[R-sig-ME] LME4: interpretation of multivariate interaction effect

[Eiko Fried]

Dear Mailing List,

My model is this:
> m1<-lmer( Y ~ -1 + as.factor(Y_index) * X + (-1+as.factor(Y_Index)|subject), data=data2, REML=FALSE)

I have 9 response variables (items from a screening instrument), and
reorganized the data to have them in one row ("Y"). The variable
"Y_index" denominates the 9 different variables for Y (e.g. Y_index=2
is my second response variable).
The data are in a long format, every subjects has 9 lines.

I have a hard time interpreting the interaction output.

Fixed effects:
                                 Estimate  Std. Error  t value
as.factor(Y_index)1      0.46177    0.05965   7.742
as.factor(Y_index)2      0.40207    0.05908   6.806
as.factor(Y_index)3      0.44255    0.07527   5.879
as.factor(Y_index)4      0.92783    0.07236  12.822
as.factor(Y_index)5      0.55113    0.07881   6.993
as.factor(Y_index)6      0.31863    0.06442   4.946
as.factor(Y_index)7      0.28208    0.06152   4.585
as.factor(Y_index)8      0.17036    0.04734   3.598
as.factor(Y_index)9      0.10635    0.03836   2.772
X                                0.02473    0.03732   0.663
as.factor(Y_index)2:X   0.04296    0.03197   1.344
as.factor(Y_index)3:X   0.16419    0.04482   3.664
as.factor(Y_index)4:X   0.10612    0.04076   2.604
as.factor(Y_index)5:X   0.09108    0.04480   2.033
as.factor(Y_index)6:X   0.06488    0.03307   1.962
as.factor(Y_index)7:X   0.03331    0.03633   0.917
as.factor(Y_index)8:X  -0.01012    0.03591  -0.282
as.factor(Y_index)9:X  -0.05029    0.03893  -1.292


Do I understand correctly that "X" here is (Y_index)1:X, and the
reference line for the interpretation of the other interaction lines?
E.g. (Y_index)5, my 5th response variable, is [Estimate] .09 higher
than (Y_index)1, my first response variable, and with a t of 2.033
probably significantly higher? That is, X affects my fifth response
variable significantly stronger than my first response variable?

Thank you for your patience
E