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A constrained regression model for an ordinal response with ordinal predictors

机译：具有序数预测因子的序数响应的约束回归模型

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摘要

A regression model is proposed for the analysis of an ordinal response variable depending on a set of multiple covariates containing ordinal and potentially other variables. The proportional odds model (McCullagh in J R Stat Soc Ser B (Methodol) 109-142, 1980) is used for the ordinal response, and constrained maximum likelihood estimation is used to account for the ordinality of covariates. Ordinal predictors are coded by dummy variables. The parameters associated with the categories of the ordinal predictor(s) are constrained, enforcing them to be monotonic (isotonic or antitonic). A decision rule is introduced for classifying the ordinal predictors' monotonicity directions, also providing information whether observations are compatible with both or no monotonicity direction. In addition, a monotonicity test for the parameters of any ordinal predictor is proposed. The monotonicity constrained model is proposed together with five estimation methods and compared to the unconstrained one based on simulations. The model is applied to real data explaining a 10-points Likert scale quality of life self-assessment variable by ordinal and other predictors.
机译：提出了一个回归模型，用于分析顺序响应变量，具体取决于一组包含顺序变量和潜在其他变量的协变量。比例赔率模型（J R Stat Soc Ser B（Methodol）109-142，1980中的McCullagh）用于序数响应，而受约束的最大似然估计用于解释协变量的序数。序数预测变量由伪变量编码。与顺序预测变量的类别相关联的参数受到约束，从而使它们成为单调的（等渗的或反渗透的）。引入了一个决策规则，用于对有序预测变量的单调性方向进行分类，还提供了信息是否与两个单调性方向兼容或不兼容。另外，建议对任何序数预测变量的参数进行单调性测试。提出了单调约束模型和五种估计方法，并与基于仿真的无约束模型进行了比较。该模型应用于真实数据，通过序数和其他预测因子解释了利克特量表的10点生活质量自我评估变量。

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