N =100  N =300   Parameter  Naive MLE  MME  Naive MLE  MME β0 = 1.00 1.37 (1.39)  -0.22 (0.27)  1.38 (1.38)  -0.20 (0.23) βx = 1.00 -0.79 (0.79)  -0.05 (0.08)  -0.79 (0.79)  -0.07 (0.08) βz = -0.50 0.38 (0.47)  0.06 (0.17)  0.36 (0.40)  0.05 (0.16) βxz =0.25  -0.20 (0.22)  -0.01 (0.10)  -0.19 (0.20)  -0.02 (0.08) θ= 1.00  -0.03 (0.21)  -0.04 (0.19)  0.03 (0.28)  -0.05 (0.15)

Table 1: Biases(RMSE) for the parameter estimates in the random intercept Poisson models.