Family of bivariate distributions on the unit square: theoretical properties and applications.

We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in Vila et al. [25] as a flexible family of bivariate distributions over the unit square. We then study its mathematical properties such as stochastic representations, quantiles, conditional distributions, independence of the marginal distributions and marginal moments. Maximum likelihood estimation method is discussed and examined through Monte Carlo simulation. Finally, the proposed model is used to analyze some soccer data sets.

A new regression model for rates and proportions data with applications.

We propose a new continuous distribution in the interval ( 0 , 1 ) based on the generalized odd log-logistic-G family, whose density function can be symmetrical, asymmetric, unimodal and bimodal. The new model is implemented using the gamlss packages in R. We propose an extended regression based on this distribution which includes as sub-models some important regressions. We employ a frequentist and Bayesian analysis to estimate the parameters and adopt the non-parametric and parametric bootstrap methods to obtain better efficiency of the estimators. Some simulations are conducted to verify the empirical distribution of the maximum likelihood estimators. We compare the empirical distribution of the quantile residuals with the standard normal distribution. The extended regression can give more realistic fits than other regressions in the analysis of proportional data.

A proportional-hazards model for survival analysis and long-term survivors modeling: application to amyotrophic lateral sclerosis data.

The majority of survival data are affected by explanatory variables. We develop a new regression model for survival data analysis. As an alternative to standard mixture models, another model is proposed to describe the eventual presence of a surviving fraction. The proposed models are based on the Marshall-Olkin extended generalized Gompertz distribution. A maximum-likelihood inference is presented in the presence of covariates and a censorship phenomenon. Explanatory variables are incorporated into the model through proportional-hazards to evaluate the effect of risk factors on overall survival under different assumptions. Parametric, semi-parametric, and non-parametric methods are applied to survival analysis of patients treated for amyotrophic lateral sclerosis. Interesting results about riluzole use and other treatment effects on patients' survival have been obtained.

Pairwise influences in dynamic choice: network-based model and application.

In this paper, we study the problem of network discovery and influence propagation, and propose an integrated approach for the analysis of lead-lag synchronization in multiple choices. Network models for the processes by which decisions propagate through social interaction have been studied before, but only a few consider unknown structures of interacting agents. In fact, while individual choices are typically observed, inferring individual influences - who influences who - from sequences of dynamic choices requires strong modeling assumptions on the cross-section dependencies of the observed panels. We propose a class of parametric models which extends the vector autoregression to the case of pairwise influences between individual choices over multiple items and supports the analysis of influence propagation. After uncovering a collection of theoretical properties (conditional moments, parameter sensitivity, identifiability and estimation), we provide an economic application to music broadcasting, where a set of songs are diffused over radio stations; we infer station-to-station influences based on the proposed methodology and assess the propagation effect of initial launching stations to maximize songs diffusion. Both on the theoretical and empirical sides, the proposed approach connects fields which are traditionally treated as separated areas: the problem of network discovery and the one of influence propagation.

Analysis of batched service time data using Gaussian and semi-parametric kernel models.

Batched data is a type of data where each observed data value is the sum of a number of grouped (batched) latent ones obtained under different conditions. Batched data arises in various practical backgrounds and is often found in social studies and management sector. The analysis of such data is analytically challenging due to its structural complexity. In this article, we describe how to analyze batched service time data, estimate the mean and variance of each batch that are latent. We in particular focus on the situation when the observed total time includes an unknown proportion of non-service time. To address this problem, we propose a Gaussian model for efficiency as well as a semi-parametric kernel density model for robustness. We evaluate the performance of both proposed methods through simulation studies and then applied our methods to analyze a batched data.

An empirical approach to determine a threshold for assessing overdispersion in Poisson and negative binomial models for count data.

Overdispersion is a problem encountered in the analysis of count data that can lead to invalid inference if unaddressed. Decision about whether data are overdispersed is often reached by checking whether the ratio of the Pearson chi-square statistic to its degrees of freedom is greater than one; however, there is currently no fixed threshold for declaring the need for statistical intervention. We consider simulated cross-sectional and longitudinal datasets containing varying magnitudes of overdispersion caused by outliers or zero inflation, as well as real datasets, to determine an appropriate threshold value of this statistic which indicates when overdispersion should be addressed.