N =100   N =300
Distribution Parameter  Naive MLE  MME  Naive MLE  MME
 Normal β0 = 0.00     0.11 (0.16)  0.01 (0.09)  0.10 (0.12)  0.01 (0.06)
  βx= 2.00  -0.51 (0.51)  -0.05 (0.07)  -0.51 (0.51)  -0.02 (0.05)
  θ = 0.25  0.00 (0.18)  0.00 (0.25)  0.00 (0.11)  0.01 (0.17)
  ϕ =1  2.99 (3.00)  0.09 (0.46)  3.00 (3.01)  0.06 (0.31)
t(3) β0= 0.00      0.10 (0.15)  0.00 (0.10)  0.10 (0.12)  0.01 (0.06)
  βx= 2.00   -0.50 (0.51)  -0.04 (0.07)  -0.50 (0.51)  -0.02 (0.05)
  θ = 0.25   0.01 (0.38)  -0.02 (0.29)  -0.01 (0.20)  -0.02 (0.17)
  ϕ=1  2.98 (2.99)  0.05 (0.48)  2.99 (3.00)  0.05 (0.28)
Table 3: Biases(RMSE) for the parameter estimates in the random intercept Poisson models.