[R-sig-ME] LME4: output interpretation of tricky model

[ONKELINX, Thierry]

Dear Eiko,

Try to write out the model by hand. E.g. if you want a prediction for Y_index = 1, time = 1, x1 = 2 and x2 = 4, which coefficient would you use? And what is the values for Y_index, time, x1 and x2 change (look especially at time = 0, x1 =  and x2 = 0)?

If the interpretation of the coefficients is important, then I would model it as

Y ~ -1 + time + Y_index:x1 + Y_index:x2 + ( - 1 + Y_index | subject)

Which gives the same model fit but with a different parametrisation.

Best regards,

Thierry

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium
+ 32 2 525 02 51
+ 32 54 43 61 85
Thierry.Onkelinx op inbo.be
www.inbo.be

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~ Sir Ronald Aylmer Fisher

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-----Oorspronkelijk bericht-----
Van: r-sig-mixed-models-bounces op r-project.org [mailto:r-sig-mixed-models-bounces op r-project.org] Namens Eiko Fried
Verzonden: zondag 20 mei 2012 13:53
Aan: r-sig-mixed-models op r-project.org
Onderwerp: [R-sig-ME] LME4: output interpretation of tricky model

Dear Mailinglist,

I would be very glad to get some assistance with interpreting a tricky model output in LME4.

The model is this:

Y ~ -1 + Y_index + time + Y_index*x1 + Y_index*x2 + ( - 1 + Y_index |
subject)

What I am doing with this is modeling 9 items of a questionnaire as a multivariate response variable Y.
Y_index is a categorical variable defining the number of item of the questionnaire (1 through 9), and I am checking with interaction effects on
x1 and x2 whether these covariates have differential effects on my multivariate response. It is a longitudinal design with 5 measurement points, and I expect that x1 only affects some of my 9 items (the same for x2).

The dataset is in long-long format (Y_index * time), so each subject has
9*5 lines.
(I found the suggestion for that kind of analysis in Hox, 2010).

The for me relevant part of the output looks like this:

Fixed effects:
                              Estimate    Std. Error    t value
Y_index1                 0.3161592  0.0780922   4.049
Y_index2                 0.4685218  0.0775360   6.043
Y_index3                 0.9531528  0.0969119   9.835
Y_index4                 0.2366093  0.0898923   2.632
Y_index5                 0.3055025  0.0955639   3.197
Y_index6                 0.2581729  0.0819606   3.150
Y_index7                 0.4556287  0.0817002   5.577
Y_index8                 0.6027990  0.0691566   8.716
Y_index9                 0.8697155  0.0620898  14.007
time                        0.5726978  0.0374384  15.297
x1                           0.0196260  0.0020225   9.704
x2                          -0.0415874  0.0350631  -1.186
Y_index2:x1            0.0023080  0.0018770   1.230
Y_index3:x1           -0.0019870  0.0027166  -0.731
Y_index4:x1           -0.0006285  0.0023784  -0.264
Y_index5:x1            0.0033737  0.0026178   1.289
Y_index6:x1            0.0067164  0.0020428   3.288
Y_index7:x1           -0.0016510  0.0021435  -0.770
Y_index8:x1           -0.0080817  0.0020414  -3.959
Y_index9:x1           -0.0140743  0.0021874  -6.434
Y_index2:x2            0.0358944  0.0325015   1.104
Y_index3:x2           -0.0675878  0.0470604  -1.436
Y_index4:x2            0.0037518  0.0411980   0.091
Y_index5:x2           -0.0456199  0.0453805  -1.005
Y_index6:x2            0.0333067  0.0353716   0.942
Y_index7:x2            0.0443440  0.0371040   1.195
Y_index8:x2            0.0595453  0.0353532   1.684
Y_index9:x2            0.0223958  0.0379038   0.591

What I don't understand is
(1) why Y_index1 is missing in my interaction output with x1 and x2 (the lists start with Y_index2), and
(2) what the interaction lines exactly mean. Is it a comparison to a baseline? Is it difference from the main effect?

I do apologize in case this is a very simple question, but I cannot get my head around it.

Thank you
--E

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