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Correlation structure in hierarchical linear modelling: An illustration with the therapeutic alliance

机译：分层线性建模中的相关结构：治疗联盟的插图

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Previous studies have found an association between therapeutic alliance and treatment outcome, but only recently have researchers begun to analyse time-lagged relationships between session-to-session measures of alliance and outcomes with hierarchical linear modelling (HLM). HLM assumes simple correlation structures between any two measurements from the same client. In this paper, we suggest that this assumption might be problematic. Session-to-session measurements of outcomes (Outcome Questionnaire-10.2) and alliance (Working Alliance Inventory) in a sample (N = 63) were used to perform HLM analyses to test time-lagged (lag +1) relations between outcomes and alliance in both directions. A first set of analyses replicated the models consistently used in the literature, whereas a second set of models considered a correlation structure as a function of time. A correlation independent of time distance resulted in a bidirectional influence between alliance and outcomes (the model commonly used in the literature), but when considering a correlation structure as a function of time, only the outcomes were predictive of alliance. Considering a more complex correlation structure as a function of time seems to be an important analytical strategy for addressing the issue of variability in within-client measurements over time. This study highlights how the misspecification of a statistical model, namely, not considering a time-dependent correlation structure of the response variable, may lead to misleading findings in HLM studies. This is particularly relevant in process-outcome research, such as studies analysing the impact of therapeutic alliance on clinical outcomes.
机译：以前的研究已经发现治疗联盟和治疗结果之间的关联，但最近只有研究人员开始分析与分层线性建模（HLM）的联盟和结果之间的会话与会话措施之间的时间滞后关系。 HLM假设来自同一客户端的任何两个测量值之间的简单相关结构。在本文中，我们建议这种假设可能是有问题的。样本（n = 63）中的结果（结果问卷-10.2）和联盟（工作联盟库存）的会话到会话测量用于执行HLM分析以测试结果和联盟之间的时间滞后（LAG +1）关系在两个方向。第一组分析复制了文献中一致使用的模型，而第二组模型被认为是作为时间的函数的相关结构。与时间距离无关的相关性导致联盟和结果之间的双向影响（文献中常用的模型），但是在考虑与时间函数的相关结构时，只有结果是预测联盟的预测。考虑到更复杂的相关结构作为时间的函数，似乎是解决客户内测量内的变异性问题的重要分析策略。本研究突出了统计模型的误解方式，即，不考虑响应变量的时间相关结构，可能导致HLM研究中的误导性发现。这在过程结果研究中特别相关，例如分析治疗联盟对临床结果的影响的研究。

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