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: This paper presents the comparative study of coded
data methods for finding the benefit of concealing the natural data
which is the mercantile secret. Influential parameters of the number
of replicates (rep), treatment effects (τ) and standard deviation (σ)
against the efficiency of each transformation method are investigated.
The experimental data are generated via computer simulations under
the specified condition of the process with the completely
randomized design (CRD). Three ways of data transformation consist
of Box-Cox, arcsine and logit methods. The difference values of F
statistic between coded data and natural data (Fc-Fn) and hypothesis
testing results were determined. The experimental results indicate
that the Box-Cox results are significantly different from natural data
in cases of smaller levels of replicates and seem to be improper when
the parameter of minus lambda has been assigned. On the other hand,
arcsine and logit transformations are more robust and obviously,
provide more precise numerical results. In addition, the alternate
ways to select the lambda in the power transformation are also
offered to achieve much more appropriate outcomes.
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.