[R] Syntax differences between aov and lmer for 2-way repeated measures design using a mixed model

[Uri Eduardo Ramírez Pasos]

Hi everyone,

I'm working with the following data frame using R. It consists of
measurements obtained from 7 subjects with two independent variables (IV1
and IV2) with two levels each (OFF/ON, ALT/ISO, respectively):

>myData
Subject      DV         IV1     IV2
        1   2.567839      OFF      ALT
        1  58.708027       ON      ALT
        1  44.504265      OFF      ISO
        1 109.555701       ON      ISO
        2  99.043735      OFF      ALT
        2  75.958737       ON      ALT
        2 182.727396      OFF      ISO
        2 364.725795       ON      ISO
        3  45.788988      OFF      ALT
        3  52.941263       ON      ALT
        3  54.719013      OFF      ISO
        3  41.909909       ON      ISO
        4 116.145279      OFF      ALT
        4 162.927971       ON      ALT
        4  34.162077      OFF      ISO
        4  74.029748       ON      ISO
        5 114.412913      OFF      ALT
        5 121.127983       ON      ALT
        5 192.379708      OFF      ISO
        5 229.192453       ON      ISO
        6 213.421076      OFF      ALT
        6 526.739206       ON      ALT
        6 150.596812      OFF      ISO
        6 217.931951       ON      ISO
        7 117.931273      OFF      ALT
        7 102.467813       ON      ALT
        7  57.823062      OFF      ISO
        7  85.181033       ON      ISO
(1) Is this a repeated measures (RM) design? Some folks have mentioned that
it is not since it isn't a longitudinal study, but I thought that as long
as there are measurements from each experimental unit for every single
level of a factor, one can say this as a RM design. What is correct? Also,
is an RM design synonymous with having a within-subject factor?

(2) I'm interested in both the main and the interaction effects of IV1 and
IV2, but due to having measurements from each subject for all level
combinations, I think I have to include Subject as a random effect. I have
looked at aov and lmer but I'm confused about the difference in syntax:
This cheat sheet recommends:

m1<-aov(DV ~ IV1*IV2 + Error(Subject/(IV1*IV2)), myData)

However it's not clear to me whether Error(x/(y*z)) means x is a random
effect and y and z are nested in x. Is this interpretation correct? If so,
would m1 be inappropriate for my data since my data isn't nested, but fully
crossed? And if so, would

m2<-aov(DV ~ IV1*IV2 + Error(Subject), myData)

be the correct syntax? I have also been told that in m2 the Error term
should be dropped - is this correct?

(3) In a previous question I was told the linear mixed effects model

m3<-lmer(DV ~ IV1*IV2 + (1|Subject), myData)
was appropriate more my data. Just to better understand lmer syntax: if I
had n subjects and for each subject measurements were obtained for both
levels of IV2 but half of the subjects were OFF and the other half ON,
would the model be

m4<-lmer(DV ~ IV1*IV2 +(1|Subject/IV1), data=myData) ?

And if there was only one measurement per IV1*IV2 combination, would that
mean this is no longer a repeated-measures design and therefore the model
is just

m5<-lmer(DV ~ IV1*IV2, data=myData) ? In which case lm would probably
suffice.

Any help would be greatly appreciated,
Uri Ramirez

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