[R-sig-ME] assessing fixed factor significance depending on reference levels ?

[Claudia Monica Campos]

Dear list,

I'm trying to fit a GLMM to assess whether some category of species
(native, mammal, bird, etc.)
from the total named by each student can be explained by differences
in the place of residence
(urban or rural), gender and/or age.

m1= lmer(cbind (n_a_bird,n_animals-n_a_bird) ~ sex*place+age+ (1 |
school/grade), data=a,family=binomial)
  where:
    sex has two levels ('f' and 'm')
    place has two levels ('r' and 'u')
    age is numerical (from 7 to 18)

As you can see from below, a$place fixed effect could be an
explanatory variable,
but it may be significant (its p-value) depending on a$sex ref level:

a$sex<-relevel(a$sex,'f');a$place<-relevel(a$place,'r')
m1_fr= lmer(cbind (n_a_bird,n_animals-n_a_bird) ~ place*sex+age+ (1 |
school/grade), data=a,family=binomial)
a$sex<-relevel(a$sex,'m');a$place<-relevel(a$place,'r')
m1_mr= lmer(cbind (n_a_bird,n_animals-n_a_bird) ~ place*sex+age+ (1 |
school/grade), data=a,family=binomial)

summary(m1_fr) ### ref levels: sex:'f' , place:'r'
  Generalized linear mixed model fit by the Laplace approximation
  Formula: cbind(n_a_bird, n_animals - n_a_bird) ~ place * sex + age +
(1 |      school/grade)
     Data: a
    AIC  BIC logLik deviance
   2125 2163  -1055     2111
  Random effects:
   Groups       Name        Variance   Std.Dev.
   grade:school (Intercept) 1.4745e-13 3.8399e-07
   school       (Intercept) 1.6971e-02 1.3027e-01
  Number of obs: 1746, groups: grade:school, 51; school, 42

  Fixed effects:
              Estimate Std. Error z value Pr(>|z|)
  (Intercept) -1.87093    0.15225 -12.289  < 2e-16 ***
  placeu       0.03351    0.07922   0.423 0.672331       <================
  sexm         0.16097    0.07476   2.153 0.031299 *
  age          0.02716    0.01099   2.472 0.013437 *
  placeu:sexm -0.32108    0.09478  -3.388 0.000705 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

  Correlation of Fixed Effects:
              (Intr) placeu sexm   age
  placeu      -0.518
  sexm        -0.253  0.443
  age         -0.918  0.237  0.028
  placeu:sexm  0.160 -0.537 -0.788  0.021

summary(m1_mr) ### ref levels: sex:'m', place: 'r'
  Generalized linear mixed model fit by the Laplace approximation
  Formula: cbind(n_a_bird, n_animals - n_a_bird) ~ place * sex + age +
(1 |      school/grade)
     Data: a
    AIC  BIC logLik deviance
   2125 2163  -1055     2111
  Random effects:
   Groups       Name        Variance   Std.Dev.
   grade:school (Intercept) 3.5201e-13 5.9330e-07
   school       (Intercept) 1.6971e-02 1.3027e-01
  Number of obs: 1746, groups: grade:school, 51; school, 42

  Fixed effects:
              Estimate Std. Error z value Pr(>|z|)
  (Intercept) -1.70995    0.15171 -11.271  < 2e-16 ***
  placeu      -0.28754    0.08484  -3.389 0.000701 ***   <================
  sexf        -0.16097    0.07476  -2.153 0.031298 *
  age          0.02716    0.01099   2.472 0.013438 *
  placeu:sexf  0.32102    0.09478   3.387 0.000706 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

  Correlation of Fixed Effects:
              (Intr) placeu sexf   age
  placeu      -0.536
  sexf        -0.239  0.467
  age         -0.908  0.245 -0.028
  placeu:sexf  0.228 -0.616 -0.788 -0.021

Doing a LRT, by removing a$place seems to show it's indeed significant:
> m0=lmer(cbind (n_a_bird,n_animals-n_a_bird) ~ sex+age+ (1 | school/grade), data=a,family=binomial, REML=F)
> m1= lmer(cbind (n_a_bird,n_animals-n_a_bird) ~ place*sex+age+ (1 | school/grade), data=a,family=binomial, REML=F)
> anova(m0,m1)
Data: a
Models:
m0: cbind(n_a_bird, n_animals - n_a_bird) ~ sex + age + (1 | school/grade)
m1: cbind(n_a_bird, n_animals - n_a_bird) ~ place * sex + age + (1 |
m1:     school/grade)
   Df    AIC    BIC  logLik  Chisq Chi Df Pr(>Chisq)
m0  5 2134.7 2162.0 -1062.3
m1  7 2124.8 2163.1 -1055.4 13.808      2   0.001004 **
---

How should I proceed with the model selection ?

To properly understand if a$place alone or its interaction with a$sex
is significant,
do I need to fit the model with different relevel-ing (in a
combinatorial way ) ?
Ie: if you see above "placeu", you'll find that shows significant for sex='m' as
reference but not for sex='f'.

Thanks a lot in advance!

Regards,

--Claudia

Claudia M. Campos
IADIZA- CONICET
CC 507 Mendoza (5500) Argentina
Correo electrónico: claudia.monica.campos at gmail.com
ccampos at lab.cricyt.edu.ar
http://www.cricyt.edu.ar/personal/ccampos