Hello all, I have two questions about anova (one is probably VERY basic...) 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)? 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? Thanks all. -- +-------------------------------------------------+ Carlos Henrique Grohmann - Guano Geologist - MSc Student at IGc-USP - Brazil Linux User #89721 ICQ: 214752832 +-------------------------------------------------+
"Pr(>F)" = probability of obtaining by chance alone an "F
value"
at least as large as what was computed. If this probability is small
(as in this case), it is not credible to believe the null hypothesis.
That is typically taken as evidence that there is a "statistically
significant" trend surface. However, it could also mean that some other
assumption, such as independent observations, is violated. I don't know
"surf.ls", but from my cursory review of the documentation, it may
assume independence, which may not be realistic in this case.
I'm not familiar with Davis, but to test increasing orders of
trend surfaces, consider the following:
> data(topo, package="MASS")
> topo.kr <- surf.ls(2, topo)
> topo.kr3 <- surf.ls(3, topo)
> anova(topo.kr, topo.kr3)
Analysis of Variance Table
Model 1: surf.ls(np = 2, x = topo)
Model 2: surf.ls(np = 3, x = topo)
Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
1 46 39958
2 42 21577 4 18381 8.9447 2.558e-05
> p.23 <- anova(topo.kr, topo.kr3)[2, "Pr(>F)"]
Analysis of Variance Table
Model 1: surf.ls(np = 2, x = topo)
Model 2: surf.ls(np = 3, x = topo)
Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
1 46 39958
2 42 21577 4 18381 8.9447 2.558e-05
> p.23
[1] 2.558186e-05
You can put this in a "for" loop to fit and evaluate increasing
orders of surfaces and put that inside a function. If you need help
with that, please consult the substantial documentation provided with R
or downloadable from "www.r-project.org" or in other references such
as
Venables and Ripley (2002) Modern Applied Statistics with S, 4th ed.
(Springer).
Hope this helps. spencer graves
Carlos Henrique Grohmann wrote:
>Hello all,
>
>I have two questions about anova (one is probably VERY basic...)
>
>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)?
>
>
>
>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?
>
>
>Thanks all.
>
>
>
>
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