From: "Richard A. O'Keefe" <ok at cs.otago.ac.nz>
Date: Wed, 4 Oct 2006 18:36:55 +1300 (NZDT)
To: <r-help at stat.math.ethz.ch>
Subject: [R] Linear model with hidden variables
I have some data on a moving vehicle where, amongst other things,
it looks as though it would be informative to fit a model with the
following structure:
Z = B.Y + errorz
Y = C.X + errorz
The X variables are observed predictor variables;
6 of the variables look promising (on the basis of what they mean).
The Z variables are observed response variables;
there are 4 of them.
There is a priori reason to believe, and scatterplots to suggest,
that the Z variables are really essentially two-dimensional, so
the Y variables are "hidden" intermediate variables.
There should be 2 of them. There are actually two physical candidates
for what they might be, but they happen not to have been measured.
There are 800 cases. (More precisely, there are 14 periods, each with
about 800 samples, and I am interested in fitting a separate model in
each period.)
A simple least squares fit for this model would minimise the sum of
error squares for the Zs. Oh, I do mean there to be constant terms.
I suppose I could go back to first principles and work it all out,
but has anyone ever done something like this in R? There seems to
be every imaginable variation on lm and some that I find unimaginable,
so presumably a means to do this is already around somewhere.