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Fixing/constraining a parameter estimate- what does this mean for "goodness/power" the model?

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Fixing/constraining a parameter estimate- what does this mean for "goodness/power" the model?

Please help, I'm not sure what is happening with my modelling. I ran the original model and noted down a parameter estimate, and manually input that for the subsequent two models.

I am sure "goodness" and "power" are not the right kind of words here.

1) Here is the "original" model code:

proc nlmixed;

parms

ED50  5 to 250 by 5        

Emax  -2 to -1  by 0.1

V     0.1             

BETA0 1               

s 1;

pred = (logbase * (Beta0)) +  (Dose**s * Emax) / ( Dose**s + ED50**s );

model R ~ normal( pred, V);

run;

2) Here is the model code with "s" constrained:

proc nlmixed;

parms

ED50  5 to 250 by 5      

Emax  -2 to -1  by 0.1  

V     0.1             

BETA0 1    

s 0.53; 

bounds s < 0.5318;

pred = (logbase * (Beta0)) +  (Dose**s * Emax) / ( Dose**s + ED50**s );

model R ~ normal( pred, V);

run;

Here's the code with "s" fixed:

proc nlmixed data=newdata;

parms

ED50  5 to 250 by 5      

Emax  -2 to -1  by 0.1  

V     0.1             

BETA0 1    ;       

pred = (logbase * (Beta0)) +  (Dose**0.53 * Emax) / ( Dose**0.53 + ED50**0.53 );

model R ~ normal( pred, V);

run;

See the output attached.

The first model has huge standard errors around the parameter estimates.

The second model has reasonable standard errors and the same fit statistics as the first model.

The third model has reasonable standard errors and better fit statistics than the first model.

Is fixing/constraining this parameter "cheating"? If it's okay to do- shouldn't I fix all of the parameters and have a brilliant AIC and BIC???

So confused

Please help

xxx


output.jpg
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