A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented.Comment: 21 pages, 3 figures, 5 tables. Computational Statistics and Data Analysis, 17 October 2011, ISSN 0167-9473 (http://www.sciencedirect.com/science/article/pii/S0167947311003628

Kumaraswamy autoregressive moving average models for double bounded environmental data

In this paper we introduce the Kumaraswamy autoregressive moving average models (KARMA), which is a dynamic class of models for time series taking values in the double bounded interval $(a,b)$ following the Kumaraswamy distribution. The Kumaraswamy family of distribution is widely applied in many areas, especially hydrology and related fields. Classical examples are time series representing rates and proportions observed over time. In the proposed KARMA model, the median is modeled by a dynamic structure containing autoregressive and moving average terms, time-varying regressors, unknown parameters and a link function. We introduce the new class of models and discuss conditional maximum likelihood estimation, hypothesis testing inference, diagnostic analysis and forecasting. In particular, we provide closed-form expressions for the conditional score vector and conditional Fisher information matrix. An application to environmental real data is presented and discussed.Comment: 25 pages, 4 tables, 4 figure

Robust semi-parametric inference for two-stage production models: A beta regression approach

The data envelopment analysis is related to a non-parametric mathematical tool used to assess the relative efficiency of productive units. In different studies on productive efficiency, it is common to employ semi-parametric procedures in two stages to determine whether any exogenous factors of interest affect the performance of productive units. However, some of these procedures, particularly those based on conventional statistical inference, generate inconsistent estimates when dealing with incoherent data-generating processes. This inconsistency arises due to the efficiency scores being limited to the unit interval, and the estimated scores often exhibit serial correlation and have limited observations. To address such inconsistency, several strategies have been suggested, with the most well-known being an algorithm based on a parametric bootstrap procedure using the truncated normal distribution and its regression model. In this work, we present a modification of this algorithm that utilizes the beta distribution and its regression structure. The beta model allows for better accommodation of asymmetry in the data distribution. Our proposed algorithm introduces inferential characteristics that are superior to the original algorithm, resulting in a more statistically coherent data-generating process and improving the consistency property. We have conducted computational experiments that demonstrate the improved results achieved by our proposal.ANCD -Agenția Națională pentru Cercetare și Dezvoltare(1200525

Does linear equating improve prediction in mapping? Crosswalking MacNew onto EQ‑5D‑5L value sets

Purpose: Preference-based measures are essential for producing quality-adjusted life years (QALYs) that are widely used for economic evaluations. In the absence of such measures, mapping algorithms can be applied to estimate utilities from disease-specific measures. This paper aims to develop mapping algorithms between the MacNew Heart Disease Quality of Life Questionnaire (MacNew) instrument and the English and the US-based EQ-5D-5L value sets. Methods: Individuals with heart disease were recruited from six countries: Australia, Canada, Germany, Norway, UK and the US in 2011/12. Both parametric and non-parametric statistical techniques were applied to estimate mapping algorithms that predict utilities for MacNew scores from EQ-5D-5L value sets. The optimal algorithm for each country-specific value set was primarily selected based on root mean square error (RMSE), mean absolute error (MAE), concordance correlation coefficient (CCC), and r-squared. Leave-one-out cross-validation was conducted to test the generalizability of each model. Results: For both the English and the US value sets, the one-inflated beta regression model consistently performed best in terms of all criteria. Similar results were observed for the cross-validation results. The preferred model explained 59 and 60% for the English and the US value set, respectively. Linear equating provided predicted values that were equivalent to observed values. Conclusions: The preferred mapping function enables to predict utilities for MacNew data from the EQ-5D-5L value sets recently developed in England and the US with better accuracy. This allows studies, which have included the MacNew to be used in cost-utility analyses and thus, the comparison of services with interventions across the health system.publishedVersio

The zero-inflated promotion cure rate model applied to financial data on time-to-default

In this paper, we extend the promotion cure rate model studied in Yakovlev and Tsodikov (1996) and Chen et al. (1999) by incorporating an excess of zeros in the modeling. Despite relating covariates to the cure fraction, the current approach does not enable us to relate covariates to the fraction of zeros. The presence of excess of zeros in credit risk survival data stems from a group of loans that became defaulted shortly after the granting process. Through our proposal, all survival data available of customers is modeled with a multinomial logistic link for the three classes of banking customers: (i) individual with an event at the starting time (zero time), (ii) non-susceptible for the event, or (iii) susceptible for the event. The model parameter estimation is reached by the maximum likelihood estimation procedure and Monte Carlo simulations are carried out to assess its finite sample performance

Cabinet formation and portfolio distribution in European multiparty systems

Government formation in multiparty systems is of self-evident substantive importance, and the subject of an enormous theoretical literature. Empirical evaluations of models of government formation tend to separate government formation per se from the distribution of key government pay-offs, such as cabinet portfolios, between members of the resulting government. Models of government formation are necessarily specified ex ante, absent any knowledge of the government that forms. Models of the distribution of cabinet portfolios are typically, though not necessarily, specified ex post, taking into account knowledge of the identity of some government ‘formateur’ or even of the composition of the eventual cabinet. This disjunction lies at the heart of a notorious contradiction between predictions of the distribution of cabinet portfolios made by canonical models of legislative bargaining and the robust empirical regularity of proportional portfolio allocations – Gamson’s Law. This article resolves this contradiction by specifying and estimating a joint model of cabinet formation and portfolio distribution that, for example, predicts ex ante which parties will receive zero portfolios rather than taking this as given ex post. It concludes that canonical models of legislative bargaining do increase the ability to predict government membership, but that portfolio distribution between government members conforms robustly to a proportionality norm because portfolio distribution follows the much more difficult process of policy bargaining in the typical government formation process