密集追踪数据的有调节的中介效应分析

doi:10.3724/SP.J.1041.2025.0915

摘要/Abstract

摘要：

密集追踪数据在心理学、管理学等领域的应用日益增多, 但密集追踪数据的分析方法研究却比较欠缺。如果将密集追踪数据的有调节的中介效应当成有调节的多水平中介效应进行分析, 则忽略了变量之间的历时性关系。本文使用动态结构方程模型建构了被层2变量调节的1-1-1、2-1-1、2-2-1密集追踪中介模型和被层1变量调节的1-1-1密集追踪中介模型。用模拟研究考察了被层2变量调节的1-1-1密集追踪中介模型的参数估计的准确性。接着用示例演示如何进行有调节的密集追踪中介效应分析, 并给出相应的Mplus程序。最后, 讨论了基于动态结构方程模型的有调节的密集追踪中介模型的前提假设以及模型的拓展。

关键词: 密集追踪数据, 有调节的中介效应, 动态结构方程模型

Abstract:

Intensive longitudinal data (ILD) is increasing in fields such as psychology and management, yet research on analytical methods for ILD remains relatively scant. Traditionally, the ILD is statistically modeled as a two-level structure, with Level 1 being the time and Level 2 being individuals. Especially, existing analytical methods treat longitudinal moderated mediation as multilevel moderated mediation, without considering the lagged relationship between variables. A possible solution is to use dynamic structural equation modeling (DSEM) for ILD moderated mediation analysis.
DSEM has recently been used for analyzing intensive longitudinal mediation (ILMed; Fang et al., 2024; McNeish & MacKinnon, 2022) and intensive longitudinal moderation (ILMod; Speyer et al., 2024). However, it remains unclear how DSEM can be employed in analyzing intensive longitudinal moderated mediation (ILMM). The purpose of this paper is to combine ILMed and ILMod based on DSEM and propose a method of moderated mediation analysis that takes into account the temporal order between variables.
For the 1-1-1 ILMed model where all variables are measured at Level 1 (i.e., all variables are ILD), it might be moderated by variables of Level 1 or Level 2. However, for the 2-1-1 ILMed model (i.e., only the independent variable is measured at Level 2) and the 2-2-1 ILMed model (i.e., only the dependent variable is measured at Level 1), they could only be moderated by variables of Level 2. Therefore, there are four basic types of ILMM models: 2-1-1 ILMed moderated by a level 2 moderator, 2-2-1 ILMed moderated by a level 2 moderator, 1-1-1 ILMed moderated by a level 2 moderator, and 1-1-1 ILMed moderated by a level 1 moderator.
This paper describes in detail how to construct the above four ILMM models with DSEM, so that empirical researchers can understand which kind of ILMM model meets their needs and how to analyze it. Mplus codes for analyzing all these ILMM models are provided.
A simulation study is conducted to examine the estimation accuracy of the 1-1-1 ILMed moderated by a level 2 moderator, with the following factors taken into account: sample size (N), number of time points (T), indirect effect sizes, and Level-2 variances and covariances. Results show that the estimates for the average mediation effect components (a and b) and the average mediation effect are generally accurate when N ≥ 100 and T ≥ 10. However, a sufficiently large N and T (e.g., T ≥ 20) are required in order to obtain accurate estimation of Level-2 variances.
Lastly, we discuss assumptions and the extensions of ILMM based on DSEM. As usual, the models used in this paper are based on the assumption that the time series is stationary. Otherwise, residual DSEM can be employed to detrend in ILMM analysis.

Key words: intensive longitudinal data, moderated mediation effect, dynamic structural equation model

中图分类号:

B841

方杰, 温忠麟, 王惠惠, 顾红磊. (2025). 密集追踪数据的有调节的中介效应分析. 心理学报, 57(5), 915-928.

FANG Jie, WEN Zhonglin, WANG Huihui, GU Honglei. (2025). Moderated mediation analyses of intensive longitudinal data. Acta Psychologica Sinica, 57(5), 915-928.

图/表 10

图1 前后路径和直接路径被调节的中介模型概念图

图2 基于动态结构方程模型的被层2变量调节的1-1-1密集追踪中介模型图

(改编自Fang et al., 2024)

表1 被层2变量调节的1-1-1密集追踪中介效应分析的数据示例(t=20)

个体(j)	时间(t)	Z	X	M	Y
1	1	1.21	0.39	1.99	0.85
1	2	1.21	−0.43	1.97	1.69
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
1	20	1.21	−0.89	2.10	−1.68
2	1	2.10	−0.78	0.59	0.83
2	2	2.10	−1.12	2.22	1.67
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
2	20	2.10	−1.13	2.45	−0.84

表1 被层2变量调节的1-1-1密集追踪中介效应分析的数据示例(t=20)

个体(j)	时间(t)	Z	X	M	Y
1	1	1.21	0.39	1.99	0.85
1	2	1.21	−0.43	1.97	1.69
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
1	20	1.21	−0.89	2.10	−1.68
2	1	2.10	−0.78	0.59	0.83
2	2	2.10	−1.12	2.22	1.67
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
2	20	2.10	−1.13	2.45	−0.84

图3 基于动态结构方程模型的被层2变量调节的2-1-1密集追踪中介模型图

图4 基于动态结构方程模型的有调节的2-2-1密集追踪中介模型图

表2 系数、方差和协方差估计的相对偏差(%)和均方误差(×100)

参数	N×T	100×10		100×20		100×50		200×10		200×20		200×50
参数	真值	RB	MSE	RB	MSE	RB	MSE	RB	MSE	RB	MSE	RB	MSE
a	0.2	1.2	0.3	0.5	0.2	2.7	0.2	0.9	0.2	0.4	0.1	1.7	0.1
b	0.2	2.9	0.3	0.6	0.2	1.5	0.2	2.4	0.2	−0.3	0.1	0.4	0.1
g	0.2	−0.1	0.3	−0.5	0.2	−0.7	0.2	0.9	0.1	−0.4	0.1	−0.3	0.1
k	0.2	0.3	0.3	−1.7	0.2	0.4	0.2	1.4	0.2	−1.2	0.1	−0.3	0.1
E(a_jb_j)	0.273	4.1	0.4	3.1	0.3	4.3	0.3	3.5	0.2	1.7	0.2	2.2	0.1
diff	0.16	0.9	0.2	−1.5	0.1	0.7	0.1	2.3	0.1	−1.1	0.1	0.2	0.1
$σ a j 2$	0.16	11.1	0.2	7.6	0.1	5.0	0.1	4.4	0.1	3.3	0.1	2.5	0.0
$σ b j 2$	0.16	16.5	0.3	9.4	0.1	8.5	0.1	10.9	0.1	4.8	0.1	4.6	0.0
$σ a j b j$	0.113	5.0	0.1	6.4	0.1	5.8	0.1	3.3	0.1	3.8	0.0	3.2	0.0
a	0.0	0.3	0.3	0.3	0.2	0.5	0.2	0.2	0.2	0.1	0.1	0.4	0.1
b	0.0	−0.1	0.3	0.3	0.2	−0.3	0.2	0.1	0.2	−0.1	0.1	−0.4	0.1
g	0.0	0.1	0.3	−0.1	0.2	−0.1	0.2	0.3	0.1	0.0	0.1	0.1	0.1
k	0.0	−0.6	0.3	−0.6	0.2	0.1	0.2	−0.6	0.2	−0.6	0.1	−0.1	0.1
E(a_jb_j)	0.0	−0.1	0.1	0.0	0.1	0.1	0.1	−0.1	0.1	0.0	0.0	0.0	0.0
$σ a j 2$	0.16	10.9	0.2	7.9	0.1	4.0	0.1	5.4	0.1	3.9	0.1	2.5	0.0
$σ b j 2$	0.16	15.6	0.3	7.9	0.1	8.2	0.1	9.7	0.1	2.6	0.1	4.4	0.0
$σ a j b j$	0.0	−0.1	0.1	0.0	0.1	0.1	0.0	−0.1	0.1	0.0	0.0	0.0	0.0

表2 系数、方差和协方差估计的相对偏差(%)和均方误差(×100)

参数	N×T	100×10		100×20		100×50		200×10		200×20		200×50
参数	真值	RB	MSE	RB	MSE	RB	MSE	RB	MSE	RB	MSE	RB	MSE
a	0.2	1.2	0.3	0.5	0.2	2.7	0.2	0.9	0.2	0.4	0.1	1.7	0.1
b	0.2	2.9	0.3	0.6	0.2	1.5	0.2	2.4	0.2	−0.3	0.1	0.4	0.1
g	0.2	−0.1	0.3	−0.5	0.2	−0.7	0.2	0.9	0.1	−0.4	0.1	−0.3	0.1
k	0.2	0.3	0.3	−1.7	0.2	0.4	0.2	1.4	0.2	−1.2	0.1	−0.3	0.1
E(a_jb_j)	0.273	4.1	0.4	3.1	0.3	4.3	0.3	3.5	0.2	1.7	0.2	2.2	0.1
diff	0.16	0.9	0.2	−1.5	0.1	0.7	0.1	2.3	0.1	−1.1	0.1	0.2	0.1
$σ a j 2$	0.16	11.1	0.2	7.6	0.1	5.0	0.1	4.4	0.1	3.3	0.1	2.5	0.0
$σ b j 2$	0.16	16.5	0.3	9.4	0.1	8.5	0.1	10.9	0.1	4.8	0.1	4.6	0.0
$σ a j b j$	0.113	5.0	0.1	6.4	0.1	5.8	0.1	3.3	0.1	3.8	0.0	3.2	0.0
a	0.0	0.3	0.3	0.3	0.2	0.5	0.2	0.2	0.2	0.1	0.1	0.4	0.1
b	0.0	−0.1	0.3	0.3	0.2	−0.3	0.2	0.1	0.2	−0.1	0.1	−0.4	0.1
g	0.0	0.1	0.3	−0.1	0.2	−0.1	0.2	0.3	0.1	0.0	0.1	0.1	0.1
k	0.0	−0.6	0.3	−0.6	0.2	0.1	0.2	−0.6	0.2	−0.6	0.1	−0.1	0.1
E(a_jb_j)	0.0	−0.1	0.1	0.0	0.1	0.1	0.1	−0.1	0.1	0.0	0.0	0.0	0.0
$σ a j 2$	0.16	10.9	0.2	7.9	0.1	4.0	0.1	5.4	0.1	3.9	0.1	2.5	0.0
$σ b j 2$	0.16	15.6	0.3	7.9	0.1	8.2	0.1	9.7	0.1	2.6	0.1	4.4	0.0
$σ a j b j$	0.0	−0.1	0.1	0.0	0.1	0.1	0.0	−0.1	0.1	0.0	0.0	0.0	0.0

表3 系数估计的可信区间覆盖率、检验力和第一类错误率

系数	N×T	100×10		100×20		100×50		200×10		200×20		200×50
系数	真值	Cov	Pow	Cov	Pow	Cov	Pow	Cov	Pow	Cov	Pow	Cov	Pow
a	0.2	0.945	0.925	0.96	0.99	0.965	0.995	0.945	1	0.94	1	0.95	1
b	0.2	0.975	0.950	0.95	0.99	0.955	1	0.94	1	0.945	1	0.95	1
g	0.2	0.950	0.945	0.945	0.975	0.97	1	0.965	1	0.96	1	0.965	1
k	0.2	0.96	0.94	0.93	0.96	0.965	0.995	0.955	1	0.94	1	0.95	1
E(a_jb_j)	0.273	0.955	1	0.955	1	0.97	1	0.96	1	0.93	1	0.95	1
diff	0.16	0.935	0.945	0.945	0.985	0.97	1	0.975	1	0.935	1	0.955	1
系数	N×T	100×10		100×20		100×50		200×10		200×20		200×50
系数	真值	Cov	Error	Cov	Error	Cov	Error	Cov	Error	Cov	Error	Cov	Error
a	0.0	0.949	0.051	0.95	0.05	0.965	0.035	0.939	0.061	0.935	0.065	0.965	0.045
b	0.0	0.96	0.04	0.94	0.06	0.975	0.025	0.949	0.051	0.96	0.04	0.955	0.035
g	0.0	0.949	0.051	0.945	0.055	0.97	0.03	0.965	0.035	0.95	0.05	0.955	0.045
k	0.0	0.934	0.066	0.955	0.045	0.96	0.04	0.955	0.045	0.965	0.035	0.945	0.055
E(a_jb_j)	0.0	0.97	0.03	0.95	0.05	0.965	0.035	0.944	0.056	0.945	0.055	0.945	0.055

表4 前后路径被调节的1-1-1密集追踪中介效应分析结果

参数	点估计	区间估计
a	0.590	[0.532, 0.652]
b	0.598	[0.531, 0.660]
g	0.410	[0.346, 0.475]
k	0.371	[0.300, 0.439]
$σ a j, b j$	0.117	[0.085, 0.151]
IND1	1.024	[0.879, 1.186]
IND2	0.172	[0.126, 0.225]
IND1−IND2	0.852	[0.700, 1.010]
c′	0.218	[0.172, 0.266]
d	0.161	[−0.192, 0.529]
f	−0.186	[−1.152, 0.739]
l_X	0.267	[0.013, 0.515]
l_M	8.995	[8.660, 9.324]
l_Y	35.151	[34.281, 36.027]
β_X	0.291	[0.269, 0.314]
β_M	0.300	[0.283, 0.317]
β_Y	0.303	[0.284, 0.312]

表4 前后路径被调节的1-1-1密集追踪中介效应分析结果

参数	点估计	区间估计
a	0.590	[0.532, 0.652]
b	0.598	[0.531, 0.660]
g	0.410	[0.346, 0.475]
k	0.371	[0.300, 0.439]
$σ a j, b j$	0.117	[0.085, 0.151]
IND1	1.024	[0.879, 1.186]
IND2	0.172	[0.126, 0.225]
IND1−IND2	0.852	[0.700, 1.010]
c′	0.218	[0.172, 0.266]
d	0.161	[−0.192, 0.529]
f	−0.186	[−1.152, 0.739]
l_X	0.267	[0.013, 0.515]
l_M	8.995	[8.660, 9.324]
l_Y	35.151	[34.281, 36.027]
β_X	0.291	[0.269, 0.314]
β_M	0.300	[0.283, 0.317]
β_Y	0.303	[0.284, 0.312]

图5 基于动态结构方程模型的条件中介效应

表5 被调节的密集追踪中介模型汇总表

调节变量	中介模型	被调节的中介路径
调节变量	中介模型	前、后路径和直接路径	前半路径和直接路径	后半路径和直接路径
Z_j	1-1-1	方程(1)-(7)	去掉方程(5)的kZ_j	去掉方程(4)的dZ_j和方程(5)的gZ_j
	2-1-1	方程(13)-(19)	去掉方程(16)的kl_MjZ_j	去掉方程(15)的dZ_j和gX_jZ_j
	2-2-1	方程(20)-(24)	去掉方程(21)的kM_jZ_j	去掉方程(24)的dZ_j和gX_jZ_j
Z_tj	1-1-1	方程(25)-(26)、(29)-(34)和(44)-(46)	去掉方程(45)的 $k j i n t m z t − 1 j c$	去掉方程(34)的 $d j Z t − 1 j c$ 和 $d j Z t − 1 j c$

表5 被调节的密集追踪中介模型汇总表

调节变量	中介模型	被调节的中介路径
调节变量	中介模型	前、后路径和直接路径	前半路径和直接路径	后半路径和直接路径
Z_j	1-1-1	方程(1)-(7)	去掉方程(5)的kZ_j	去掉方程(4)的dZ_j和方程(5)的gZ_j
	2-1-1	方程(13)-(19)	去掉方程(16)的kl_MjZ_j	去掉方程(15)的dZ_j和gX_jZ_j
	2-2-1	方程(20)-(24)	去掉方程(21)的kM_jZ_j	去掉方程(24)的dZ_j和gX_jZ_j
Z_tj	1-1-1	方程(25)-(26)、(29)-(34)和(44)-(46)	去掉方程(45)的 $k j i n t m z t − 1 j c$	去掉方程(34)的 $d j Z t − 1 j c$ 和 $d j Z t − 1 j c$

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