Hi Chetan,
We’ve had some discussion on your project here, and I wanted to follow up and give you the attached project. Dan parameterized the model in terms of clearance for both the Phoenix Model and WNL Classic, and got a nice match in the parameter values, and also pointed out that WNL Classic is more stable with the clearance parameterization.
Bob also reminded me that REML adjusts for degrees of freedom so the standard errors and CV% do not match between the REML (WNL Classic) and ML (Phoenix Model), unless you figure out what ratio you need to multiply by to adjust for this difference in methods: From Bob:
There are 9 observations and 5 fitted parameters (other than sigma). So there are 9-5=4 dof. If you adjust for dof (which REML does), you will get an estimate of the std deviation of EPS which is sqrt(9/4) = 3/2 = 150% of the maximum likelihood estimate of the std deviation of EPS. Indeed, if you look at the parameters as listed in the Core Output file for the Phoenix Model for the Ke parameterization, it gives both the ML estimate (EPS_STD_DEV=0.143), and the REML estimate (EPS_STD_DEV_WNL = 0.215 ) (i.e., this shows this 1.5 ratio). Note that the Cl parameterization gives identical estimates for V and EPS and std error of V as the Ke parameterization.
0.32890933E+01 1 1 THETA BOUNDS: -0.100+101 0.100+101
0.79139570E-02 2 1 THETA BOUNDS: -0.100+101 0.100+101
0.32045903E+01 3 1 THETA BOUNDS: -0.100+101 0.100+101
0.82420337E-01 4 1 THETA BOUNDS: -0.100+101 0.100+101
0.81057477E-01 5 1 THETA BOUNDS: -0.100+101 0.100+101
0.14374254E+00 1 1 EPS_STD_DEV BOUNDS: 0.000E+00 0.100+101
0.20661917E-01 1 1 EPS_VARIANCE
0.67361710E+02 1 1 -LOGLIKE
0.11818253E+03 1 1 ELSOBJ
0.21561380E+00 1 1 EPS_STD_DEV_WNL
0.46489312E-01 1 1 EPS_VARIANCE_WNL
For the Ke parameterized model, the CV of V is 14.1%, while for the Cl parameterization it is also 14.1% (using the maximum likelihood EPS). The REML value will be 50% higher. In fact, for both the Ke and Cl parameterizations, identical V=.00791 estimates are obtained, and identical std errors of V are of .00112 are obtained, as theory predicts for the single subject case. Also as theory predicts, the -2LL values are identical at 134.72 for the two different parameterizations (changing the parameterization only matters in the population case).
ClearanceParameters.phxproj (1.1 MB)