[R] Safe prediction does not work for bivariate polynomial terms?

[Prof Brian Ripley]

On 24/01/2014 02:09, Xing Zhao wrote:
> Hi everyone,
>
> R documents says the safe prediction is implemented, when basis
> functions are used, such as poly(), bs(), ns()
>
> This works for univariate basis, but fails in my bivariate polynomial setting.
> Can anyone explain the reason?

Because there is a makepredictcall() method for class "poly", and 
bivariate polynomials are not of that class (see ?poly).  The 
documentation only says safe prediction is available for 'polynomial' 
fits, and 'bivariate polynomial' is not conventionally included in 
'polynomial'.

Your call is really to polym(), not to poly(), and it may be better to 
call polym() explicitly to remind yourself.

>
>
> The following is a small example.
>
> set.seed(731)
> x<-runif(300)
> y<-runif(300)
>
> f <- function(x, y) {  0.5+2*x+13*x^2-14*y^2+12*x*y+y }
>
> z <- f(x,y)+rnorm(length(x))*0.2
>
> # default orthogonal polynomials basis
> mod <- lm (z ~ poly(x,y,degree = 2))
>
> # raw polynomials basis
> mod1 <- lm (z ~ poly(x,y,degree = 2, raw = T))
>
> # data points to evaluate, just the first five data
> new <- data.frame(x=x[1:5],y= y[1:5])
>
> z[1:5]
> [1]  9.796620 10.397851  1.280832  4.028284  4.811709
>
> # two predicted values differ dramatically, and the orthogonal
> polynomials basis fails
> predict(mod, new)
>          1         2         3         4         5
> 121.46776  40.85002  18.67273  31.82417  20.81673
> predict(mod1, new)
>          1         2         3         4         5
>   9.981091 10.418628  1.223148  4.031664  4.837099
>
> # However, the fitted.values are the same
> mod$fitted.values[1:5]
>          1         2         3         4         5
>   9.981091 10.418628  1.223148  4.031664  4.837099
> mod1$fitted.values[1:5]
>          1         2         3         4         5
>   9.981091 10.418628  1.223148  4.031664  4.837099
>
>
> Thanks in advance
> Xing
>
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>


-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595