Beta regression for time series analysis of bounded data, with application to Canada Google® Flu Trends

Guolo, Annamaria; Varin, Cristiano

doi:10.1214/13-aoas684

Cited by 63 publications

(56 citation statements)

References 25 publications

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“…Our method is obviously not restricted to AR models and can be directly extended to several other settings. For example, we could envision an extension to ARMA time series models for the errors (see Guolo and Varin 2014).…”

Section: Resultsmentioning

confidence: 99%

Partially linear beta regression model with autoregressive errors

Ferreira

Figueroa-Zúñiga

Castro

2015

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This paper is focused on developing a methodology to deal with time series data on the unit interval modeled by a partially linear model with correlated disturbances from a Bayesian perspective. In this context, the linear predictor of the beta regression model incorporates an unknown smooth function with time as an auxiliary covariate and a set of regressors. In addition, an autoregressive dependence structure is proposed for the errors of the model. This formulation can capture the dynamic evolution of curves using both non-stochastic explanatory variables and non-parametric components, allowing an accurate fit with a limited number of parameters. Diagnostic measures are derived from the case-deletion approach and an influence measure based on the Kullback-Leibler divergence is studied and thus, a new method to determine the optimal order of the autoregressive processes through an adaptive procedure using the conditional predictive ordinate statistic is presented. A simulation study is conducted to assess some properties of the Bayesian estimator. Finally, the proposed methodology is illustrated in two real-life applications.

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Section: Resultsmentioning

confidence: 99%

Partially linear beta regression model with autoregressive errors

Ferreira

Figueroa-Zúñiga

Castro

2015

TEST

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“…An attractive feature of the Gaussian copula approach is that various forms of dependence can be expressed through suitable parametrization of the correlation matrix P. For example, longitudinal data can be modelled with the working correlation matrices considered in generalized estimating equations (Song 2007, § 6), serial dependence in time series with a correlation matrix corresponding to an autoregressive and moving average process (Guolo and Varin 2014), spatial dependence with a correlation matrix induced by a Gaussian random field (Bai et al 2014).…”

Section: Gaussian Copula Regressionmentioning

confidence: 99%

Gaussian Copula Regression in R

Masarotto¹,

Varin²

2017

J. Stat. Soft.

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This article describes the R package gcmr for fitting Gaussian copula marginal regression models. The Gaussian copula provides a mathematically convenient framework to handle various forms of dependence in regression models arising, for example, in time series, longitudinal studies or spatial data. The package gcmr implements maximum likelihood inference for Gaussian copula marginal regression. The likelihood function is approximated with a sequential importance sampling algorithm in the discrete case. The package is designed to allow a flexible specification of the regression model and the dependence structure. Illustrations include negative binomial modeling of longitudinal count data, beta regression for time series of rates and logistic regression for spatially correlated binomial data.

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“…However, to better estimate topical trends, the continuous distribution has to approximate the real topical trends. Indeed, recently, the Beta distribution has drawn a lot of attentions for accommodating a variety of shapes given an x-axis interval [14]. Therefore, we choose to use a Beta distribution since it can more accurately fit the various shapes of topical trends.…”

Section: Integrating the Time Dimension In The Vb Approachmentioning

confidence: 99%

“…We propose a time-sensitive VB (TVB) approach for social media data that embraces the time dimension of social media data. We extend the traditional VB approach by incorporating a Beta distribution, which is reported to fit various patterns [14]. The employed Beta continuous distribution is used to represent each topic's volume over time, i.e.…”

Section: Introductionmentioning

confidence: 99%

Exploring Time-Sensitive Variational Bayesian Inference LDA for Social Media Data

Fang

Macdonald

Ounis

et al. 2017

Lecture Notes in Computer Science

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Abstract. There is considerable interest among both researchers and the mass public in understanding the topics of discussion on social media as they occur over time. Scholars have thoroughly analysed samplingbased topic modelling approaches for various text corpora including social media; however, another LDA topic modelling implementationVariational Bayesian (VB)-has not been well studied, despite its known efficiency and its adaptability to the volume and dynamics of social media data. In this paper, we examine the performance of the VB-based topic modelling approach for producing coherent topics, and further, we extend the VB approach by proposing a novel time-sensitive Variational Bayesian implementation, denoted as TVB. Our newly proposed TVB approach incorporates time so as to increase the quality of the generated topics. Using a Twitter dataset covering 8 events, our empirical results show that the coherence of the topics in our TVB model is improved by the integration of time. In particular, through a user study, we find that our TVB approach generates less mixed topics than state-of-the-art topic modelling approaches. Moreover, our proposed TVB approach can more accurately estimate topical trends, making it particularly suitable to assist end-users in tracking emerging topics on social media.

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Beta regression for time series analysis of bounded data, with application to Canada Google® Flu Trends

Cited by 63 publications

References 25 publications

Partially linear beta regression model with autoregressive errors

Partially linear beta regression model with autoregressive errors

Gaussian Copula Regression in R

Exploring Time-Sensitive Variational Bayesian Inference LDA for Social Media Data

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