Hello,
I'm running mixed models in GAMM4 with 2 (non-nested) random intercepts and
I want to include a spline term for one of my exposure variables. However,
when I include a spline term, I always get reported degrees of freedom of
less than 1, even when I know that my spline is using more than 1 degree of
freedom. For example, here is the code for my model:
> global.gamm4<-gamm4(zcog~s(adjpatx, fx=TRUE, k=5)+int234+cogagec+cogagesq
+
+ + oldfran +newus +alc2 +alc3 +alc4 +alcmiss +smk2 +smk3
+ +mdinc10c +mdinc10sq+ pwhtc +pwhtsq +edu2+ edu3 +husbgs
+husbcol+ husbmiss
+ +currpmh +pastpmh +neverpmh, random= ~(1|id)
+(1|cogtest), data=global)
Using > summary(global.gamm4$mer), I get the following output for my spline
term, indicating that I use the expected 4 degrees of freedom.
Xs(adjpatx)Fx1 0.1018943 0.1073225 0.949
Xs(adjpatx)Fx2 -0.0708114 0.1123845 -0.630
Xs(adjpatx)Fx3 0.7459511 0.6836413 1.091
Xs(adjpatx)Fx4 -0.2062321 0.0923569 -2.233
However, when I use > summary(global.gamm4$gam). I get an estimate of
degrees of freedom that is not 4:
Approximate significance of smooth terms:
edf Ref.df F p-value
s(adjpatx) 0.7588 0.7588 1.346 0.234
This degree of freedom = 0.76 also shows up on my plot.
Ultimately, I would like to use a cubic regression penalized spline,
allowing R to choose the degrees of freedom for me using GCV. However, when
I use the correct code for this or variants of it using mgcv, I also get
degrees of freedom less than 1. For example, in the following code provides
a degree of freedom of less than 1 as well:
> global.gamm4<-gamm4(zcog~s(adjpatx, fx=FALSE)+int234+cogagec+cogagesq +
+ + oldfran +newus +alc2 +alc3 +alc4 +alcmiss +smk2 +smk3
+ +mdinc10c +mdinc10sq+ pwhtc +pwhtsq +edu2+ edu3 +husbgs
+husbcol+ husbmiss
+ +currpmh +pastpmh +neverpmh, random= ~(1|id)
+(1|cogtest), data=global)
Output indicating that this spline should probably look linear:
> summary(global.gamm4$mer)
Random effects:
Groups Name Variance Std.Dev.
id (Intercept) 0.1823454 0.427019
cogtest (Intercept) 0.0025498 0.050496
Xr.1 s(adjtibx) 0.0000000 0.000000
Residual 0.7782969 0.882211
Xs(adjtibx)Fx1 -0.0387360 0.0215596 -1.797
Output getting a df for this spline of 0.20.
> summary(global.gamm4$gam)
Approximate significance of smooth terms:
edf Ref.df F p-value
s(adjtibx) 0.2009 0.2009 16.07 NA
The plot looks linear, but reports a df =0.20.
So...to summarize my questions:
1. Are the splines produced by s(exp, fx=FALSE) or s(exp, fx=TRUE, k=k)
correct even though the reported degrees of freedom appears to be wrong?
2. Can I believe my plot?
3. How can I get the true df used when I use s(exp, fx=FALSE)?
Thanks for any and all help you can provide!
Melinda
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