R：nls和lm不相同的加权指数函数

Question

im struggeling with something. If i estimate an exponential function with lm and using transformation ie.

    leastsquares.complete=lm(log(PPPrate)~Highest+Mortrate5Y+Crate+DummieJan+DummieDec,weights=Notional)
b.completebestin= predict.lm(leastsquares.completebestout)
Forecast.completebestin= exp(b.completebestin)

I get different result than using a weighted nls

form<-as.formula(PPPrate~exp(alfa0+alfa1*Highest+alfa2*Mortrate5Y+alfa3*Crate+alfa4*DummieJan+alfa5*DummieDec))
nlsresultshehe=nls(
  form,
  data=AllDataXX,
  start=list(alfa0=1,alfa1=1,alfa2=1,alfa3=1,alfa4=1,alfa5=1),trace=TRUE,
  weight=Notional,control=nls.control(minFactor=0.0001,maxiter = 5000))
T=summary(nlsresultshehe)$parameters
Forecast=exp(T[1,1]+Highest*T[2,1]+Mortrate5Y*T[3,1]+Crate*T[4,1]+DummieJan*T[5,1]+DummieDec*T[6,1])

Does it have something to do with the weighting scheme? im kinda lost here

Answer 1

You're fitting two different models.

• The lm call fits a straight line through the log-transformed response. It's finding the line that minimises the sum of squared residuals on the log scale.
• The nls call fits an exponential line without transforming anything. It's finding the line that minimises the sum of squared residuals on the original scale.

In general, you're not going to get the same result from both these cases.