Table 3.

Results of a simulation study from 500 replications under the exponential model. The locations of subjects were sampled uniformly over the region [0, $\sqrt{n}$]², where n is the number of subjects. The true parameters were β₀ = 0, β_x = 0.5, $\theta =1{\sigma }_{\epsilon }^2=0.3,{\sigma }_{\mathrm{\sum }}^2=1.2,{\sigma }_e^2=0.5$ and α₀ = 1.4. The measurement error variance ${\sigma }_u^2=0.5$. Inside the brackets are estimated standard errors

Sample Size	Para meter	Mean of naive est	model based Var. of naive est	MSE	Mean of MLE	model based Var. of MLE	MSE
49	β0	0.223	0.145 (0.179)	0.228	−0.030	0.187 (0.239)	0.239
	βx	0.339	0.010 (0.012)	0.038	0.528	0.0270 (0.0323)	0.033
	θ	1.079	0.220 (0.268)	0.274	0.966	0.191 (0.235)	0.236
	${\sigma }_{\epsilon }^2$	0.408	0.0535 (0.0670)	0.079	0.364	0.052 (0.063)	0.067
100	β0	0.216	0.062 (0.073)	0.108	−0.021	0.071 (0.079)	0.079
	βx	0.350	0.0057 (0.0058)	0.028	0.509	0.012 (0.013)	0.013
	θ	1.037	0.114 (0.130)	0.131	0.982	0.113 (0.134)	0.134
	${\sigma }_{\epsilon }^2$	0.399	0.037 (0.042)	0.038	0.314	0.036 (0.037)	0.037
400	β0	0.168	0.009 (0.010)	0.038	−0.002	0.011 (0.011)	0.011
	βx	0.374	0.0015 (0.0015)	0.017	0.495	0.0026 (0.0026)	0.0026
	θ	1.037	0.040 (0.030)	0.031	1.010	0.037 (0.045)	0.045
	${\sigma }_{\epsilon }^2$	0.387	0.022 (0.014)	0.021	0.298	0.020 (0.024)	0.024