[R] mgcv (bam) very large standard error difference between versions 1.7-11 and 1.7-17, bug?

Martijn Wieling wieling at gmail.com
Sun Jun 3 19:45:04 CEST 2012


Dear useRs,

I've ran some additional analyses (see below), which strongly suggest
the standard errors of the bam (and gam) function are much too low in
mgcv version 1.7-17, at least when including an s(X,bs="re") term.
Until this issue has been clarified, it's perhaps best to use an older
version of mgcv (unfortunately, however, in earlier versions the
p-value calculation of s(X,bs="re") is not correct). All analyses were
conducted in R 2.15.0.

My approach was the following: I created a mixed-effects regression
model with a single random intercept and only linear predictors. In my
view, the results using lmer (lme4) should be comparable to those of
bam and gam (mgcv). This was the case when using an older version of
mgcv (version 1.7-13), but this is not the case anymore in version
1.7-17. In version 1.7-17, the standard errors and p-values are much
lower and very similar to those of a linear model (which does not take
the random-effects structure into account). The R-code and results are
shown below. (The results using gam are not shown, but show the same
pattern.)

Furthermore, note that the differences in standard errors become less
severe (but still noticeable) when less data is involved (e.g., using
only 500 rows as opposed to >100.000). Finally, when not including an
s(X,bs="re") term, but another non-random-effect smooth, the standard
errors do not appear to be structurally lower (only for some
variables, but not by a great deal - see also below).

With kind regards,
Martijn Wieling
University of Groningen

#### lme4 model (most recent version of lme4)
modelLMER <- lmer(RefPMIdistMeanLog.c ~ SpYearBirth.z*IsAragon +
SpIsMale + (1|Key), data=wrddst)
#                        Estimate Std. Error t value
#SpYearBirth.z          -0.012084   0.004577  -2.640
#IsAragon                0.138959   0.010040  13.840
#SpIsMale               -0.003087   0.008290  -0.372
#SpYearBirth.z:IsAragon  0.015429   0.010159   1.519


#### mgcv 1.7-13, default (method = "REML") - almost identical to modelLMER
modelBAMold <- bam(RefPMIdistMeanLog.c ~ SpYearBirth.z*IsAragon +
SpIsMale + s(Key,bs="re"), data=wrddst)
#                        Estimate Std. Error t value Pr(>|t|)
#SpYearBirth.z          -0.012084   0.004578  -2.640  0.00829 **
#IsAragon                0.138959   0.010042  13.838  < 2e-16 ***
#SpIsMale               -0.003087   0.008292  -0.372  0.70968
#SpYearBirth.z:IsAragon  0.015429   0.010160   1.519  0.12886


#### mgcv 1.7-17, method = "REML" - standard errors greatly reduced
# (comparable to standard errors of LM without random intercept)
modelBAMnew <- bam(RefPMIdistMeanLog.c ~ SpYearBirth.z*IsAragon +
SpIsMale + s(Key,bs="re"), data=wrddst); print(testje,cor=F)
#                        Estimate Std. Error t value Pr(>|t|)
#SpYearBirth.z          -0.012084   0.001159 -10.428  < 2e-16 ***
#IsAragon                0.138959   0.002551  54.472  < 2e-16 ***
#SpIsMale               -0.003087   0.002098  -1.471    0.141
#SpYearBirth.z:IsAragon  0.015429   0.002587   5.965 2.45e-09 ***

#### lm results, standard errors comparable to mgcv 1.7-17
modelLM <- lm(RefPMIdistMeanLog.c ~ SpYearBirth.z*IsAragon + SpIsMale,
data=wrddst)
#                        Estimate Std. Error t value Pr(>|t|)
#(Intercept)            -0.025779   0.001653 -15.595  < 2e-16 ***
#SpYearBirth.z          -0.011906   0.001182 -10.070  < 2e-16 ***
#IsAragon                0.139323   0.002603  53.531  < 2e-16 ***
#SpIsMale               -0.003076   0.002140  -1.437    0.151
#SpYearBirth.z:IsAragon  0.015252   0.002639   5.780 7.49e-09 ***


#### mgcv 1.7-17, default (method = "fREML") - completely different
from previous models
modelBAMfREML <- bam(RefPMIdistMeanLog.c ~ SpYearBirth.z*IsAragon +
SpIsMale + s(Key,bs="re"), data=wrddst); print(testje,cor=F)
#                        Estimate Std. Error t value Pr(>|t|)
#(Intercept)            -0.025391   0.106897  -0.238    0.812
#SpYearBirth.z          -0.012084   0.076300  -0.158    0.874
#IsAragon                0.138959   0.166697   0.834    0.405
#SpIsMale               -0.003087   0.138291  -0.022    0.982
#SpYearBirth.z:IsAragon  0.015429   0.168260   0.092    0.927
#
#Approximate significance of smooth terms:
#          edf Ref.df     F p-value
#s(Key) -38.95    310 15.67  <2e-16 ***


#### differences w.r.t. standard smooths
#### mgcv version 1.7-13
m2old <- bam(RefPMIdistMeanLog.c ~ s(GeoX,GeoY) +
SpYearBirth.z*IsAragon + SpIsMale, data=wrddst, method="REML")
## RESULTS
#Family: gaussian
#Link function: identity
#
#Formula:
#RefPMIdistMeanLog.c ~ s(GeoX, GeoY) + SpYearBirth.z * IsAragon +
#    SpIsMale
#
#Parametric coefficients:
#                        Estimate Std. Error t value Pr(>|t|)
#(Intercept)            -0.001386   0.004982  -0.278   0.7809
#SpYearBirth.z          -0.012950   0.001167 -11.097  < 2e-16 ***
#IsAragon                0.020532   0.023608   0.870   0.3845
#SpIsMale               -0.004788   0.002219  -2.158   0.0309 *
#SpYearBirth.z:IsAragon  0.015611   0.002600   6.005 1.92e-09 ***
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
#Approximate significance of smooth terms:
#               edf Ref.df     F p-value
#s(GeoX,GeoY) 27.11  28.14 126.2  <2e-16 ***
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
#R-sq.(adj) =  0.0555   Deviance explained = 5.58%
#REML score =  39232  Scale est. = 0.11734   n = 112608


#### mgcv version 1.7-17
m2new <- bam(RefPMIdistMeanLog.c ~ s(GeoX,GeoY) +
SpYearBirth.z*IsAragon + SpIsMale, data=wrddst, method="REML")
#Family: gaussian
#Link function: identity
#
#Formula:
#RefPMIdistMeanLog.c ~ s(GeoX, GeoY) + SpYearBirth.z * IsAragon +
#    SpIsMale
#
#Parametric coefficients:
#                        Estimate Std. Error t value Pr(>|t|)
#(Intercept)            -0.001388   0.003938  -0.352   0.7245
#SpYearBirth.z          -0.012950   0.001167 -11.098  < 2e-16 ***
#IsAragon                0.020543   0.018055   1.138   0.2552
#SpIsMale               -0.004788   0.002215  -2.161   0.0307 *
#SpYearBirth.z:IsAragon  0.015611   0.002600   6.005 1.92e-09 ***
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
#Approximate significance of smooth terms:
#               edf Ref.df     F p-value
#s(GeoX,GeoY) 27.11  28.14 126.2  <2e-16 ***
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
#R-sq.(adj) =  0.0555   Deviance explained = 5.58%
#REML score =  39232  Scale est. = 0.11734   n = 112608


On Sat, Jun 2, 2012 at 6:25 PM, Martijn Wieling <wieling at gmail.com> wrote:
> Dear useRs,
>
> I reran an analysis with bam (mgcv, version 1.7-17) originally
> conducted using an older version of bam (mgcv, version 1.7-11) and
> this resulted in the same estimates, but much lower standard errors
> (in some cases 20 times as low) and lower p-values. This obviously
> results in a larger set of significant predictors. Is this result
> expected given the improvements in the new version? Or this a bug and
> are the p-values of bam in mgcv 1.7-17 too low? The summaries of both
> versions are shown below to enable a comparison.
>
> In addition, applying the default method="fREML" (mgcv version 1.7-17)
> on the same dataset yields only non-significant results, while all
> results are highly significant using method="REML". Furthermore, it
> also results in large negative (e.g., -8757) edf values linked to
> s(X,bs="RE") terms. Is this correct, or is this a bug? The summary of
> the model using method="fREML" is also shown below.
>
> I hope someone can shed some light on this.
>
> With kind regards,
> Martijn Wieling,
> University of Groningen
>
> #################################
> ### mgcv version 1.7-11
> #################################
>
> Family: gaussian
> Link function: identity
>
> Formula:
> RefPMIdistMeanLog.c ~ s(GeoX, GeoY) + RefVratio.z + IsSemiwordOrDemonstrative +
>    RefSoundCnt.z + SpYearBirth.z * IsAragon + PopCntLog_residGeo.z +
>    s(Word, bs = "re") + s(Key, bs = "re")
>
> Parametric coefficients:
>                           Estimate Std. Error t value Pr(>|t|)
> (Intercept)               -0.099757   0.020234  -4.930 8.23e-07 ***
> RefVratio.z                0.105705   0.013328   7.931 2.19e-15 ***
> IsSemiwordOrDemonstrative  0.289828   0.046413   6.245 4.27e-10 ***
> RefSoundCnt.z              0.119981   0.021202   5.659 1.53e-08 ***
> SpYearBirth.z             -0.011396   0.002407  -4.734 2.21e-06 ***
> IsAragon                   0.055678   0.033137   1.680  0.09291 .
> PopCntLog_residGeo.z      -0.006504   0.003279  -1.984  0.04731 *
> SpYearBirth.z:IsAragon     0.015871   0.005459   2.907  0.00365 **
> ---
> Signif. codes:  0 â***â 0.001 â**â 0.01 â*â 0.05 â.â 0.1 â â 1
>
> Approximate significance of smooth terms:
>                edf Ref.df      F p-value
> s(GeoX,GeoY)  24.01  24.21  31.16  <2e-16 ***
> s(Word)      352.29 347.00 501.57  <2e-16 ***
> s(Key)       269.75 289.25  10.76  <2e-16 ***
> ---
> Signif. codes:  0 â***â 0.001 â**â 0.01 â*â 0.05 â.â 0.1 â â 1
>
> R-sq.(adj) =  0.693   Deviance explained = 69.4%
> REML score = -22476  Scale est. = 0.038177  n = 112608
>
>
> #################################
> ### mgcv version 1.7-17, much lower p-values and standard errors than
> version 1.7-11
> #################################
>
> Family: gaussian
> Link function: identity
>
> Formula:
> RefPMIdistMeanLog.c ~ s(GeoX, GeoY) + RefVratio.z + IsSemiwordOrDemonstrative +
>    RefSoundCnt.z + SpYearBirth.z * IsAragon + PopCntLog_residGeo.z +
>    s(Word, bs = "re") + s(Key, bs = "re")
>
> Parametric coefficients:
>                            Estimate Std. Error t value Pr(>|t|)
> (Intercept)               -0.0997566  0.0014139 -70.552  < 2e-16 ***
> RefVratio.z                0.1057049  0.0006565 161.010  < 2e-16 ***
> IsSemiwordOrDemonstrative  0.2898285  0.0020388 142.155  < 2e-16 ***
> RefSoundCnt.z              0.1199813  0.0009381 127.905  < 2e-16 ***
> SpYearBirth.z             -0.0113956  0.0006508 -17.509  < 2e-16 ***
> IsAragon                   0.0556777  0.0057143   9.744  < 2e-16 ***
> PopCntLog_residGeo.z      -0.0065037  0.0007938  -8.193 2.58e-16 ***
> SpYearBirth.z:IsAragon     0.0158712  0.0014829  10.703  < 2e-16 ***
> ---
> Signif. codes:  0 â***â 0.001 â**â 0.01 â*â 0.05 â.â 0.1 â â 1
>
> Approximate significance of smooth terms:
>                edf Ref.df       F p-value
> s(GeoX,GeoY)  24.01  24.21   31.15  <2e-16 ***
> s(Word)      352.29 347.00  587.26  <2e-16 ***
> s(Key)       269.75 313.00 4246.76  <2e-16 ***
> ---
> Signif. codes:  0 â***â 0.001 â**â 0.01 â*â 0.05 â.â 0.1 â â 1
>
> R-sq.(adj) =  0.693   Deviance explained = 69.4%
> REML score = -22476  Scale est. = 0.038177  n = 112608
>
>
> #################################
> ### mgcv version 1.7-17, default: method="fREML", all p-values
> non-significant and negative edf's of s(X,bs="re")
> #################################
>
> Family: gaussian
> Link function: identity
>
> Formula:
> RefPMIdistMeanLog.c ~ s(GeoX, GeoY) + RefVratio.z + IsSemiwordOrDemonstrative +
>    RefSoundCnt.z + SpYearBirth.z * IsAragon + PopCntLog_residGeo.z +
>    s(Word, bs = "re") + s(Key, bs = "re")
>
> Parametric coefficients:
>                           Estimate Std. Error t value Pr(>|t|)
> (Intercept)               -0.099757   1.730235  -0.058    0.954
> RefVratio.z                0.105705   1.145329   0.092    0.926
> IsSemiwordOrDemonstrative  0.289828   4.167237   0.070    0.945
> RefSoundCnt.z              0.119981   1.901158   0.063    0.950
> SpYearBirth.z             -0.011396   0.034236  -0.333    0.739
> IsAragon                   0.055678   0.298629   0.186    0.852
> PopCntLog_residGeo.z      -0.006504   0.041981  -0.155    0.877
> SpYearBirth.z:IsAragon     0.015871   0.077142   0.206    0.837
>
> Approximate significance of smooth terms:
>               edf Ref.df       F p-value
> s(GeoX,GeoY) -1376      1   7.823 0.00516 **
> s(Word)      -8298    347 577.910 < 2e-16 ***
> s(Key)       -1421    316  13.512 < 2e-16 ***
> ---
> Signif. codes:  0 â***â 0.001 â**â 0.01 â*â 0.05 â.â 0.1 â â 1
>
> R-sq.(adj) =  0.741   Deviance explained = 69.4%
> fREML score = -22476  Scale est. = 0.038177  n = 112608



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