针对有序或区间尺度数据的连续充分目标函数的表征
Characterizations of continuous adequate objective functions for ordinal or interval scaled data
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中文总结 AI 辅助
本文针对有序或区间尺度数据，研究连续充分目标函数的表征，聚焦仿射严格递增变换，通过区间尺度数据的充分不相似系数验证了所提充分性概念的合理性。
中文摘要 AI 辅助
例如在聚类分析、因子分析、（线性）结构方程模型、（线性）回归、多维标度、选择理论及效用理论中所考虑的目标函数（需被优化的优度准则）必须是充分的，即需仔细适配观测数据的结构。按本文术语，目标函数的充分性指其自变量的某些变换（如涉及量的度量单位变化）不会影响优化过程的解。本文聚焦于仿射严格递增变换，并相应纳入连续充分目标函数的情形。针对区间尺度数据的充分不相似系数的表征，证明了本文所提出的充分性概念的合理性。
英文摘要
Objective functions (goodness criteria which have to be optimized) that are considered, for instance, in cluster analysis, factor analysis, (linear) structural equation modeling, (linear) regression, multidimensional scaling, choice theory, and utility theory, must be {\em adequate}, i.e. carefully adapted to the structure of the observed data. Adequateness of an objective function means, in our terminology, that (certain) transformations of its arguments, e.g. changes in the unit measures of the quantities involved, do not influence the solutions of the optimization procedure. In this paper we concentrate our attention on affine strictly increasing transformations and we also incorporate the case of continuous adequate objective functions accordingly. The characterization of adequate dissimilarity coefficients for interval scaled data shows the appropriateness of the concept of adequateness that is developed in this paper.
