R help - Aug 2009 - lmer with random slopes for 2 or more first-level factors?

I have data from a design in which items are completely nested within  
subjects.  Subject is the only second-level factor, but I have  
multiple first-level factors (IVs).  Say there are 2 such independent  
variables that I am interested in.  What is the proper syntax to fit a  
mixed-effects model with a by-subject random intercept, and by-subject  
random slopes for both the 2 IVs?

I can think of at least two possibilities:

lmer(DV ~ IV1 + IV2 + (1 + IV1 + IV2 | Subject))

lmer(DV ~ IV1 + IV2 + (1 + IV1 | Subject) + (1 + IV2 | Subject))

Or maybe there is some other way to do it?  Maybe the correct syntax  
depends on whether the random effect of subjects on the intercept and  
slopes are correlated or not?  (If so, how do I proceed?)

Finally, what would be the syntax if I wanted to include a random  
subject effect for the INTERACTION of IV1 and IV2?

Thanks very much,
~jason

PS: additional search terms: multi-level linear model, MLM,  
hierarchical, repeated measures

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Jason R. Finley
Department of Psychology
University of Illinois, Urbana-Champaign
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Dear Jason,

Both models have a correct syntax. Although I would write the last model
rather as lmer(DV ~ IV1 + IV2 + (1|Subject) + (IV1 - 1| Subject) + (IV2
- 1| Subject))

The only difference is indeed the correlation between the random
effects. The random effects in the model I wrote are all independent
(not correlated). In your first model all random effects are correlated.
In your second model the first random intercept is correlated with the
random slope of IV1. The second random intercept with the random slope
of IV2.

Depending on if you want your interaction to be indepentend or not your
can use either

lmer(DV ~ IV1 + IV2 + (IV1 * IV2 | Subject))
lmer(DV ~ IV1 + IV2 + (1 | Subject) + (IV1 -1 | Subject) + (IV2 - 1|
Subject) + (IV1:IV2 - 1| Subject))


Note that IV1 * IV2 is equivalent to 1 + IV1 + IV2 + IV1:IV2

HTH,

Thierry

PS R-Sig-mixed-models is a better list for this kind of questions. 


------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature
and Forest
Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
methodology and quality assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium
tel. + 32 54/436 185
Thierry.Onkelinx at inbo.be
www.inbo.be

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to
say what the experiment died of.
~ Sir Ronald Aylmer Fisher

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of
data.
~ John Tukey

-----Oorspronkelijk bericht-----
Van: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
Namens Jason R. Finley
Verzonden: woensdag 19 augustus 2009 3:47
Aan: r-help at r-project.org
Onderwerp: [R] lmer with random slopes for 2 or more first-level
factors?

I have data from a design in which items are completely nested within
subjects.  Subject is the only second-level factor, but I have multiple
first-level factors (IVs).  Say there are 2 such independent variables
that I am interested in.  What is the proper syntax to fit a
mixed-effects model with a by-subject random intercept, and by-subject
random slopes for both the 2 IVs?

I can think of at least two possibilities:

lmer(DV ~ IV1 + IV2 + (1 + IV1 + IV2 | Subject))

lmer(DV ~ IV1 + IV2 + (1 + IV1 | Subject) + (1 + IV2 | Subject))

Or maybe there is some other way to do it?  Maybe the correct syntax
depends on whether the random effect of subjects on the intercept and
slopes are correlated or not?  (If so, how do I proceed?)

Finally, what would be the syntax if I wanted to include a random
subject effect for the INTERACTION of IV1 and IV2?

Thanks very much,
~jason

PS: additional search terms: multi-level linear model, MLM,
hierarchical, repeated measures

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Jason R. Finley
Department of Psychology
University of Illinois, Urbana-Champaign
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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Since nobody has answered yet, let me try.  I'm not 100% sure.  (So
why bother?  To check my own understanding.)

On 08/18/09 20:47, Jason R. Finley wrote:
> I have data from a design in which items are completely nested within  
> subjects.  Subject is the only second-level factor, but I have  
> multiple first-level factors (IVs).  Say there are 2 such independent  
> variables that I am interested in.  What is the proper syntax to fit a  
> mixed-effects model with a by-subject random intercept, and by-subject  
> random slopes for both the 2 IVs?
> 
> I can think of at least two possibilities:
> 
> lmer(DV ~ IV1 + IV2 + (1 + IV1 + IV2 | Subject))
> 
> lmer(DV ~ IV1 + IV2 + (1 + IV1 | Subject) + (1 + IV2 | Subject))
> 
> Or maybe there is some other way to do it?  Maybe the correct syntax  
> depends on whether the random effect of subjects on the intercept and  
> slopes are correlated or not?  (If so, how do I proceed?)
I think that the first way assumes correlations of IV1, IV2, and the
Subject intercept.  The second way assumes that each of IV1 and IV2 is
correlated with the Subject intercept, and the intercept is computed
separately for IV1 and IV2.

There are other ways.  You can do, for example, 

lmer(DV ~ IV1 + IV2 + (1 | Subject) + (1 | Subject)) + 
                (0 + IV1 | Subject) + (0 + IV2| Subject))

This assumes, I think, that intercepts and slopes are uncorrelated.
If you can tolerate that assumption, an advantage of doing it this way
is that you can use mcmc sampling, and thus you can use pvals.fnc() in
the languageR package.  (What I do not know are the consequences of
making this assumption if it is false.)
> Finally, what would be the syntax if I wanted to include a random  
> subject effect for the INTERACTION of IV1 and IV2?
lmer(DV ~ IV1 + IV2 + (1 + IV1 * IV2 | Subject))

-- 
Jonathan Baron, Professor of Psychology, University of Pennsylvania
Home page: http://www.sas.upenn.edu/~baron