[R-sig-ME] mixed effects models and pseudo replication

[ONKELINX, Thierry]

Dear Eli,

I find it strange that the summary tables of the models yield different
df for the fixed effects. Can you provide us with those summaries?

HTH,

Thierry

------------------------------------------------------------------------
----
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek
team Biometrie & Kwaliteitszorg
Gaverstraat 4
9500 Geraardsbergen
Belgium

Research Institute for Nature and Forest
team Biometrics & 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-sig-mixed-models-bounces at r-project.org 
> [mailto:r-sig-mixed-models-bounces at r-project.org] Namens 
> Kvingedal, Eli
> Verzonden: woensdag 10 maart 2010 15:08
> Aan: r-sig-mixed-models at r-project.org
> Onderwerp: [R-sig-ME] mixed effects models and pseudo replication
> 
> Hi, 
> 
> I am analysing effects of local population density on fish 
> performance (e.g. weight). My dataset is based on fish 
> sampled from different sites (17 stations) and in addition to 
> measures on individual performance, I have information on age 
> (0 and 1). On site level, I have information on fish 
> densities for both age groups. I am interesting in estimating 
> the effects of fish density on performance and particularly 
> interested in determining possible differences between age 
> groups in the density response. 
> 
> Traditionally, these kind of data are analysed based on mean 
> values (ancovas). However, based on mixed effects model, the 
> among individual variance will be included in the analysis 
> and not just averaged out. I started by using lmer (lme4 
> package), but realizing that the variance is increasing with 
> density, I switched to lme (nlme package) and applied
> variance structures. 
> 
> My starting model is thus: 
> 
> m1 <- lme(weight ~ age*density0 + age*density1, random = 
> ~1|station, weights=....) 
> 
> with station and age as factors.  
> 
> Now, my issue is pseudo-replication. The summary table shows 
> that the factors age and age*density have very high degrees 
> of freedom (~700) and accordingly low p-values. It seems to 
> me like age and the interactions between age and density are 
> analysed as if the samples were independent, and if so, it 
> means pseudo-replication, doesn't it? 
> 
> If I set up an alternative random structure allowing for 
> random variance between age classes within station: 
> m2 <- lme(weight ~ age*density0 + age*density1, random = 
> ~1|station/age, weights=....) 
> 
> the summary table is more like I think it should be: 14 df 
> for all fixed effects parameters and interactions, and the 
> p-values seem more realistic.  
> 
> When comparing m1 and m2 (REML estimation), however, m2 do 
> not provide better fit, and based on literature (e.g. Zuur et 
> al. 2009), then I should use m1. 
> 
> Testing the significance of the interaction terms by model 
> comparisons (which is what I do to find the optimal model), 
> the significance levels of the likelihood ratio test for 
> specific interaction terms are equivalent whether I use
> station or station/age as random factors. Which is sort of 
> comforting. 
> 
> So, my question is, do I really control for 
> pseudo-replication in the estimation of all fixed effects and 
> interactions when using m1? If so, why these high dfs in the 
> summary table?? 
> 
> I would really appreciate if someone could enlighten me! 
> 
> Regards, 
> 
> Eli 
> 
> 
> ________________________________________________________________
> 
> Eli Kvingedal
> PhD Student
> 
> Norwegian Institute for Nature Research - NINA Postal
> address: NO-7485 Trondheim, NORWAY Delivery/Visiting address: 
> Tungasletta 2, NO-7047 Trondheim, NORWAY
> Phone: +47 73 80 14 00 * Fax: +47 73 80 14 01 * www.nina.no
> 
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list 
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> 

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