Zero-inflated Poisson Regression Models Research Articles

Urban landscape pattern mainly drives the early epidemic distribution of dengue fever in Hangzhou, China

ContextA new dengue fever (DF) epidemic in Hangzhou, China has placed a serious burden on the urban sustainable development. However, the key drivers of DF epidemic are still unclear, especially the effects of urban landscape patterns.ObjectivesIn the present study, the spatial relationships between DF epidemic and urban landscape attributes in Hangzhou were investigated based on the framework and approach of landscape epidemiology.MethodsThe landscape indices of green space, waterbody, and built-up area were calculated based on land cover and land use (LULC) data. Population density, road density, GDP, and property price were used to represent socioeconomic conditions. The densities of social gathering places (SGPs) such as restaurants, malls, services, entertainment, traditional markets, and parks were recorded. A geographically weighted zero-inflated poisson regression (GWZIPR) model was applied to analyze the effects of LULC patterns, socioeconomic conditions, and SGPs on the risk of DF epidemics. An additional ZIPR-LASSO algorithm was used to explore the dominant drivers of spatial patterns of DF risk to construct the optimal model.ResultsDF cases were mainly clustered in central Hangzhou. Landscape patterns involving LULC and SGPs played a more important role in DF epidemic than the socioeconomic conditions. Among these factors, the total area of built-up area had the greatest effect to DF risk. Furthermore, property price, density of entertainment and services could better explain the spatial variation of DF risk in Hangzhou.ConclusionsOverall, the contribution of landscape patterns to the DF epidemic was more important than socioeconomic conditions within the urban region, especially in the new epidemic region. These findings revealed the key role of landscape epidemiology in public health management and landscape governance to improve the urban sustainable development and human well-being.

Tobacco exposures are associated with health care utilization (HCU) and health care costs in pregnant persons and their newborn babies.

Identifying health care utilization and costs associated with active and passive smoking during pregnancy could help improve health management strategies. Data are from the Newborn Epigenetics STudy (NEST), a birth cohort enrolled from 2005-2011 in Durham and adjacent counties in North Carolina, United States. Participants included those for whom prenatal serum samples were assayed and for whom administrative data were obtainable (N=1,045). Zero-inflated Poisson (ZIP) regression models were used to assess associations between cotinine, adjusted for covariates (e.g., race and ethnicity, age at delivery, cohabitation status, education), and health care utilization outcomes. Generalized linear regression models were used to estimate average total charges. Simulation models were conducted to determine the economic benefits of reducing SHS and smoking during pregnancy. Increasing levels of cotinine were positively associated with parent's number of ED visits (coefficient(b)=0.0012, standard error (SE)=0.0002; P<.001), the number of ICU hours (b=0.0079, SE=0.0025; P=.002)), time spent in the ICU (b=0.0238, SE=0.0020, P<.001), and the number of OP visits (b=0.0003, SE=0.0001; P<.001). For infants, higher cotinine levels were associated with higher number of ED (b=0.0012, SE=0.0004; P=.005), ICU (b=0.0050, SE=0.001; P<.001), and OP (b=0.0006, SE=0.0002; P<.001) visits and longer time spent in the ED (b=0.0025, SE=0.0003; P<.001), ICU (b=0.0005, SE=0.0001; P<.001), and IP (b=0.0020, SE=0.0002; P<.001). Simulation results showed that a 5% reduction in smoking would correspond to a potential median cost savings of $150,533 from ED visits of parents and infants. Our findings highlight the importance of smoke exposure cessation during pregnancy to reduce health care utilization and costs for both parents and infants. This study reinforces the importance of reducing smoking and secondhand smoke exposure during pregnancy. Focusing on expanding cessation services to this group could help reduce morbidities observed within this population. Furthermore, there is the potential for health care costs savings to health care systems, especially to those with high delivery numbers. These cost savings are represented by potential reductions in ED, OP, and ICU hours and visits.

Participation and Persistence in High School Elective Music Ensembles

In this study, we examined demographic patterns of participation and persistence in high school elective music ensembles. We extend prior research that has only compared music and non-music students by explicitly modeling persistence across multiple years of ensemble enrollment. The research draws on data from the High School Longitudinal Study of 2009 and employs a zero-inflated Poisson regression model to analyze the data. This hurdle model, suitable for count data with a large number of zero observations, allows us to jointly examine factors related to enrolling in at least 1 year of a music ensemble (moving from 0 years to 1 year of music) and those factors related to accruing additional years of music ensemble enrollment (moving beyond 1 year to multiple years). We found that family socioeconomic status, birth-assigned sex, academic achievement, shared parent/student outside arts event attendance, and out-of-school arts engagement were significant predictors of both students’ music participation and persistence. By examining persistence, we add important nuance to the prior research examining demographic predictors of elective high school music enrollment, particularly for issues of birth-assigned sex and socioeconomic status in the choral context.

Predicting the multivariate zero-inflated counts: A novel model averaging method under Pearson loss.

Excessive zeros in multivariate count data are often observed in scenarios of biomedicine and public health. To provide a better analysis on this type of data, we first develop a marginalized multivariate zero-inflated Poisson (MZIP) regression model to directly interpret the overall exposure effects on marginal means. Then, we define a multiple Pearson residual for our newly developed MZIP regression model by simultaneously taking heterogeneity and correlation into consideration. Furthermore, a new model averaging prediction method is introduced based on the multiple Pearson residual, and the asymptotical optimality of this model averaging prediction is proved. Simulations and two empirical applications in medicine are used to illustrate the effectiveness of the proposed method.

Modeling clustered count data using mixed effect discrete Weibull regression model with cubic splines

This paper investigates the use of mixed-effect discrete Weibull (DW) regression model with cubic splines for clustered count data. DW regression model can be used for both over and under-dispersed data thus, it can be an appropriate choice for researchers to use without having the risk to violate assumptions for using a particular model distribution. We used a cubic spline function to model the non-linear relationship between the outcome variable and the covariate. The proposed model is applied to a clustered dataset from the eighth Korean National Health and Nutrition Examination Survey (KNHANES VIII) from 2019 to assess the factors influencing the amount of alcohol drink in 17 different regions. We compared the results with our proposed model with those of Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial regression models in the presence of spline function. The results show that using DW regression model with cubic spline gives the best fit. We also held a simulation study to investigate the performance and the robustness of DW with a spline function. It turns out that DW regression model with a spline function can flexibly model clustered count data with various dispersion and data with many zeros.

Long-term effects of childhood difficulties on depressive symptoms among older adults: Role of adulthood income and income satisfaction.

This study examines how childhood difficulties are associated with late-life depression. Using the concept of agency within the structure of the life course perspective, this study investigates how subjective income satisfaction in adulthood plays a role in the relationship between adulthood objective income and late-life depressive symptoms among older adults who have experienced childhood difficulties. Using data from two waves (2006, 2021) of the Korean Welfare Panel Study (N = 1822), we identified respondents with and without childhood difficulties, and performed a series of hierarchical zero-inflated Poisson regression models. Childhood difficulties (β, 0.07; 95% confidence interval [CI], 0.04-0.11), adulthood low income (β, 0.17; 95% CI, 0.13-0.21), and low income satisfaction (β, 0.16; 95% CI, 0.12-0.21) are associated with an increased level of depressive symptoms in late life. In the context of the association between objective income level and late-life depressive symptoms, the buffering effect of income satisfaction in adulthood was found among the respondents who had experienced childhood difficulties (β, 0.22; 95% CI, 0.09-0.34). Childhood difficulties are a critical risk factor impacting late-life psychological well-being. How an individual subjectively evaluates his or her economic status in adulthood plays a major role in mitigating the negative impact of childhood difficulties on late-life health inequality. Interventions to reduce the risk of childhood difficulties and their negative long-lasting impact may alleviate individuals' exposure to depression in late life. Geriatr Gerontol Int 2024; 24: 246-252.

Evaluating the Performance of Mixed Zero-Inflated Poisson Regression Models with Time-dependent and Time-independent Covariates

One of the issues that researchers may encounter in count data is having many zeros. One of the solutions to model these data is using zero-inflated Poisson (ZIP) regression models. Recently, researchers have started to model longitudinal count data with time-dependent covariates. However, it has not been considered whether a model with time-dependent covariates provides a better fit than a model with time-independent covariates. In this paper, the fit between a mixed ZIP model with time-dependent covariates and a mixed ZIP model with time-independent covariates is compared using simulation. Using the deviance information criterion as a measure of fit, we found that the model with time-dependent covariates exhibits a better fit than the model with time-independent covariates. KEYWORDS correlated data, count data, excess zeros, longitudinal, mixed models, model fit

Associations between screen viewing at 2 and 3.5 years and drawing ability at 3.5 years among children from the French nationwide Elfe birth cohort

The effect of screen viewing on children’s cognitive development has been of concern among parents and researchers. This study investigated the association between children screen time, as reported by parents, and drawing ability, and the confounding effects of socioeconomic characteristics (such as parental education, household income, migration status) and children’s competing activities (such as drawing practice, extracurricular activity, outdoor time, sleep time, time playing with parents). Participants included 7577 children aged 3.5 years (50% girls) who underwent the Draw-a-person test (McCarthy score [range = 0–12 points]) in the French nationwide Elfe birth cohort, initiated in 2011. Sex-stratified zero-inflated Poisson regression models were used. Increased screen time was associated with a higher likelihood to obtain a null score in boys (OR 1.15, 95% CI 1.07–1.23) and girls (1.13 [1.03–1.24]) and a lower score in girls only (β = − 0.02, 95% CI − 0.04; − 0.01). After adjusting for SES, associations were no longer observed, indicating that the association between screen time and drawing abilities was confounded by socioeconomic characteristics.

New antipsychotic prescription and recurrent infections among adult sepsis survivors: A population-based cohort study.

Antipsychotic agents, which may increase the risk of infection through dopaminergic dysregulation, are prescribed to a fraction of patients following critical illness. We compared the rate of recurrent sepsis among patients who filled a prescription for antipsychotics with high- or low-D2 affinity. Population-based cohort with active comparator design. We included sepsis survivors older than 65 years with intensive care unit admission and new prescription of antipsychotics in Ontario 2008-2019. The primary outcome were recurrent sepsis episodes within 1 year of follow-up. Patients who filled a prescription within 30 days of hospital discharge for high-D2 affinity antipsychotics (e.g., haloperidol) were compared with patients who filled a prescription within 30 days of hospital discharge for low-D2 affinity antipsychotics (e.g., quetiapine). Multivariable zero-inflated Poisson regression models with robust standard errors adjusting for confounding at baseline were used to estimate incidence rate ratios (IRR) and 95% confidence intervals (CI). Overall, 1879 patients filled a prescription for a high-D2, and 1446 patients filled a prescription for a low-D2 affinity antipsychotic. Patients who filled a prescription for a high-D2 affinity antipsychotic did not present a higher rate of recurrent sepsis during 1 year of follow-up, compared with patients who filled a prescription for a low-D2 affinity antipsychotic (IRR: 1.12; 95% CI: 0.94, 1.35). We did not find conclusive evidence of a higher rate of recurrent sepsis associated with the prescription of high-D2 affinity antipsychotics (compared with low-D2 affinity antipsychotics) by 1 year of follow-up in adult sepsis survivors with intensive care unit admission.

Epidemiology of engagement in physical activity behaviors in people with epilepsy from National Health Interview Survey 2017

ObjectivePhysical activity (PA) participation may be beneficial for people with epilepsy (PWE) but has been discouraged due to a fear that it may induce seizures. Using data from the 2017 National Health Interview Survey, we aimed to describe current rates of PA sufficient to meet US PA Aerobic and Strength Training Guidelines (Aim #1), compare the average time PWE spend on aerobic activity and strength training activity (Aim #2), and compare rates of engagement with various types of PA (e.g., moderate, vigorous, strength training, and mind–body activities) among PWE to the general population (Aim #3). MethodsCross-sectional data (n = 26,728) were analyzed via logistic and zero-inflated Poisson regression models. PA participation was analyzed based on the US PA Guidelines (neither, strength training [≥2 times/wk], moderate to vigorous physical activity [MVPA; ≥ 150 min/wk], or both; Aim #1), time spent on activity/week (Aim #2), and activity participation (yes/no; Aim #3). Epilepsy status was coded as active epilepsy (doctor-diagnosed and either taking antiepileptic medication or had at least one seizure in 12 months; n = 335), inactive epilepsy (doctor-diagnosed, not taking antiepileptic medication nor had a seizure in 12 months; n = 213), and no history of epilepsy (n = 26,180). ResultsPeople with active epilepsy were more likely to report meeting neither (68 %, 95 % CI = 63–74 %) of the PA Guidelines compared to people with no history of epilepsy (59 %, 58–60 %). The mean duration of time reported on vigorous activity for people with inactive epilepsy was significantly higher than people with no history of epilepsy (p = 0.01). People with active epilepsy were 32–39 % less likely to report participating in any moderate or vigorous activity compared to people with no history of epilepsy. SignificanceThis study highlights activity disparities among PWE and the general population, indicating substantially lower activity and higher likelihood of inactivity in PWE, particularly active epilepsy.

Prescribed fires, smoke exposure, and hospital utilization among heart failure patients

BackgroundPrescribed fires often have ecological benefits, but their environmental health risks have been infrequently studied. We investigated associations between residing near a prescribed fire, wildfire smoke exposure, and heart failure (HF) patients’ hospital utilization.MethodsWe used electronic health records from January 2014 to December 2016 in a North Carolina hospital-based cohort to determine HF diagnoses, primary residence, and hospital utilization. Using a cross-sectional study design, we associated the prescribed fire occurrences within 1, 2, and 5 km of the patients’ primary residence with the number of hospital visits and 7- and 30-day readmissions. To compare prescribed fire associations with those observed for wildfire smoke, we also associated zip code-level smoke density data designed to capture wildfire smoke emissions with hospital utilization amongst HF patients. Quasi-Poisson regression models were used for the number of hospital visits, while zero-inflated Poisson regression models were used for readmissions. All models were adjusted for age, sex, race, and neighborhood socioeconomic status and included an offset for follow-up time. The results are the percent change and the 95% confidence interval (CI).ResultsAssociations between prescribed fire occurrences and hospital visits were generally null, with the few associations observed being with prescribed fires within 5 and 2 km of the primary residence in the negative direction but not the more restrictive 1 km radius. However, exposure to medium or heavy smoke (primarily from wildfires) at the zip code level was associated with both 7-day (8.5% increase; 95% CI = 1.5%, 16.0%) and 30-day readmissions (5.4%; 95% CI = 2.3%, 8.5%), and to a lesser degree, hospital visits (1.5%; 95% CI: 0.0%, 3.0%) matching previous studies.ConclusionsArea-level smoke exposure driven by wildfires is positively associated with hospital utilization but not proximity to prescribed fires.

Zero-Inflated Poisson Regression Modeling of Plant Protein Consumption

Summary This research fitted a discrete distribution for modeling count data. Specifically, Zero-Inflated Poisson (ZIP) regression was used to model plant protein consumption by 400 randomly sampled individuals in Wukari. The data was collected by questionnaire. The ZIP regression model was used based on its ability to model data with excess zeros present in the collected data. Variables considered and used for the analysis are Age, Body Mass Index, Blood Pressure, Occupation, Gender, Weight, Height, Body Reaction, and Consumption Class. The parameters of the ZIP model were estimated using the maximum likelihood estimation technique. The model was tested for Goodness of Fit (GoF) using deviance, scaled deviance, Pearson–χ 2 and scaled Pearson–χ 2 statistics. The results obtained showed that Age, Gender, and Reaction were significant at 5%, and the GoF tests revealed that the Zero-Inflated Poisson regression produces a good fit and is a good model for overcoming the overdispersion effect.

Statistical Inference in Marginalized Zero-inflated Poisson Regression Models with Missing Data in Covariates

Statistical Inference in Marginalized Zero-inflated Poisson Regression Models with Missing Data in Covariates

The effect of non-medical cannabis retailer proximity on use of mental health services for psychotic disorders in Ontario, Canada.

Cannabis is associated with the onset and persistence of psychotic disorders. Evidence suggests that accessibility of substances is associated with an increased risk of use-related harms. We sought to examine the effect of residing in proximity to non-medical cannabis retailers on the prevalence of health service use for psychosis. We conducted a cross-sectional study using linked health administrative data, and used geospatial analyses to determine whether people in Ontario, Canada (aged 14-60 years) resided within walking (1.6 km) or driving (5.0 km) distance of non-medical cannabis retailers (open as of February-2020). We identified outpatient visits, emergency department (ED) visits, and hospitalizations for psychotic disorders between 01-April-2019 and 17-March-2020. We used zero-inflated Poisson regression models and gamma generalized linear models to estimate the association between cannabis retailer proximity and indicators of health service use. Non-medical cannabis retailers were differentially located in areas with high levels of marginalization and pre-existing health service use for psychosis. People residing within walking or driving distance of a cannabis retailer had a higher rate of psychosis-related outpatient visits, ED visits, and hospitalizations, compared to people living outside these areas. This effect was stronger among those with no prior service use for psychosis. Proximity to a non-medical cannabis retailer was associated with higher health service use for psychosis, even after adjustment for prior health service use. These findings suggest that opening of non-medical cannabis retailers could worsen the burden of psychosis on mental health services in areas with high-risk populations.

Mental Health Care Use by Ethnicity and Preferred Language in a National Cohort of Community Health Center Patients.

Disparities in U.S. mental health care by race and ethnicity have long been documented. The authors sought to compare specialty mental health service use among non-Hispanic White, English-preferring Hispanic, and Spanish-preferring Hispanic patients who accessed care in community health centers (CHCs). Retrospective electronic medical records data were extracted for patients ages ≥18 years who received care in 2012-2020 at a national CHC network. Zero-inflated Poisson regression models were used to estimate the likelihood of receiving mental health services, which was compared with expected annual rates of mental health service use. Of the 1,498,655 patients who received care at a CHC during the study, 14.4% (N=215,098) received any specialty mental health services. English- and Spanish-preferring Hispanic patients were less likely to have had a mental health visit (OR=0.69, 95% CI=0.61-0.77, and OR=0.65, 95% CI=0.54-0.78, respectively). Compared with non-Hispanic White patients, Spanish-preferring Hispanic patients had an estimated annualized rate of 0.59 (95% CI=0.46-0.76) mental health visits. Among patients who were likely to receive specialty mental health services, Spanish-preferring patients had a significantly lower rate of mental health care use. Although overall access to mental health care is improving, unequal access to recurring specialty mental health care remains among patients who do not prefer to use English.

Estimation of zero-inflated bivariate Poisson regression with missing covariates

Zero-inflated bivariate Poisson regression (ZIBP) models are most often applied to correlated bivariate count data that contain a large proportion of zeros. These models have been applied in various fields, such as medical research, health economics, insurance, sports, etc. Because, in practice, some of the covariates involved in ZIBP regression modeling often have missing values, we propose methods for estimating the parameters of the ZIBP regression model with missing at random covariates. Assuming that the selection probability is unknown and estimated non parametrically (by a kernel estimator), we propose inverse probability weighting (IPW) and multiple imputation (MI) methods for estimating the parameters of the ZIBP regression model with missing at random covariates. Asymptotic properties of the proposed estimators are studied under certain regularity conditions. A simulation study is conducted to evaluate the performance of the proposed methods. Finally, the practical application of the proposed methodology is illustrated with data from the health-care field.

Relationships between common pre-season screening measures and dance-related injuries in pre-professional ballet dancers.

OBJECTIVE: To examine modifiable and non-modifiable factors for associations with dance-related injury among pre-professional ballet dancers over five academic years. DESIGN: Prospective cohort study METHODS: Full-time pre-professional ballet dancers [n=452; 399 female, median (range) age: 15 years (11-21)] participated across five academic years at a vocational school. Participants completed baseline screening and online weekly injury questionnaires including dance exposure (hours/week). Zero-inflated Poisson regression models were used to examine associations between potential risk factors measured at baseline and self-reported dance-related injury. RESULTS: In count model coefficients, left one leg standing score [log coefficient estimate: -0.249 (95%CI: -0.478, -0.02); p=0.033] and right unipedal dynamic balance time [log coefficient estimate: -0.0294 (95%CI: -0.048, -0.01); p>0.001] carried a protective effect with increased years of training when adjusted for Athletic Coping Skills Inventory (ACSI) score. A significant association was found for left unipedal dynamic balance time and dance-related injury [log coefficient estimate: 0.013 (95%CI: 0.000, 0.026); p=0.045] when adjusted for years training and ACSI score. There were no significant associations between dance-related injury and ankle and hip range of motion, active straight leg raise or Y-balance test measures. CONCLUSION: When adjusted for years of previous dance training and psychological coping skills, there was a significant association between limb-specific lumbopelvic control and dynamic balance tasks, and self-reported dance-related injury in pre-professional ballet.

Spatio-temporal analysis of childhood vaccine uptake in Nigeria: a hierarchical Bayesian Zero-inflated Poisson approach

BackgroundGlobally, child mortality and morbidity remain a serious health challenge and infectious diseases are the leading causes. The use of count models together with spatial analysis of the number of doses of childhood vaccines taken is limited in the literature. We used a Bayesian zero-inflated Poisson regression model with spatio-temporal components to assess the number of doses of childhood vaccines taken among children aged 12–23 months and their associated factors.MethodsData of 19,564 children from 2003, 2008, 2013 and 2018 population-based cross-sectional Nigeria Demographic and Health Survey were used. The childhood vaccines include one dose of Bacillus-Calmette-Guérin; three doses of Diphtheria-Pertussis-Tetanus; three doses of Polio and one dose of Measles. Uptake of all nine vaccines was regarded as full vaccination. We examined the multilevel factors associated with the number of doses of childhood vaccines taken using descriptive, bivariable and multivariable Bayesian models. Analysis was conducted in Stata version 16 and R statistical packages, and visualization in ArcGIS.ResultsThe prevalence of full vaccination was 6.5% in 2003, 14.8% in 2008, 21.8% in 2013 and 23.3% in 2018. Full vaccination coverage ranged from 1.7% in Sokoto to 51.9% in Anambra. Factors associated with the number of doses of childhood vaccines taken include maternal age (adjusted Incidence “risk” Ratio (aIRR) = 1.05; 95% Credible Interval (CrI) = 1.03–1.07) for 25–34 years and (aIRR = 1.07; 95% CrI = 1.05–1.10) for 35–49 years and education: (aIRR = 1.11, 95% CrI = 1.09–1.14) for primary and (aIRR = 1.16; 95% CrI = 1.13–1.19) for secondary/tertiary education. Other significant factors are wealth status, antenatal care attendance, working status, use of skilled birth attendants, religion, mother’s desire for the child, community poverty rate, community illiteracy, and community unemployment.ConclusionAlthough full vaccination has remained low, there have been improvements over the years with wide disparities across the states. Improving the uptake of vaccines by educating women on the benefits of hospital delivery and vaccines through radio jingles and posters should be embraced, and state-specific efforts should be made to address inequality in access to routine vaccination in Nigeria.

REGRESI ZERO INFLATED POISSON UNTUK PEMODELAN ANGKA POSITIF PENYAKIT MALARIA DI JAWA TIMUR

The number of confirmed cases of malaria in East Java from 2020 to 2022 is a count data with numerous zero values and is exhibiting overdispersion. With Zero Inflated Poisson (ZIP) regression, this work seeks to solve the overdispersion issue that plagues Poisson regression. The ZIP model is superior to the Poisson regression model, according to the results. Data modeling with ZIP regression carries out model fit testing with the G test, parameter significance testing with the Wald test, and parameter estimation using Maximum Likelihood Estimation. For case data of malaria positivity, the ZIP regression model in this research is log(𝜇𝑖) = 3,695 + 0,0057X1 − 0,0569X2 − 0,0085X3 − 0,0619X4 + 0,0604X5 − 0,0118X6 − 0,012X8, and logit(𝜔𝑖) = −5,5185 + 0,0039X2 − 0,592X6. The test's findings indicate that factors such as population density, poverty levels, the proportion of households with access to clean water and sanitation, the morbidity rate, the number of medical facilities, the number of health complaints, and the percentage of public spaces that adhere to health standards all significantly influence the number of confirmed cases of malaria in East Java.Keywords: Malaria, excess zeros, overdispersion, Zero Inflated Poisson.

Mixed-Effects Zero-Inflated Negative Binomial Crash Predictive Models for Unsignalized Intersections along Two-Lane Highways with Minor Roads Operating with Very Low Traffic Volumes

Current and past investigations into road accidents have mainly focused on high-volume roads which have experienced a significant number of collisions. However, low-volume roads also record crash data which merit analysis to understand the causes of accidents and find potential countermeasures. This study focuses on unsignalized intersections linking major highways and minor stop-controlled local roads that operate with very low traffic volumes. In this scenario, an over-abundance of zero observations has to be accounted for. To address this issue, zero-inflated Poisson and negative binomial regression models have been calibrated and analyzed to find the geometric and operational factors which contribute most to the crash rate. Random effects have also been considered to account for unobserved heterogeneity inherent in the grouping of intersections within the database. The results indicate that the mixed-effect negative binomial model had the best prediction performance. Developing models for subgroups of crashes, for example, failure-to-yield and other types of crash, resulted in better prediction performance. The major road’s average annual daily traffic and the surface type (i.e., paved or unpaved) of minor road approaches had a significant effect on the frequency of all crash types. The type of intersection (three- or four-legs), the skew angle of intersection, deviation angle of near curves, and operating speed differences also had statistically significant effects on the frequency of crashes that do not include the failure-to-yield.