[R-sig-ME] LRT significant but new variable's beta not

[Clara Neudecker]

Dear all,

I'm looking for some hints on how to interprete my results. I have a
logistic mixed effects model in which I include a single new variable.
Comparing the old and new model with a likelihood ratio test yields a
significant difference (p < .001), but when I look at the new variable's
beta it's not significant at all.

How do I interprete this? After thinking and googling I have only one
suspicion left: Is it possible that including the new variable makes the
other variables more informative because there is some kind of supressor
effect in the data? Or is there another explanation?

(The phenomenon cannot be a coincidence; the same happens with other
variables as well.)

I attach some output in case it helps.

Best regards and thanks in advance,
Clara Neudecker 



My model without the new variable:

> summary(fm501)
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: umzug50000 ~ 1 + gebjahr_c + sex + (1 | zp12401) + (1 | ror96)
   Data: master_5

     AIC      BIC   logLik deviance df.resid 
  1077.9   1110.7   -534.0   1067.9     5167 

Scaled residuals: 
   Min     1Q Median     3Q    Max 
-0.547 -0.169 -0.102 -0.065 35.188 

Random effects:
 Groups  Name        Variance Std.Dev.
 ror96   (Intercept) 0.23757  0.4874  
 zp12401 (Intercept) 0.01509  0.1229  
Number of obs: 5172, groups:  ror96, 96; zp12401, 7

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept) -4.433991   0.001499 -2957.3   <2e-16 ***
gebjahr_c    0.075061   0.001449    51.8   <2e-16 ***
sex.L        0.113758   0.001498    75.9   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
          (Intr) gbjhr_
gebjahr_c -0.001       
sex.L      0.000  0.000




With the new variable pol_fit_ror:

> summary(fm510)
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) ['glmerMod']
 Family: binomial  ( logit )
Formula: umzug50000 ~ 1 + gebjahr_c + sex + pol_fit_ror + (1 | zp12401)
+      (1 | ror96)
   Data: master_5

     AIC      BIC   logLik deviance df.resid 
  1027.6   1066.5   -507.8   1015.6     4857 

Scaled residuals: 
   Min     1Q Median     3Q    Max 
-0.564 -0.171 -0.104 -0.066 33.626 

Random effects:
 Groups  Name        Variance  Std.Dev.
 ror96   (Intercept) 0.2125987 0.46108 
 zp12401 (Intercept) 0.0008857 0.02976 
Number of obs: 4863, groups:  ror96, 88; zp12401, 7

Fixed effects:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept) -4.086460   0.351692 -11.619   <2e-16 ***
gebjahr_c    0.074675   0.006972  10.711   <2e-16 ***
sex.L        0.158924   0.132901   1.196    0.232    
pol_fit_ror -0.256504   0.288639  -0.889    0.374    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) gbjhr_ sex.L 
gebjahr_c   -0.293              
sex.L        0.084 -0.152       
pol_fit_ror -0.872 -0.030 -0.010

LRT of the two models:

> anova(fm501, fm510)
Data: master_5
Models:
fm501: umzug50000 ~ 1 + gebjahr_c + sex + (1 | zp12401) + (1 | ror96)
fm510: umzug50000 ~ 1 + gebjahr_c + sex + pol_fit_ror + (1 | zp12401) + 
fm510:     (1 | ror96)
      Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)    
fm501  5 1077.9 1110.7 -533.96   1067.9                             
fm510  6 1027.5 1066.5 -507.78   1015.5 52.362      1  4.615e-13 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1