Bounded continuous data are encountered in many applications of item response theory, including the measurement mood, personality, and times analyses summed scores. Although different theory models exist to analyze such bounded data, most assume be an open interval cannot accommodate a closed interval. As result, ad hoc transformations needed prevent scores on bounds observed variables. To moti...

Background: The instrumental activities of daily living (IADLs) are important index of physical functioning in older adult studies. These count outcomes with a large proportion of zeros are often collected in longitudinal studies. Data were from the Hispanic Established Population for Epidemiological Study of the Elderly (HEPESE), a four wave (seven years) longitudinal study of community-dwelli...

Several kinds of models have been developed in modeling the occurrence of crashes, but most of these models have deficiencies and lack good results. Single and multivariate deterministic models have illustrated some influences of causal factors on crashes, but the inherent deterministic characteristic of these models makes explaining crash events a difficult task for these kinds of models. Stoc...

Word embeddings are a widely-used tool to analyze language, and exponential family embeddings (Rudolph et al., 2016) generalize the technique to other types of data. One challenge to fitting embedding methods is sparse data, such as a document/term matrix that contains many zeros. To address this issue, practitioners typically downweight or subsample the zeros, thus focusing learning on the non...

Zero inflation problem is very common in ecological studies as well as other areas. We propose the COnstrained Zero-Inflated Generalized Additive Model (COZIGAM) for analyzing zero-inflated data. Our approach assumes that the response follows some distribution from the zero-inflated 1-parameter exponential family, with the further assumption that the probability of zero inflation is some monoto...

The generalized Poisson regression model has been used to model dispersed count data. It is a good competitor to the negative binomial regression model when the count data is over-dispersed. Zero-inflated Poisson and zero-inflated negative binomial regression models have been proposed for the situations where the data generating process results into too many zeros. In this paper, we propose a z...

Mixture distributions provide flexibility in modeling data collected from populations having unexplained heterogeneity. While interpretations of regression parameters from traditional finite mixture models are specific to unobserved subpopulations or latent classes, investigators are often interested in making inferences about the marginal mean of a count variable in the overall population. Rec...