[R-sig-ME] Comparing mixed models

Wed May 11 08:49:41 CEST 2016

I have argued for allowing negative random effect estimates to be 
output, as was and I expect still is the case for Genstat mixed model 
fits.  What does asreml-R do? The negative value is needed so that 
the variance-covariance matrix, which does have to be positive definite 
(or at least semi-definite) is correctly estimated.  

The negative value, if more negative than can be ascribed to chance, is
a useful warning device.  Someone at Rothamsted told me about getting
data where blocks had been chosen in which treatment plots moved
successively further away from the stream.  The additional systematic
within block variance thereby induced called for a negative between 
blocks random effect so that the variance-covariance matrix would come 
out ‘right’.  Maybe Nelder’s paper mentions this specific type of effect?

John Maindonald             email: john.maindonald at anu.edu.au

> 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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>> 
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> 
> 
> -- 
> Paul V. Debes
> DFG Research Fellow
> 
> Division of Genetics and Physiology
> Department of Biology
> University of Turku
> PharmaCity, 7th floor
> Itainen Pitkakatu 4
> 20014 Finland
> 
> Email: paul.debes at utu.fi
> 
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