Question (Hierarchical Linear Model) In this question, we use simulations to decide whether we should include partial information from the observed dependent variable as covariates. (1). We start from a hierarchical linear model without random effects 112, N(0, o where i 0,1,... n, j 1,2 N. Note here the index i starts from 0. The level-2 explanatory variable 2 is the observation of Yu when i 0. Say, Additionally, we have We want to compare the following five models. Model 1: N(0, o where i 0.1 n, j 1,2 ,N. Model 2: N(0, Where i 1,... n, 1,2 Model 3 Question (Hierarchical Linear Model) In this question, we use simulations to decide whether we should include partial information from the observed dependent variable as covariates. (1). We start from a hierarchical linear model without random effects 112, N(0, o where i 0,1,... n, j 1,2 N. Note here the index i starts from 0. The level-2 explanatory variable 2 is the observation of Yu when i 0. Say, Additionally, we have We want to compare the following five models. Model 1: N(0, o where i 0.1 n, j 1,2 ,N. Model 2: N(0, Where i 1,... n, 1,2 Model 3