The Effects of Weighting on the Estimator of 3-Level Growth Model in the analysis of missing longitudinal data

This study seeks to clarify the effect of weighting on the fixed effect and random effect parameter estimators of the 3-level growth model. This study considered five weighting methods; ① non-weighting, ② sampling weighting, ③ longitudinal weighting, ④ multi-level weighting, ⑤ scaled multi-level weighting. The simulation study was conducted to statistically reveal the effect of weighting methods on the parameter estimation of the multi-level growth model. For the study, population, sampling data, and missing longitudinal data were each generated. The parameters of the 3-level growth model were estimated for each of the five weighting conditions using the missing longitudinal data. All conditions were repeated 100 times. The properties of the estimator were evaluated with bias, relative bias, and RMSE(root mean square error) from the viewpoint of bias and efficiency. The result is as follows. First, all fixed and random effects parameters were estimated inconsistently when non-weights or scaled multi-level weights were used in the 3-level growth model. Second, the 3-level growth model had the highest efficiency of fixed-effect and random-effect parameter estimators when non-weights or scaled multi-level weights were used. Based on the above results, suggestions for researchers and follow-up studies were presented.