| Model Comparison Statistics | 
        Empty Model | 
        Random Intercept | 
        Random Coefficient | 
       
      
        | -2 log likelihood | 
        9788.8416 | 
        9665.768 | 
        9650.66 | 
       
      
        | Deviance based on    chi-square | 
        206.57 | 
        123.0736 | 
        15.108 | 
       
      
        | Tabulated value of    chi-square | 
        5.991 | 
        41.337 | 
        10.075 | 
       
      
        | P-value | 
        0.000* | 
        0.000* | 
        0.0099* | 
       
      
        | AIC | 
        9792.842 | 
        9729.768 | 
        9724.66 | 
       
      
        | Degree of freedom | 
        2 | 
        32 | 
        37 | 
       
      |