Tesio Luigi
Department of Rehabilitation, Salvatore Maugeri Foundation, IRCCS, Pavia, Italy.
J Rehabil Med. 2003 May;35(3):105-15. doi: 10.1080/16501970310010448.
Variables present in an individual, for example, independence, pain, balance, fatigue, depression and knowledge, cannot be measured directly (hence the term "latent" variables). They are usually assessed by measuring related behaviours, defined by sets of standardized items. The homogeneity of the different items, and proportionality of raw counts to measure, can only be postulated. In 1960 Georg Rasch proposed a statistical model that complied with the fundamental assumptions made in measurements in physical sciences. It allowed for the transformation of the cumulative raw scores (achieved by a subject across items, or by an item across subjects) into linear continuous measures of ability (for subjects) and difficulty (for items). These 2 parameters, only, govern the probability that "pass" rather than "fail" occurs. The discrepancies between model-expected scores (continuous between 0 and 1) and observed scores (discrete, either 0 or 1) provide indexes of inconsistency of individual subjects, items and classes of subjects. In subsequent years the same principles were extended to rating scales, with items graded on more than 2 levels, and to "many-facet" contexts where, beyond items and subjects, multiple raters, times of administration, etc. converge in determining the observed scores. Rasch modelling has increasing application in rehabilitation medicine. New scales with unprecedented metric validity (including internal consistency and reliability) can be built. Existing scales can be improved or rejected on a sound theoretical basis. In clinical trials the consistency and the linearity of measures of either subjects or raters can be validly matched with those of physical and chemical measures. The stability of the item difficulties across time, cultures, diagnostic groups and time of administration can be estimated, thus making it possible to compare homogeneous measures or foster diagnostic procedures on the reasons for differential item functioning.
个体中存在的变量，例如独立性、疼痛、平衡、疲劳、抑郁和知识，无法直接测量（因此称为“潜在”变量）。它们通常通过测量相关行为来评估，这些行为由一组标准化项目定义。不同项目的同质性以及原始计数与测量的比例关系只能假定。1960年，格奥尔格·拉施提出了一种统计模型，该模型符合物理科学测量中的基本假设。它允许将累积原始分数（由受试者在各个项目上获得，或由项目在各个受试者上获得）转换为能力（针对受试者）和难度（针对项目）的线性连续测量。仅这两个参数决定了“通过”而非“失败”发生的概率。模型预期分数（在0到1之间连续）与观察分数（离散，要么为0要么为1）之间的差异提供了个体受试者、项目和受试者类别不一致的指标。在随后的几年中，相同的原则被扩展到评分量表，项目被分为两级以上，并且扩展到“多方面”情境，在这种情境中，除了项目和受试者之外，多个评分者、施测时间等共同决定观察分数。拉施模型在康复医学中的应用越来越广泛。可以构建具有前所未有的度量效度（包括内部一致性和可靠性）的新量表。现有量表可以在合理的理论基础上得到改进或被摒弃。在临床试验中，受试者或评分者测量的一致性和线性可以有效地与物理和化学测量的一致性和线性相匹配。可以估计项目难度在不同时间、文化、诊断组和施测时间的稳定性，从而能够比较同质测量或促进基于项目功能差异原因的诊断程序。
