# [R] interpretation of F-statistics in GAMs

robert.ptacnik at niva.no robert.ptacnik at niva.no
Fri Jun 15 09:06:53 CEST 2007

```

dear listers,
I use gam (from mgcv) for evaluation of shape and strength of relationships
between a response variable and several predictors.
How can I interpret the 'F' values viven in the GAM summary? Is it
appropriate to treat them in a similar manner as the T-statistics in a
linear model, i.e. larger values mean that this variable has a stronger
impact than a variable with smaller F?
When I run my analysis for two different response varables (but identical
predictors), is there a way to compare the F values among tests (like to
standardize them by teh sum of F within each test?) I append two summaries
below.
Robert

### example 1 ###

Family: gaussian

Formula:
dep[sel, i] ~ s(date, k = 3) + s(depth, k = kn) + s(temp, k = kn) +
s(light, k = kn) + s(PO4, k = kn) + s(DIN, k = kn) + s(prop.agpla,
k = kn)

Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)   5.1048     0.0384   132.9   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Approximate significance of smooth terms:
edf Est.rank      F  p-value
s(date)       1.669        2 12.161 1.07e-05 ***
s(depth)      1.671        2 36.125 4.85e-14 ***
s(temp)       1.927        2  6.686  0.00156 **
s(light)      1.886        2 12.604 7.20e-06 ***
s(PO4)        1.676        2  3.237  0.04143 *
s(DIN)        1.000        1 38.428 3.41e-09 ***
s(prop.agpla) 1.405        2 15.987 3.79e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

R-sq.(adj) =  0.687   Deviance explained = 70.5%
GCV score = 0.31995   Scale est. = 0.30076   n = 204

### example 2 ###
Family: gaussian

Formula:
dep[sel, i] ~ s(date, k = 3) + s(depth, k = kn) + s(temp, k = kn) +
s(light, k = kn) + s(PO4, k = kn) + s(DIN, k = kn) + s(prop.agpla,
k = kn)

Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  7.13588    0.05549   128.6   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Approximate significance of smooth terms:
edf Est.rank      F  p-value
s(date)       1.944        2 15.997 3.67e-07 ***
s(depth)      1.876        2 25.427 1.52e-10 ***
s(temp)       1.000        1  2.866   0.0921 .
s(light)      1.751        2  4.212   0.0162 *
s(PO4)        1.950        2 10.632 4.14e-05 ***
s(DIN)        1.805        2 10.745 3.73e-05 ***
s(prop.agpla) 1.715        2  2.674   0.0715 .
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

R-sq.(adj) =  0.479   Deviance explained = 50.9%
GCV score = 0.6863   Scale est. = 0.64348   n = 209

```