Semiparametric Additive Beta Regression Models
Inference and Local Influence Diagnostics
DOI:
https://doi.org/10.57805/revstat.v19i2.342Keywords:
beta distribution, diagnostic techniques, maximum penalized likelihood estimates, penalized likelihood function, semiparametric additive modeAbstract
In this paper, we study a semiparametric additive beta regression model using a parameterization based on the mean and a dispersion parameter. This model is useful for situations where the response variable is continuous and restricted to the unit interval, in addition to being related to other variables through a semiparametric regression structure. First, we formulate the model and then estimation of its parameters is discussed. A back-fitting algorithm is derived to attain the maximum penalized likelihood estimates by using natural cubic smoothing splines. We provide closed-form expressions for the score function, Fisher information matrix and its inverse. Local influence methods are derived as diagnostic tools. Finally, a practical illustration based on real data is presented and discussed.
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