[R-sig-ME] Understanding/plotting fixed effects estimates & standard errors
Rafael Maia
queirozrafaelmv at yahoo.com.br
Thu Jun 21 18:51:19 CEST 2012
Dear all,
I have ran a mixed effects binomial model and am trying to understand how the estimates of my model relate to its conclusions. It is a fairly simple model with one fixed categorical factor (2 levels) and a nested random effect. I am using lmer and the Wald test result, the likelihood ratio test and running a similar model using MCMCglmm all seem to point in the direction that the fixed effect is significant and important. However, as I am trying to extract the estimates and their standard errors to plot the results (by running a model without the intercept or releveling the factor), it is clear that there is a huge overlap in the estimates of the two levels of the fixed effect.
In the main model (below), the standard error has a very small standard error, but the SE for the intercept is fairly large, and encompasses the estimate of the second level.
So I am trying to understand - am I interpreting something wrong? Converting them from the log-odds scale doesn't seem to help much. If not, how should I reconcile these two pieces of evidence? Is the releveling/removing intercept approach to understand estimates from a model not valid for mixed models?
Many thanks for any help! below you will find the results:
>m1=lmer(cbind(success,fail) ~ factor+ (1|spp/variable), bb, family='binomial')
> summary(m1)
Generalized linear mixed model fit by the Laplace approximation
Formula: cbind(success, fail) ~ factor + (1 | spp/variable)
Data: bb
AIC BIC logLik deviance
166.8 173.8 -79.41 158.8
Random effects:
Groups Name Variance Std.Dev.
variable:spp (Intercept) 0.014916 0.12213
spp (Intercept) 1.907228 1.38102
Number of obs: 42, groups: variable:spp, 42; spp, 7
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.43834 0.52289 2.751 0.00595 **
factor1 0.21081 0.04269 4.938 7.88e-07 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr)
factor1 -0.040
> m0=lmer(cbind(success,fail) ~ 1+ (1|spp/variable), bb, family='binomial')
> anova(m0,m1)
Data: bb
Models:
m0: cbind(success, fail) ~ 1 + (1 | spp/variable)
m1: cbind(success, fail) ~ factor + (1 | spp/variable)
Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
m0 3 183.16 188.37 -88.579
m1 4 166.81 173.76 -79.406 18.346 1 1.842e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> m3=lmer(cbind(success,fail) ~ factor-1+ (1|spp/variable), bb, family='binomial')
> summary(m3)
Generalized linear mixed model fit by the Laplace approximation
Formula: cbind(success, fail) ~ factor - 1 + (1 | spp/variable)
Data: bb
AIC BIC logLik deviance
166.8 173.8 -79.41 158.8
Random effects:
Groups Name Variance Std.Dev.
variable:spp (Intercept) 0.014916 0.12213
spp (Intercept) 1.907221 1.38102
Number of obs: 42, groups: variable:spp, 42; spp, 7
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
factor0 1.4383 0.5229 2.751 0.00595 **
factor1 1.6491 0.5229 3.154 0.00161 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
factor0
factor1 0.997
Abraços,
Rafael Maia
---
webpage: http://gozips.uakron.edu/~rm72
"A little learning is a dangerous thing; drink deep, or taste not the Pierian spring." (A. Pope)
Graduate Student - Integrated Bioscience
University of Akron
http://gozips.uakron.edu/~shawkey/
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