[R-sig-ME] location-scale models in nlme
Ben Bolker
bbo|ker @end|ng |rom gm@||@com
Sun Jan 14 21:00:39 CET 2024
For varIdent (from ?nlme::varIdent),
For identifiability reasons, the
coefficients of the variance function represent the ratios between
the variances and a reference variance (corresponding to a
reference group level).
I assume that this is internally parameterized via something like (1)
a model matrix constructed with ~ <grouping factor> and (2) a log link,
to ensure that the ratios are all positive
For varPower,
s2(v) = |v|^(2*t)
-- notice it uses the absolute value of the covariate. So that term
will also be positive.
varComb uses a product; the product of two positive values will also be
positive ...
On 2024-01-14 11:40 a.m., Simon Harmel wrote:
> Dear Ben and List Members,
>
> I'm following up on this
> (https://stat.ethz.ch/pipermail/r-sig-mixed-models/2023q4/030552.html
> <https://stat.ethz.ch/pipermail/r-sig-mixed-models/2023q4/030552.html>)
> thread. There, Ben noted that my MODEL (below) qualifies as a
> "location-scale" model.
>
> Q: Usually for the scale part of a location-scale model, the linear
> model uses a log link to guarantee that the estimate of scale is positive:
>
> log(scale_i) = a_0 + b_1*x_i1+ ... + b_n*x_ip (for p predictors of scale)
>
> But in the MODEL that I sketched below, how such a guarantee is made?
>
> Thanks, Simon
> MODEL <- nlme::lme(y ~ X1_categorical + X2_numeric ...,
> random = ~1| subject,
> data = data,
> correlation = corSymm(~1|subject),
> weights = varComb(varIdent(form = ~ 1 | X1_categorical ),
> varPower(form = ~ X2_numeric )))
>
--
Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
(Acting) Graduate chair, Mathematics & Statistics
> E-mail is sent at my convenience; I don't expect replies outside of
working hours.
More information about the R-sig-mixed-models
mailing list