University of Nevada, Reno, NV, USA.
Indiana University, Bloomington, IN, USA.
Behav Res Methods. 2020 Feb;52(1):131-150. doi: 10.3758/s13428-019-01210-8.
Single-case experimental design (SCED) research plays an important role in establishing and confirming evidence-based practices. Due to multiple measures of a target behavior in such studies, missing information is common in their data. The expectation-maximization (EM) algorithm has been successfully applied to deal with missing data in between-subjects designs, but only in a handful of SCED studies. The present study extends the findings from Smith, Borckardt, and Nash (2012) and Velicer and Colby (2005b, Study 2) by systematically examining the performance of EM in a baseline-intervention (or AB) design under various missing rates, autocorrelations, intervention phase lengths, and magnitudes of effects, as well as two fitted models. Three indicators of an intervention effect (baseline slope, level shift, and slope change) were estimated. The estimates' relative bias, root-mean squared error, and relative bias of the estimated standard error were used to assess EM's performance. The findings revealed that autocorrelation impacted the estimates' qualities most profoundly. Autocorrelation interacted with missing rate in impacting the relative bias of the estimates, impacted the root-mean squared error nonlinearly, and interacted with the fitted model in impacting the relative bias of the estimated standard errors. A simpler model without autocorrelation can be used to estimate baseline slope and slope change in time-series data. EM is recommended as a principled method to handle missing data in SCED studies. Two decision trees are presented to assist researchers and practitioners in applying EM. Emerging research directions are identified for treating missing data in SCED studies.
单病例实验设计（SCED）研究在建立和确认循证实践方面发挥着重要作用。由于此类研究中目标行为有多个测量值，因此数据中通常会存在缺失信息。期望最大化（EM）算法已成功应用于处理组间设计中的缺失数据，但仅在少数 SCED 研究中有所应用。本研究通过系统地检查 EM 在各种缺失率、自相关、干预阶段长度和效应幅度下的表现，以及两种拟合模型，扩展了 Smith、Borckardt 和 Nash（2012）以及 Velicer 和 Colby（2005b，研究 2）的发现。估计了干预效果的三个指标（基线斜率、水平偏移和斜率变化）。使用干预效果估计的相对偏差、均方根误差和估计标准误差的相对偏差来评估 EM 的性能。研究结果表明，自相关对估计质量的影响最为深远。自相关与缺失率相互作用，影响估计的相对偏差，对均方根误差产生非线性影响，并与拟合模型相互作用，影响估计标准误差的相对偏差。没有自相关的简单模型可以用于估计时间序列数据中的基线斜率和斜率变化。建议将 EM 作为处理 SCED 研究中缺失数据的一种原则性方法。提出了两个决策树来帮助研究人员和实践者应用 EM。确定了处理 SCED 研究中缺失数据的新兴研究方向。
