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

[Katerina Pappa (PGR)]

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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