I have a question about some strange results I get when using lmer to
build a logistic mixed effects model. I have a data set of about 30k
points, and I'm trying to do backwards selection to reduce the number
of fixed effects in my model. I've got 3 crossed random effects and
about 20 or so fixed effects. At a certain point, I get a model (m17)
where the fixed effects are like this (full output is at end of
message):
print(m17, corr=F)
...
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.97887 0.19699 -10.045 < 2e-16 ***
sexM 0.45553 0.14387 3.166 0.001544 **
...
is_discTRUE 0.24676 0.15204 1.623 0.104576
poly(wfreq, 2)1 -119.72397 11.00516 -10.879 < 2e-16 ***
poly(wfreq, 2)2 17.35646 5.44456 3.188 0.001433 **
poly(wlen_p, 2)1 -13.60798 7.26926 -1.872 0.061208 .
poly(wlen_p, 2)2 -6.43167 5.24119 -1.227 0.219770
...
where poly(wlen_p,2)2 is the least significant factor left in the
model. So I then build a model (m18) with exactly the same random and
fixed effects except removing poly(wlen_p,2)2. Then I do an anova,
and I get:
anova(m17,m18)
Data:
Models:
m18: is_err ~ sex + starts_turn + before_hes + after_hes + before_part +
m17: after_part + first_rep + is_open + is_disc + poly(wfreq,
m18: 2) + wlen_p + poly(utt_rate, 2) + poly(dur, 2) + pmean +
m17: poly(log_prange, 2) + poly(imean, 2) + poly(irange, 2) +
m18: (1 | speaker) + (1 | corpus) + (1 | ref)
m17: is_err ~ sex + starts_turn + before_hes + after_hes + before_part +
m18: after_part + first_rep + is_open + is_disc + poly(wfreq,
m17: 2) + poly(wlen_p, 2) + poly(utt_rate, 2) + poly(dur, 2) +
m18: pmean + poly(log_prange, 2) + poly(imean, 2) + poly(irange,
m17: 2) + (1 | speaker) + (1 | corpus) + (1 | ref)
Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
m18 27 25928 26153 -12937
m17 28 25925 26159 -12934 5.2136 1 0.02241 *
So my first question is: Should I be concerned that the significance
level shown in the original m17 is so different from the one shown by
the anova? It's hard for me to see how this could happen. I noticed
that there is a post on the FAQ about significance levels in linear
mixed models, but I'm not sure whether it applies to the logistic
case and if so how.
Now, my second question is a result of removing one more factor
(is_disc) from the model, creating m19. I do another anova:
anova(m19,m18)
Data:
Models:
m19: is_err ~ sex + starts_turn + before_hes + after_hes + before_part +
m18: after_part + first_rep + is_open + poly(wfreq, 2) + wlen_p +
m19: poly(utt_rate, 2) + poly(dur, 2) + pmean + poly(log_prange,
m18: 2) + poly(imean, 2) + poly(irange, 2) + (1 | speaker) + (1 |
m19: corpus) + (1 | ref)
m18: is_err ~ sex + starts_turn + before_hes + after_hes + before_part +
m19: after_part + first_rep + is_open + is_disc + poly(wfreq,
m18: 2) + wlen_p + poly(utt_rate, 2) + poly(dur, 2) + pmean +
m19: poly(log_prange, 2) + poly(imean, 2) + poly(irange, 2) +
m18: (1 | speaker) + (1 | corpus) + (1 | ref)
Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
m19 26 25925 26142 -12936
m18 27 25928 26153 -12937 0 1 1
and now it seems that m19 (which contains fewer parameters than m18)
is a better fit. I don't see how it's possible to remove parameters
from a model and get a better likelihood, but I will confess that I
don't entirely understand how these kinds of models are estimated.
Does this have something to do with approximations that R is making to
fit the models, or numerical rounding errors? Could either problem be
due to correlations among variables? All my fixed effects are either
binary or numeric, and there are some fairly high correlations between
a few pairs of them (maybe as high as .6 or .65 using Kendall tau) but I
figured that this would be ok given the large number of data points.
I think each value of each binary feature is observed at least
70-100 times.
In case it matters, I'm running R 2.5.1 on Linux, with lme4 0.99875-8, and
below is a full printout of all my output:
On Dec 28, 2007 9:35 AM, Sharon Goldwater <sgwater at stanford.edu> wrote:
I have a question about some strange results I get when using lmer to
build a logistic mixed effects model. I have a data set of about 30k
points, and I'm trying to do backwards selection to reduce the number
of fixed effects in my model. I've got 3 crossed random effects and
about 20 or so fixed effects. At a certain point, I get a model (m17)
where the fixed effects are like this (full output is at end of
message):
print(m17, corr=F)
...
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.97887 0.19699 -10.045 < 2e-16 ***
sexM 0.45553 0.14387 3.166 0.001544 **
...
is_discTRUE 0.24676 0.15204 1.623 0.104576
poly(wfreq, 2)1 -119.72397 11.00516 -10.879 < 2e-16 ***
poly(wfreq, 2)2 17.35646 5.44456 3.188 0.001433 **
poly(wlen_p, 2)1 -13.60798 7.26926 -1.872 0.061208 .
poly(wlen_p, 2)2 -6.43167 5.24119 -1.227 0.219770
...
where poly(wlen_p,2)2 is the least significant factor left in the
model. So I then build a model (m18) with exactly the same random and
fixed effects except removing poly(wlen_p,2)2. Then I do an anova,
and I get:
So my first question is: Should I be concerned that the significance
level shown in the original m17 is so different from the one shown by
the anova? It's hard for me to see how this could happen. I noticed
that there is a post on the FAQ about significance levels in linear
mixed models, but I'm not sure whether it applies to the logistic
case and if so how.
It can happen that the significance levels reported by the different
tests will be different. The test in the summary is based on a local
approximation to the conditional mean and assumes that the variances
of the random effects will not change substantially when fitting the
model with and without that term. Did they?
One thing I noticed is your output (and thank you for including that)
is that it reports that corpus has only two levels. Is that correct?
If so, I would not advise using a random effect for corpus. It is
very difficult to estimate a variance from only two levels of a
factor. I suggest using a fixed effect for corpus instead.
Now, my second question is a result of removing one more factor
(is_disc) from the model, creating m19. I do another anova:
anova(m19,m18)
Data:
Models:
m19: is_err ~ sex + starts_turn + before_hes + after_hes + before_part +
m18: after_part + first_rep + is_open + poly(wfreq, 2) + wlen_p +
m19: poly(utt_rate, 2) + poly(dur, 2) + pmean + poly(log_prange,
m18: 2) + poly(imean, 2) + poly(irange, 2) + (1 | speaker) + (1 |
m19: corpus) + (1 | ref)
m18: is_err ~ sex + starts_turn + before_hes + after_hes + before_part +
m19: after_part + first_rep + is_open + is_disc + poly(wfreq,
m18: 2) + wlen_p + poly(utt_rate, 2) + poly(dur, 2) + pmean +
m19: poly(log_prange, 2) + poly(imean, 2) + poly(irange, 2) +
m18: (1 | speaker) + (1 | corpus) + (1 | ref)
Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
m19 26 25925 26142 -12936
m18 27 25928 26153 -12937 0 1 1
and now it seems that m19 (which contains fewer parameters than m18)
is a better fit. I don't see how it's possible to remove parameters
from a model and get a better likelihood, but I will confess that I
don't entirely understand how these kinds of models are estimated.
Does this have something to do with approximations that R is making to
fit the models, or numerical rounding errors? Could either problem be
due to correlations among variables? All my fixed effects are either
binary or numeric, and there are some fairly high correlations between
a few pairs of them (maybe as high as .6 or .65 using Kendall tau) but I
figured that this would be ok given the large number of data points.
I think each value of each binary feature is observed at least
70-100 times.
The difference could be due to approximations or due to poor
convergence. For some models the Laplace approximation can be
generalized to a higher-order approximation, called adaptive
Gauss-Hermite quadrature (AGQ), but that isn't feasible when you have
crossed random effects (and, besides, I still haven't written the
code for AGQ even in the case where you don't have crossed random
effects).
First I suggest that you check the value stored as the log-likelihood
dput(logLik(m17))
dput(logLik(m18))
to see how different they really are.
You could, if you are feeling brave, try the development version of
the lme4 package from http://r-forge.r-project.org. To do that,
however, you will need to install a new version of R (R-2.6.1 is
preferred) and a new version of the Matrix package. Then you can
install the new lme4 with
install.packages("lme4", repos = "http://r-forge.r-project.org")
If you prefer, you can contact me off-list and I can try to fit your
models for you using the development version.
In case it matters, I'm running R 2.5.1 on Linux, with lme4 0.99875-8, and
below is a full printout of all my output: