On 11/05/2016, at 17:39, Paul Debes <paul.debes at utu.fi> wrote:
Dear Jean-Philippe,
There are some papers that deal with the special case that the variance of an experimental design random term becomes negative due to a negative intraclass correlation. In old ANOVA models this could be detected as negative variance (this term will earn head shaking...), whereas in mixed models, where the design term is modeled at the random level, this is often not detectable because the design term variance may just be fixed at zero / converge to zero (if restrained to be positive). As a consequence, it happens that people tend to remove design terms from their models (because a zero variance random term clearly does not improve the model) and make inferences about, let's say treatments, based on observational rather than experimental units (that would only be represented by including the experimental design term) and this can lead to unrepeatable and overconfident inferences.
This problem cannot always be simply accounted for by leaving the random design term with a zero variance in the model. For example asreml-R does not account for zero-variance terms in F-tests (the denominator degrees of freedom inflate to observational level numbers), not sure what happens in lme4 / nlme models.
Here are some references about this very special topic that only covers the issue of zero-variance design terms that may in fact be negative, and how the experimental design can be accounted for at the residual level (with the associated consequences on prediction ability) in alternative to having zero-variance random terms:
Nelder, J. A. 1954. The interpretation of negative components of variance. Biometrika 41:544-548.
Wang, C. S., B. S. Yandell, and J. J. Rutledge. 1992. The dilemma of negative analysis of variance estimators of intraclass correlation. Theoretical and Applied Genetics 85:79-88.
Pryseley, A., C. Tchonlafi, G. Verbeke, and G. Molenberghs. 2011. Estimating negative variance components from Gaussian and non-Gaussian data: A mixed models approach. Computational Statistics & Data Analysis 55:1071-1085.
I hope that is not too special case for your question, but I think it is a very important case for making inferences that account for an experimental design, i.e., when a non-significant random term should be left in the model.
Best,
Paul
On Wed, 11 May 2016 05:52:24 +0300, Jean-Philippe Laurenceau <jlaurenceau at psych.udel.edu> wrote:
Dear Ben et al.--I agree with the general practice of trying to estimate and retain as many random effects as possible (without estimation issues) in a mixed model. However, I was wondering whether anyone had some references recommending or arguing for this approach. I am aware of a paper on this topic with some simulation work by Barr et al. (2013; Journal of Memory and Language), but I would be interested in whether there are others. Thanks, J-P
Jean-Philippe Laurenceau, Ph.D.
Department of Psychological & Brain Sciences
University of Delaware
-----Original Message-----
From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Ben Bolker
Sent: Saturday, May 7, 2016 11:35 AM
To: Carlos Barboza <carlosambarboza at gmail.com>
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Comparing mixed models
My only other comment would be that my standard approach would be to retain all random effects in the model unless they are causing difficulty in model fitting -- this depends on your goal (confirmation/testing, prediction, exploration)
On Sat, May 7, 2016 at 11:26 AM, Carlos Barboza <carlosambarboza at gmail.com>
wrote:
Dear Dr. Ben Bolker
My name is Carlos Barboza and I am a Marine Biologist from the Rio de
Janeiro University, Brazil. First it's a pleasure to again have the
opportunity to send you a message.The reason for it is a simple doubt:
Can I compare AIC from:
1. glmmADMB: Density ~ 1 + 1|Site
2. glmmADMB: Density ~ Sector + 1|Site + Cage
Note that they have different random and fixed structures. I know that
this is not the best choice to model selection but, I think that the
AIC values can be compared.
thank you very much for your attention
is Cage a random effect? Are you intentionally leaving out the
intercept in the second case (it will be included anyway unless you
use -1)? In any case, I don't see any obvious reason you can't
compare AIC values; see
https://rawgit.com/bbolker/mixedmodels-misc/master/glmmFAQ.html#can-i-
use-aic-for-mixed-models-how-do-i-count-the-number-of-degrees-of-freed
om-for-a-random-effect
Follow-ups to r-sig-mixed-models at r-project.org, please ...
sorry, yes, cage was included only to examplify a different random
structure in the second case...it should be coded (1|Site) + (1|Cage)
yes, I know that the intercept will be included in the second model
it's an example of comparing AIC values from mixed models with
different fixed and random structures:
1. Density ~ 1 + 1|Site
2. Density ~ Sector + 1|Site + 1|Cage
comparing AIC...I beleive that both values can be compared
again, thank you very much for your very fast message
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