Table 6.

Parameter estimates for the Van der Pol oscillator model with T = 150, true initial condition = random, fitted initial condition = random.

	True θ	Mean θ̂	RMSE	rBias	$a\widehat{\mathrm{S}\mathrm{E}}$	MC SD	RDSE	Power/type I error
ζ0	3.00	2.92	0.08	−0.03	0.047	0.216	−0.78	1.00
ζ1	0.50	0.46	0.04	−0.08	0.012	0.066	−0.81	1.00
ζ2	0.50	0.46	0.04	−0.08	0.012	0.063	−0.80	1.00
μx1	0.00	0.00	0.00	–	0.001	0.069	−0.99	0.99
μx2	0.00	0.00	0.00	–	0.006	0.087	−0.93	0.95
μ1	0.00	0.00	0.00	–	0.004	0.005	−0.11	0.10
μ2	0.00	−0.00	0.00	–	0.004	0.004	−0.07	0.05
μ3	0.00	0.00	0.00	–	0.004	0.005	−0.13	0.11
λ21	0.70	0.70	0.00	−0.00	0.003	0.004	−0.22	1.00
λ31	1.20	1.20	0.00	−0.00	0.003	0.006	−0.45	1.00
${\sigma }_{e1}^2$	0.50	0.50	0.00	0.00	0.004	0.008	−0.51	1.00
${\sigma }_{e2}^2$	0.50	0.50	0.00	0.00	0.004	0.005	−0.25	1.00
${\sigma }_{e3}^2$	0.50	0.50	0.00	0.00	0.004	0.011	−0.63	1.00
${\sigma }_{b_{\zeta }}^2$	0.50	0.57	0.07	0.13	0.053	0.186	−0.71	1.00
${\sigma }_{b_{x1}}^2$	1.00	1.10	0.10	0.10	0.110	0.116	−0.05	1.00
${\sigma }_{b_{x2}}^2$	1.00	1.23	0.23	0.23	0.131	0.184	−0.29	1.00
σbx1,x2	0.30	0.16	0.14	−0.45	0.123	0.112	0.09	0.29

% of retained cases =93%, correlation between true and estimated b_ζ,i = 0.65, true θ = true value of a parameter, mean $\mathrm{\theta ̂}=\frac{1}{H}{\sum }_{h=1}^H{\mathrm{\theta ̂}}_h$, where θ̂_h = estimate of θ from the hth Monte Carlo replication, $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{H}{\sum }_{h=1}^H{({\mathrm{\theta ̂}}_h-\text{true}\theta )}^2}$, rBias relative bias = $\frac{1}{H}{\sum }_h^H({\mathrm{\theta ̂}}_h-\text{true}\theta )/\text{true}\theta$, SE standard deviation of θ̂ across Monte Carlo runs, $a\widehat{\mathrm{S}\mathrm{E}}$ = average standard error estimate across Monte Carlo runs, RDSE average relative deviance of $\widehat{\mathrm{S}\mathrm{E}}=(a\widehat{\mathrm{S}\mathrm{E}}-\mathrm{S}\mathrm{E})/\mathrm{S}\mathrm{E}$, power/type I error = 1 − the proportion of 95% confidence intervals (CIs) that contain 0 across the Monte Carlo replications.