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