Hello everyone:
Having not heard back about the design below, perhaps a quicker more
strait-forward question is in order.
Specifically, *how do you design a model with a between group treatment?*

For example, suppose I have a multilevel design with predictor A within
groups of B. I expose groups to some treatment C, such that half of the
groups get treatment C1 and half C2. How do I design a model for this
between-groups treatment? What if we believe C might interact with A?

If every group received both treatments, we could model the interaction
between C and B as a variable slope
M1 <- DV ~ A*C + (0 + C | B) + (1|B)

We could also include the varying interaction between A and C for each
group by using model M2
M2 <- DV ~ A*C + (0 + C + A:C | B) + (1|B)

BUT in our case there is only 1 C variable for each B. (This is what I find
confusing).
Would M1 and M2 still be correct?
Or do we need to get rid of the variable slope of C with respect to B?

M3 <- DV ~ A*C + (0 + A:C | B) + (1|B)

For bonus points, what if C had many more factors and we wanted to model it
as a random effect.
In the case where each group received multiple treatments we could write
R1 <- DV ~ A + (0 + A|C) + (1|B/C)

BUT in our case there is only 1 C variable for each B - so would this be
correct?
R2 <- DV ~ A + (0 + A|C) + (1|B)

What about this?
R3 <- DV ~ A + (0 + A|C) + (1|B) + (1|C)

Many thanks again for your help interpreting these designs!!
Derek
--
Derek Dunfield, PhD
Postdoctoral Fellow, MIT Intelligence Initiative
Sloan School of Management
MIT Center for Neuroeconomics, Prelec Lab
77 Massachusetts Ave E62-585
Cambridge MA 02139


On Wed, Nov 30, 2011 at 12:16 PM, Derek Dunfield <dunfield@mit.edu> wrote:
> Dear all:
> I am currently working with a multilevel model with ITEMS (and
> covariate V1) nested within SUBJECT. Items were not repeated across
> subjects (each item looked at was novel).   SUBJECTS were given a
> treatment (V2) in a between subject design. The dependent variable
> (DV) is per ITEM. I've included a dummy data set with a similar design
> below.
>
> I am interested in V1 and V2 as predictors, as well as the potential
> interaction of V1:V2. In addition, I expect varying intercepts and
> varying slopes for V1 within each SUBJECT.
>
> I believe this would correspond to the model:
>
> model1 <- glmer(DV ~ V1*V2 + (0 + V1|SUBJECT) +
> (1|SUBJECT),testdataset,family="binomial")
>
> However, I also expect V1 to have varying intercepts and slopes with
> respect to V2. I believe varying intercepts should be accounted for by
> (1|SUBJECT) because of the between subjects treatment design.
> Similarly, I don't believe (0 + V2|SUBJECT) would make sense, since
> each subject only has one value of V2.
>
> Instead, I ran a model accounting for varying slopes of the
> interaction V2:V1. This seemed to make sense since each V2:V1 factor
> should have a different slope if V1 slopes vary with respect to V2.
> This gives us the model:
>
> model2 <- glmer(DV ~ V1*V2 + (0 + V2:V1|SUBJECT) +
> (1|SUBJECT),testdataset,family="binomial")
>
> Model2 does give me different results than model1. However, because of
> the between subjects design for V2 treatment, I'm not clear why model2
> is any different from model1. Shouldn't V2:V1 should be 0 for the
> non-treated value of V2 within a subject?
>
> Many thanks for help interpreting this question / design.
> Yours,
> Derek
>
>
> TESTDATASET:
>
> SUBJECT V2      ITEM    V1      V1.nested       DV
> S1      A       1       a       A:a     N
> S1      A       2       a       A:a     N
> S1      A       3       a       A:a     N
> S1      A       4       a       A:a     Y
> S1      A       5       a       A:a     Y
> S1      A       6       b       A:b     Y
> S1      A       7       b       A:b     Y
> S1      A       8       b       A:b     Y
> S1      A       9       b       A:b     Y
> S1      A       10      b       A:b     N
> S2      A       11      a       A:a     N
> S2      A       12      a       A:a     N
> S2      A       13      a       A:a     Y
> S2      A       14      a       A:a     Y
> S2      A       15      a       A:a     Y
> S2      A       16      b       A:b     Y
> S2      A       17      b       A:b     Y
> S2      A       18      b       A:b     Y
> S2      A       19      b       A:b     N
> S2      A       20      b       A:b     Y
> S3      A       21      a       A:a     N
> S3      A       22      a       A:a     Y
> S3      A       23      a       A:a     N
> S3      A       24      a       A:a     N
> S3      A       25      a       A:a     N
> S3      A       26      b       A:b     Y
> S3      A       27      b       A:b     Y
> S3      A       28      b       A:b     Y
> S3      A       29      b       A:b     Y
> S3      A       30      b       A:b     Y
> S4      A       31      a       A:a     N
> S4      A       32      a       A:a     N
> S4      A       33      a       A:a     N
> S4      A       34      a       A:a     N
> S4      A       35      a       A:a     N
> S4      A       36      b       A:b     Y
> S4      A       37      b       A:b     Y
> S4      A       38      b       A:b     N
> S4      A       39      b       A:b     Y
> S4      A       40      b       A:b     N
> S5      B       41      a       B:a     N
> S5      B       42      a       B:a     N
> S5      B       43      a       B:a     Y
> S5      B       44      a       B:a     N
> S5      B       45      a       B:a     Y
> S5      B       46      b       B:b     Y
> S5      B       47      b       B:b     Y
> S5      B       48      b       B:b     N
> S5      B       49      b       B:b     Y
> S5      B       50      b       B:b     N
> S6      B       51      a       B:a     N
> S6      B       52      a       B:a     Y
> S6      B       53      a       B:a     Y
> S6      B       54      a       B:a     N
> S6      B       55      a       B:a     N
> S6      B       56      b       B:b     Y
> S6      B       57      b       B:b     Y
> S6      B       58      b       B:b     N
> S6      B       59      b       B:b     N
> S6      B       60      b       B:b     Y
> S7      B       61      a       B:a     N
> S7      B       62      a       B:a     N
> S7      B       63      a       B:a     Y
> S7      B       64      a       B:a     N
> S7      B       65      a       B:a     N
> S7      B       66      b       B:b     N
> S7      B       67      b       B:b     Y
> S7      B       68      b       B:b     Y
> S7      B       69      b       B:b     Y
> S7      B       70      b       B:b     N
> S8      B       71      a       B:a     N
> S8      B       72      a       B:a     N
> S8      B       73      a       B:a     N
> S8      B       74      a       B:a     N
> S8      B       75      a       B:a     Y
> S8      B       76      b       B:b     Y
> S8      B       77      b       B:b     Y
> S8      B       78      b       B:b     N
> S8      B       79      b       B:b     Y
> S8      B       80      b       B:b     N
> S9      B       81      a       B:a     Y
> S9      B       82      a       B:a     N
> S9      B       83      a       B:a     N
> S9      B       84      a       B:a     N
> S9      B       85      a       B:a     N
> S9      B       86      b       B:b     N
> S9      B       87      b       B:b     N
> S9      B       88      b       B:b     N
> S9      B       89      b       B:b     Y
> S9      B       90      b       B:b     Y
>
> --
> Derek Dunfield, PhD
> Postdoctoral Fellow, MIT Intelligence Initiative
> Sloan School of Management
> MIT Center for Neuroeconomics, Prelec Lab
> 77 Massachusetts Ave E62-585
> Cambridge MA 02139

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