LRT significant but new variable's beta not

library(lme4)
ss <- subset(sleepstudy,Days<8)
fm1 <- lmer(Reaction~Days+(1|Subject),data=sleepstudy)
fm2 <- lmer(Reaction~(1|Subject),data=ss)
anova(fm1,fm2)

The first model has 5172 obs
The second model has 4863 obs

That is a difference of 309 obs. Clearly the new variable has a bunch of missing values. I would pay attention to that. You are fitting models in different groups, although they do overlap.

-----Original Message-----
From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Clara Neudecker
Sent: Tuesday, April 19, 2016 3:21 AM
To: R-sig-mixed-models at r-project.org
Subject: [R-sig-ME] LRT significant but new variable's beta not

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