[R-sig-ME] LRT significant but new variable's beta not
Ben Bolker
bbolker at gmail.com
Tue Apr 19 20:35:25 CEST 2016
I agree with Alex. I do find these results *mildly* surprising, but note that:
- estimated coefficient of gebjahr_c doesn't change much, but Z-score
goes from 52 (model 1) to 11 (model 2)
- fixed effects in first model are nearly perfectly independent
- fairly strong correlation (-0.88) between the new variable and gebjahr_c
Note that these kinds of questions are not specific to mixed models,
but are general to essentially all linear/generalized models as soon
as the experimental/observation design no longer provides
orthogonal/independent estimates of the coefficients.
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 ***
---
Correlation of Fixed Effects:
(Intr) gbjhr_
gebjahr_c -0.001
sex.L 0.000 0.000
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
--
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
On Tue, Apr 19, 2016 at 2:29 PM, Alex Fine <abfine at gmail.com> wrote:
> The LRT is robust to multicollinearity but the coefficient-based test is
> not, so that could be it (collinearity involving the new predictor could be
> inflating the standard error on the coefficient).
>
> On Tue, Apr 19, 2016 at 4:20 AM, Clara Neudecker <
> clara.hildegard.ruecker at uni-jena.de> wrote:
>
>> 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
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>
>
>
> --
> Alex Fine
> Ph. (336) 302-3251
> web: http://internal.psychology.illinois.edu/~abfine/
> <http://internal.psychology.illinois.edu/~abfine/AlexFineHome.html>
>
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