# Visualize partially-summed effects in GAM

#### Motoki Saito

    library(gamutil)

This package facilitates daily modeling routines with GA(M)Ms by the mgcv package (Wood, 2017). Suppose you already fitted a GAM below, using mgcv::gam or mgcv::bam:

    print(mdl)
    #>
    #> Family: gaussian
    #> Link function: identity
    #>
    #> Formula:
    #> y ~ s(x0) + s(x1) + s(x2) + ti(x0, x1) + ti(x0, x2) + ti(x1,
    #>     x2) + ti(x0, x1, x2)
    #>
    #> Estimated degrees of freedom:
    #>  5.34  5.51  5.03  9.38  8.29 10.88  7.08
    #>  total = 52.51
    #>
    #> GCV score: 1.048869

## Summed effects

Summed-effects can be visualized by mgcv::vis.gam, or itsadug::fvisgam (van Rij, 2020). The same plot can also be plotted by mgcv::plot_contour as below:

    library(mgcv)
    #> Loading required package: nlme
    #> This is mgcv 1.9-4. For overview type '?mgcv'.
    vis.gam(mdl, view=c('x1','x2'), plot.type='contour')

    plot_contour(mdl, view=c('x1','x2'))

There is no correct way in choosing the number of contour lines and their values. In gamutil::plot_contour, you can use user-defined contour lines by the optional arguments “contour.line.breaks” and “contour.color.breaks” for contour lines and contour colors respectively:

    lbr <- seq(-10, 10, by=1.0)
    cbr <- seq(-10, 10, by=0.1)
    plot_contour(mdl, view=c('x1','x2'),
             contour.line.breaks=lbr, contour.color.breaks=cbr)

## Partial effects

Partial effects can be visualized by mgcv::plot.gam or itsadug::pvisgam. The same plot can be obtained with gamutil::plot_contour as below:

    plot.gam(mdl, select=6)

    lbr <- seq(-5, 5, by=0.50)
    cbr <- seq(-5, 5, by=0.05)
    plot_contour(mdl, view=c('x1','x2'), summed=FALSE, terms.size='min',
             verbose=TRUE, contour.line.breaks=lbr, contour.color.breaks=cbr)
    #> Selected:
    #> ti(x1,x2)

The optional argument “terms.size=‘min’” ensures that you include only the term that contains the variables specified in “view”, namely “x1” and “x2” in this example.

## Partially-summed effects

The argument “terms.size” can take three values. They are “min”, “medium”, and “max”. “min” is intended to plot only one term, i.e., partial effects. “medium” includes all the terms that contain the variables specified in “view” but no other variables. In the current example, it would include “s(x1)”, “s(x2)”, and “ti(x1,x2)”. Note that “ti(x0, x1)”, “ti(x0,x2)”, and ti(x0, x1, x2) are excluded, although they contain one of the variables in “view”. They are excluded because they also contain the variables that are not specified in “view”.

    plot_contour(mdl, view=c('x1','x2'), summed=FALSE, terms.size='medium',
             verbose=TRUE)
    #> Selected:
    #> s(x1)
    #> s(x2)
    #> ti(x1,x2)

In contrast, “terms.size=‘max’” plots all the terms that include at least one of the variables specified in the “view” argument. In the current example, it would include “s(x1)”, “s(x2)”, “ti(x0,x1)”, “ti(x0,x2)”, “ti(x1,x2)”, and “ti(x0,x1,x2)”.

    plot_contour(mdl, view=c('x1','x2'), summed=FALSE, terms.size='max',
             verbose=TRUE)
    #> Selected:
    #> s(x1)
    #> s(x2)
    #> ti(x0,x1)
    #> ti(x0,x2)
    #> ti(x1,x2)
    #> ti(x0,x1,x2)

## Notes

The return value of gamutil::plot_contour is a ggplot object. Therefore, you can modify the plot afterwards.

    library(ggplot2)
    plt <- plot_contour(mdl, view=c('x1','x2'), summed=FALSE, terms.size='medium',
                verbose=TRUE)
    #> Selected:
    #> s(x1)
    #> s(x2)
    #> ti(x1,x2)
    plt <- plt + theme(text=element_text(size=25))
    plt