3 x 2 mixed factorial design - which model is correct

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3 x 2 mixed factorial design - which model is correct

apappa1
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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Re: 3 x 2 mixed factorial design - which model is correct

Bert Gunter-2
Please note, per the posting guide linked below:

"*Questions about statistics:* The R mailing lists are primarily intended
for questions and discussion about the R software. However, questions about
statistical methodology are sometimes posted. If the question is well-asked
and of interest to someone on the list, it *may* elicit an informative
up-to-date answer. See also the Usenet groups sci.stat.consult (applied
statistics and consulting) and sci.stat.math (mathematical stat and
probability)."

So do not be surprised if you do not get a helpful response here.
https://stats.stackexchange.com/  may be a better place for you to post
your queries.

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) <
[hidden email]> 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
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

        [[alternative HTML version deleted]]

______________________________________________
[hidden email] mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.