Abstract

Categorical scale data are only ordinal and defined on a finite set. Continuous scale data are only ordinal and defined on a bounded interval. Due to that character, the statistical methods for scale data ought to be based on orders between outcomes only and not any metric involving distance measure. For simple two-sample scale data, variants of classical rank methods are suitable. For regression type of problems, there are known good generalized linear models for separate categories for a long time. In the present article is suggested a new generalized linear type of model based on non parametric statistics for the whole scale. Asymptotic normality for those statistics is also shown and illustrated. Both fixed and random effects are considered.

摘要

分类尺度数据只是有序的，并且是在有限集上定义的。连续尺度数据只是有序的并且在有界区间上定义。由于这一特点，尺度数据的统计方法应该仅基于结果之间的顺序，而不是任何涉及距离度量的度量。对于简单的双样本规模数据，经典排名方法的变体是合适的。对于回归类型的问题，很长一段时间以来，已知良好的广义线性模型用于单独的类别。在本文中，提出了一种基于全尺度非参数统计的新型广义线性模型。还显示并说明了这些统计数据的渐近正态性。固定效应和随机效应都被考虑在内。