Table 5.

Parameter estimates for the Van der Pol oscillator model with T = 300, true initial condition = fixed, 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	3.22	0.22	0.07	0.054	0.124	−0.56	1.00
ζ1	0.50	0.45	0.05	−0.10	0.012	0.031	−0.61	1.00
ζ2	0.50	0.45	0.05	−0.10	0.012	0.030	−0.60	1.00
μx1	1.00	1.00	0.00	−0.00	0.006	0.009	−0.34	1.00
μx2	1.00	1.01	0.01	0.01	0.015	0.024	−0.39	1.00
μ1	0.00	−0.00	0.00	–	0.003	0.003	−0.06	0.08
μ2	0.00	−0.00	0.00	–	0.003	0.003	0.04	0.00
μ3	0.00	−0.00	0.00	–	0.003	0.003	0.12	0.05
λ21	0.70	0.70	0.00	−0.00	0.002	0.002	−0.08	1.00
λ31	1.20	1.20	0.00	−0.00	0.002	0.003	−0.27	1.00
${\sigma }_{e1}^2$	0.50	0.50	0.00	−0.00	0.003	0.003	0.07	1.00
${\sigma }_{e2}^2$	0.50	0.50	0.00	0.00	0.003	0.003	0.12	1.00
${\sigma }_{e3}^2$	0.50	0.50	0.00	−0.00	0.003	0.003	−0.03	1.00
${\sigma }_{b_{\zeta }}^2$	0.50	0.49	0.01	−0.02	0.049	0.096	−0.49	1.00
${\sigma }_{b_{x1}}^2$	0.00	0.01	0.01	–	0.001	0.002	−0.68	1.00
${\sigma }_{b_{x2}}^2$	0.00	0.05	0.05	–	0.103	0.011	8.62	0.00
σbx1,x2	0.00	−0.01	0.01	–	0.005	0.003	0.37	0.41

% of retained cases = 98%, correlation between true and estimated b_ζ,i = 0.88, 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.