Make a 'between-and-within-factors' ANOVA with lmer function

Hi there,

I'm trying to understand how to use the function lmer in order to do a
'between-and-within-factors' ANOVA, but without any success. I know about
the usage of the function aov, but this holds only for balanced designs;
its documentation say to use lme function (package nlme) for unbalanced
designs. Furthermore I found the lmer function (package lme4) is an
evolution of lme, so I wish to use this last function in order to perform
my ANOVA. But I'm not able to understand how to do this.

More precisely, imagine you have a dependent variable DV and four
independent variables IV1, IV2, IV3, IV4, where IV1, IV2 are
between-factors and IV3, IV4 are within-factors. Moreover you have a
variable called Subject in order to identify the subject on which
measurements are done (like for example this dataset:
http://personality-project.org/r/datasets/R.appendix5.data). If I use the
aov function, my 'between-and-within-factors' ANOVA would stand as follows:

aov(DV~(IV1*IV2*IV3*IV4)+Error(Subject/(IV3*IV4))).

Now can you write me the precise syntax in order to obtain the same result
with the lmer function?

Thanks a lot in advance!
Vanni Rovera



*Additional details:* The problem is that no one seems to be interested in
explain the relations of 'within-factor' and 'between-factor' concepts with
those of 'fixed-effect' and 'random-effect'. Textbooks and papers about
ANOVA talk about between and within factors, while documentations and
papers about lmer function talk about mixed-effects models, i.e. they talk
about fixed and random effects, without mentioning between and within
factors. *Thus I am not able to understand the relations between the two,
since I think they are completely uncorrelated each others, and hence I am
not able to use the syntax in lmer in order to distinguish between factors
from within factors.*

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