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

[Alex Fine]

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
>
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-- 
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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