Generalized additive models for location, scale and shape
Generalized additive models for location, scale and shape
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DOI：
10.1111/j.1467-9876.2005.00510.x
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发表时间：
2005-01-01
影响因子：
1.6
通讯作者：
Stasinopoulos, DM
中科院分区：
文献类型：
--
作者：
Rigby, RA;Stasinopoulos, DM
本文提出了一类单变量响应变量的统计模型，我们称之为位置、尺度和形状的广义加性模型（GAMLSS）。该模型假设响应变量y的独立观测值，给定参数、解释变量和随机效应值。响应变量的分布可以从非常一般的分布族中选择，包括高度偏斜或峰度连续和离散分布。该模型的系统部分被扩展，不仅允许建模的平均值（或位置），但也y的分布的其他参数，作为参数和/或添加剂的非参数（平滑）函数的解释变量和/或随机效应项。最大（惩罚）似然估计用于拟合（非）参数模型。使用Newton-Raphson或Fisher评分算法来最大化（惩罚）可能性。模型中的加性项采用后拟合算法进行拟合。删失数据很容易纳入框架。五个数据集从不同的应用领域进行了分析，强调的通用性的GAMLSS类模型。
A general class of statistical models for a univariate response variable is presented which we call the generalized additive model for location, scale and shape (GAMLSS). The model assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects. The distribution for the response variable in the GAMLSS can be selected from a very general family of distributions including highly skew or kurtotic continuous and discrete distributions. The systematic part of the model is expanded to allow modelling not only of the mean (or location) but also of the other parameters of the distribution of y, as parametric and/or additive nonparametric (smooth) functions of explanatory variables and/or random-effects terms. Maximum (penalized) likelihood estimation is used to fit the (non)parametric models. A Newton-Raphson or Fisher scoring algorithm is used to maximize the (penalized) likelihood. The additive terms in the model are fitted by using a backfitting algorithm. Censored data are easily incorporated into the framework. Five data sets from different fields of application are analysed to emphasize the generality of the GAMLSS class of models.