This chapter provides a synthesis of spatial data mining models for analyzing multivariate count responses. Geo-referenced multivariate count responses are common in regional science (e.g., registered vehicle counts by body type and firm/job counts by industry type), but are computationally difficult to model especially when sample size is large. This chapter synthesizes relevant research and o...

In this paper we introduce the Hinde-Demétrio (HD) regression models for analyzing overdispersed count data and, mainly, investigate the e¤ect of dispersion parameter. The HD distributions are discrete additive exponential dispersion models (depending on canonical and dispersion parameters) with a third real index parameter p and have been characterized by its unit variance function + p. For p ...

It is often convenient to define models for the process of chiasma formation at meiosis as stationary renewal models. However, count-location models are also useful, particularly to capture the biological requirement of at least one chiasma per chromosome. The Sturt model and truncated Poisson model are both count-location models with this feature. We show that the truncated Poisson model can a...

Education researchers often study count variables, such as times a student reached a goal, discipline referrals, and absences. Most researchers that study these variables use typical regression methods (i.e., ordinary least-squares) either with or without transforming the count variables. In either case, using typical regression for count data can produce parameter estimates that are biased, th...

Statistical models that involve a two-part mixture distribution are applicable in a variety of situations. Frequently, the two parts are a model for the binary response variable and a model for the outcome variable that is conditioned on the binary response. Two common examples are zero-inflated or hurdle models for count data and two-part models for semicontinuous data. Recently, there has bee...

Language models (LMs) are statistical models that calculate probabilities over sequences of words or other discrete symbols. Currently two major paradigms for language modeling exist: count-based n-gram models, which have advantages of scalability and test-time speed, and neural LMs, which often achieve superior modeling performance. We demonstrate how both varieties of models can be unified in...

In this study, a two-state Markov switching count-data model is proposed as an alternative to zero-inflated models to account for the preponderance of zeros sometimes observed in transportation count data, such as the number of accidents occurring on a roadway segment over some period of time. For this accident-frequency case, zero-inflated models assume the existence of two states: one of the ...

In this paper we have considered several regression models to fit the count data that encounter in the field of Biometrical, Environmental, Social Sciences and Transportation Engineering. We have fitted Poisson (PO), Negative Binomial (NB), Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) regression models to run-off-road (ROR) crash data which collected on arterial roads ...

Five methods for count data clusterization based on Poisson mixture models are described. Two of them are parametric, the others are semi-parametric. The methods emlploy the plug-in Bayes classification rule. Their performance is investigated by making use of computer simulation and compared mainly by the clusterization error rate. We also apply the clusterization procedures to real count data ...