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: Zero inflated Strict Arcsine model is a newly developed model which is found to be appropriate in modeling overdispersed count data. In this study, maximum likelihood estimation method is used in estimating the parameters for zero inflated strict arcsine model. Bootstrapping is then employed to compute the confidence intervals for the estimated parameters.
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: Zero inflated strict arcsine model is a newly developed
model which is found to be appropriate in modeling overdispersed
count data. In this study, we extend zero inflated strict arcsine model
to zero inflated strict arcsine regression model by taking into
consideration the extra variability caused by extra zeros and
covariates in count data. Maximum likelihood estimation method is
used in estimating the parameters for this zero inflated strict arcsine
regression model.
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.
Abstract: The purpose of this study is mainly to predict collision
frequency on the horizontal tangents combined with vertical curves
using artificial neural network methods. The proposed ANN models
are compared with existing regression models. First, the variables
that affect collision frequency were investigated. It was found that
only the annual average daily traffic, section length, access density,
the rate of vertical curvature, smaller curve radius before and after
the tangent were statistically significant according to related
combinations. Second, three statistical models (negative binomial,
zero inflated Poisson and zero inflated negative binomial) were
developed using the significant variables for three alignment
combinations. Third, ANN models are developed by applying the
same variables for each combination. The results clearly show that
the ANN models have the lowest mean square error value than those
of the statistical models. Similarly, the AIC values of the ANN
models are smaller to those of the regression models for all the
combinations. Consequently, the ANN models have better statistical
performances than statistical models for estimating collision
frequency. The ANN models presented in this paper are
recommended for evaluating the safety impacts 3D alignment
elements on horizontal tangents.