On Sat, Feb 28, 2009 at 9:00 AM, Jeroen Ooms <

[hidden email]> wrote:

> I am making a little GUI for lme4, and I was wondering if there is a function

> that automatically detects on which level every variable exists.

> Furtheremore I got kind of confused about what a random effects model

> actually calculates.

Questions such as this may be answered more quickly if you send them

to the R-SIG-Mixed-Models mailing list, which I am cc:ing on this

reply.

> I have some experience with commercial software packages for multilevel

> analysis, like HLM6, and I was surprised that lme4 does not require the user

> to specify the level for every predictor variable. Is this because the

> function automatically detects the level by testing on which levels the

> predictor has variance, or is this information simply not needed?

In some ways, exposure to software like HLM or MLWin can be more of a

hindrance than a help when learning about mixed models. In

presentation of the model and in the software itself these packages

emphasize "levels" of random effects leading to the impression that we

can only associate random effects with factors that are nested. This

is a misconception. There are many cases where is it eminently

sensible to associate random effects with factors that are completely

crossed ('subject' and 'item' are a prime example) or partially

crossed. The archetypal example used in multilevel modeling,

achievement scores on students nested in classes nested in schools

nested in ..., becomes partially crossed when we track students over

time and they move from class to class or school to school.

I imagine that the reason for defining the model in terms of nested

factors for random effects is computational. If you insist that the

random effects must always be defined with respect to nested factors

then you can employ methods that take advantage of this, with

considerable simplification in the storage and computational burden.

The lme4 package adopts a different approach based on sparse matrix

storage and decomposition methods. It turns out that these methods

are competitive with the best methods for models based on nested

factors, in the cases to which they apply, and these methods allow for

fitting much more general models.

An unfortunate side-effect of the emphasis on levels in MLWin and HLM

is the perception that other covariates must be characterized by the

level at which they vary, even if these covariates only determine

fixed-effects parameters. This is quite untrue and misleading. The

only constraints on the covariates and the model matrix for the

fixed-effects parameters is that the model matrix must be of full

column rank. In models that define random effects for slopes, or in

general for the coefficients associated with a covariate, the

constraint is that the covariate cannot be constant within each level

of the grouping factor of the random effect. For example, we cannot

estimate a random effect for the coefficients for sex (M/F) within

subject (assuming we do not have transgender people in the study).

My advice would be to avoid phrasing the model in terms of levels of

random effects. Although I realize that those with a background of

using MLWin or HLM may find this more comfortable, I think it would be

propagating bad practices and misconceptions.

> I was taught that a crosslevel interaction predicts the regression

> coefficient of the lower level variable, which is also what is implied by

> the HLM gui. However, in an lme4 formula, a crosslevel interaction has the

> same syntax as a regular interaction term. Furthermore, lme4 also allows

> adding crosslevel interactions without a random slope for the lower level

> variable. Now I'm confused. Is there a fundamental difference between a

> crosslevel interaction, or is the same thing as a regular interaction when

> the model also holds an error term for the lower level variable?

>

>

>

>

> -----

> Jeroen Ooms * Dept. of Methodology and Statistics * Utrecht University

>

> Visit

http://www.jeroenooms.com www.jeroenooms.com to explore some of my

> current projects.

>

>

>

>

>

>

> --

> View this message in context:

http://www.nabble.com/lme4-and-Variable-level-detection-tp22262944p22262944.html> Sent from the R help mailing list archive at Nabble.com.

>

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