steepest  R Documentation 
These functions provide the path of steepest ascent (or descent)
for a fitted response surface produced by rsm
.
steepest (object, dist = seq(0, 5, by = .5), descent = FALSE)
canonical.path(object, which = ifelse(descent, length(object$b), 1),
dist = seq(5, 5, by = 0.5), descent = FALSE, ...)
object 

dist 
Vector of desired distances along the path of steepest ascent or descent.
In 
descent 
Set this to 
which 
Which canonical direction (eigenvector) to use. 
... 
Optional arguments passed to 
steepest
returns the linear path of steepest ascent for firstorder models, or a path obtained by ridge analysis (see Draper 1963) for secondorder models. In either case, the path begins at the origin.
canonical.path
applies only to secondorder models (at least a TWI
term present). It determines a linear path along one of the canonical variables, originating at the stationary point (not the origin). We need to specify which canonical variable to use.
The eigenvalues obtained in the canaonical analysis are always in decreasing order, so the first canonical direction will be the path of steepest ascent (or slowest descent, if all eigenvalues are negative) from the stationary point, and the last one will be the path of steepest descent (or slowest ascent, if all eigenvalues are positive). These are the defaults for which
when descent=FALSE
and descent=TRUE
respectively.
All eigenvalues less (in absolute value than) threshold
are taken to be zero. Increasing this threshold may bring the stationary point, and hence the canonical path, much closer to the design center, and thus less extrapolation.
With either function, the path in uncoded units depends on how the data are coded. Accordingly, it is important to code the predictor variables appropriately before fitting the responsesurface model. See coded.data
and its relatives for more information.
A data.frame
of points along the path of steepest ascent (or descent).
For steepest
, this path originates from the center of the experiment; for canonical.path
,
it starts at the stationary point.
If coding information is available, the data frame also includes the uncoded values of the variables.
For firstorder response surfaces, only steepest
may be used; the path is linear in that case.
For secondorder surfaces, steepest
uses ridge analysis, and the path may be curved.
Take careful note of the fitted values along the outputted path (labeled yhat
). For example, if the stationary point is a maximum
(all eigenvalues negative), the fitted values from steepest
will increase as far as the stationary point, then they will decrease as we proceed along what is now the path of slowest descent.
Russell V. Lenth
Draper, NR (1963), “Ridge analysis of response surfaces”, Technometrics, 5, 469–479.
Lenth RV (2009). “ResponseSurface Methods in R, Using rsm”, Journal of Statistical Software, 32(7), 1–17. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v032.i07")}
rsm
, coded.data
library(rsm)
heli.rsm = rsm (ave ~ block + SO(x1, x2, x3, x4), data = heli)
steepest(heli.rsm)
canonical.path(heli.rsm)
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