[R] 3 x 2 mixed factorial design - which model is correct

[Bert Gunter]

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As an editorial comment -- meaning feel free to ignore or dismiss -- the
reply to statistical questions like yours generally depend on the specific
research hypotheses of interest as well as the data. Clarifying the
research questions may increase your chance of success in further posts.
And a multivariate treatment of the data may also be more appropriate as
the responses among the various brain regions are likely correlated. Etc.

Cheers,
Bert

Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Tue, Feb 9, 2021 at 7:54 AM Katerina Pappa (PGR) <
a.pappa.1 using research.gla.ac.uk> wrote:

> Hello everyone,
>
> I was hoping you could help with a few R-related questions.
>
> I have a 3 x 2 mixed factorial design. This is a longitudinal design,
> where two groups of participants were assessed over three time points.
>
> Factor Time has 3 levels (time 1, 2 and 3)
> Factor Group has 2 levels (groups 1 and 2)
> Dependent variables are continuous and represent gray matter volumes for 6
> regions of interest
>
> I have arranged the data as indicated below:
>
> A tibble: 111 x 13
>
> ##    ID      Age Time  Group  lCau  rCau  lHip  rHip  lPut  rPut  T2vT1
> T3vT1 G
>
> ##    <fct> <dbl> <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>
> <dbl>
>
> ##  1 BT02     22 T1-P… G2     2.65  2.71  2.58  2.83  3.17  3.05 -0.333
> -0.333  -0.5
>
> ##  2 BT02     22 T2-E… G2     2.69  2.76  2.62  2.90  2.95  3.09  0.667
> -0.333 -0.5
>
> ##  3 BT02     22 T3-P… G2     2.66  2.72  2.56  2.87  2.99  2.96 -0.333
> 0.667 -0.5
>
> ##  4 BT03     22 T1-P… G1     2.20  2.37  2.46  2.81  3.51  3.45 -0.333
> -0.333  0.5
>
> ##  5 BT03     22 T2-E… G1     2.18  2.38  2.47  2.77  3.38  3.48  0.667
> -0.333 0.5
>
> ##  6 BT03     22 T3-P… G1     2.18  2.33  2.44  2.78  3.61  3.66 -0.333
> 0.667 0.5
>
> ##  7 BT04     19 T1-P… G2     2.93  3.10  2.89  3.19  3.57  3.70 -0.333
> -0.333 -0.5
>
> ##  8 BT04     19 T2-E… G2     2.91  3.07  2.86  3.18  3.46  3.60  0.667
> -0.333 -0.5
>
> ##  9 BT04     19 T3-P… G2     2.84  3.01  2.90  3.23  3.54  3.71 -0.333
> 0.667 -0.5
>
> taking the left caudate, .i.e. lCau, as an example:
>
> Q1: Anova model
> aov (lCau ~ Time*Group + Error(ID))  —> is this model correct?
>
> Q2: lm model
> And then i used dummy coding for the lm model
>
> lmer(lCau ~ (T2vT1 + T3vT1)*G+ (1 |ID))  —> is this model correct?
>
> Are these models correct for this type of data?
>
> Q3: any thoughts on how to deal with unbalanced design (I have missing
> data for one participant for Time2)
>
>
> Thank you!
> Katerina
>
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>
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