[R-sig-ME] mixed effects models and pseudo replication
Kvingedal, Eli
Eli.Kvingedal at nina.no
Thu Mar 11 12:15:41 CET 2010
Dear Thierry,
Here are the summary tables for the alternative models:
> M1 <- lme(weight ~ age*density0 + age*density1, random=~1|station, weights=varComb(varIdent(form=~1|age), varPower(form=~density0|age)), method="ML")
> summary(M1)
Linear mixed-effects model fit by maximum likelihood
Data: NULL
AIC BIC logLik
3061.287 3111.566 -1519.643
Random effects:
Formula: ~1 | station
(Intercept) Residual
StdDev: 0.2394472 0.3304975
Combination of variance functions:
Structure: Different standard deviations per stratum
Formula: ~1 | age
Parameter estimates:
0 1
1.00000 18.32243
Structure: Power of variance covariate, different strata
Formula: ~density0 | age
Parameter estimates:
0 1
0.12277823 -0.01863642
Fixed effects: weight ~ age * density0 + age * density1
Value Std.Error DF t-value p-value
(Intercept) 2.548689 0.1280585 694 19.902539 0.0000
age1 12.094327 0.5960983 694 20.289150 0.0000
density0 -0.002892 0.0007015 14 -4.122892 0.0010
density1 0.002138 0.0058263 14 0.366970 0.7191
age1:density0 -0.009194 0.0029657 694 -3.100081 0.0020
age1:density1 0.053147 0.0252106 694 2.108131 0.0354
Correlation:
(Intr) age1 dnsty0 dnsty1 ag1:d0
age1 -0.054
density0 0.065 -0.006
density1 -0.697 0.042 -0.639
age1:density0 -0.005 0.212 -0.056 0.035
age1:density1 0.044 -0.743 0.035 -0.060 -0.722
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.4011664 -0.6931402 -0.1359044 0.6256529 3.6626548
Number of Observations: 714
Number of Groups: 17
> summary(M2)
Linear mixed-effects model fit by maximum likelihood
Data: NULL
AIC BIC logLik
3063.287 3118.137 -1519.643
Random effects:
Formula: ~1 | station
(Intercept)
StdDev: 0.2394471
Formula: ~1 | age %in% station
(Intercept) Residual
StdDev: 9.335646e-05 0.3304975
Combination of variance functions:
Structure: Different standard deviations per stratum
Formula: ~1 | age
Parameter estimates:
0 1
1.00000 18.32243
Structure: Power of variance covariate, different strata
Formula: ~density.trout0 | age
Parameter estimates:
0 1
0.12277827 -0.01863644
Fixed effects: weight ~ age * density0 + age * density1
Value Std.Error DF t-value p-value
(Intercept) 2.548689 0.1280584 680 19.902548 0.0000
age1 12.094327 0.5960982 14 20.289153 0.0000
density0 -0.002892 0.0007015 14 -4.122894 0.0010
density1 0.002138 0.0058263 14 0.366970 0.7191
age1:density0 -0.009194 0.0029657 14 -3.100082 0.0078
age1:density1 0.053147 0.0252106 14 2.108131 0.0535
Correlation:
(Intr) age1 dnsty0 dnsty1 ag1:d0
age1 -0.054
density0 0.065 -0.006
density1 -0.697 0.042 -0.639
age1:density0 -0.005 0.212 -0.056 0.035
age1:density1 0.044 -0.743 0.035 -0.060 -0.722
Standardized Within-Group Residuals:
Min Q1 Med Q3 Max
-2.4011661 -0.6931402 -0.1359044 0.6256530 3.6626539
Number of Observations: 714
Number of Groups:
station age %in% station
17 34
Thank you for considering my case!
Eli
-----Original Message-----
From: ONKELINX, Thierry [mailto:Thierry.ONKELINX at inbo.be]
Sent: 11. mars 2010 11:04
To: Kvingedal, Eli; r-sig-mixed-models at r-project.org
Subject: RE: [R-sig-ME] mixed effects models and pseudo replication
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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