and Poisson regression models. Results There was a consistent and significant increase in anticipated times to help-seeking for 12 of 13 cancer symptoms, with the largest increases for breast changes (OR = 1.54, 95% CI 1.22–1–96) and unexplained bleeding (OR = 1.50, 1.26–1.79). Respondents were more likely to report barriers to help-seeking in the post wave, most notably worry about what the doctor may find (OR = 1.58, 1.35–1.84) and worry about wasting the doctor’s time (OR = 1.48, 1.25–1.74). Women and older individuals were the most affected. Conclusions Participants reported longer waiting times to help-seeking for cancer symptoms after the pandemic. There is an urgent need for public interventions encouraging people to consult their physicians with symptoms suggestive of cancer and counteracting the main barriers perceived during the pandemic situation.

Challenging the Link Between Early Childhood Television Exposure and Later Attention Problems: A Multiverse Approach

2021 ◽  
pp. 095679762097165
Author(s):  
Matthew T. McBee ◽  
Rebecca J. Brand ◽  
Wallace E. Dixon
Keyword(s):  
Early Childhood ◽  
Regression Models ◽  
Propensity Score Analysis ◽  
Harmful Effect ◽  
Attention Problems ◽  
Linear Regression Models ◽  
Data Set ◽  
Logistic Regression Models ◽  
Score Analysis ◽  
Television Exposure

In 2004, Christakis and colleagues published an article in which they claimed that early childhood television exposure causes later attention problems, a claim that continues to be frequently promoted by the popular media. Using the same National Longitudinal Survey of Youth 1979 data set ( N = 2,108), we conducted two multiverse analyses to examine whether the finding reported by Christakis and colleagues was robust to different analytic choices. We evaluated 848 models, including logistic regression models, linear regression models, and two forms of propensity-score analysis. If the claim were true, we would expect most of the justifiable analyses to produce significant results in the predicted direction. However, only 166 models (19.6%) yielded a statistically significant relationship, and most of these employed questionable analytic choices. We concluded that these data do not provide compelling evidence of a harmful effect of TV exposure on attention.

A Test for Functional Form Against Nonparametric Alternatives

1992 ◽  
Vol 8 (4) ◽  
pp. 452-475 ◽  
Author(s):  
Jeffrey M. Wooldridge
Keyword(s):  
Alternative Model ◽  
Regression Models ◽  
Functional Form ◽  
Parametric Model ◽  
Finite Sample ◽  
Test Statistic ◽  
Sieve Estimation ◽  
Finite Sample Properties ◽  
Standard Normal ◽  
Nonparametric Alternatives

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

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