[R] questions about anova

[Roger Bivand]

On Sat, 28 Feb 2004, Carlos Henrique Grohmann wrote:

> Hello all,
> 
> I have two questions about anova (one is probably VERY basic...)
> 

About surf.ls() in the spatial package, and documented in Venables & 
Ripley Modern Applied Statistics with S ...

> 1 - when one asks for a summary of a trend surface created with surf.ls,
> he/she gets:
> 
> > summary(g3r)
> Analysis of Variance Table
>  Model: surf.ls(np = 3, x = gradiente$east, y = gradiente$north, z =
> gradiente$num1)
>              Sum Sq    Df      Mean Sq  F value     Pr(>F)
> Regression 215.7182     9 23.968693976 2686.508 < 2.22e-16
> Deviation  480.1218 53814  0.008921876
> Total      695.8401 53823
> Multiple R-Squared: 0.31,       Adjusted R-squared: 0.3099
> AIC: (df = 53814) -146390.9
> Fitted:
>      Min       1Q   Median       3Q      Max
> 0.007852 0.075619 0.100498 0.139042 0.338186
> Residuals:
>      Min       1Q   Median       3Q      Max
> -0.29758 -0.04418 -0.01411  0.02536  0.51484
> >
> 
> So, what's the meaning of the "Pr(>F)?
> 

Roughly here that, if the model assumptions are met, that the reduction of 
sum of squares from total to deviation could have occurred at random, and 
that the reduction represented by the cubic trend surface does make a 
difference. Note that the observations are probably not independent, so 
the assumptions may not be met, and with the number of observations you 
have here, almost anything will appear to be significant.

> 
> 
> 2 - I have six trend surfaces, and I like to make a anova for the significance
> of increasing the degree of polynomial (like in Davis, 1986, p.422, Statistics
> and data analysis in geology).
> 
> is there a way I can do it automatically or should I do it manually?
> 

See the example in help(anova.trls):

anova(topo0, topo1, topo2, topo3, topo4)

which compares the trend surfaces from 0 to 4th order. There are concerns 
about trying to fit higher-order surfaces because of co-linearity.

> 
> Thanks all.
> 
> 
> 

-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Breiviksveien 40, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93
e-mail: Roger.Bivand at nhh.no