置信区间宽度等高线图在线性混合效应模型样本量规划中的应用  

Confidence interval width contours:Sample size planning for linear mixed-effects models

作　　者：刘玥[1] 徐雷 刘红云 韩雨婷 游晓锋 万志林 LIU Yue;XU Lei;LIU Hongyun;HAN Yuting;YOU Xiaofeng;WAN Zhilin(Institute of Brain and Psychological Sciences,Sichuan Normal University,Chengdu 610066,China;Beijing Key Laboratory of Applied Experimental Psychology,Beijing Normal University,Beijing 100875,China;Faculty of Psychology,Beijing Normal University,Beijing 100875,China;School of Psychology,Beijing Language and Culture University,Beijing,100083,China;School of Mathematics and Information Science,Nanchang Normal University,Nanchang 360111,China)

机构地区：[1]四川师范大学脑与心理科学研究院,成都610066 [2]应用实验心理北京市重点实验室 [3]北京师范大学心理学部,北京100875 [4]北京语言大学心理学院,北京100083 [5]南昌师范学院数学与信息科学学院,南昌360111

出　　处：《心理学报》2024年第1期124-138,I0001-I0042,共57页Acta Psychologica Sinica

基　　金：国家自然科学基金项目(32071091,32200920);四川省自然科学基金青年项目(2022NSFSC1788,2022NSFSC1631,2022NSFSC1691)。

摘　　要：线性混合效应模型在分析具有嵌套结构的心理学实验数据时具有明显优势。本文提出了置信区间宽度等高线图用于该模型的样本量规划。通过等高线图,确定同时符合检验力、效应量准确性以及置信区间宽度要求的被试量和试次数。结合关注被试内实验效应和被试变量调节效应的两类典型模型,通过两个模拟研究,采用基于蒙特卡洛模拟方法,探索效应量、随机效应大小和被试变量类型对置信区间宽度等高线图及样本量规划结果的影响。Hierarchical data,which is observed frequently in psychological experiments,is usually analyzed with the linear mixed-effects models(LMEMs),as it can account for multiple sources of random effects due to participants,items,and/or predictors simultaneously.However,it is still unclear of how to determine the sample size and number of trials in LMEMs.In history,sample size planning was conducted based purely on power analysis.Later,the influential article of Maxwell et al.(2008)has made clear that sample size planning should consider statistical power and accuracy in parameter estimation(AIPE)simultaneously.In this paper,we derive a confidence interval width contours plot with the codes to generate it,providing power and AIPE information simultaneously.With this plot,sample size requirements in LMEMs based on power and AIPE criteria can be decided.We also demonstrated how to run sensitivity analysis to assess the impact of the magnitude of experiment effect size and the magnitude of random slope variance on statistical power,AIPE and the results of sample size planning.There were two sets of sensitivity analysis based on different LMEMs.Sensitivity analysisⅠinvestigated how the experiment effect size influenced power,AIPE and the requirement of sample size for within-subject experiment design,while sensitivity analysisⅡinvestigated the impact of random slope variance on optimal sample size based on power and AIPE analysis for the cross-level interaction effect.The results for binary and continuous between-subject variables were compared.In these sensitivity analysis,two factors regarding sample size varied:number of subjects(I=10,30,50,70,100,200,400,600,800),number of trials(J=10,20,30,50,70,100,150,200,250,300).The additional manipulated factor was the effect size of experiment effect (standard coefficient of experiment condition = 0.2, 0.5, 0.8, in sensitivity analysis I) and the magnitude ofrandom slope variance (0.01, 0.09 and 0.25, in sensitivity analysis Ⅱ). A random slope model was used insensitivity a

关 键 词：线性混合效应模型 多水平模型 检验力分析 效应量 置信区间宽度 

分 类 号：B841[哲学宗教—基础心理学]