When noncompliance happens to longitudinal experiments, the randomness for drawing causal inferences is contaminated. In such cases, the longitudinal Complier Average Causal Effect (CACE) is often estimated. The Latent Growth Model (LGM) is very useful in estimating longitudinal trajectories and can be easily adapted for estimating longitudinal CACE.

Two popular CACE approaches, the Standard IV approach and the Mixture Model Based (MMB) approach, are both readily applicable to the LGM framework. The Standard IV approach is simple in modelling and has a low computational burden, but it is also criticized for ignoring distributions of subgroups and leading to biased estimations. The MMB approach is capable of not only estimating the CACE but also answering research questions regarding distributions of subpopulations, but this method may yield unstable results under unfavorable conditions, especially when the estimation model is complicated.

Previous studies laid out a theoretical background for applying LGMs to longitudinal CACE estimation using both approaches. However, 1) very little was known regarding the factors that might influence the longitudinal CACE estimation, 2) the three compliance classes scenario was not thoroughly investigated, and 3) it was still unclear about how and to what extent the Standard IV approach would perform better or worse than the MMB approach in the longitudinal CACE estimation.

The present study used an intensive simulation design to investigate the performance of the Standard IV and the MMB approaches while manipulating six factors that were related to most experimental designs: sample size, compliance composition, effect size, reliability of measurements, mean distances, and noncomplier-complier Level 2 covariance ratio. Their performance was evaluated on four criteria, estimation success rate, estimation bias, power, and type I error rate. With the analysis result, suggestions regarding experiment designs were provided for researchers and practitioners.