Modeling the Rainfall Count data Using Some Zero Type models with application

Statistical modelling for falls count data

In recent years, there has been considerable interest in regression models based on zero-inflated distributions. These models are commonly encountered in many disciplines, such as medicine, public health, and environmental sciences, among others. The zero-inflated Poisson (ZIP) model has been typically considered for these types of problems. However, the ZIP model can fail if the non-zero counts are overdispersed in relation to the Poisson distribution, hence the zero-inflated negative binomial (ZINB) model may be more appropriate. In this paper, we present a Bayesian approach for fitting the ZINB regression model. This model considers that an observed zero may come from a point mass distribution at zero or from the negative binomial model. The likelihood function is utilized to compute not only some Bayesian model selection measures, but also to develop Bayesian case-deletion influence diagnostics based on q-divergence measures. The approach can be easily implemented using standard Bayesian software, such as WinBUGS. The performance of the proposed method is evaluated with a simulation study. Further, a real data set is analyzed, where we show that ZINB regression models seems to fit the data better than the Poisson counterpart.

Modeling Vehicle-pedestrian Crashes With Excess Zero Along Malaysia Federal Roads

ObjectiveTo propose a more realistic model for disease cluster detection, through a modification of the spatial scan statistic to account simultaneously for inflated zeros and overdispersion.IntroductionSpatial Scan Statistics [1] usually assume Poisson or Binomial distributed data, which is not adequate in many disease surveillance scenarios. For example, small areas distant from hospitals may exhibit a smaller number of cases than expected in those simple models. Also, underreporting may occur in underdeveloped regions, due to inefficient data collection or the difficulty to access remote sites. Those factors generate excess zero case counts or overdispersion, inducing a violation of the statistical model and also increasing the type I error (false alarms). Overdispersion occurs when data variance is greater than the predicted by the used model. To accommodate it, an extra parameter must be included; in the Poisson model, one makes the variance equal to the mean.MethodsTools like the Generalized Poisson (GP) and the Double Poisson [2] may be a better option for this kind of problem, modeling separately the mean and variance, which could be easily adjusted by covariates. When excess zeros occur, the Zero Inflated Poisson (ZIP) model is used, although ZIP’s estimated parameters may be severely biased if nonzero counts are too dispersed, compared to the Poisson distribution. In this case the Inflated Zero models for the Generalized Poisson (ZIGP), Double Poisson (ZIDP) and Negative Binomial (ZINB) could be good alternatives to the joint modeling of excess zeros and overdispersion. By one hand, Zero Inflated Poisson (ZIP) models were proposed using the spatial scan statistic to deal with the excess zeros [3]. By the other hand, another spatial scan statistic was based on a Poisson-Gamma mixture model for overdispersion [4]. In this work we present a model which includes inflated zeros and overdispersion simultaneously, based on the ZIDP model. Let the parameter p indicate the zero inflation. As the the remaining parameters of the observed cases map and the parameter p are not independent, the likelihood maximization process is not straightforward; it becomes even more complicated when we include covariates in the analysis. To solve this problem we introduce a vector of latent variables in order to factorize the likelihood, and obtain a facilitator for the maximization process using the E-M (Expectation-Maximization) algorithm. We derive the formulas to maximize iteratively the likelihood, and implement a computer program using the E-M algorithm to estimate the parameters under null and alternative hypothesis. The p-value is obtained via the Fast Double Bootstrap Test [5].ResultsNumerical simulations are conducted to assess the effectiveness of the method. We present results for Hanseniasis surveillance in the Brazilian Amazon in 2010 using this technique. We obtain the most likely spatial clusters for the Poisson, ZIP, Poisson-Gamma mixture and ZIDP models and compare the results.ConclusionsThe Zero Inflated Double Poisson Spatial Scan Statistic for disease cluster detection incorporates the flexibility of previous models, accounting for inflated zeros and overdispersion simultaneously.The Hanseniasis study case map, due to excess of zero cases counts in many municipalities of the Brazilian Amazon and the presence of overdispersion, was a good benchmark to test the ZIDP model. The results obtained are easier to understand compared to each of the previous spatial scan statistic models, the Zero Inflated Poisson (ZIP) model and the Poisson-Gamma mixture model for overdispersion, taken separetely. The E-M algorithm and the Fast Double Bootstrap test are computationally efficient for this type of problem.

Testing overdispersion in the zero-inflated Poisson model

This paper makes a theoretical contribution by presenting a detailed derivation of a zero-inflated Poisson (ZIP) model, and then deriving the parameters of the ZIP model using a fishing data set. This model has several practical applications, and is largely performed to model count data that have an excess number of zero counts. In the scope of the paper, we introduce the complete formulae, the likelihood and log-likelihood functions and the estimating equation of the ZIP model. We then investigate the theory of large sample properties of this model under some regularity conditions. A simulation study and a fishing data set are studied for the ZIP model. The results in the actual application in this work are meaningful, useful and crucial in reality. The results also provide reliable evidence for obtaining the largest number of fish while fishing. This is the contribution of this research in terms of applications. Finally, the important applications of this model in practice, some conclusions, and future work is also presented for consideration.

The authors investigated the theoretical and clinical role of depression among cocaine abusers in treatment. Eighty-nine cocaine-abusing patients underwent 2 weeks of substance abuse treatment. Posttreatment major depressive disorder, depressive symptoms before and after substance abuse treatment, and alcohol diagnoses were assessed and their relation to pretreatment substance use, cravings in high-risk situations, and 3-month follow-up status was examined. High rates of major depressive disorder were found but were unrelated to pretreatment substance use. The decrease in depressive symptoms during treatment was independent of major depressive disorder or alcohol diagnoses and predicted treatment attrition. Higher levels of depressive symptoms during treatment were associated with greater urge to use cocaine, alcohol, and other drugs in high-risk situations. Concurrent major depressive disorder and depressive symptoms did not predict cocaine use at follow-up. However, patients who had an alcohol relapse episode experienced more depressive symptoms during treatment than did those who abstained. The results highlight the relationship of depression to alcohol use among cocaine abusers and suggest a need for further studies of the association between depression and substance use disorders.

Background: Although religious and cultural factors have been related to substance use in various populations, research is needed regarding associations for Arab Americans. Objectives: We examined how ethnic identity and religiosity relate to the odds and frequency of alcohol and cannabis use in Arab American college students during the COVID-19 pandemic, as well as differences by biological sex and Muslim upbringing Methods:Arab American college students (N = 173; Mage = 20.1, range 17–23; 60.7% female; 44.5% Christian upbringing, 43.9% Muslim upbringing) were recruited through electronic flyers and a psychology subject pool in California. Participants reported their ethnic identity affirmation (i.e. feeling positively about being Arab American) and search (i.e. learning about Arab culture), religiosity, and past-year alcohol and cannabis use Results: Greater ethnic identity affirmation was related to less frequent alcohol (OR = .68, p = .046) and cannabis use over the past year (OR = .58, p = .030), whereas greater ethnic identity search was related to lower odds of alcohol (OR = 0.66, p = .025) and cannabis use (OR = 0.68, p = .025). Greater ethnic identity search was also related to less frequent alcohol use among individuals from Muslim upbringings (OR = .37, p = .004). Greater religiosity was related to less frequent alcohol (OR = .61, p = .015) and cannabis use (OR = .44, p = .005). It was also related to lower odds of using alcohol and cannabis, with significantly stronger associations among individuals from Muslim upbringings (OR = .39, p = .040; OR = .40, p = .048) Conclusion: Ethnic identity and religiosity buffered substance use risk. Culturally tailored interventions and supporting cultural experiences may reduce Arab American students’ substance use.

Zero-inflated count data are characterized by an excessive frequency of zeros that cannot be adequately analyzed by a single distribution, such as Poisson or negative binomial. This problem is pervasive in many practical applications, including document–keyword matrix derived from text corpora, where most keyword frequencies are zero. Conventional statistical approaches, such as the zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models, explicitly separate a structural zero component from a count component, but they typically assume independent observations and can be unstable when covariates are high-dimensional and sparse. To address these limitations, this paper proposes a graph-based zero-inflated learning framework that combines simple graph convolution (SGC) with zero-inflated count regression heads such as ZIP and ZINB. We first construct an observation graph by connecting similar samples, and then apply SGC to propagate and smooth features over the graph, producing convolutional representations that incorporate neighborhood information while remaining computationally lightweight. The resulting representations are used as covariates in ZIP and ZINB heads, which preserve probabilistic interpretability through maximum likelihood learning. Our experiments on simulated zero-inflated datasets with controlled zero ratios demonstrate that the proposed ZIP+SGC and ZINB+SGC consistently reduce prediction errors compared with their non-graph baselines, as measured by mean absolute error and root mean squared error. Overall, the proposed approach provides an efficient and interpretable way to integrate graph neural computation with zero-inflated modeling for sparse count prediction problems.

Although stress is often related to substance use, it remains unclear whether substance use is related to individual differences in how adolescents respond to stress. Therefore the present study examined associations between substance use and daily emotional reactivity to stress within a year across adolescence. Adolescents (N = 330; Mage = 16.40, SD = 0.74 at study entry; n = 186 female; n = 138 Latine; n = 101 European American; n = 72 Asian American; n = 19 identifying as another ethnicity including African American and Middle Eastern) completed a longitudinal study, including three assessments between the 10th grade and 3-years post-high school. At each assessment, participants reported frequency of alcohol and cannabis use and the number of substances they had ever used. They also completed 15 daily checklists, in which they reported the number of daily arguments and their daily emotion. Multilevel models suggested that more frequent alcohol and cannabis use were related to attenuated positive emotional reactivity to daily stress (i.e., smaller declines in positive emotion on days when they experienced more arguments) for both male and female adolescents. Associations for negative emotional reactivity to stress varied by sex; more frequent alcohol use and use of more substances in one’s lifetime were related to greater anxious emotional reactivity to stress among female adolescents, whereas more frequent alcohol and cannabis use and higher lifetime substance use were related to attenuated depressive emotional reactivity to stress among male adolescents. Taken together, substance use was related to emotional reactivity to daily stress within the same year during adolescence, although associations differed by valence and adolescent sex.

Generalized Extreme Value models for count data: Application to worker telecommuting frequency choices

To measure the prevalence and frequency of alcohol and tobacco use among secondary school teachers in Zimbabwe. Cross sectional survey. 17 secondary schools in Harare, Mashonaland East and West and Matabeleland North Provinces (including Bulawayo). 442 secondary school teachers, of whom half were males. Prevalence of self-reported experience with alcohol and tobacco, frequency of alcohol use, alcohol type preferences and use of alcohol and tobacco by age and school type. Prevalence of alcohol was significantly higher among teachers at private schools as compared with the other school categories. Smoking varied between the school types for women but not for men. Except for private schools, both tobacco and alcohol prevalence among female teachers were significantly lower than for male teachers. Of the male teachers 44.6% and 64.1% of female teachers reported never drinking; 38.6% of male teachers and 8.2% of female teachers reported drinking every day or at least weekly. Alcohol type preferences varied in general across school categories and between male and female teachers. The study reveals a mixed picture of smoking and alcohol drinking among secondary school teachers. Relatively high levels of beer drinking among men as well as the particularly high levels of use programmes among private school teachers may constitute negative influence on the habits of students. This aspect should not be ignored when designing school-based prevention of substance use programmes among school children in Zimbabwe.

S ome P oints of D iscussion • Why hasn't the PIG model been widely used before this? • What types of data are best modeled using a PIG regression? • How do we model data with a very high initial peak and long right skew? • How do we know whether a PIG is a better-fitted model than negative binomial or Poisson models? P oisson I nverse G aussian M odel A ssumptions The Poisson inverse Gaussian (PIG) model is similar to the negative binomial model in that both are mixture models. The negative binomial model is a mixture of Poisson and gamma distributions , whereas the inverse Gaussian model is a mixture of Poisson and inverse Gaussian distributions . Those of you who are familiar with generalized linear models will notice that there are three GLM continuous distributions: normal, gamma, and inverse Gaussian. The normal distribution is typically parameterized to a lognormal distribution when associated with count models, presumably because the log link forces the distribution to have only nonnegative values. The Poisson and negative binomial (both NB2 and NB1) models have log links. Recall that the negative binomial is a mixture of the Poisson and gamma distributions, with variances of μ and μ 2 / v , respectively. We inverted v so that there is a direct relationship between the mean, dispersion, and variance function. Likewise, the inverse Gaussian is a mixture of Poisson and inverse Gaussian distributions, with an inverse Gaussian variance of μ 3 Φ.

Increased weight gain and sucrose intake during extinction of nicotine self-administration in adult male rats

The purpose of the study was to identify characteristics associated with higher levels of alcohol use in individuals who are between 24 and 25 years of age. Data from the 1982 and 1986 U.S. High School and Beyond longitudinal study (n = 8,875) were used to examine the relationship between the response variables, frequency, and intensity of alcohol use in 1986, and the explanatory variables which included alcohol use in 1982. Comparison of alcohol use in the two time periods revealed an increase in the percentage of respondents who consumed high levels of alcohol, while abstention from drinking remained relatively constant. Frequency of alcohol use in 1986 was related to use in 1982, gender, ethnicity, and family orientation.