[FORGED] different models

Hi all,

This might be a very dumb question that shows I have very little idea of
what I am talking about, but I'll risk it:

What is the difference between fitting a model using these 3 different
syntaxes?

1/ fit1 <- ppm(ppp, ~covariate),
2/ fit2 <- ppm(ppp, ~x+y+Z, covariates=list(Z=covariate))
3/ fit3 <- ppm(ppp, ~x+y+covariate)

where ppp is my point pattern and "covariate" is a pixel image? I realise
the outputs of 2 and 3 are the same and different to that of 1, so I guess
the question really is

a/ Is there any difference, practical or in the actual computations of the
model, between using 2 and 3?
b/ What is the difference between (2&3) and 1?

(1) There is essentially no difference between fits 2 & 3.  The fit 2 
syntax is provided so that the user can have the relevant covariates 
bundled up in a list without any need to extract these covariates from 
that list.   With the fit 2 syntax you don't need to have all covariates 
present in your workspace.

E.g.: fit <- ppm(bei ~ elev + grad, data=bei.extra)

(2) The fit 2 syntax is essentially the same as that used by lm() and 
glm() and was designed in imitation thereof.

(3) The preferred structure of a call to ppm() is

     fit2 <- ppm(ppp ~ x + y + Z, data=list(Z=covariate))

Note:  "data" rather than "covariates"; no comma between the name of the 
response variable ("ppp") and the formula.

This makes the syntax identical to that of lm() and glm().

The syntax that you used is a remnant of earlier versions of spatstat 
and remains acceptable for reasons of backward compatibility.

(4) The difference between model 1 and models 2 and 3 is that models 2 
and 3 involve the Cartesian coordinates "x" and "y".  Model 1 is such 
that the model intensity takes the form

    exp(beta_0 + beta_1 * covariate)

In models 2 and 3 the model intensity takes the (more complex) form

    exp(beta_0 + beta_1 * x + beta_2 *y beta_3 * covariate)

Note that "x" and "y" are *reserved* names.  You cannot use these names 
for any covariates *other than* the Cartesian coordinates.

(5) The name "covariate" is probably *not* a good name for a covariate.
As fortune(77) puts it "Would you call your dog 'dog'?"

(6) Likewise (and even more so) "ppp" is *not* a good name for a point 
pattern, since it clashes the name of the creator function ppp().

cheers,

Rolf Turner

Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276