A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of counts. The distribution of the responses is not restricted to exponential families, which is a severe restriction in generalized mixed models. Generalized mixed models use fixed distributions for responses, for example the Poisson distribution in count data, which has the disadvantage of not accounting for overdispersion. By using a response function and a thresholds function the proposed mixed thresholds model can account for a variety of alternative distributions that often show better fits than fixed distributions used within the generalized linear model framework. A particular strength of the model is that it provides a tool for joint modeling, responses may be of different types, some can be discrete, others continuous. In addition to introducing the mixed thresholds model parameter sparsity is addressed. Random effects models can contain a large number of parameters, in particular if effects have to be assumed as measurement-specific. Methods to obtain sparser representations are proposed and illustrated. The methods are shown to work in the thresholds model but could also be adapted to other modeling approaches.

翻译：提出一种通用随机效应模型，可兼容连续型与离散型响应变量。响应变量可包括无界连续、有界连续、二元、有序分类及计数形式。该模型不将响应分布限制于指数族（这是广义混合模型的主要局限）。广义混合模型采用固定分布（如计数数据中的泊松分布）处理响应，但此类分布无法解释过度离散现象。通过引入响应函数与阈值函数，所提出的混合阈值模型可容纳多种替代分布，通常比广义线性模型框架内的固定分布具有更优拟合效果。该模型的显著优势在于为联合建模提供工具支持——响应变量可包含不同类型，部分为离散型，其余为连续型。除引入混合阈值模型外，本文还关注参数稀疏性问题。随机效应模型可能包含大量参数（尤其是当效应需按测量项分别假设时）。本文提出并阐释了实现稀疏化表征的方法，并通过实例验证其有效性。这些方法在阈值模型中表现良好，且可适配其他建模策略。