Defining arbitrary function in PHX’s modeling language

Phoenix Certara Forums Modelling and Simulation
1

Dear all,

I’m interested how PHX performs with the NIST’s reference datasets (background info). I’m fine with ASCII-codes, but I’m completely lost with the new syntax.
The most simple model is y = b1*(1-exp(-b2*x)). No idea. Hey, that’s even PK!

2

Hi Helmut,

I think what you’re asking is how this would look as a model and I believe it would be something like;

test(){
covariate(x)

error(e = 1)
observe(y = b1*(1-exp(-b2*x)) + e)

fixef(b1 = c(, 500, ))
fixef(b2 = c(, 0.001, ))
}

(I started from a simple PD model just to remind me of the ‘house keeping’). I am not sure if there is a significance to the fact we are testing a set that was for Nonlinear Least Squares Regression yet the Phoenix engine is a maximum likelihood - but that’s more your field ;0)

That code gives;

Parameter Estimate Units Stderr CV% 2.5% CI 97.5% CI Var. Inf. factor
b1 238.934 2.524995 1.0567751 233.37651 244.49149 705.98
b2 0.000550179 6.7790855E-06 1.23216 0.00053525829 0.00056509971 5.0883E-09
stdev0 0.0943214 0.018128707 19.220141 0.054420282 0.13422252

which seems to look OK to their certified values;

          Starting values                  Certified Values
 
        Start 1     Start 2           Parameter     Standard Deviation
  b1 =   500         250           2.3894212918E+02  2.7070075241E+00
  b2 =     0.0001      0.0005      5.5015643181E-04  7.2668688436E-06

and quickly looking at the second set of inital estimates too.

Does that help as a starting point?

Simon.

NIST_Misra1a.phxproj (623 KB)

3

Hi Simon,

THX!

I am not sure if there is a significance to the fact we are testing a set that was for Nonlinear Least Squares Regression yet the Phoenix engine is a maximum likelihood - but that’s more your field ;0)

Doesn’t worry me too much. :wink: WNL-ACSII (which uses LS) didn’t perform that good, actually.

That code gives;

Parameter Estimate
b1 238.934
b2 0.000550179

Strange. When I opened your project (and when I re-executed as well):

Parameter Estimate
b1 238.932
b2 0.000550177

I got the same results with the second initial estimates.

which seems to look OK to their certified values

Yep. Should agree by more than 4 significant digits by TRUNC(-LOG10( ABS(estimate-certified) / ABS(certified))). Actually 5-6. Mine are closer to the certified ones than yours. I’m using 6.4.0.768 (64bit) on Win7 and the project was created with 6.3.0395.

BTW, if I want to get one more significant digit I had to grab it from Core Status/Optimal Parameters.

4

Hi Helmut,

You can also grap the ouput from dmp.txt that can be saved to file and then automatically sourced into R.

It should have all the outputs and significant digits.

Regards,

Samer