[R] mgcv (bam) very large standard error difference between versions 1.7-11 and 1.7-17, bug?
Martijn Wieling
wieling at gmail.com
Wed Jun 6 09:09:37 CEST 2012
Dear useRs,
I ran an additional analysis with another dataset and (logistic
regression), but also in this case I obtain very different p-values
comparing version 1.7-11 and 1.7-17. Any ideas about this? Which is
the good one?
Below, I'll first show the model based on 1.7-11, then of version
1.7-17: summary(model) followed by summary(model, freq=F). Data can be
sent offline if required.
With kind regards,
Martijn Wieling,
University of Groningen
# call in all versions
model = bam(NoStandard3 ~
te(GeoX,GeoY,WordFreqLog.z,by=OldSpeakerContrast,d=c(2,1)) +
OldSpeakerContrast + PopCntLog.z + s(Word,bs="re") +
s(Placename,bs="re") + s(Word,PopAvgIncomeLog.z,bs="re") +
s(Word,PopAvgAgeLog_residIncome.z,bs="re") +
s(Word,PopCntLog.z,bs="re") +
s(Word,YearRec.z,bs="re"),data=lexdst,family="binomial",method="REML")
### mgcv, version 1.7-11
#Family: binomial
#Link function: logit
#
#Formula:
#NoStandard3 ~ te(GeoX, GeoY, WordFreqLog.z, by = OldSpeakerContrast,
# d = c(2, 1)) + OldSpeakerContrast + PopCntLog.z + s(Word,
# bs = "re") + s(Placename, bs = "re") + s(Word, PopAvgIncomeLog.z,
# bs = "re") + s(Word, PopAvgAgeLog_residIncome.z, bs = "re") +
# s(Word, PopCntLog.z, bs = "re") + s(Word, YearRec.z, bs = "re")
#
#Parametric coefficients:
# Estimate Std. Error z value Pr(>|z|)
#(Intercept) -0.41610 0.14027 -2.966 0.00301 **
#OldSpeakerContrast1 0.44508 0.01934 23.009 < 2e-16 ***
#PopCntLog.z -0.11673 0.02725 -4.284 1.83e-05 ***
#---
#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 Chi.sq p-value
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast0 54.05 69.06 223.3 < 2e-16
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast1 59.17 74.83 327.6 < 2e-16
#s(Word) 166.41 167.84 13756.0 < 2e-16
#s(Placename) 157.64 188.02 692.7 < 2e-16
#s(Word,PopAvgIncomeLog.z) 137.83 160.05 829.9 < 2e-16
#s(Word,PopAvgAgeLog_residIncome.z) 121.13 151.13 435.5 < 2e-16
#s(Word,PopCntLog.z) 97.12 133.97 205.5 7.01e-05
#s(Word,YearRec.z) 128.98 155.27 585.7 < 2e-16
#
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast0 ***
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast1 ***
#s(Word) ***
#s(Placename) ***
#s(Word,PopAvgIncomeLog.z) ***
#s(Word,PopAvgAgeLog_residIncome.z) ***
#s(Word,PopCntLog.z) ***
#s(Word,YearRec.z) ***
#---
#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) = 0.372 Deviance explained = 32.4%
#REML score = 97450 Scale est. = 1 n = 69259
### version 1.7-17, summary(model)
#Family: binomial
#Link function: logit
#
#Formula:
#NoStandard3 ~ te(GeoX, GeoY, WordFreqLog.z, by = OldSpeakerContrast,
# d = c(2, 1)) + OldSpeakerContrast + PopCntLog.z + s(Word,
# bs = "re") + s(Placename, bs = "re") + s(Word, PopAvgIncomeLog.z,
# bs = "re") + s(Word, PopAvgAgeLog_residIncome.z, bs = "re") +
# s(Word, PopCntLog.z, bs = "re") + s(Word, YearRec.z, bs = "re")
#
#Parametric coefficients:
# Estimate Std. Error z value Pr(>|z|)
#(Intercept) -0.98150 0.16742 -5.863 4.56e-09 ***
#OldSpeakerContrast1 0.65497 0.30268 2.164 0.0305 *
#PopCntLog.z -0.11724 0.01064 -11.016 < 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 Chi.sq p-value
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast0 53.62 68.48 221.4 <2e-16
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast1 58.64 74.14 324.9 <2e-16
#s(Word) 166.41 168.00 14351.7 <2e-16
#s(Placename) 157.79 209.00 1160.0 <2e-16
#s(Word,PopAvgIncomeLog.z) 137.84 170.00 1062.1 <2e-16
#s(Word,PopAvgAgeLog_residIncome.z) 121.15 170.00 686.7 <2e-16
#s(Word,PopCntLog.z) 97.10 169.00 434.0 <2e-16
#s(Word,YearRec.z) 128.98 170.00 867.4 <2e-16
#
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast0 ***
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast1 ***
#s(Word) ***
#s(Placename) ***
#s(Word,PopAvgIncomeLog.z) ***
#s(Word,PopAvgAgeLog_residIncome.z) ***
#s(Word,PopCntLog.z) ***
#s(Word,YearRec.z) ***
#---
#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) = 0.372 Deviance explained = 32.4%
#REML score = 97449 Scale est. = 1 n = 69259
### mgcv 1.7-17, summary(model,freq=F)
#Family: binomial
#Link function: logit
#
#Formula:
#NoStandard3 ~ te(GeoX, GeoY, WordFreqLog.z, by = OldSpeakerContrast,
# d = c(2, 1)) + OldSpeakerContrast + PopCntLog.z + s(Word,
# bs = "re") + s(Placename, bs = "re") + s(Word, PopAvgIncomeLog.z,
# bs = "re") + s(Word, PopAvgAgeLog_residIncome.z, bs = "re") +
# s(Word, PopCntLog.z, bs = "re") + s(Word, YearRec.z, bs = "re")
#
#Parametric coefficients:
# Estimate Std. Error z value Pr(>|z|)
#(Intercept) -0.98150 0.52485 -1.870 0.0615 .
#OldSpeakerContrast1 0.65497 0.68628 0.954 0.3399
#PopCntLog.z -0.11724 0.02726 -4.300 1.71e-05 ***
#---
#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 Chi.sq p-value
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast0 53.62 68.48 221.4 <2e-16
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast1 58.64 74.14 324.9 <2e-16
#s(Word) 166.41 168.00 14351.7 <2e-16
#s(Placename) 157.79 209.00 1160.0 <2e-16
#s(Word,PopAvgIncomeLog.z) 137.84 170.00 1062.1 <2e-16
#s(Word,PopAvgAgeLog_residIncome.z) 121.15 170.00 686.7 <2e-16
#s(Word,PopCntLog.z) 97.10 169.00 434.0 <2e-16
#s(Word,YearRec.z) 128.98 170.00 867.4 <2e-16
#
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast0 ***
#te(GeoX,GeoY,WordFreqLog.z):OldSpeakerContrast1 ***
#s(Word) ***
#s(Placename) ***
#s(Word,PopAvgIncomeLog.z) ***
#s(Word,PopAvgAgeLog_residIncome.z) ***
#s(Word,PopCntLog.z) ***
#s(Word,YearRec.z) ***
#---
#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) = 0.372 Deviance explained = 32.4%
#REML score = 97449 Scale est. = 1 n = 69259
On Tue, Jun 5, 2012 at 11:06 AM, Martijn Wieling <wieling at gmail.com> wrote:
> Dear useRs, Simon,
>
> @Simon: I'll send the data offline.
> The command summary(...,freq=F) yields the same result as before. Why
> did the default change from freq=F in version 1.7-13 to freq=T in
> version 1.7-17? Especially since the original default appeared to be
> better.
>
> I noticed that some of my commands were slightly off in the R-example
> of my previous e-mail (cut-paste errors...). They should be:
>
> modelLMER <- lmer(RefPMIdistMeanLog.c ~ SpYearBirth.z*IsAragon +
> SpIsMale + (1|Key), data=wrddst)
> print(modelLMER,cor=F)
>
> # using version 1.7-13, default = "REML"
> modelBAMold <- bam(RefPMIdistMeanLog.c ~ SpYearBirth.z*IsAragon +
> SpIsMale + s(Key,bs="re"), data=wrddst)
> summary(modelBAMold)
>
> # using version 1.7-17, explicitly stating method="REML"
> modelBAMnew <- bam(RefPMIdistMeanLog.c ~ SpYearBirth.z*IsAragon +
> SpIsMale + s(Key,bs="re"), data=wrddst, method="REML")
> summary(modelBAMnew)
> summary(modelBAMnew,freq=F) # same results as modelBAMold
>
> # using version 1.7-17, default: fREML - contains a bug
> modelBAMfREML <- bam(RefPMIdistMeanLog.c ~ SpYearBirth.z*IsAragon +
> SpIsMale + s(Key,bs="re"), data=wrddst)
> summary(modelBAMfREML)
>
> With kind regards,
> Martijn Wieling
>
> --
> *******************************************
> Martijn Wieling
> http://www.martijnwieling.nl
> wieling at gmail.com
> +31(0)614108622
> *******************************************
> University of Groningen
> http://www.rug.nl/staff/m.b.wieling
> *******************************************
>
>
> On Sun, Jun 3, 2012 at 7:45 PM, Martijn Wieling <wieling at gmail.com> wrote:
>> 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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