Multilevel models allow researchers to test hypotheses at multiple levels of analysis-for example, assessing the effects of both individual-level and school-level predictors on a target outcome. To assess these effects with the greatest clarity, researchers are well-advised to cluster mean center all Level 1 predictors and explicitly incorporate the cluster means into the model at Level 2. When an outcome of interest is continuous, this unconflated model specification serves both to increase model accuracy, by separating the level-specific effects of each predictor, and to increase model interpretability, by reframing the random intercepts as unadjusted cluster means. When an outcome of interest is binary or ordinal, however, only the first of these benefits is fully realized: In these models, the intuitive cluster mean interpretations of Level 2 effects are only available on the metric of the linear predictor (e.g., the logit) or, equivalently, the latent response propensity, yij∗. Because the calculations for obtaining predicted probabilities, odds, and ORs operate on the entire combined model equation, the interpretations of these quantities are inextricably tied to individual-level, rather than cluster-level, outcomes. This is unfortunate, given that the probability and odds metrics are often of greatest interest to researchers in practice. To address this issue, I propose a novel rescaling method designed to calculate cluster average success proportions, odds, and ORs in two-level binary and ordinal logistic and probit models. I apply the approach to a real data example and provide supplemental R functions to help users implement the method easily. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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个体级概率和集群级比例：在二元结果的非合并多级模型中实现可解释的二级估计。


多层次模型允许研究人员在多个分析层次上检验假设，例如，评估个人层面和学校层面的预测因素对目标结果的影响。为了最清晰地评估这些影响，建议研究人员对所有 1 级预测变量进行聚类均值中心，并明确地将聚类均值合并到 2 级模型中。当感兴趣的结果是连续的时，这种未合并的模型规范既可以用于通过分离每个预测变量的特定水平效应来提高模型的准确性，并通过将随机截距重新构建为未调整的聚类均值来提高模型的可解释性。然而，当感兴趣的结果是二元或序数时，只有第一个好处得到充分实现：在这些模型中，2 级效应的直观聚类均值解释仅适用于线性预测变量的度量（例如，logit ) 或等价的潜在反应倾向 yij*。由于获得预测概率、赔率和 OR 的计算是在整个组合模型方程上进行的，因此这些量的解释与个体级别（而不是集群级别）的结果密不可分。这是不幸的，因为实践中研究人员通常最感兴趣的是概率和优势指标。为了解决这个问题，我提出了一种新颖的重新调整方法，旨在计算两级二元和序数逻辑和概率模型中的集群平均成功比例、几率和 OR。我将该方法应用于真实的数据示例，并提供补充 R 函数来帮助用户轻松实现该方法。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。