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Tweedie regression models and its geometric sums for (semi‐)continuous data

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Abstract Tweedie regression models (TRMs) are flexible tools to deal with non‐negative right‐skewed data and can handle semi‐continuous data, that is, continuous data with probability mass at zero. The geometric sums of Tweedie random variables lead to the geometric Tweedie distributions. Their corresponding regression models (GTRMs) provide not only additional flexibility to deal with continuous, semi‐continuous, heavily right‐skewed data but also a possibility of under‐variation than TRMs. Estimation and inference based on the likelihood approach for TRMs and GTRMs are challenging owing to the presence of an infinity sum and an intractable integral in the probability function along with non‐trivial restrictions on the Tweedie power parameter space. Thus, methods based on quasi‐likelihood have been proposed and successfully applied for estimation and inference in these classes of regression models. In this paper, our central focus is upon characterizing as well as comparing TRMs and GTRMs taking into consideration their variation and zero‐mass indices. Besides, we attempt to illustrate their application through some data analyses. Furthermore, we discuss the challenges for the computational implementation of such probability distributions and corresponding regression models referring to some available implementations in R. This article is categorized under: Statistical Models > Fitting Models Statistical Models > Generalized Linear Models Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms
Plot of the density functions of Twp(m, ϕ) with p = 2, m = 1 and different values of ϕ corresponding to 0 < ϕ < 1 and ϕ ≥ 1
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Histogram (a) and dispersion diagram with fitted values by MLE (b) and QMLE (c)
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Time series plot for Curitiba rainfall data with fitted values and confidence intervals by fitted models
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Probability density functions of the geometric Tweedie distribution by parameter configurations. Symbols in the left show the density at zero
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Probability density functions of the Tweedie distribution by parameter configurations. Symbols in the left demonstrate the density at zero
[ Normal View | Magnified View ]

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Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms
Statistical Models > Generalized Linear Models
Statistical Models > Fitting Models

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