mixed effects models and pseudo replication
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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