From: Stephen Duffull <*stephen.duffull*>

Date: Mon, 24 Aug 2009 12:49:17 +1200

Mats

Just a comment on your comments below:

"All models are wrong and I see no reason why the exponential error model w=

ould be different although I think it is better than the proportional error=

for most situations. "

"Why would you not be able to get sensible information from models that don=

't have an additive error component?"

I agree that for estimation purposes a purely proportional or exponential e=

rror model often seems to work well and under the principles of "all models=

are wrong" it may well be appropriately justified. This is probably becau=

se estimation processes that we use in standard software are fairly robust =

to trivial solutions. The theory of optimal design is less forgiving in th=

is light and if you stated that your error was proportional to the observat=

ion then it would conclude that there would be no error when there is no ob=

servation (which we know is not true due to LOD issues). All designs are o=

ptimal when there is zero error since the information matrix would be infin=

ite. Practically, the smallest observation will have least error and hence=

be in some sense close to optimal.

So, a proportional or exponential only error model should be used with caut=

ion in anything other than estimation and not used for the purposes of opti=

mal design.

Steve

--

Received on Sun Aug 23 2009 - 20:49:17 EDT

Date: Mon, 24 Aug 2009 12:49:17 +1200

Mats

Just a comment on your comments below:

"All models are wrong and I see no reason why the exponential error model w=

ould be different although I think it is better than the proportional error=

for most situations. "

"Why would you not be able to get sensible information from models that don=

't have an additive error component?"

I agree that for estimation purposes a purely proportional or exponential e=

rror model often seems to work well and under the principles of "all models=

are wrong" it may well be appropriately justified. This is probably becau=

se estimation processes that we use in standard software are fairly robust =

to trivial solutions. The theory of optimal design is less forgiving in th=

is light and if you stated that your error was proportional to the observat=

ion then it would conclude that there would be no error when there is no ob=

servation (which we know is not true due to LOD issues). All designs are o=

ptimal when there is zero error since the information matrix would be infin=

ite. Practically, the smallest observation will have least error and hence=

be in some sense close to optimal.

So, a proportional or exponential only error model should be used with caut=

ion in anything other than estimation and not used for the purposes of opti=

mal design.

Steve

--

Received on Sun Aug 23 2009 - 20:49:17 EDT