Bivariate Poisson Model Research Articles

Children's toothbrushing: a population survey on behaviours, attitudes, and knowledge in parents of Callao, Peru.

To determine the factors associated with behaviours, attitudes and knowledge of parents about children's toothbrushing (CTB). This is a cross-sectional analytical study of a calculated sample of 3,534 parents/guardians (92.6% female; 7.4% male; average age = 34 years [29-37]) of schoolchildren aged 3 to 8 years in 19 public schools in the province of Callao (Peru). A 31-item face-to-face/virtual questionnaire was divided into: 5 behavioural (18 (IQR)=3]; good 76%), 5 attitudes (13 [IQR=4]; negative 74.2%) and 10 knowledge (12 [IQR=4]; low 92.8%) (KMO≥0.537, Bartlett<0,001) and reliability (ω≥0.537) and 11 demographic domains. Bivariate and multivariate linear Poisson models were used with a P<0.05. Children of parents with a higher education showed good behaviours related to CTB. Negative parental attitudes and low knowledge about CTB were associated with a lower parental education and toothbrushing frequency.

Comparison of univariate and bivariate Poisson regression methods in the analysis of determinants of female schooling and fertility in Malawi

Recent research has established existence of a correlation between women’s education and fertility, suggesting that they share similar risk factors. However, in many studies, the two variables were analysed separately, which could bias the conclusions by undermining the apparent correlations of such paired outcomes. In this article, the univariate and bivariate Poisson regression models were applied to nationally representative sample of 24,562 women from the 2015-16 Malawi demographic and health survey to examine the risk factors of women’s education levels and fertility. The R software version 4.1.2 was used for the analyses. The results showed that estimates from the bivariate Poisson model were consistent with those obtained from the separate univariate Poisson models. The sizes of estimates of coefficients, their standard errors, p-values, and directions were comparable in both bivariate and univariate Poisson models. Using either the univariate or bivariate Poisson model, it was found that the age of a woman at first sexual experience, her current age, household wealth index, and contraceptive usage were significantly associated with both the woman’s schooling and fertility. The study further revealed that ethnicity, religion, and region of residence impacted education level only and not fertility. Similarly, marital status and occupation impacted fertility only and not education. The study also found that higher education levels were linked to a lower number of children, with a strong negative correlation of -0.62 between the two variables. The study recommends using bivariate Poisson regression for analysing paired count response data, when there is an apparent covariance between the outcome variables. The results suggest that efforts by policymakers to achieve the desired women’s sexual and reproductive health in sub-Saharan Africa should be intertwined with improving women’s and girls’ education attainment in the region.

Comparative analysis of the yields of dicentrics and chromosomal translocations

Purpose Chromosomal dicentrics and translocations are commonly employed as biomarkers to estimate radiation doses. The main goal of this article is to perform a comparative analysis of yields of both types of aberrations. The objective is to determine if there are relevant distinctions between both yields, allowing for a comprehensive assessment of their respective suitability and accuracy in the estimation of radiation doses. Materials and methods The analysis involved data from a partial-radiation simulation study with the calibration data obtained through two scoring methods: conventional and PAINT modified. Subsequently, a Bayesian bivariate zero-inflated Poisson model was employed to compare the posterior marginal density of the mean of dicentrics and translocations and assess the differences between them. Results When employing the conventional method of scoring, the findings indicate that there is no notable disparity between the yield of observed translocations and dicentrics. However, when utilizing the PAINT modified method, a notable discrepancy is observed for higher doses, indicating a relevant difference in the mean number of the two types of aberrations. Conclusions The choice of scoring method significantly influences the analysis of radiation-induced aberrations, especially when distinguishing between complex and simple chromosomal formations. Further research and analysis are necessary to gain a deeper understanding of the factors and mechanisms impacting the formation of dicentrics and translocations.

Health care access barriers among metropolitan and nonmetropolitan populations of eight geographically diverse states, 2018.

Nonmetropolitan populations face frequent health care access barriers compared to their metropolitan counterparts, but differences in the number of these barriers across groups are not known. Our objective was to examine the differences in health care access barriers across metropolitan, micropolitan, and noncore populations. We used Behavioral Risk Factor Surveillance System data from the optional "Health Care Access" module to perform a cross-sectional analysis examining access barriers across levels of rurality using bivariate analyses and Poisson models. Access barriers were operationalized as a count ranging from 0 to 5, reflective of the number of financial barriers and nonfinancial barriers. Micropolitan and noncore respondents had lower educational attainment, were older, and were less racially/ethnically diverse than metropolitan respondents. They also reported more barriers, including lacking health insurance, medical debt, and foregoing care or medication due to cost. These barriers were most pronounced in non-Hispanic Black, Hispanic, and American Indian/Alaska Native nonmetropolitan populations, compared to their White counterparts. In adjusted analysis, micropolitan respondents reported more barriers compared to metropolitan (prevalence rate ratio=1.06; 95% confidence interval: 1.02-1.10) as did women, racial/ethnic minority populations, and those with less education. Micropolitan populations experience more barriers to health care, and nonmetropolitan respondents report more cost-related barriers than their metropolitan counterparts, raising concerns on health care disparities and financial burdens for these underserved populations. This underscores the need to mitigate these barriers, particularly among those in micropolitan areas and minorized populations.

Analyzing Correlated Road Accident Count Data Using Zero Truncated Bivariate Poisson Regression Model

This paper aims to determine the significant factors which influence two correlated count responses, namely the total number of cars involved in an accident and the total number of fatalities due to that accident, of United Kingdom (UK) road accident count data. The bivariate Poisson (BVP) of two different forms and zero truncated bivariate Poisson regression (ZTBVP) models are considered to analyze UK road accident count data and the best model is selected based on the AIC and BIC values. From the data analysis, it is observed that the ZTBVP model provides the best fit (AIC value: 20563.26) for the UK road accident count data compared to all two variants of the BVP model (AIC value: &gt;20563.26). From the results obtained from ZTBVP model, it is also observed that sex of driver, area, serious severity, and light condition are the significant covariates for the total number of cars involved in an accident while area, fatal severity, serious severity, light condition and year 2021 are the significant covariates for the total number of fatalities due to that accident. Dhaka Univ. J. Sci. 72(1): 24-29, 2024 (January)

A bivariate Poisson regression to analyse impact of outlier women on correlation between female schooling and fertility in Malawi

BackgroundWomen’s levels of education and fertility are commonly associated. In Sub-Saharan Africa, the pace of decreasing fertility rates varies greatly, and this is linked to women’s levels of education. However, this association may be influenced by unusual females who have uncommon measurements on both variables. Despite this, most studies that researched this association have only analysed the data descriptively, without taking into account the effect of potential outliers. This study aimed to examine the presence and impact of outlier women on the relationship between female education and fertility in Malawi, using regression methods.MethodsTo analyse the correlation between women’s schooling and fertility and evaluate the effect of outliers on this relationship, a bivariate Poisson model was applied to three recent demographic and health surveys in Malawi. The R software version 4.3.0 was used for model fitting, outlier computations, and correlation analysis. The STATA version 12.0 was used for data cleaning.ResultsThe findings revealed a correlation of -0.68 to -0.61 between schooling and fertility over 15 years in Malawi. A few outlier women were identified, most of whom had either attended 0 or at least 9 years of schooling and had born either 0 or at least 5 children. The majority of the outliers were non-users of modern contraceptive methods and worked as domestic workers or were unemployed. Removing the outliers from the analysis led to marked changes in the fixed effects sizes and slight shifts in correlation, but not in the direction and significance of the estimates. The woman’s marital status, occupation, household wealth, age at first sex, and usage of modern contraceptives exhibited significant effects on education and fertility outcomes.ConclusionThere is a high negative correlation between female schooling and fertility in Malawi. Some outlier women were identified, they had either attended zero or at least nine years of schooling and had either born zero or at least five children. Most of them were non-users of modern contraceptives and domestic workers. Their impact on regression estimates was substantial, but minimal on correlation. Their identification highlights the need for policymakers to reconsider implementation strategies for modern contraceptive methods to make them more effective.

Sports Data Analysis by using Bivariate Poisson Models in the Bayesian Framework

Bivariate distribution models are commonly used to analyze sports data and data from various fields. These models are used to analyze discrete count data with two dependent variables in the data. In this research article, we have used Bivariate Poisson and Diagonally Inflated Bivariate Poisson regression models. We have proposed an estimation procedure in the Bayesian framework in conjunction with the augmentation of data. For parameter estimation, we use Gaussian priors and beta priors for both models. To illustrate the fitting performances of our suggested models we have performed real data analysis on English Premier League soccer data.

Zero-Dependent Bivariate Poisson Distribution with Applications

The bivariate Poisson model is the most widely used model for bivariate counts, and in recent years, several bivariate Poisson regression models have been developed in order to analyse two response variables that are possibly correlated. In this paper, a particular class of bivariate Poisson model, developed from the bivariate Bernoulli model, will be presented and investigated. The proposed bivariate Poisson models use dependence parameters that can model positively and negatively correlated data, whereas more well-known models, such as Holgate’s bivariate Poisson model, can only be used for positively correlated data. As a result, the proposed model contributes to improving the properties of the more common bivariate Poisson regression models. Furthermore, some of the properties of the new bivariate Poisson model are outlined. The method of maximum likelihood and moment method were used to estimate the parameters of the proposed model. Additionally, real data from the healthcare utilization sector were used. As in the case of healthcare utilization, dependence between the two variables may be positive or negative in order to assess the performance of the proposed model, in comparison to traditional bivariate count models. All computations and graphs shown in this paper were produced using R programming language.

Modeling the Impact of Driving Styles on Crash Severity Level Using SHRP 2 Naturalistic Driving Data

Previous studies have examined driving styles and how they are associated with crash risks relying on self-report questionnaires to categorize respondents based on pre-defined driving styles. Naturalistic driving studies provide a unique opportunity to examine this relationship differently. The current study aimed to study how driving styles, derived from real-road driving, may relate to crash severity. To study the relationship, this study retrieved safety critical events (SCEs) from the SHRP 2 database and adopted joint modelling of the number of the aggregated crash severity levels (crash vs. non-crash) using the Diagonal Inflated Bivariate Poisson (DIBP) model. Variables examined included driving styles and various driver characteristics. Among driving styles examined, styles of maintenance of lower speeds and more adaptive responses to driving conditions were associated with fewer crashes given an SCE occurred. Longer driving experiences, more miles driven last year, and being female also reduced the number of crashes. Interestingly, older drivers were associated with both an increased number of crashes and increased number of non-crash SCEs. Future work may leverage more variables from the SHRP 2 database and widen the scope to examine different traffic conditions for a more complete picture of driving styles.

A cross-sectional study examining consideration of self-managed abortion among people seeking facility-based care in the United States

IntroductionWith increasing restrictions on abortion across the United States, we sought to understand whether people seeking abortion would consider ending their pregnancy on their own if unable to access a facility-based abortion.MethodsFrom January to June 2019, we surveyed patients seeking abortion at 4 facilities in 3 US states. We explored consideration of self-managed abortion (SMA) using responses to the question: “Would you consider ending this pregnancy on your own if you are unable to obtain care at a health care facility?” We used multivariable Poisson regression to assess associations between individual sociodemographic, pregnancy and care-seeking characteristics and prevalence of considering SMA. In bivariate Poisson models, we also explored whether consideration of SMA differed by specific obstacles to abortion care.ResultsOne-third (34%) of 741 participants indicated they would definitely or probably consider ending the pregnancy on their own if unable to obtain care at a facility. Consideration of SMA was higher among those who reported no health insurance (adjusted prevalence ratio [aPR] = 1.66; 95% Confidence Interval [CI] 1.12–2.44), described the pregnancy as unintended (aPR = 1.53; 95% CI 1.08–2.16), were seeking abortion due to concerns about their own physical or mental health (aPR = 1.50, 95% CI 1.02, 2.20), or experienced obstacles that delayed their abortion care seeking (aPR = 2.26, 95% CI 1.49, 3.40). Compared to those who would not consider SMA, participants who would consider SMA expressed higher difficulty finding an abortion facility (35 vs. 27%, p = 0.019), figuring out how to get to the clinic (29 vs 21%, p = 0.021) and needing multiple clinic visits (23 vs 17%, p = 0.044).Conclusions.One in three people seeking facility-based abortion would consider SMA if unable to obtain abortion care at a facility. As abortion access becomes increasingly restricted in the US, SMA may become more common. Future research should continue to monitor people’s consideration and use of SMA and ensure that they have access to safe and effective methods.

The role of network embeddedness across multiple social networks: Evidence from mobile social network games

This article examines peer influences from network relationships within a social network game (i.e., embeddedness) and across such games (i.e., multiplexity). Drawing on social influence theory, we develop a bivariate Poisson model of users’ repeated visits and latent attrition that accommodates peer interaction after controlling for homophily. We estimate the model using data from two social network games with considerable overlap among network members. We find that friends who are only multiplex across games exert greater peer influence on users’ game visits than members who are embedded within a single game. We also determined that ignoring network multiplexity across games may lead firms to mistarget users due to biased peer influences of embedded friends. This result provides an unresearched explanation—strength of peer influence—for the mixed findings in previous literature on network embeddedness. We utilized our results to conduct several scenario analyses to demonstrate how firms can effectively manage users’ engagement and target users in multiple social network games.

Forecasting football matches by predicting match statistics

This paper considers the use of observed and predicted match statistics as inputs to forecasts for the outcomes of football matches. It is shown that, were it possible to know the match statistics in advance, highly informative forecasts of the match outcome could be made. Whilst, in practice, match statistics are clearly never available prior to the match, this leads to a simple philosophy. If match statistics can be predicted pre-match, and if those predictions are accurate enough, it follows that informative match forecasts can be made. Two approaches to the prediction of match statistics are demonstrated: Generalised Attacking Performance (GAP) ratings and a set of ratings based on the Bivariate Poisson model which are named Bivariate Attacking (BA) ratings. It is shown that both approaches provide a suitable methodology for predicting match statistics in advance and that they are informative enough to provide information beyond that reflected in the odds. A long term and robust gambling profit is demonstrated when the forecasts are combined with two betting strategies.

Estimating the change in soccer's home advantage during the Covid-19 pandemic using bivariate Poisson regression.

In wake of the Covid-19 pandemic, 2019–2020 soccer seasons across the world were postponed and eventually made up during the summer months of 2020. Researchers from a variety of disciplines jumped at the opportunity to compare the rescheduled games, played in front of empty stadia, to previous games, played in front of fans. To date, most of this post-Covid soccer research has used linear regression models, or versions thereof, to estimate potential changes to the home advantage. However, we argue that leveraging the Poisson distribution would be more appropriate and use simulations to show that bivariate Poisson regression (Karlis and Ntzoufras in J R Stat Soc Ser D Stat 52(3):381–393, 2003) reduces absolute bias when estimating the home advantage benefit in a single season of soccer games, relative to linear regression, by almost 85%. Next, with data from 17 professional soccer leagues, we extend bivariate Poisson models estimate the change in home advantage due to games being played without fans. In contrast to current research that suggests a drop in the home advantage, our findings are mixed; in some leagues, evidence points to a decrease, while in others, the home advantage may have risen. Altogether, this suggests a more complex causal mechanism for the impact of fans on sporting events.

Estimation in the zero-inflated bivariate Poisson model, with an application to health-care utilization data

Data on the demand for medical care is usually measured by a number of different counts. These count data are most often correlated and subject to high proportions of zeros. However, excess zeros and the dependence between these data can jointly affect several utilization measures.In this paper, the zero-inflated bivariate Poisson regression model (ZIBP) was used to analyze health-care utilization data. First, the asymptotic properties of the maximum likelihood estimator (MLE) of this model were investigated theoretically.Then, a simulation study is conducted to evaluate the behaviour of the estimator in finite samples. Finally, an application of the ZIBP model to health care demand data is provided by way of illustration.

Estimation in the zero-inflated bivariate Poisson model, with an application to health-care utilization data

Data on the demand for medical care is usually measured by a number of different counts. These count data are most often correlated and subject to high proportions of zeros. However, excess zeros and the dependence between these data can jointly affect several utilization measures.In this paper, the zero-inflated bivariate Poisson regression model (ZIBP) was used to analyze health-care utilization data. First, the asymptotic properties of the maximum likelihood estimator (MLE) of this model were investigated theoretically. Then, a simulation study is conducted to evaluate the behaviour of the estimator in finite samples. Finally, an application of the ZIBP model to health care demand data is provided by way of illustration.

A bivariate autoregressive Poisson model and its application to asthma-related emergency room visits.

There are no gold standard methods that perform well in every situation when it comes to the analysis of multiple time series of counts. In this paper, we consider a positively correlated bivariate time series of counts and propose a parameter-driven Poisson regression model for its analysis. In our proposed model, we employ a latent autoregressive process, AR(p) to accommodate the temporal correlations in the two series. We compute the familiar maximum likelihood estimators of the model parameters and their standard errors via a Bayesian data cloning approach. We apply the model to the analysis of a bivariate time series arising from asthma-related visits to emergency rooms across the Canadian province of Ontario.

Discrete Weibull regression for modelling football outcomes

We propose the use of the discrete Weibull distribution for modelling football match results, as an alternative to existing Poisson and generalised Poisson models. The number of goals scored by the two teams playing a football match are regarded as a pairwise observation and are modelled first through two independent discrete Weibull variables, and then through two dependent discrete Weibull variables, using a copula approach that accommodates non-null correlation. The parameters of the bivariate discrete Weibull distributions are assumed to depend on covariates such as the attack and defence abilities of the two teams and the 'home effect'. Several discrete Weibull regression models are proposed and then applied to the 2015-2016 Italian Serie A. Even if the interpretation of parameters is less immediate than in the case of bivariate Poisson models, nevertheless these models represent a suitable alternative, which can be applied also in other fields than sport data analysis.

Analyzing the effect of duration on the daily new cases of COVID-19 infections and deaths using bivariate Poisson regression: a marginal conditional approach.

The whole world is devastated by the impact of the COVID-19 pandemic. The socioeconomic and other effects of COVID-19 on people are visible in all echelons of society. The main goal of countries is to stop the spreading of this pandemic by reducing the COVID-19 related new cases and deaths. In this paper, we analyzed the correlated count outcomes, daily new cases, and fatalities, and assessed the impact of some covariates by adopting a generalized bivariate Poisson model. There are different effects of duration on new cases and deaths in different countries. Also, the regional variation found to be different, and population density has a significant impact on outcomes.

A Bivariate Zero-Inflated Poisson Model with Skew-Normal Random Effect

A Bivariate Zero-Inflated Poisson Model with Skew-Normal Random Effect

Ranking soccer teams on the basis of their current strength: A comparison of maximum likelihood approaches

We present 10 different strength-based statistical models that we use to model soccer match outcomes with the aim of producing a new ranking. The models are of four main types: Thurstone–Mosteller, Bradley–Terry, independent Poisson and bivariate Poisson, and their common aspect is that the parameters are estimated via weighted maximum likelihood, the weights being a match importance factor and a time depreciation factor giving less weight to matches that are played a long time ago. Since our goal is to build a ranking reflecting the teams’ current strengths, we compare the 10 models on the basis of their predictive performance via the Rank Probability Score at the level of both domestic leagues and national teams. We find that the best models are the bivariate and independent Poisson models. We then illustrate the versatility and usefulness of our new rankings by means of three examples where the existing rankings fail to provide enough information or lead to peculiar results.