Summary on 'F-tests for lme-results'

Regula Suter (
Mon, 19 Jan 1998 08:46:09 +0100

Those are the answers I got concerning my question on F-tests for lme-results:

1 from Jose Pinheiro, Bell Laboratories,

Type III sum of squares, mean squares, and F-values are generally
associated with some type of least squares fit, which is not what is
used in lme (neither in PROC MIXED). They are extensively used in
PROC GLM for the analysis of ANOVA models and what is included in
PROC MIXED is based on a "linearization" of the mixed-effects model
using Wald-type of tests. For linear mixed-effects it is probably
safer to use likelihood ratio tests, instead of F-tests, to test the
significance of factors (e.g. race and group in your model
specification). The function anova.lme can be used for that
purpose. You can use, for example,

> fp1 <- lme(fixed = TS ~ C(race, sum) + C(group,sum) + BCS + LG + SKL,
+ random= ~ -1, cluster= ~ LaufNummer,
+ re.structure = "identity", data =, est.method = "ML"))

(Note: likelihood ratio tests are not meaningful for RML fits of
models with different fixed effects structures)

> fp2 <- lme(fixed = TS ~ C(group,sum) + BCS + LG + SKL,
+ random= ~ -1, cluster= ~ LaufNummer,
+ re.structure = "identity", data =, est.method = "ML"))

> anova(fp1, fp2) # testing the effect of "race"

2 from Prof Brian Ripley

I suspect you will get very little sympathy, as Type III Sums of
Squares are regarded as misguided (at best) by most of the authors
in that area.

3 from Roy Pardee

I think it may not be possible to get sums of squares for this
analysis--at least not in PROC MIXED. See:

MIXED uses maximum likelihood, and so doesn't need to compute sums of
squares. If lme() works the same (I have no idea whether that is so) then
you may have to do without them...


>From our own SAS-consultant I got the information that SAS is calculating
F-tests for fixed effects, but in an approximative way.

>From Jon Binkley ( I got information concerning
literature about the mixed-effects-topic: This is "Mixed Effects Models and
Classes for S and Splus", Feb 1995, by Jose C. Pinheiro and Douglas M.
Bates (

You can also find information about lme() in the supplement of the
S-Plus-Documentation from MathSoft and in "Modern Applied Statistics with
S-PLUS" by Venables and Ripley. Second Edition.
(More info on

Thanks to all those, who helped me!

Regula Suter


Regula Suter
Swiss Federal Institute of Technology
Institute of Animal Science
Animal Breeding
Research-Station Chamau
CH-6331 Huenenberg
phone: +41 41 780 10 47
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