# PharmPK Discussion - Sum squared errors

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• On 15 Sep 2003 at 09:49:32, "Ravi Kuppuraj" (rkuppuraj.aaa.innaphase.com) sent the message
`The following message was posted to: PharmPKHello,   can somebody comment on what should happen to SSEs when you "fix" aparameter in a PK model, and why?thanksRavi Kuppuraj`
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• On 15 Sep 2003 at 15:37:21, "Bonate, Peter" (pbonate.aaa.ilexonc.com) sent the message
`The following message was posted to: PharmPKRavi Kuppuraj writes:    can somebody comment on what should happen to SSEs when you "fix" aparameter in a PK model, and why?That depends on what you fix it to.  If you fix a value to its maximumlikelihood estimate, SSE should be unaffected.  If you fix it tosomething other than SSE than then SSE should increase.  Now, MSE, onthe other hand, will change.  The denominator of MSE is (n-p) where pis the number of estimable parameters.  Because you have fixed MSE, pis smaller and so MSE will increase.  Hope this helps,Pete Bonate`
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• On 16 Sep 2003 at 12:46:13, "J.H.Proost" (j.H.Proost.at.farm.rug.nl) sent the message
`The following message was posted to: PharmPKDear Ravi Kuppuraj,With respect to your question:>   can somebody comment on what should happen to SSEs when you "fix" a> parameter in a PK model, and why?SSE (Sum of squared errors) will always increase if a parameter isfixed during fitting of a model. This is simply so because fixing aparameter does not allow to explore the entire parameter space to findthe minimum SSE. So there will be always a different value for thefixed parameter resulting in a lower SSE (unless you fixed the value atthe minimum, but this makes no sense; see below).Please note that the SSE is only one possible 'objective function' tobe minimized during fitting; e.g. the objective function may be 'minustwo log-likelihood' or any expressed related to it (including SSE). Thenumerical value of the objective function is usually not relevant; itis used only to find the minimum (and AIC, see below).In case of ordinary least=squares (OLS) or weighted least-squares(WLS), 'minus two log-likelihood' can be replaced by log(SSE) andlog(WSSE), respectively (log refers to natural logarithm with base e),leaving out various constant terms.Whether or not the change of the objective function by fixing orvarying a particular parameter is 'relevant', is usually judged fromAkaike's Information Criterion (AIC):AIC = -2 log(likelihood) + 2 Pwhere P is the number of estimated parameters. Comparing two models,the one with lowest AIC is the 'best' model.So, fixing a parameter decreases P and increased -2 log(likelihood).Besides, fixing a parameter implies that the number of assumptionsabout the model increases; one investigates only a restricted model.This can be done only if there is some plausible value for thatparameter, e.g. a value obtained from an independent source. Fixing aparameter simply because the fitting procedure does not provide aplausible estimate (e.g. a negative or zero value) is definitely notgood practice! (although reporting a negative PK parameter is also notrecommended). Here we are in the darker side of modeling ...Best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlandstel. 31-50 363 3292fax  31-50 363 3247Email: j.h.proost.aaa.farm.rug.nl`
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