Distributional structured additive regression provides a flexible framework for modelling each parameter of a potentially complex response distribution in dependence of covariates. Structured additive predictors allow for an additive decomposition of covariate effects with non-linear effects and time trends, unit- or cluster-specific heterogeneity, spatial heterogeneity and complex interactions between covariates of different type. Within this framework, we present a simultaneous estimation approach for multiplicative random effects that allow for cluster-specific heterogeneity with respect to the scaling of a covariate′s effect. More specifically, a possibly non-linear function f(z) of a covariate z may be scaled by a multiplicative and possibly spatially correlated cluster-specific random effect (1+αc). Inference is fully Bayesian and is based on highly efficient Markov Chain Monte Carlo (MCMC) algorithms. We investigate the statistical properties of our approach within extensive simulation experiments for different response distributions. Furthermore, we apply the methodology to German real estate data where we identify significant district-specific scaling factors. According to the deviance information criterion, the models incorporating these factors perform significantly better than standard models without (spatially correlated) random scaling factors.

中文翻译：

---

贝叶斯分布回归模型中的随机缩放因子在房地产数据中的应用

分布结构加法回归提供了一个灵活的框架，用于对依赖于协变量的潜在复杂响应分布的每个参数进行建模。结构化加性预测器允许对具有非线性效应和时间趋势、单位或集群特定异质性、空间异质性和不同类型协变量之间复杂相互作用的协变量效应进行加法分解。在此框架内，我们提出了一种乘法随机效应的同时估计方法，该方法允许在协变量效应的缩放方面具有特定于集群的异质性。更具体地说，协变量 z 的可能非线性函数 f(z) 可以通过乘法和可能空间相关的集群特定随机效应 (1+αc) 进行缩放。推理是完全贝叶斯的，并且基于高效的马尔可夫链蒙特卡罗 (MCMC) 算法。我们在针对不同响应分布的广泛模拟实验中研究了我们方法的统计特性。此外，我们将该方法应用于德国房地产数据，我们确定了重要的地区特定比例因子。根据偏差信息标准，包含这些因素的模型的性能明显优于没有（空间相关）随机缩放因子的标准模型。我们将该方法应用于德国房地产数据，并在其中确定重要的地区特定比例因子。根据偏差信息标准，包含这些因素的模型的性能明显优于没有（空间相关）随机缩放因子的标准模型。我们将该方法应用于德国房地产数据，并在其中确定重要的地区特定比例因子。根据偏差信息标准，包含这些因素的模型的性能明显优于没有（空间相关）随机缩放因子的标准模型。