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Discrete Weibull generalized additive model: an application to count fertility data

机译：离散Weibull广义加性模型：用于计算生育力数据的应用

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摘要

Fertility plans, measured by the number of planned children, have been found to be affected by education and family background via complex tail dependences. This challenge was previously met with the use of non-parametric jittering approaches. The paper shows how a novel generalized additive model based on a discrete Weibull distribution provides partial effects of the covariates on fertility plans which are comparable with jittering, without the inherent drawback of conditional quantiles crossing. The model has some additional desirable features: both overdispersed and underdispersed data can be modelled by this distribution, the conditional quantiles have a simple analytic form and the likelihood is the same as that of a continuous Weibull distribution with interval-censored data. Because the likelihood is like that of a continuous Weibull distribution, efficient implementations are already available, in the R package gamlss, for a range of models and inferential procedures, and at a fraction of the time compared with the jittering and Conway-Maxwell-Poisson approaches, showing potential for the wide applicability of this approach to the modelling of count data.
机译：已经发现，以计划生育的孩子数量来衡量的生育计划，受复杂的尾巴依赖关系受教育程度和家庭背景的影响。以前通过使用非参数抖动方法可以解决该挑战。本文显示了基于离散威布尔分布的新型广义加性模型如何在不考虑条件分位数交叉的固有缺点的情况下，将协变量对生育力计划的部分影响与抖动相提并论。该模型还具有其他一些理想的功能：通过这种分布可以对过度分散和欠分散的数据进行建模，条件分位数具有简单的分析形式，并且其可能性与具有区间删失数据的连续Weibull分布的可能性相同。由于可能性类似于连续的威布尔分布，因此在R包游戏中，对于一系列模型和推论过程，已经存在有效的实现方式，与抖动和Conway-Maxwell-Poisson相比，花费的时间很少这些方法表明了这种方法在计数数据建模中的广泛应用的潜力。

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