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Designing A Three Level Multilevel Model

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Model
This section is divided into several parts. The parameter estimates are shown in Table XX along with relevant model statistics. As the study makes use of a three-level multilevel model, a two-level null model with individuals nested within region-years is presented first to determine whether a three-level model is a better choice. Next, the simple model with only the parameters of interest added will be interpreted. A full model including all relevant variables, including a decomposition of the main variable of interest (‘important to understand different people’), concludes the model selection process.
Two-level null model
The simple two-level null model with individuals nested within regions is defined as follows (using notation in accordance with Rabe-Hesketh and Skrondal (2004)): trstep_ij=η_0j+ϵ_ij where η_0j=γ_00+ζ_0j
Here, ϵ_ij are the level-1 residual terms, γ_00 is the mean intercept and ζ_0j is the deviation of the school-specific intercept from the mean. As with most multilevel models, it is assumed that the clusters j are independent. Furthermore the level-1 residuals are assumed to be normally distributed with mean 0 and variance Var(e_ij) , while the level-2 residual are assumed to be normally distributed with mean 0 and variance Var(ζ_0j). (ADD THE THIRD ASSUMPTION?).
The two-level model estimates the mean trust in the EP to be 4.46. An likelihood ratio test between the two-level null model and a single-level null models (LR test statistic = 4065 with

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