Python Code for Statistical Mirroring-based Ordinalysis

Statistical mirroring-based ordinalysis (SM-based ordinalysis) measures the proximity or deviation of an individual's composite set of ordinal assessment scores from the highest positive ordinal scale point [3]. Within the framework of Kabirian-based optinalysis [1] and statistical mirroring [2], Statistical mirroring-based ordinalysis is conceptualized as the isoreflectivity (isoreflective pairing) of the composite set of ordinal assessment scores of an individual to the highest positive ordinal scale point of an established ordinal assessment scale, under customized and optimized choice of parameters. This represents the underlying assumption of statistical mirroring-based ordinalysis. The process of Statistical mirroring-based ordinalysis comprises three distinct phases: a) Adaptive customization and optimization phase [3]: This phase represents the core of the methodology. This involves the adaptive customization and optimization of parameters to suit the requirements for statistical mirroring estimation in the given task [3]. b) Statistical mirroring computation phase [2]: This involves applying the adopted statistical mirroring type based on the phase 1 adaption. c) Optinalytic model calculation phase [1]: This phase is focused on computing estimates (such as the Kabirian coefficient of proximity, the probability of proximity, and the deviation) based on Kabirian-based isomorphic optinalysis models. References: [1] K.B. Abdullahi, Kabirian-based optinalysis: A conceptually grounded framework for symmetry/asymmetry, similarity/dissimilarity, and identity/unidentity estimations in mathematical structures and biological sequences, MethodsX 11 (2023) 102400. https://doi.org/10.1016/j.mex.2023.102400 [2] K.B. Abdullahi, Statistical mirroring: A robust method for statistical dispersion estimation, MethodsX 12 (2024) 102682. https://doi.org/10.1016/j.mex.2024.102682 [3] K.B. Abdullahi, Statistical mirroring-based ordinalysis: A sensitive, robust, efficient, and ordinality-preserving descriptive method for analyzing ordinal assessment data, MethodsX 14 (2024) 103427. https://doi.org/10.1016/j.mex.2025.103427基于统计镜像的序级分析（Statistical mirroring-based ordinalysis，简称SM-based ordinalysis）用于衡量个体的序级评估得分复合集与既定序度量表最高正向序分值之间的接近程度或偏差程度[3]。在基于卡比尔的最优分析（Kabirian-based optinalysis）[1]与统计镜像（statistical mirroring）[2]的框架下，基于统计镜像的序级分析被概念化为个体序级评估得分复合集与既定序度量表最高正向序分值之间的等反射性（即等反射配对，isoreflective pairing），且参数需经自定义与优化，这便是基于统计镜像的序级分析的核心假设。 基于统计镜像的序级分析流程包含三个独立阶段： a) 自适应定制与优化阶段[3]：此阶段为该方法的核心环节，涉及针对给定任务中统计镜像估计的需求，对参数进行自适应定制与优化[3]。 b) 统计镜像计算阶段[2]：该阶段需基于第一阶段的自适应适配结果，应用选定的统计镜像类型。 c) 最优分析模型计算阶段[1]：此阶段聚焦于基于卡比尔式同构最优分析模型，计算各类估计值（如卡比尔接近度系数、接近度概率与偏差值）。 参考文献： [1] K.B. Abdullahi，基于卡比尔的最优分析：数学结构与生物序列中对称性/非对称性、相似性/非相似性及同一性/非同一性估计的概念化框架，《方法学X》11 (2023) 102400。https://doi.org/10.1016/j.mex.2023.102400 [2] K.B. Abdullahi，统计镜像：一种稳健的统计离散度估计方法，《方法学X》12 (2024) 102682。https://doi.org/10.1016/j.mex.2024.102682 [3] K.B. Abdullahi，基于统计镜像的序级分析：一种用于序级评估数据分析的灵敏、稳健、高效且保序级的描述性方法，《方法学X》14 (2024) 103427。https://doi.org/10.1016/j.mex.2025.103427