Partially linear beta regression model with autoregressive errors

In this paper we introduce the class of beta seasonal autoregressive moving average (β SARMA) models for modeling and forecasting time series data that assume values in the standard unit interval. It generalizes the class of beta autoregressive moving average models [Rocha and Cribari-Neto, Test, 2009] by incorporating seasonal dynamics to the model dynamic structure. Besides introducing the new class of models, we develop parameter estimation, hypothesis testing inference, and diagnostic analysis tools. We also discuss out-of-sample forecasting. In particular, we provide closed-form expressions for the conditional score vector and for the conditional Fisher information matrix.We also evaluate the finite sample performances of conditional maximum likelihood estimators and white noise tests using Monte Carlo simulations. An empirical application is presented and discussed.Univariate time series modeling is commonly used in many fields. Most conventional time series models are based on the Gaussianity assumption [1]. A well-known class of this linear models is the class of autoregressive integrated moving average models (ARIMA) [2]. However, it has been recognized that the Gaussian assumption is too restrictive for many applications [3]. As a consequence, there has been increased interest in non-Gaussian time series models [4]. Some models for discrete variate time series are considered in [5,6,7]. In [8] is proposed a quasi-likelihood approach to regression models for discrete and continuous time series. In [9] is focused on time series modeling under non-Gaussian innovations. Non-Gaussian time series models are considered as instantaneous transformations of Gaussian time series in [10,1]. Time series models based on generalized linear models (GLM) [11] are considered in [12,13,14,15]. Other important and recent works on non-Gaussian time series modeling are [16,17,3,18,19,20,4]. A comprehensive reference on general models for time series analysis is [21]. * F. M. Bayer is with the

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“…An approach that has been used to model this type of data is based on the beta distribution." Recent related works include [32,29,33,34].…”

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confidence: 99%

Beta seasonal autoregressive moving average models

Bayer

Cintra

Cribari‐Neto

2018

Journal of Statistical Computation and Simulation

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“…Huang & Oosterlee (2011) discussed frequentist random effects models and Smithson (2012) andFigueroa-Zúñiga, Arellano-Valle &Ferrari (2013) discussed mixed-effects Bayesian beta regression models. Time-series beta regression models have been discussed by Guolo & Varin (2014) and Ferreira, Figueroa-Zúñiga & de Castro (2015). Beta regression models for spatial data have been considered by Cepeda-Cuervo & Núñez-Antón (2013), Mandal, Srivastav & Simonovic (2016), Lagos-Álvarez et al (2017) and da-Silva & de Oliveira Lima (2017.…”

Section: Literature Reviewmentioning

confidence: 99%

Regression modelling with the tilted beta distribution: A Bayesian approach

Hahn

2020

Can J Statistics

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Beta regression models are commonly used in the case of a dependent variable y that exists on the range (0,1). However, when y can additionally take on the values of zero and/or one, limitations of the beta distribution and beta regression models become apparent. One recent approach is to use an inflated beta regression model which has discrete point-valued components. In this article, we introduce a new class of regression models for y ∈ [0, 1] that is fully continuous. This allows the entirety of y to be treated as a continuum instead of discontinuously, which appears to be a new development for the literature. We use a Bayesian approach for estimation. We also illustrate the impact of different choices of prior distributions on empirical findings and perform a simulation study examining model fit.

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“…And then in the M-step, (11) and (12) functions are maximized using Newton-Raphson method. M-step of the EM algorithm, estimation of variance components, the scale parameter of NB part, and their corresponding standard errors are given in the Appendix.…”

Section: Parameter Estimation Using Expectation Maximization Algorithmmentioning

confidence: 99%

“…Zimprich [10] and Figueroa et al [11] extended Beta regression to longitudinal data analysis through adding a random effect in the mean and precision parameters respectively. Another extension of the Beta regression was used by [12] to analyze time series rate data with correlated errors using Bayesian approach. Other extensions of the Beta regression includes spatial data analysis [13] and spatial analysis of structured additive regression model [14].…”

Section: Introductionmentioning

confidence: 99%

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

Tapak

Hamidi

Sadeghifar

et al. 2019

Preprint

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Objectives Zero-inflated proportion or rate data nested in clusters due to the sampling structure can be found in many disciplines. Sometimes, the rate response may not be observed for some study units because of some limitations (false negative) like failure in recording data and the zeros are observed instead of the actual value of the rate/proportions (low incidence). In this study, we proposed a multilevel zero-inflated censored Beta regression model that can address zero-inflation rate data with low incidence.Methods We assumed that the random effects are independent and normally distributed. The performance of the proposed approach was evaluated by application on a three level real data set and a simulation study. We applied the proposed model to analyze brucellosis diagnosis rate data and investigate the effects of climatic and geographical position. For comparison, we also applied the standard zero-inflated censored Beta regression model that does not account for correlation.Results Results showed the proposed model performed better than zero-inflated censored Beta based on AIC criterion. Height (p-value <0.0001), temperature (p-value <0.0001) and precipitation (p-value = 0.0006) significantly affected brucellosis rates. While, precipitation in ZICBETA model was not statistically significant (p-value =0.385). Simulation study also showed that the estimations obtained by maximum likelihood approach had reasonable in terms of mean square error.Conclusions The results showed that the proposed method can capture the correlations in the real data set and yields accurate parameter estimates.

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Partially linear beta regression model with autoregressive errors

Cited by 7 publications

References 33 publications

Beta seasonal autoregressive moving average models

Beta seasonal autoregressive moving average models

Regression modelling with the tilted beta distribution: A Bayesian approach

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

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