Count Data Models Research Articles

Climate change adaptation strategies by smallholder farmers in Nigeria: does non-farm employment play any role?

Non-farm employment in agrarian communities in developing countries has received a lot of attention. However, its role in implementing climate change adaptation strategies is rarely discussed. This study employs a cross-sectional data to examine whether rural households in Southwest Nigeria are increasing the extent of climate change adaptation practices through their participation in non-farm employment. To account for selectivity bias, the study used endogenous treatment effect for count data model (precisely Poisson) augmented with the inverse probability-weighted-regression-adjustment (IPWRA) estimator. Both estimators found that rural non-farm jobs increase smallholder farmers' adaptive capacities and that participants would have used less adaptation techniques if they had not participated in non-farm work. Efforts to boost rural development must provide more employment opportunities for farmers, particularly during the off-cropping time. This will help farmers improve their ability to adopt more climate change adaptation strategies and, consequently increase farm productivity.

Solving unobserved heterogeneity with latent class inflated Poisson regression model

Inflated data and over-dispersion are two common problems when modeling count data with traditional Poisson regression models. In this study, we propose a latent class inflated Poisson (LCIP) regression model to solve the unobserved heterogeneity that leads to inflations and over-dispersion. The performance of the model estimation is evaluated through simulation studies. We illustrate the usefulness of introducing a latent class variable by analyzing the Behavioral Risk Factor Surveillance System (BRFSS) data, which contain several excessive values and characterized by over-dispersion. As a result, the new model we proposed displays a better fit than the standard Poisson regression and zero-inflated Poisson regression models for the inflated counts.

Can Generalized Poisson model replace any other count data models? An evaluation

BackgroundCount data represents the number of occurrences of an event within a fixed period of time. In count data modelling, overdispersion is inevitable. Sometimes, this overdispersion may not be just due to the excess zeros but may be due to the presence of two or more mixtures. Hence the main objective is to examine for the presence of mixtures if any, with excess zeros and compare Generalized Poisson model, Mixture models with other count data models using real time and simulated data. MethodsThree real time over-dispersed datasets were used for the comparison of the models. The real time data models were compared using information criteria like AIC and BIC and regression coefficients. Data was also simulated using mixture Poisson with excess zeros. The simulation was repeated for different sample sizes were used to identify the better model. ResultsGeneralized Poisson showed consistently lower bias and MSE when compared to the other models for varying sample of sizes. AIC and BIC values were almost similar for Generalized Poisson, ZIP and Mixture Poisson model. Similar findings were also obtained from real time data. ConclusionGeneralized Poisson models provides a better fit for overdispersed data due to excess zeros, consistently in real time and simulated with varying sample sizes. Negative Binomial models can be redistricted or re-evaluated against Generalized Poisson model.

Zero-Inflated Models for Count Data: An Application to Number of Antenatal Care Service Visits

The risk of maternal death in developing countries is projected to be one in 61, while for developed countries it is estimated to be one in 2800. Antenatal care is a protective obstetric health care system aimed at improving the outcome of the pregnant fetus by routine pregnancy monitoring. One of the most important functions of antenatal care is to offer health information and services that can significantly improve the health of women and their infants. 6450 pregnant women from Ethiopian Demographic and Health Survey of 2016 were used to analyze the determinants of the barriers in number of antenatal care service visits among pregnant women in Ethiopia. The data were found to have excess zeros (35%); thus several count data models such as Poisson, Negative Binomial, Zero Inflated Poisson, Zero Inflated Negative Binomial and Hurdle regression models were modeled and fitted. From the exploratory analysis the results showed that among those eligible pregnant women, it was seen that 2240 (34.7%) of them did not visit antenatal care service during their periods of pregnancy months. The visualization of data using scatter plot depicts that all of the variables selected for modeling have an influence on the event of not visiting antenatal care cervices while each of these variables had opposite slope in non-zero number of such events in their respective categories. To select the model which best fits the data, models were compared based on their Akaike information criterion value by using the simulation study. The simulation experiment revealed that models for zero-inflated data such as; Zero Inflated Poisson, Zero Inflated Negative Binomial and Hurdle were models that fitted the data better than the classical models Poisson and Negative Binomial. Each of these zero-inflated models was compared using Voung test and Hurdle model was better fitted the data which was characterized by excess zeros and high variability in the non-zero outcome than any other zero-inflated models. In this study, maternal education, partner education level, age of mothers, religion of mothers and wealth index are major predictors of antenatal care service utilization. Through simulation experiment, it was found that Zero Inflated Poisson, Zero Inflated Negative Binomial and Hurdle models were better fitted zero-inflated data than Poisson and Negative Binomial. Voung test suggests that Hurdle model was better fitted zero-inflated (ZI) data than any other zero inflated models and therefore, it was selected as the best parsimonious model.

A New Regression Model for the Analysis of Overdispersed and Zero-Modified Count Data

Count datasets are traditionally analyzed using the ordinary Poisson distribution. However, said model has its applicability limited, as it can be somewhat restrictive to handling specific data structures. In this case, the need arises for obtaining alternative models that accommodate, for example, overdispersion and zero modification (inflation/deflation at the frequency of zeros). In practical terms, these are the most prevalent structures ruling the nature of discrete phenomena nowadays. Hence, this paper’s primary goal was to jointly address these issues by deriving a fixed-effects regression model based on the hurdle version of the Poisson–Sujatha distribution. In this framework, the zero modification is incorporated by considering that a binary probability model determines which outcomes are zero-valued, and a zero-truncated process is responsible for generating positive observations. Posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the g-prior method. Intensive Monte Carlo simulation studies were performed to assess the Bayesian estimators’ empirical properties, and the obtained results have been discussed. The proposed model was considered for analyzing a real dataset, and its competitiveness regarding some well-established fixed-effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian p-value and the randomized quantile residuals were considered for the task of model validation.

Majoritarian politics and hate crimes against religious minorities: Evidence from India, 2009–2018

• In 2014, the Hindu nationalist BJP won the national parliamentary elections in India. • The BJP’s exclusivist, nationalist ideology has constructed Muslims as the ‘other’. • BJP’s electoral victory in 2014 increased hate crimes against religious minorities. • Accounting for unobserved confounders does not change the results qualitatively. Did the unprecedented victory of the right-wing, Hindu nationalist Bharatiya Janata Party (BJP) in the 2014 national elections in India increase hate crimes against religious minorities? I investigate this question using a difference-in-difference methodology and a novel state-level panel data set for the period 2009–18. To provide context, I offer a brief historical account of Hindu nationalism and a descriptive account of anti-minority hate crimes in India between 2009 and 2018. Turning to the econometric analysis, I estimate a binary treatment regression model (states where BJP won the largest plurality of votes in the 2014 national elections form the treatment group). My results show that BJP’s electoral victory in 2014 caused an increase in the incidence of hate crimes against religious minorities, especially Muslims. I test for robustness of my results by using two falsification tests and a count data model specification. I account for possible omitted variable bias and compute bias-adjusted treatment effects. I conclude that unobserved confounders are unlikely to nullify the results.

The effect of data aggregation on dispersion estimates in count data models.

For the modelling of count data, aggregation of the raw data over certain subgroups or predictor configurations is common practice. This is, for instance, the case for count data biomarkers of radiation exposure. Under the Poisson law, count data can be aggregated without loss of information on the Poisson parameter, which remains true if the Poisson assumption is relaxed towards quasi-Poisson. However, in biodosimetry in particular, but also beyond, the question of how the dispersion estimates for quasi-Poisson models behave under data aggregation have received little attention. Indeed, for real data sets featuring unexplained heterogeneities, dispersion estimates can increase strongly after aggregation, an effect which we will demonstrate and quantify explicitly for some scenarios. The increase in dispersion estimates implies an inflation of the parameter standard errors, which, however, by comparison with random effect models, can be shown to serve a corrective purpose. The phenomena are illustrated by γ-H2AX foci data as used for instance in radiation biodosimetry for the calibration of dose-response curves.

THE IMPACTS OF SPOUSES’ EDUCATION AND MATERNAL HEALTH ON FERTILITY IN PAKISTAN: AN ECONOMETRIC ANALYSIS

Purpose of the study: This paper primarily aims to recognize, develop, and examine the impacts of spouses’ education and maternal health status in cooperation with a variety of other covariates (demographic, social, economic, cultural, and attitudinal) on fertility in Pakistan.
 Methodology: This study mainly aimed to discover how spouse’s education and maternal health inputs help in controlling high fertility using four data sets of Pakistan Demographic and Health Survey (1990-91, 2006-07, 2012-13 and 2017-18) through count data model (Poisson regression).
 Main Findings: Our empirical results proved the hypotheses that educated spouses and healthy mothers practice family planning tools (contraceptives) to lower down the total fertility rates.
 Application of this study: Educated husband and wife will keep their family size smaller to devote more on children’s nutrition, health, and education. In general, rise in intentional birth control method make the education policy more helpful in reducing fertility. Findings draw government attention for embarking on public enlightenment campaigns to generate wakefulness regarding the long-term significance of fertility regulation in Pakistan.
 Novelty/Originality: The study is one of its kind because it attempted to explore the link among spouse’s education, maternal health inputs, and child’s health outcomes with fertility that could be used to benchmark for additional research in Pakistan.

Bayesian regression models for ecological count data in PyMC3

Ecological inferences need structurally flexible statistical models to accommodate complex ecological phenomena. PyMC3 is a Probabilistic Programming Language (PPL) and allows for custom statistical distributions to build complex statistical models. This study used PyMC3 to implement Bayesian generalized Poisson (GP), zero-inflated GP, and hurdle GP regression models for over- and under-dispersed counts. The Bayesian GP regression models were fitted to simulated counts and real-world counts of over- and under-dispersion, respectively. Coefficient estimates of the Bayesian regression models were consistent with the known values used in the simulations and those of published work or models. Simulations demonstrated that Bayesian GP regression models with the NUTS sampler worked correctly for under-dispersed counts if the number of non-zero frequency classes was five or more. PyMC3 is not only flexible for building complex statistical models using custom likelihood functions, but also syntactically concise. The programming flexibility of PyMC3 can provide ecologists and environmental scientists with flexible, robust Bayesian computational platforms.

How do air pollution and meteorological parameters contribute to the spread of COVID-19 in Saudi Arabia?

The current global health crisis is unprecedented in modern times. It has killed numerous people, caused great suffering, and turned many people’s lives upside down. This study seeks to investigate the role of some pollutants and the meteorological parameters in the transmission of the virus (SARS-CoV-2). The number of infections identified in Saudi Arabia, a country with a hot climate, was studied for a period between March 9, 2020 and November 19, 2020, which was characterized by a single wave with a peak of 4,919 cases on June 17, 2020. Based on count data models, we observed that air pollution and meteorological parameters considerably influenced the daily evolution of infections in most affected cities of Saudi Arabia (Riyadh, Jeddah, and Makkah) where the prevalence of the disease was relatively high during summer 2020. Our study suggests that air pollution could be a significant risk factor for respiratory infections and virus transmission. On the other hand, meteorological factors and high concentration of air pollutants should be taken into account by public decision-makers in Saudi Arabia when seeking to limit COVID-19 transmission.

Comparing Regression Models with Count Data to Artificial Neural Network and Ensemble Models for Prediction of Generic Escherichia coli Population in Agricultural Ponds Based on Weather Station Measurements

Indicator microorganisms are monitored in agricultural waters to foster produce safety. Various prediction models are used to estimate the population of indicator microorganisms and pathogens when no observation is available. The purpose of this study was to compare the performance of regression models with count data (zero-inflated Poisson and hurdle negative binomial) to artificial neural network and ensemble models (random forest and AdaBoost) for the prediction of generic Escherichia coli population in agricultural surface waters in relation with weather station measurements. Two-part count data models were built on E. coli population count frequencies (0, [1,10), [10,100), [100,1000), [1000, 10000), (>=10000)) based on the data structure. The use of artificial neural network, AdaBoost, and random forest were determined based on the mean absolute error (MAE) value over pre-tested six models. The MAE was also used to compare the performance of two-part count data models with artificial neural network and ensemble models. Over-dispersed E. coli population count frequencies was calculated between 2.2 and 52.2% for all ponds. Observed and predicted zero E. coli population counts for all ponds were matched from 82 to 100% for zero-inflated Poisson and 100% for hurdle negative binomial regression models. Overdispersion reduced the performance of tested models. AdaBoost-Twelve Estimators had the best performance with the lowest MAE values for all ponds (from 0.87 to 46.60). The ensemble models used in this study provided more promising performance when compared to tested regression models with count data.

Air Pollution, Health, and Avoidance Behavior: Evidence from South Korea

Using detailed data on the beneficiaries of the Korean National Health Insurance Service (c.2006-2015), this paper estimates the health effects of air pollution in South Korea while controlling for avoidance behaviors. In particular, I investigate changes in the respiratory hospitalization rates due to increases in PM10 and O3 concentrations. To address the endogeneity of air pollution, this paper applies the historical average concentration of air pollution that includes rich information about the meteorological and geographical factors that affect regional air pollution levels as an instrumental variable and compares the results with other count data models. I find that a 10mg/m3 increase in PM10 and a 10ppb increase in O3 lead to an increase in daily respiratory hospital visits of up to 10.39% (95% confidence intervals (CI): 4.04--16.80) and 10.93% (95% CI: 9.23-12.63), which results in additional health care costs of $67 million USD and $70 million USD, respectively. This paper also shows that the effects of PM10 and O3 are greater in more populated cities, on children's health, and for non-chronic respiratory patients.

Air Pollution, Health, and Avoidance Behavior: Evidence from South Korea

Using detailed data on the beneficiaries of the Korean National Health Insurance Service (c.2006–2015), this paper estimates the health effects of air pollution in South Korea while controlling for avoidance behaviors. In particular, we investigate changes in respiratory hospitalization rates due to increases in PM $$_{10}$$ and O $$_{3}$$ concentrations. To address the endogeneity of air pollution, this paper applies the historical average concentration of air pollution, which includes rich information about the meteorological and geographical factors that affect regional air pollution levels, as an instrumental variable and compares the results with other count data models. We find that a 10 $$\upmu$$ g/m $$^{3}$$ increase in PM $$_{10}$$ and a 10 ppb increase in O $$_{3}$$ lead to an increase in daily respiratory hospital visits of up to 10.39% [95% confidence interval (CI) 4.04–16.80] and 10.93% (95% CI 9.23–12.63), resulting in additional health care costs of US$67 million and US$70 million, respectively. This paper also shows that the effects of PM $$_{10}$$ and O $$_{3}$$ are elevated in highly populated cities, children, and patients without chronic respiratory diseases.

A zero-inflated non-negative matrix factorization for the deconvolution of mixed signals of biological data.

A latent factor model for count data is popularly applied in deconvoluting mixed signals in biological data as exemplified by sequencing data for transcriptome or microbiome studies. Due to the availability of pure samples such as single-cell transcriptome data, the accuracy of the estimates could be much improved. However, the advantage quickly disappears in the presence of excessive zeros. To correctly account for this phenomenon in both mixed and pure samples, we propose a zero-inflated non-negative matrix factorization and derive an effective multiplicative parameter updating rule. In simulation studies, our method yielded the smallest bias. We applied our approach to brain gene expression as well as fecal microbiome datasets, illustrating the superior performance of the approach. Our method is implemented as a publicly available R-package, iNMF.

Big science and innovation: gestation lag from procurement to patents for CERN suppliers

CERN, the European Organization for Nuclear Research, is the most important laboratory for particle physics in the world. It requires cutting edge technologies to deliver scientific discoveries. This paper investigates the time span needed for technology suppliers of CERN to absorb the knowledge acquired during the procurement relation and develop it into a patent. We estimate count data models relying on a sample of CERN suppliers for the Large Hadron Collider (LHC), a particle accelerator. Firms in our sample received their first LHC-related order over a long-time span (1995–2008). This fact is exploited to estimate the time lag that separates the beginning of the procurement relationship and the filing date of patents. Becoming a supplier of CERN is associated with a statistically significant increase in the number of patent applications by firms. Moreover, such an effect requires a relatively long gestation lag in the range of five to eight years.

A Reply to Campbell and Mau

In Bloom et al. (2016, Bloom, Draca and Van Reenen (BDVR)), we have a set of nine results on the impact of Chinese trade. The first three showed that Chinese trade increased technical change in European firms measured by patents, productivity, and the adoption of Information Technology (IT). The last six showed that Chinese trade led to reallocation towards more technologically advanced firms: those with more patents, higher productivity and IT adoption had faster growth and lower exit rates. Campbell and Mau (2020, “CM”) argue that one of these results, the effect of Chinese imports on patenting, is sensitive to specification changes. This article focuses on CM’s critique of our count data models—we discuss other aspects of CM in a longer response.1

Modeling and comparison of count data containing zero values: a case study of Setipinna taty in the south inshore of Zhejiang, China.

To effectively use the fishery count data containing zero values, Setipinna taty in the coastal waters of south inshore of Zhejiang in China from 2017 to 2019 was used in this study. Environmental factors, such as water temperature, water depth, and salinity, were selected to establish models and compare based on the generalized additive model (GAM) of the Tweedie distribution (Tweedie-GAM) and two-stage GAM, Ad hoc method, and generalized additive mixed model (GAMM). The results showed that each station accounted for a higher proportion of zero values and the two-stage GAM model had a higher deviation interpretation rate, and GAM I and GAM II had 19.6% and 60.4% deviation interpretation rates. The cross-validation results showed that the performance evaluation of the two-stage GAM model was the best and showed the highest R2 value, the lowest average absolute error, and the relatively small root mean square error. This study found that the abundance of S. taty in the south inshore of Zhejiang was highest at around 21°C and 18°C in spring and autumn, and the abundance reached the highest at a water depth of about 20 m. In spatial distribution, the high value of the abundance of S. taty was mostly distributed in the coastal waters in the south of 28°N. In future research, models should be fitted and compared for different sampling zero-value ratios, and more environmental factors should be included to accurately find an optimal model and provide references for the conservation of fishery resources.

Modelling count data with an excess of zero values applied to childhood bone tumour incidence in Iraq.

Bone tumours are rarely found in children and adolescents (0- 19 years old), but there are reports from some provinces in Iraq indicating possible increases in the incidence of childhood bone cancer. Since counts are very low and often zero, or near zero, we fitted zero-inflated Poisson, zero-inflated negative binomial, Poisson hurdle, and negative binomial hurdle regression models to investigate these changes. We used data covering the 2000-2015 period taking age, gender and province into account with the aim of identifying potential health disparities. The results indicate that the zero-inflated Poisson is the most appropriate approach. We also found that, the incidence rate ratio of bone tumours for age groups of 5-9, 10-14 and 15-19 years were 134%, 490% and 723% higher, respectively, compared to the 0-4 year olds. The incidence rate was higher by 49% higher in males compared to females. Compared to 2000-2004, the rate was higher during 2005-2009 and 2010-2015 by 23% and 50%, respectively. In addition, the provinces Al-Muthana and Al-Diwaniyah in the South were found to have a higher incidence rate than other provinces. Join point analysis showed that the age-adjusted incidence rate had a significant, increasing trend, with an average percentage change of 3.1% during 2000-2015. The study suggests that further research into childhood tumours, bone tumours in particular, is needed. Reference to the effect of environmental factors in this group of medical disorders would be of special interest.

Randomized controlled trial assessing the effects of xylazine sedation in 2- to 6-week-old dairy calves disbudded with a cautery iron

The use of local anesthesia and a nonsteroidal anti-inflammatory drug (NSAID) can reduce indicators of pain and inflammation and encourage self-rewarding behavior in calves following disbudding. Although the use of sedation may be recommended as a best practice for disbudding, there is little research in this area. The objective of this study was to evaluate the effects of xylazine sedation in conjunction with a local anesthetic and an NSAID in calves undergoing cautery disbudding. One hundred twenty-two group-housed female and male Holstein calves fed milk with automated feeders, aged 13 to 44 d, were enrolled over 9 replicates and randomly allocated to 1 of 2 treatments: (1) sedated: lidocaine cornual nerve block, 0.5 mg/kg meloxicam (administered subcutaneously) and 0.2 mg/kg xylazine (administered intramuscularly), or (2) nonsedated: lidocaine cornual nerve block and meloxicam. Outcomes collected consisted of feeding behavior (collected using automated milk feeders), latency to drink milk following disbudding, play behavior (induced by adding bedding), lying behavior, mechanical nociceptive threshold (MNT, measured using a pressure force algometer), struggling behavior during disbudding, length of time to administer the nerve block, length of time to disbud, and serum haptoglobin concentrations. Data were analyzed using mixed models with a fixed effect for baseline values and a random effect for trial replicate. Linear regression was used to assess continuous outcomes, logistic regression for binary outcomes, and Poisson and negative binomial models for count data with negative binomial models used if the over dispersion term was significant. There were no detected differences between the treatment groups in mean daily milk consumption in the 72-h following disbudding. Sedated calves had reduced average milk drinking speed from 0 to 24 h and 24 to 48 h following disbudding compared with nonsedated calves, but no difference was detected from 48 to 72 h. Sedated calves had reduced MNT at 0, 60, and 240 min after disbudding, but no differences were detected between groups at 24 h after disbudding. Nonsedated calves had 4.5 times the odds (95% CI: 1.5-13.2) of struggling more than twice during the disbudding procedure compared with sedated calves, and it took less time to administer a nerve block to sedated calves compared with nonsedated. At +3 h, nonsedated calves were 79 times (95% CI: 22.4 to 279.2) more likely to play compared with sedated calves, and 24 h after disbudding, sedated calves were 2 times more likely to play compared with nonsedated calves (95% CI: 0.93-4.3). The results indicate that calves sedated with xylazine for cautery disbudding responded less to painful stimuli (disbudding and MNT) both during and following the procedure and had a higher rate of play behavior 24 h following sedation compared with the nonsedated calves, but xylazine may also have a prolonged carryover effect that affects suckling behavior for 48 h following sedation.

Statistical modeling of COVID-19 deaths with excess zero counts

Abstract Objectives Modeling and forecasting possible trajectories of COVID-19 infections and deaths using statistical methods is one of the most important topics in present time. However, statistical models use different assumptions and methods and thus yield different results. One issue in monitoring disease progression over time is how to handle excess zeros counts. In this research, we assess the statistical empirical performance of these models in terms of their fit and forecast accuracy of COVID-19 deaths. Methods Two types of models are suggested in the literature to study count time series data. The first type of models is based on Poisson and negative binomial conditional probability distributions to account for data over dispersion and using auto regression to account for dependence of the responses. The second type of models is based on zero-inflated mixed auto regression and also uses exponential family conditional distributions. We study the goodness of fit and forecast accuracy of these count time series models based on autoregressive conditional count distributions with and without zero inflation. Results We illustrate these methods using a recently published online COVID-19 data for Tunisia, which reports daily death counts from March 2020 to February 2021. We perform an empirical analysis and we compare the fit and the forecast performance of these models for death counts in presence of an intervention policy. Our statistical findings show that models that account for zero inflation produce better fit and have more accurate forecast of the pandemic deaths. Conclusions This paper shows that infectious disease data with excess zero counts are better modelled with zero-inflated models. These models yield more accurate predictions of deaths related to the pandemic than the generalized count data models. In addition, our statistical results find that the lift of travel restrictions has a significant impact on the surge of COVID-19 deaths. One plausible explanation of the outperformance of zero-inflated models is that the zero values are related to an intervention policy and therefore they are structural.