协变量相关对时变效应模型参数估计的影响

时变效应模型被广泛应用于密集追踪研究中，研究者往往会同时纳入2个或以上协变量。然而，协变量相关对其参数估计的影响较少被研究者关注。本研究在不同类型协变量的情境下，采用蒙特卡洛模拟，探讨协变量相关对时变效应模型参数估计的影响，结果表明：（1）在两种协变量类型的情境下，协变量相关都会影响时变效应模型斜率函数β_1和斜率函数β_2参数估计的准确性；（2）两种协变量类型的情境下，协变量相关和样本量的交互作用都会影响时变效应模型斜率函数β_1和斜率函数β_2参数估计的准确性；（3）两种协变量类型的情境下，样本量、观测数据缺失率主要通过主效应影响时变效应模型参数估计的准确性。

The Effect of Covariates Correlation on The Parameter Estimation in Time-Varying Effects Model

Longitudinal study has its unique and irreplaceable advantages in causal inference, which has received more and more attention and has been frequently used in the fields of developmental, educational and clinical psychology. Recently, the intensive longitudinal study has been favored by researchers, which is based on longer observation time, more measurement times and more accurate depiction of development trends.The Time-varying Effects Model has been widely used in the intensive longitudinal study, and researchers usually include two or more moderators both in simulation and empirical studies. It is common to recognize correlation in psychology field, while previous studies didn’t explore whether covariate correlation will influence the model estimation result. The effect of covariate correlation on the performance of the Time-varying Effects Model remains unknown.In view of the above situations, this study intends to use Monte Carlo simulation to explore whether the covariate correlation will affect the accuracy of parameter estimation in the Time-varying Effects Model with two moderators. Different situations were set by varying the covariant type (time-varying, time-invariant), the sample size and the miss rate of data. The main results of the study are as follows:(1) For both time-varying and time-invariant covariates, the degree of correlation of the covariates affects the accuracy of estimating the slope β_1 and slope β_2. Under each condition, as the correlation of covariate increases, the mean absolute deviation error of the slope β_1 and slope β_2 increases, but the intercept is not affected by the degree of covariate correlation;(2) For both time-varying and time-invariant covariates, the sample size and the miss rate under the most conditions affect the accuracy of the parameter estimation of the Time-varying Effects Model. The mean absolute deviation error of the interception, slope β_1 and slope β_2 decrease as the sample size increases, and increase as the miss rate increases;(3) For both time-varying and time-invariant covariates, the interaction between covariate correlation and the sample size affects the accuracy of the parameter estimation of the slope β_1 and slope β_2. At each sample level, the mean absolute deviation error of slope β_1 and slope β_2 increase with increasing covariate correlation, while the errors are still within acceptable limits under most conditions. While when the sample size is 50 and covariate correlation reaches 0.8, the result is beyond acceptance.