Mediation analysis of intensive longitudinal data

doi:10.3724/SP.J.1042.2025.0717

Abstract

Abstract:

With the widespread use of intensive longitudinal data in the social sciences, how to analysis intensive longitudinal mediation (ILM) effect has attracted the attention of many researchers. A conventional approach is using multilevel models or multilevel structural equation models. In that case, the temporal sequence of variables is ignored, with the dynamic relationship between variables remaining unexplored.

In this paper, taking 1-1-1 [i.e., 1 (independent at Level 1) - 1 (mediator at Level 1) - 1 (dependent at Level 1)] ILM model as an example, we summarize five types of ILM analysis approaches: 1) multilevel autoregressive model (MAM); 2) residual multilevel autoregressive model (RMAM); 3) dynamic structural equation model (DSEM); 4) residual dynamic structural equation model (RDSEM). 5) cross-classified dynamic structural equation model (cross-classified DSEM). In both RMAM and RDSEM, we first statistically remove the trend from the variables with a regression of each variable on time, and then construct the ILM model using the residuals from the previous step.

There are two methods developed for analyzing the ILM effect. One of them is based on manifest variables. The multilevel model and the temporal sequence of variables are combined to develop MAM, which is extended to RMAM when detrending is required. The other method is based on latent variables. The multilevel structural equation model and the temporal sequence of variables are combined to develop DSEM, which is extended to RDSEM when detrending is required.

In the present study, we propose a procedure to conduct ILM analysis. The first step is to decide whether one would like to get ILM effects with time changes. If yes, cross-classified DSEM should be adopted to analyze ILM effects with time changes. It is a suitable detrending approach to include time as a time-varying covariate in the cross-classified DSEM. Otherwise, one will proceed with the second step, which is to decide whether it is necessary to detrend. If detrending is necessary, RDSEM should be adopted to analyze ILM effects with individual changes. Otherwise, DSEM should be adopted to analyze ILM effects with individual changes. The third step is to check whether RDSEM or DSEM converges. If either of them converges, their result should be reported. Otherwise, MAM or RMAM should be adopted to analyze ILM effects with individual changes. This paper exemplifies how to conduct the proposed procedure and provides corresponding Mplus and R codes.

Directions for future research on mediation analysis of intensive longitudinal data are discussed at the end of the paper. According to the level of the variable, there are seven ILM models: 1-1-1, 2-1-1, 2-2-1, 2-1-2, 1-2-2, 1-2-1 and 1-1-2. However, only the first four mediation models are discussed in the existing literature, and it is found that as long as there is a level-2 variable in the ILM model, the mediation effect can only occur at level-2. The analytical methods of the last three models, 1-2-2, 1-2-1 and 1-1-2 ILM, can be inferred from those of the first four.

Key words: intensive longitudinal data, mediation, multilevel autoregressive model, dynamic structural equation model, detrending

CLC Number:

B841

FANG Jie, WEN Zhonglin, DONG Yuming, WANG Xiaojie. Mediation analysis of intensive longitudinal data[J]. Advances in Psychological Science, 2025, 33(4): 717-728.

Figures/Tables 8

被试(j)	时间(t)	X	M	Y
1	1	0.33	0.43	−1.72
1	2	−0.48	−0.68	−1.61
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
1	20	0.14	0.26	1.05
2	1	0.31	0.68	0.15
2	2	0.46	0.03	−0.94
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
2	20	−0.86	0.51	−0.56

被试(j)	时间(t)	X	M	Y
1	1	0.33	0.43	−1.72
1	2	−0.48	−0.68	−1.61
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
1	20	0.14	0.26	1.05
2	1	0.31	0.68	0.15
2	2	0.46	0.03	−0.94
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
2	20	−0.86	0.51	−0.56

参数估计	DSEM		MAM		交叉分类DSEM
参数估计	估计值	95% CI	估计值	95% CI	估计值	95% CI
a	0.618	[0.525, 0.713]	0.621	[0.540, 0.703]	0.576	[0.551, 0.598]
b	0.725	[0.594, 0.851]	0.762	[0.638, 0.879]	0.734	[0.684, 0.780]
c′	0.044	[0.005, 0.085]	0.037	[−0.017, 0.092]	0.010	[−0.019, 0.039]
${{\sigma }_{{{a}_{j}}{{b}_{j}}}}$	0.158	[0.093, 0.253]	0.110	[0.061, 0.171]
${{\sigma }_{{{a}_{t}}{{b}_{t}}}}$					0.001	[−0.002, 0.004]
β_X	0.301	[0.265, 0.338]	0.277	[0.227, 0.336]	0.302	[0.269, 0.335]
β_M	0.293	[0.263, 0.323]	0.285	[0.245, 0.324]	0.335	[0.305, 0.363]
β_Y	0.280	[0.247, 0.314]	0.256	[0.214, 0.298]	0.324	[0.292, 0.355]
l_X	−0.074	[−0.220, 0.071]	0.000	[−0.027, 0.027]	−0.076	[−0.206, 0.050]
l_M	0.075	[−0.061, 0.210]	0.000	[−0.021, 0.022]	0.073	[−0.046, 0.195]
l_Y	1.926	[1.776, 2.075]	0.000	[−0.028, 0.027]	1.925	[1.794, 2.055]
ω_X	−1.922	[−2.167, −1.680]			−1.922	[−2.136, −1.712]
ω_M	−4.172	[−4.483, −3.861]			−3.259	[−3.531, −2.994]
ω_Y	−1.875	[−2.104, −1.650]			−1.667	[−1.853, −1.481]
var(μ₁_j)	0.519	[0.381, 0.732]	0.014	[0.010, 0.019]	0.402	[0.304, 0.544]
var(μ₂_j)	0.458	[0.334, 0.649]	0.011	[0.008, 0.015]	0.354	[0.268, 0.479]
var(μ₃_j)	0.526	[0.378, 0.756]	0.014	[0.011, 0.019]	0.409	[0.307, 0.561]
var(μ₄_j)	0.015	[0.007, 0.029]	0.032	[0.022, 0.046]	0.007	[0.001, 0.016]
var(μ₅_j)	0.016	[0.011, 0.025]	0.027	[0.020, 0.038]	0.012	[0.008, 0.020]
var(μ₆_j)	0.016	[0.009, 0.027]	0.028	[0.020, 0.040]	0.012	[0.007, 0.019]
var(μ₇_j)	0.213	[0.155, 0.300]	0.167	[0.124, 0.222]
var(μ₈_j)	0.331	[0.227, 0.501]	0.286	[0.197, 0.407]
var(μ₉_j)	0.009	[0.003, 0.019]	0.038	[0.025, 0.056]
var(μ₇_t)					0.002	[0.001, 0.006]
var(μ₈_t)					0.008	[0.003, 0.018]
var(μ₉_t)					0.003	[0.001, 0.008]
var(μ₁₀_j)	1.455	[1.058, 2.060]			1.098	[0.825, 1.500]
var(μ₁₁_j)	2.377	[1.740, 3.354]			1.811	[1.367, 2.457]
var(μ₁₂_j)	1.233	[0.897, 1.743]			0.838	[0.628, 1.142]

参数估计	DSEM		MAM		交叉分类DSEM
参数估计	估计值	95% CI	估计值	95% CI	估计值	95% CI
a	0.618	[0.525, 0.713]	0.621	[0.540, 0.703]	0.576	[0.551, 0.598]
b	0.725	[0.594, 0.851]	0.762	[0.638, 0.879]	0.734	[0.684, 0.780]
c′	0.044	[0.005, 0.085]	0.037	[−0.017, 0.092]	0.010	[−0.019, 0.039]
${{\sigma }_{{{a}_{j}}{{b}_{j}}}}$	0.158	[0.093, 0.253]	0.110	[0.061, 0.171]
${{\sigma }_{{{a}_{t}}{{b}_{t}}}}$					0.001	[−0.002, 0.004]
β_X	0.301	[0.265, 0.338]	0.277	[0.227, 0.336]	0.302	[0.269, 0.335]
β_M	0.293	[0.263, 0.323]	0.285	[0.245, 0.324]	0.335	[0.305, 0.363]
β_Y	0.280	[0.247, 0.314]	0.256	[0.214, 0.298]	0.324	[0.292, 0.355]
l_X	−0.074	[−0.220, 0.071]	0.000	[−0.027, 0.027]	−0.076	[−0.206, 0.050]
l_M	0.075	[−0.061, 0.210]	0.000	[−0.021, 0.022]	0.073	[−0.046, 0.195]
l_Y	1.926	[1.776, 2.075]	0.000	[−0.028, 0.027]	1.925	[1.794, 2.055]
ω_X	−1.922	[−2.167, −1.680]			−1.922	[−2.136, −1.712]
ω_M	−4.172	[−4.483, −3.861]			−3.259	[−3.531, −2.994]
ω_Y	−1.875	[−2.104, −1.650]			−1.667	[−1.853, −1.481]
var(μ₁_j)	0.519	[0.381, 0.732]	0.014	[0.010, 0.019]	0.402	[0.304, 0.544]
var(μ₂_j)	0.458	[0.334, 0.649]	0.011	[0.008, 0.015]	0.354	[0.268, 0.479]
var(μ₃_j)	0.526	[0.378, 0.756]	0.014	[0.011, 0.019]	0.409	[0.307, 0.561]
var(μ₄_j)	0.015	[0.007, 0.029]	0.032	[0.022, 0.046]	0.007	[0.001, 0.016]
var(μ₅_j)	0.016	[0.011, 0.025]	0.027	[0.020, 0.038]	0.012	[0.008, 0.020]
var(μ₆_j)	0.016	[0.009, 0.027]	0.028	[0.020, 0.040]	0.012	[0.007, 0.019]
var(μ₇_j)	0.213	[0.155, 0.300]	0.167	[0.124, 0.222]
var(μ₈_j)	0.331	[0.227, 0.501]	0.286	[0.197, 0.407]
var(μ₉_j)	0.009	[0.003, 0.019]	0.038	[0.025, 0.056]
var(μ₇_t)					0.002	[0.001, 0.006]
var(μ₈_t)					0.008	[0.003, 0.018]
var(μ₉_t)					0.003	[0.001, 0.008]
var(μ₁₀_j)	1.455	[1.058, 2.060]			1.098	[0.825, 1.500]
var(μ₁₁_j)	2.377	[1.740, 3.354]			1.811	[1.367, 2.457]
var(μ₁₂_j)	1.233	[0.897, 1.743]			0.838	[0.628, 1.142]

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