[R] [FORGED] Regression with factors ?

[stn021]

Hello,

thank you for the replies. Sorry about the html-email, I forgot.
Should be OK with this email.


Don't be fooled be the apparent simplicity of the problem. I have
tried to reduce it to only a single relatively simple question.

The idea here is to model cooperation of two persons. The model is
about one specific aspect of that cooperation, namely that two persons
with similar abilities may be able to produce better results that two
very different persons.

That is only one part of the model with other parts modeling for
example the fact that of course two persons with a higher degree of
ability will produce better results per se.


It is not classic regression with factors. That can be easily done by
something like lm( y ~ (p1-p2)^2 ).

This expands to lm( y ~ p1^2 - 2*p1*p2 + p2^2 ). This contains a
multiplicagtions and for lm() this implies interactions between the
factor-levels and produces one parameter for each combination of
factor-levels that occurs in the data. That is not what the question
is about.

Also p1 and p2 are different levels of the same factor, while for lm()
it would be two different factors with different levels.


As for the sensical part: this has a real world application therefore
it makes sense.

Also it is not so difficult to solve with non-linear optimization. I
was hoping to be able to use R for that purpose because then the
results could easily be checked with statistical tests.

So my question is not "how to solve" but "how to solve with R".


As for the excess degrees of freedom, in real observations there would
of course be added noise due to either random variations or factors
not included in the model. So to generate a more reality-conforming
example I could add some random normal-distributed noise to the
dependent variable y. I previously left that part out because to me it
did not seem relevant.


Would you like me to make a complete example dataset with more records
and noise ?


The answer I look for would be the numerical values of the
factor-levels and numerical values for the multiplier (f) and the
offset (o), with p1 and p2 given as names (here: persons) and y given
as some level of achievement they reach by cooperating.

y = f * ( o - ( p1 - p2 )^2 )

Is that what you meant by "answer" ?


THX
stefan




2016-07-10 2:27 GMT+02:00 Jeff Newmiller <jdnewmil at dcn.davis.ca.us>:
>
> I have seen less sensical questions.
>
> It would be nice if the example were a bit more complete (as in it should have excess degrees of freedom and an answer) and less like a homework problem (which are off topic here). It would of course also be helpful if the OP were to conform to the Posting Guide, particularly in respect to using plain text email.
>
> It looks like the kind of nonlinear optimization problem that evolutionary algorithms are often applied to. It doesn't look (to me) like a typical problem that factors get applied to in formulas though, because multiple instances of the same factor variable are present.
> --
> Sent from my phone. Please excuse my brevity.
>
> On July 9, 2016 4:59:30 PM PDT, Rolf Turner <r.turner at auckland.ac.nz> wrote:
> >On 09/07/16 20:52, stn021 wrote:
> >> Hello,
> >>
> >> I would like to analyse a model like this:
> >>
> >> y = 1 *  ( 1 - ( x1 - x2 )  ^ 2   )
> >>
> >> x1 and x2 are not continuous variables but factors, so the
> >observation
> >> contain the level.
> >> Its numerical value is unknown and is to be estimated with the model.
> >>
> >>
> >> The observations look like this:
> >>
> >> y        x1     x2
> >> 0.96  Alice  Bob
> >> 0.84  Alice  Charlie
> >> 0.96  Bob   Charlie
> >> 0.64  Dave Alice
> >> etc.
> >>
> >> Each person has a numerical value. Here for example Alice = 0.2 and
> >Bob =
> >> 0.4
> >>
> >> Then y = 0.96 = 1* ( 1- ( 0.2-0.4 ) ^ 2 ) , see first observation.
> >>
> >> How can this be done in R ?
> >
> >
> >This question makes about as little sense as it is possible to imagine.
> >
> >cheers,
> >
> >Rolf Turner
>