[R-sig-ME] Varying slopes in a multilevel model with a between subjects treatment

[Derek Dunfield]

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