Graphics Reference
In-Depth Information
Figure
.
.
A nonparametric estimate of a regression surface relating the mean level of a catch score to
latitude and longitude, using data from the Great Barrier Reef
Figure
.
displays a smooth estimate of a regression surface derived from data
on a catch score, representing the abundance of marine life on the sea bed at vari-
ous sampling points in a region near the Great Barrier Reef, as a function of latitude
and longitude. Poiner et al. (
) describe the background to these data and Bow-
man and Azzalini (
) illustrate the application of smoothing techniques on var-
ious subsets. Here, the data for two successive years are examined to investigate the
relationship between the catch score and the covariates latitude and longitude.
Severaltypesofgraphicaldisplayareavailablefortheresultingestimate.Figure
.
uses both colour shading and contour levels to indicate the height of the estimated
regressionsurface.hesimultaneous useofbothishelpfulinenhancing theinterpre-
tation in a form familiar to users of geographical maps. However, three-dimensional
projections are also easy to construct with many sotware packages and the ability to
rendersurfacestoahighdegreeofvisual quality isnowcommonly available. hedis-
play is further enhanced by animated rotation, providing a very realistic perception
of a real three-dimensional object. Figure
.
displays this kind of representation in
static form.
Figures
.
and
.
were produced with the smoothing parameters
(
h
, h
)=
(
selected by AIC and equivalent to
degrees of freedom. his choice
was based on a single underlying parameter h, which was then scaled by the sample
standard deviations, s
, s
, of the covariates to provide a pair of smoothing parame-
ters,
.
,
.
)
.Acommonsmoothing parameterforeachdimension orunrestricted
choices of h
and h
could also be allowed.
(
hs
, hs
)
