NLS or better: NLM

I have to correct my previous post (or have I already did it?): I used NLM,
not NLS.

Are you taking advantage of the fact that four of your five parameters
are conditionally linear?  You can use 

No. I used my fingers before my brain.

You would write the model as

 nls(y ~ x4^b4*cbind(1, x1, x2, x3), data = mydata, start = c(b4 = 0),
     alg = "plinear", trace = TRUE)

This works fine.

Do you really expect 0 to be a sensible value for this parameter?  If
so, have you already fit the linear regression model
  y ~ 1 + x1 + x2 + x3
and found it to be adequate?  Why then do you think that x4 determines
the response in this fashion is your best guess at the value of b4 is
the value that makes x4 of no consequence.

Probably wrongly, but exatly for this reason. x1, x2 and x3 are number of
adu1t males, females and children in the household, y is energy intake, and x4
is log(income)/head. Plotting the data indicated difference, so I choose 0 to
see if there is one.

it converges very quickly, and to the wrong solution.

Please explain this further.  An independent evaluation of the

Not that I am aware of.  However, R is an open source system and you
are welcome to contribute a superior nonlinear least squares
implementation at any time.

Well, I did not wanted to blame the minimizer engine (nor R!). I just observed
these things and behaved like a consumer of software bloathed with AI-like
features, not like a craftsman with a precision tool. I hope R will teach me
to be more the latter.

But one question still remains for me. OK, I should have noticed and exploited
the structure of the problem. But what if I do not? Should the other way give
so different results?

Thanks,
Zsombor

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