How can I set a minimum value for basis dimension in mgcv?

Question

Using a penalized spline of mgcv, I want to obtain effective degrees of freedom (EDF) of 10 /year in the example data (60 for the entire period). ``` library(mgcv) library(dlnm) df <- chicagoNMMAPS df1<-subset(df, as.Date(date) >= '1995-01-01') mod1 <-gam(resp ~ s(time,bs='cr',k=6*15, fx=F)+ s(temp,k=6, bs='cr') + as.factor(dow) ,family=quasipoisson,na.action=na.omit,data=df1) ``` In the example data the basis dimension for time as measured by edf for time is 56.117, which is less than 10 per year. ``` summary(mod1) Approximate significance of smooth terms: edf Ref.df F p-value s(time) 56.117 67.187 5.369 <2e-16 *** s(temp) 2.564 3.204 0.998 0.393 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 R-sq.(adj) = 0.277 Deviance explained = 28.2% GCV score = 1.1297 Scale est. = 1.0959 n = 2192 ``` Manually I will change the edf a by supplying smoothing parameters as follows ``` mod1$sp s(time) s(temp) 23.84809 17.23785 ``` Then I will plug the sp output into a new model and…

Accepted Answer

I don't understand the details of your model, but if you are looking to minimize (or maximize) `edf` for models fitted with different `sp`, `optim` will do the job. First, create a function that returns just the `edf` given different values of `sp`.

```
edf.by.sp<-function(sp) {
  model <-gam(resp ~ s(time,bs='cr',k=6*15, fx=F)+ s(temp,k=6, bs='cr') + 
                as.factor(dow),
              family=quasipoisson,
              na.action=na.omit,
              data=df1, 
              sp= c(sp,  17.23785) # Not sure if this quite right.
  )
  abs(summary(model)$s.table['s(time)','edf']-60) # Subtract 60 and flip sign so 60 is lowest.
}
```

Now, you can just run `optim` to minimize `edf`:

```
# You could pick any reasonable starting sp value.
# Many optimization methods are available, but in your case
# they work equally well.
best<-optim(12,edf.by.sp,method='BFGS')$par
best
# 16.82708
```

and, subbing back in, you get nearly 0 (exactly 60 before transforming) when plugging in the function:

```
edf.by.sp(best) # 2.229869e-06
```

How can I set a minimum value for basis dimension in mgcv?

Solution

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