[R-sig-ME] p-values from lme::anova VS fixed-effects of lme
Karl Ove Hufthammer
karl at huftis.org
Sun Dec 11 11:08:55 CET 2016
K Imran M skreiv 10. des. 2016 10:57:
> #### LME ######
>
> res <- lme(distance ~ age*Sex, random = ~ 1 | Subject, data = Orthodont)
>
> summary(res)
> […]
> Next, if I run 'anova(res)', I would obtain this
> […]
> I do not understand why the p-values for age and age:Sex (from anova) are
> similar with (lme::anova) BUT for sex: it is different (anova, p-val =
> 0.0054 vs lme::anova, p-val = 0.508).
The P-values are only identical for the interaction, *not* for age and
*not* for Sex. The P-values for age just happened to both be very small.
It’s easier to see this for a smaller dataset, with larger P-values:
set.seed(1)
d = Orthodont[sample(nrow(Orthodont), 20),]
res = lme(distance ~ age*Sex, random = ~ 1 | Subject, data = d)
Now, summary(res) gives us:
Value Std.Error DF t-value p-value
(Intercept) 19.259688 1.7255889 13 11.161226 0.0000
age 0.581252 0.1428037 3 4.070286 0.0268
SexFemale -1.859006 2.3131153 13 -0.803681 0.4360
age:SexFemale -0.224017 0.1865328 3 -1.200955 0.3159
while anova(res) gives us:
numDF denDF F-value p-value
(Intercept) 1 13 1306.1220 <.0001
age 1 3 24.4811 0.0158
Sex 1 13 10.3881 0.0067
age:Sex 1 3 1.4423 0.3159
So only the interaction age:Sex gives the same P-value. The reason is
that anova(res) gives the *sequential* tests (first the effect of age,
then the effect of Sex given age, and then the effect of age:Sex given
age and sex). Only the last test will be identical.
For a similar test using anova(), you have to request marginal tests:
> anova(res, type="marginal")
numDF denDF F-value p-value
(Intercept) 1 13 124.57297 <.0001
age 1 3 16.56723 0.0268
Sex 1 13 0.64590 0.4360
age:Sex 1 3 1.44229 0.3159
Mind you, the marginal tests (usually) don’t make much sense when you
have an interaction. In your original example, the marginal P-value of
0.51 for ‘Sex’ does *not* mean that sex doesn’t have an effect on the
outcome variable. Since the age:Sex interaction is statistically
significant (P-value ~0.01), Sex *obviously* has en effect; it’s just
that the effect of sex depends on the age of the individual. And the
P-values for the ‘marginal effects’ depend very much on the
parametrisation. For example, if you change ‘age’ by adding or
subtracting a constant (e.g. instead of measuring age as ‘years from
birth’, you measure it as ‘years since starting school’ or ‘years until
the person turns eighteen’), the ‘marginal’ P-value for ‘Sex’ will
change (perhaps to a very low or high P-value).
--
Karl Ove Hufthammer
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