A New Bivariate Random Coefficient INAR(1) Model with Applications

Excess zeros is a common phenomenon in time series of counts, but it is not well studied in asymmetrically structured bivariate cases. To fill this gap, we first considered a new first-order, bivariate, random coefficient, integer-valued autoregressive model with a bivariate innovation, which follows the asymmetric Hermite distuibution with five parameters. An attractive advantage of the new model is that the dependence between series is achieved by innovative parts and the cross-dependence of the series. In addition, the time series of counts are modeled with excess zeros, low counts and low over-dispersion. Next, we established the stationarity and ergodicity of the new model and found its stochastic properties. We discuss the conditional maximum likelihood (CML) estimate and its asymptotic property. We assessed finite sample performances of estimators through a simulation study. Finally, we demonstrate the superiority of the proposed model by analyzing an artificial dataset and a real dataset.

Identification of Cell-Type-Specific Spatially Variable Genes Accounting for Excess Zeros

Spatial transcriptomic techniques can profile gene expressions while retaining the spatial information, thus offering unprecedented opportunities to explore the relationship between gene expression and spatial locations. The spatial relationship may vary across cell types, but there is a lack of statistical methods to identify cell-type-specific spatially variable (SV) genes by simultaneously modeling excess zeros and cell-type proportions. We develop a statistical approach CTSV to detect cell-type-specific SV genes. CTSV directly models spatial raw count data and considers zero-inflation as well as overdispersion using a zero-inflated negative binomial distribution. It then incorporates cell-type proportions and spatial effect functions in the zero-inflated negative binomial regression framework. The R package pscl (Zeileis et al., 2008) is employed to fit the model. For robustness, a Cauchy combination rule is applied to integrate p-values from mutliple choices of spatial effect functions. Simulation studies show that CTSV not only outperforms the competing methods at the aggregated level but also achieves more power at the cell-type level. By analyzing pancreatic ductal adenocarcinoma spatial transcriptomic data, SV genes identified by CTSV reveal meaningful biological insights at the cell-type level. The R package to implement CTSV is available on GitHub https://github.com/jingeyu/CTSV.

Generalized Confidence Intervals for Zero-Inflated Pareto Distribution

This paper considers interval estimations for the mean of Pareto distribution with excess zeros. Three approaches for interval estimation are proposed based on fiducial generalized pivotal quantities (FGPQs), respectively. Simulation studies are performed to assess the performance of the proposed methods, along with three measurements to determine comparisons with competing approaches. The advantages and disadvantages of each method are provided. The methods are illustrated using a real phone call dataset.

PEMODELAN JUMLAH KEMATIAN BAYI DI KOTA BANDUNG DENGAN MENGGUNAKAN REGRESI ZERO-INFLATED POISSON

Kematian bayi merupakan salah satu indikator dalam menentukan tingkat kesehatan masyarakat. Salah satu upaya untuk mengurangi jumlah kematian bayi adalah dengan mengkaji faktor-faktor penyebabnya. Banyaknya kasus kematian bayi yang berupa data diskrit dan faktor-faktor yang mempengaruhinya dapat dimodelkan menggunakan regresi Poisson. Namun, dalam analisis regresi Poisson sering ditemukan kondisi overdispersi yakni nilai varians dari variabel respon lebih besar dari nilai mean. Overdispersi dapat terjadi karena terlalu banyaknya nilai nol (excess zeros) pada variabel respon. Model regresi Zero-Inflated Poisson merupakan salah satu metode yang dapat mengatasi masalah overdispersi. Pada penelitian ini, data kasus jumlah kematian bayi memiliki terlalu banyak nilai nol, sehingga regresi Zero-Inflated Poisson lebih tepat digunakan untuk memodelkan jumlah kematian bayi dan faktor-faktor yang mempengaruhinya di Kota Bandung Tahun 2019. Hasil analisis menunjukkan bahwa faktor-faktor yang berpengaruh secara signifikan terhadap kasus jumlah kematian bayi adalah persentase berat badan bayi lahir rendah (BBLR), persentase kunjungan neonatal selama 3× dan persentase bayi yang diberikan ASI eksklusif.Kata Kunci: Excess Zeros, Overdispersi, Regresi Poisson, Regresi Zero-Inflated Poisson

Influence of meteorological conditions on road accidents. A model for observations with excess zeros

Road accidents are one of the basic road safety determinants. Most research covers large territorial areas. The results of such research do not take into account the differences between individual regions, which often leads to incorrect results and their interpretation. What makes it difficult to conduct analyses in a narrow territorial area is the small number of observations. The narrowing of the research area means that the number of accidents in time units is often very low. There are many zero observations in the data sets, which may affect the reliability of the research results. Such data are usually aggregated, which leads to information loss. The authors have therefore applied a model that addresses such problems. They proposed a method that does not require data aggregation and allows for the analysis of sets with an excess of zero observations. The presented model can be implemented in different territorial areas.

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.