# [Rd] buglet?? in nlme:::corRatio documentation

From: Ben Bolker <bolker_at_zoo.ufl.edu>
Date: Mon, 03 Sep 2007 11:15:14 -0400

[hoping to redeem myself for my last spurious bug report]

From ?corRatio:

Letting d denote the range and n denote the nugget effect, the

```     correlation between two observations a distance r apart is
(r/d)^2/(1+(r/d)^2) when no nugget effect is present and
(1-n)*(r/d)^2/(1+(r/d)^2) when a nugget effect is  assumed.

```

This disagrees with the C code (corStruct.c)

/* Rational class */

static double
ratio_corr(double val)
{

double val2 = val * val;
return(1/(1+val2));
}

and with common sense (correlation structures should start from 1 and reach zero for large distances; the structure listed in the documentation starts at 0 and goes to 1 [or (1-n)] for large distances) -- if you don't want to think about it, use R instead:

curve(x^2/(1+x^2),from=0,to=5)
curve(1/(1+x^2),add=TRUE,col=2,from=0)

What's odd, and makes me really nervous, is that the expression found in the documentation is also that found in Pinheiro and Bates 2000 (Table 5.2, p. 232). It's not listed in the errata for the first printing http://cm.bell-labs.com/cm/ms/departments/sia/project/nlme/MEMSS/Errata ; I have the second printing.

(I haven't dug out my geostats books to check this, but found at least one paper that cites the "correct" (1/(1+(d/r)^2) formula -- see below

cheers

Ben Bolker

@ARTICLE{Ekstrom+2005,
author = {Ekstr{\o}m, Claus T. and Bak, S{\o}ren and Rudemo, Mats},   title = {Pixel-level Signal Modelling with Spatial Correlation for Two-Colour

Microarrays},
journal = {Statistical Applications in Genetics and Molecular Biology},   year = {2005},
volume = {4},
number = {1}
timestamp = {2007.09.03},
url = {http://www.bepress.com/sagmb/vol4/iss1/art6}
}

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