Dear Adrian and Rolf,
Thank you for your comments.
I am considering your comments to understand them.
I will send such questions to the package authors.
Regards,
Hiroshi Saito
On Mon, 11 Feb 2013 13:56:42 +0800
<adrian.badde...@csiro.au> wrote:
>
> On 02/08/2013 01:48 PM, Hiroshi Saito wrote:
> >>> I am analyzing a spatial point data set.
> >>> I would like to test how fit the model fitted by ppm is.
> >>> For this objective, I used kstest.
>
> This is a question about the 'spatstat' package.
> Questions about this package should preferably be sent to the package authors.
>
> >>> Unfortunately, however, I am not sure that the test actually tests the
> >>> fit of the model for the data set on the two dimensional space.
>
> Yes, it does.
>
> >>> For example, if I set the covariate = x, it means (in my understanding)
> >>> that the projection of the data set to the x-axis is tested.
>
> That is correct.
>
> In general, the Kolmogorov-Smirnov test compares the observed distribution of
> some numerical variable with the expected or theoretical distribution of the
> same variable.
>
> To apply the K-S test to spatial data, each point in the data and each
> spatial location in the window must be assigned a numerical value. In
> 'kstest' this is specified by the argument 'covariate'.
>
> If you specify covariate="x" then the numerical value assigned to each point
> is its x-coordinate. Thus, effectively the data points are projected onto the
> x-axis. Then the observed distribution of these x-coordinates is compared
> with the theoretical distribution of the x-coordinate according to the fitted
> model.
>
> Another possible choice would be covariate = function(x,y){ 2 * x + y}.
> More realistically, we would often have some other data in the form of a
> pixel image Z,
> and we could then use covariate=Z.
>
> The choice of covariate is arbitrary. Different choices of covariate lead to
> different tests, each of which is equally valid, and all of which have the
> same significance level (probability of type I error), but which will have
> different power (probability of type II error) depending on the true origin
> of the data.
>
> The appropriate choice of covariate depends on the *suspected* type of
> deviation from the null hypothesis.
>
> regards
> Adrian Baddeley
>
> Prof Adrian Baddeley FAA
> School of Earth and Environment
> University of Western Australia
> 35 Stirling Hwy, Crawley WA 6009, Australia
> and
> CSIRO Mathematics, Informatics & Statistics
> Leeuwin Centre, 65 Brockway Road, Floreat WA 6014, Australia
> Tel: 08 9333 6177 | Fax: 08 9333 6121 | Skype: adrian.baddeley
*************************
Hiroshi Saito:
E-MAIL: saito.hiro...@lab.ntt.co.jp
http://www9.plala.or.jp/hslab/
PHONE: +81 422 59 4300
FAX: +81 422 59 6364
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