Abstract: In this paper, zero-one inflated negative binomial distribution is considered, along with some of its structural properties, then its parameters were estimated using the method of moments. It is found that the method of moments to estimate the parameters of the zero-one inflated negative binomial models is not a proper method and may give incorrect conclusions.
Abstract: This paper focuses on the assessment of the air
pollution and morbidity relationship in Tunisia. Air pollution is
measured by ozone air concentration and the morbidity is measured
by the number of respiratory-related restricted activity days during
the 2-week period prior to the interview. Socioeconomic data are also
collected in order to adjust for any confounding covariates. Our
sample is composed by 407 Tunisian respondents; 44.7% are women,
the average age is 35.2, near 69% are living in a house built after
1980, and 27.8% have reported at least one day of respiratory-related
restricted activity. The model consists on the regression of the
number of respiratory-related restricted activity days on the air
quality measure and the socioeconomic covariates. In order to correct
for zero-inflation and heterogeneity, we estimate several models
(Poisson, negative binomial, zero inflated Poisson, Poisson hurdle,
negative binomial hurdle and finite mixture Poisson models).
Bootstrapping and post-stratification techniques are used in order to
correct for any sample bias. According to the Akaike information
criteria, the hurdle negative binomial model has the greatest goodness
of fit. The main result indicates that, after adjusting for
socioeconomic data, the ozone concentration increases the probability
of positive number of restricted activity days.
Abstract: Many researchers have suggested the use of zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) models in modeling overdispersed medical count data with extra variations caused by extra zeros and unobserved heterogeneity. The studies indicate that ZIP and ZINB always provide better fit than using the normal Poisson and negative binomial models in modeling overdispersed medical count data. In this study, we proposed the use of Zero Inflated Inverse Trinomial (ZIIT), Zero Inflated Poisson Inverse Gaussian (ZIPIG) and zero inflated strict arcsine models in modeling overdispered medical count data. These proposed models are not widely used by many researchers especially in the medical field. The results show that these three suggested models can serve as alternative models in modeling overdispersed medical count data. This is supported by the application of these suggested models to a real life medical data set. Inverse trinomial, Poisson inverse Gaussian and strict arcsine are discrete distributions with cubic variance function of mean. Therefore, ZIIT, ZIPIG and ZISA are able to accommodate data with excess zeros and very heavy tailed. They are recommended to be used in modeling overdispersed medical count data when ZIP and ZINB are inadequate.
Abstract: Road crashes not only claim lives and inflict injuries but also create economic burden to the society due to loss of productivity. The problem of deaths and injuries as a result of road traffic crashes is now acknowledged to be a global phenomenon with authorities in virtually all countries of the world concerned about the growth in the number of people killed and seriously injured on their roads. However, the road crash scenario of a developing country like Bangladesh is much worse comparing with this of developed countries. For developing proper countermeasures it is necessary to identify the factors affecting crash occurrences. The objectives of the study is to examine the effect of district wise road infrastructure, socioeconomic and demographic features on crash occurrence .The unit of analysis will be taken as individual district which has not been explored much in the past. Reported crash data obtained from Bangladesh Road Transport Authority (BRTA) from the year 2004 to 2010 are utilized to develop negative binomial model. The model result will reveal the effect of road length (both paved and unpaved), road infrastructure and several socio economic characteristics on district level crash frequency in Bangladesh.
Abstract: Dengue fever has become a major concern for health
authorities all over the world particularly in the tropical countries.
These countries, in particular are experiencing the most worrying
outbreak of dengue fever (DF) and dengue haemorrhagic fever
(DHF). The DF and DHF epidemics, thus, have become the main
causes of hospital admissions and deaths in Malaysia. This paper,
therefore, attempts to examine the environmental factors that may
influence the recent dengue outbreak. The aim of this study is twofold,
firstly is to establish a statistical model to describe the
relationship between the number of dengue cases and a range of
explanatory variables and secondly, to identify the lag operator for
explanatory variables which affect the dengue incidence the most.
The explanatory variables involved include the level of cloud cover,
percentage of relative humidity, amount of rainfall, maximum
temperature, minimum temperature and wind speed. The Poisson and
Negative Binomial regression analyses were used in this study. The
results of the analyses on the 915 observations (daily data taken from
July 2006 to Dec 2008), reveal that the climatic factors comprising of
daily temperature and wind speed were found to significantly
influence the incidence of dengue fever after 2 and 3 weeks of their
occurrences. The effect of humidity, on the other hand, appears to be
significant only after 2 weeks.
Abstract: The zero truncated model is usually used in modeling
count data without zero. It is the opposite of zero inflated model.
Zero truncated Poisson and zero truncated negative binomial models
are discussed and used by some researchers in analyzing the
abundance of rare species and hospital stay. Zero truncated models
are used as the base in developing hurdle models. In this study, we
developed a new model, the zero truncated strict arcsine model,
which can be used as an alternative model in modeling count data
without zero and with extra variation. Two simulated and one real
life data sets are used and fitted into this developed model. The
results show that the model provides a good fit to the data. Maximum
likelihood estimation method is used in estimating the parameters.
Abstract: The zero inflated models are usually used in modeling
count data with excess zeros where the existence of the excess zeros
could be structural zeros or zeros which occur by chance. These type
of data are commonly found in various disciplines such as finance,
insurance, biomedical, econometrical, ecology, and health sciences
which involve sex and health dental epidemiology. The most popular
zero inflated models used by many researchers are zero inflated
Poisson and zero inflated negative binomial models. In addition, zero
inflated generalized Poisson and zero inflated double Poisson models
are also discussed and found in some literature. Recently zero
inflated inverse trinomial model and zero inflated strict arcsine
models are advocated and proven to serve as alternative models in
modeling overdispersed count data caused by excessive zeros and
unobserved heterogeneity. The purpose of this paper is to review
some related literature and provide a variety of examples from
different disciplines in the application of zero inflated models.
Different model selection methods used in model comparison are
discussed.