Dear R users,
I am using lmer combined with AIC model selection and averaging (in the
MuMIn package) to try and assess how isotope values (which indicate diet)
vary within a population of animals.
I have multiple measures from individuals (variable 'Tattoo') and multiple
individuals within social groups within 4 locations (A, B, C ,D) crucially I
am interested if there are differences between sexes and age classes
(variable AGECAT2) and whether this differs with location.
However, whether or not I get a significant sex:location interaction depends
on which location is my reference level and I cannot understand why this is
the case. It seems to be due to the fact that the standard error associated
with my interactions varies depending on which level is the reference.
Any help or advice would be appreciated,
Andrew Robertson
Below is the example code of what I am doing and an example of the model
summary and model averaging results with location A as the ref level or
location B.
if A is the reference level...
#full model
Amodel<-lmer(d15N~(AGECAT2+Sex+Location1+AGECAT2:Location1+Sex:Location1+AGE
CAT2:Sex+(1|Year)+(1|Location1/Socialgroup/Tattoo)), REML=FALSE,
data=nocubs)
#standardise model
Amodels<-standardize(Amodel, standardize.y=FALSE)
#dredge models
summary(model.avg(get.models(Adredge,cumsum(weight)<0.95)))
Then the average model coefficients indicate no sex by location interaction
Component models:
df logLik AICc Delta Weight
235 13 -765.33 1557.28 0.00 0.68
1235 15 -764.55 1559.91 2.63 0.18
3 9 -771.64 1561.57 4.29 0.08
12345 17 -763.67 1562.37 5.09 0.05
Term codes:
AGECAT2 c.Sex Location1 AGECAT2:c.Sex
c.Sex:Location1
1 2 3 4
5
Model-averaged coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 8.673592 0.474524 18.279 <2e-16 ***
c.Sex 0.095375 0.452065 0.211 0.833
Location1B -3.972882 0.556575 7.138 <2e-16 ***
Location1C -3.633331 0.531858 6.831 <2e-16 ***
Location1D -3.348665 0.539143 6.211 <2e-16 ***
c.Sex:Location1B -0.372653 0.513492 0.726 0.468
c.Sex:Location1C 0.428299 0.511254 0.838 0.402
c.Sex:Location1D -0.757582 0.512586 1.478 0.139
AGECAT2OLD -0.179772 0.150842 1.192 0.233
AGECAT2YEARLING -0.009596 0.132328 0.073 0.942
AGECAT2OLD:c.Sex 0.045963 0.296471 0.155 0.877
AGECAT2YEARLING:c.Sex -0.323985 0.268919 1.205 0.228
---
And the full model summary looks like this..
Linear mixed model fit by maximum likelihood
Formula: d15N ~ (AGECAT2 + Sex + Location1 + AGECAT2:Location1 +
Sex:Location1 + AGECAT2:Sex + (1 | Year) + (1 |
Location1/Socialgroup/Tattoo))
Data: nocubs
AIC BIC logLik deviance REMLdev
1568 1670 -761.1 1522 1534
Random effects:
Groups Name Variance Std.Dev.
Tattoo:(Socialgroup:Location1) (Intercept) 0.35500 0.59582
Socialgroup:Location1 (Intercept) 0.35620 0.59682
Location1 (Intercept) 0.00000 0.00000
Year (Intercept) 0.00000 0.00000
Residual 0.49584 0.70416
Number of obs: 608, groups: Tattoo:(Socialgroup:Location1), 132;
Socialgroup:Location1, 22; Location1, 4; Year, 2
Fixed effects:
Estimate Std. Error t value
(Intercept) 8.83179 0.52961 16.676
AGECAT2OLD -0.44101 0.41081 -1.074
AGECAT2YEARLING 0.01805 0.38698 0.047
SexMale -0.11346 0.51239 -0.221
Location1B -3.97880 0.63063 -6.309
Location1C -4.04816 0.60404 -6.702
Location1D -3.36389 0.63304 -5.314
AGECAT2OLD:Location1B 0.44198 0.54751 0.807
AGECAT2YEARLING:Location1B -0.22134 0.52784 -0.419
AGECAT2OLD:Location1C 0.20684 0.50157 0.412
AGECAT2YEARLING:Location1C 0.24132 0.47770 0.505
AGECAT2OLD:Location1D 0.53653 0.52778 1.017
AGECAT2YEARLING:Location1D 0.51755 0.51038 1.014
SexMale:Location1B -0.02442 0.57546 -0.042
SexMale:Location1C 0.74680 0.58128 1.285
SexMale:Location1D -0.41800 0.59505 -0.702
AGECAT2OLD:SexMale -0.08907 0.32513 -0.274
AGECAT2YEARLING:SexMale -0.40146 0.30409 -1.320
If location B is the reference level then the average model coefficients
indicate an age by sex interaction in location C.
Component models:
df logLik AICc Delta Weight
235 13 -765.33 1557.28 0.00 0.68
1235 15 -764.55 1559.91 2.63 0.18
3 9 -771.64 1561.57 4.29 0.08
12345 17 -763.67 1562.37 5.09 0.05
Term codes:
AGECAT2 c.Sex Location2 AGECAT2:c.Sex
c.Sex:Location2
1 2 3 4
5
Model-averaged coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 4.700710 0.294275 15.974 <2e-16 ***
c.Sex -0.277278 0.248093 1.118 0.2637
Location2A 3.972882 0.556575 7.138 <2e-16 ***
Location2C 0.339551 0.379873 0.894 0.3714
Location2D 0.624217 0.390063 1.600 0.1095
c.Sex:Location2A 0.372653 0.513492 0.726 0.4680
c.Sex:Location2C 0.800952 0.345898 2.316 0.0206 *
c.Sex:Location2D -0.384929 0.346832 1.110 0.2671
AGECAT2OLD -0.179772 0.150842 1.192 0.2333
AGECAT2YEARLING -0.009596 0.132328 0.073 0.9422
AGECAT2OLD:c.Sex 0.045963 0.296471 0.155 0.8768
AGECAT2YEARLING:c.Sex -0.323985 0.268919 1.205 0.2283
And the full model summary looks like this..
---
Linear mixed model fit by maximum likelihood
Formula: d15N ~ (AGECAT2 + Sex + Location2 + AGECAT2:Location2 +
Sex:Location2 + AGECAT2:Sex + (1 | Year) + (1 |
Location2/Socialgroup/Tattoo))
Data: nocubs
AIC BIC logLik deviance REMLdev
1568 1670 -761.1 1522 1534
Random effects:
Groups Name Variance Std.Dev.
Tattoo:(Socialgroup:Location2) (Intercept) 0.35500 0.59582
Socialgroup:Location2 (Intercept) 0.35618 0.59681
Location2 (Intercept) 0.00000 0.00000
Year (Intercept) 0.00000 0.00000
Residual 0.49584 0.70416
Number of obs: 608, groups: Tattoo:(Socialgroup:Location2), 132;
Socialgroup:Location2, 22; Location2, 4; Year, 2
Fixed effects:
Estimate Std. Error t value
(Intercept) 4.852982 0.342364 14.175
AGECAT2OLD 0.000986 0.361951 0.003
AGECAT2YEARLING -0.203275 0.358971 -0.566
SexMale -0.137881 0.261931 -0.526
Location2A 3.978806 0.630652 6.309
Location2C -0.069353 0.444658 -0.156
Location2D 0.614917 0.479262 1.283
AGECAT2OLD:Location2A -0.441995 0.547521 -0.807
AGECAT2YEARLING:Location2A 0.221330 0.527840 0.419
AGECAT2OLD:Location2C -0.235146 0.434839 -0.541
AGECAT2YEARLING:Location2C 0.462657 0.357815 1.293
AGECAT2OLD:Location2D 0.094536 0.442264 0.214
AGECAT2YEARLING:Location2D 0.738882 0.375638 1.967
SexMale:Location2A 0.024425 0.575468 0.042
SexMale:Location2C 0.771228 0.351708 2.193
SexMale:Location2D -0.393576 0.364486 -1.080
AGECAT2OLD:SexMale -0.089071 0.325140 -0.274
AGECAT2YEARLING:SexMale -0.401467 0.304098 -1.320
The results are also different if location C or D are the reference levels
Andrew Robertson
PhD student
Centre for Ecology and Conservation
University of Exeter, Cornwall Campus
Tremough, Cornwall. TR10 9EZ
UK
Tel: 01326 371852
Email: <mailto:ar...@exeter.ac.uk> ar...@exeter.ac.uk
Web page:
<http://biosciences.exeter.ac.uk/staff/postgradresearch/andrewrobertson/>
http://biosciences.exeter.ac.uk/staff/postgradresearch/andrewrobertson/
LinkedIn: <http://uk.linkedin.com/pub/andrew-robertson/39/91a/504>
http://uk.linkedin.com/pub/andrew-robertson/39/91a/504
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