# ppr

##### Projection Pursuit Regression

Fit a projection pursuit regression model.

- Keywords
- regression

##### Usage

`ppr(x, …)`# S3 method for formula
ppr(formula, data, weights, subset, na.action,
contrasts = NULL, …, model = FALSE)

# S3 method for default
ppr(x, y, weights = rep(1, n),
ww = rep(1, q), nterms, max.terms = nterms, optlevel = 2,
sm.method = c("supsmu", "spline", "gcvspline"),
bass = 0, span = 0, df = 5, gcvpen = 1, trace = FALSE, …)

##### Arguments

- formula
a formula specifying one or more numeric response variables and the explanatory variables.

- x
numeric matrix of explanatory variables. Rows represent observations, and columns represent variables. Missing values are not accepted.

- y
numeric matrix of response variables. Rows represent observations, and columns represent variables. Missing values are not accepted.

- nterms
number of terms to include in the final model.

- data
a data frame (or similar: see

`model.frame`

) from which variables specified in`formula`

are preferentially to be taken.- weights
a vector of weights

`w_i`

for each*case*.- ww
a vector of weights for each

*response*, so the fit criterion is the sum over case`i`

and responses`j`

of`w_i ww_j (y_ij - fit_ij)^2`

divided by the sum of`w_i`

.- subset
an index vector specifying the cases to be used in the training sample. (NOTE: If given, this argument must be named.)

- na.action
a function to specify the action to be taken if

`NA`

s are found. The default action is given by`getOption("na.action")`

. (NOTE: If given, this argument must be named.)- contrasts
the contrasts to be used when any factor explanatory variables are coded.

- max.terms
maximum number of terms to choose from when building the model.

- optlevel
integer from 0 to 3 which determines the thoroughness of an optimization routine in the SMART program. See the ‘Details’ section.

- sm.method
the method used for smoothing the ridge functions. The default is to use Friedman's super smoother

`supsmu`

. The alternatives are to use the smoothing spline code underlying`smooth.spline`

, either with a specified (equivalent) degrees of freedom for each ridge functions, or to allow the smoothness to be chosen by GCV.Can be abbreviated.

- bass
super smoother bass tone control used with automatic span selection (see

`supsmu`

); the range of values is 0 to 10, with larger values resulting in increased smoothing.- span
super smoother span control (see

`supsmu`

). The default,`0`

, results in automatic span selection by local cross validation.`span`

can also take a value in`(0, 1]`

.- df
if

`sm.method`

is`"spline"`

specifies the smoothness of each ridge term via the requested equivalent degrees of freedom.- gcvpen
if

`sm.method`

is`"gcvspline"`

this is the penalty used in the GCV selection for each degree of freedom used.- trace
logical indicating if each spline fit should produce diagnostic output (about

`lambda`

and`df`

), and the supsmu fit about its steps.- …
arguments to be passed to or from other methods.

- model
logical. If true, the model frame is returned.

##### Details

The basic method is given by Friedman (1984), and is essentially the
same code used by S-PLUS's `ppreg`

. This code is extremely
sensitive to the compiler used.

The algorithm first adds up to `max.terms`

ridge terms one at a
time; it will use less if it is unable to find a term to add that makes
sufficient difference. It then removes the least
important term at each step until `nterms`

terms
are left.

The levels of optimization (argument `optlevel`

)
differ in how thoroughly the models are refitted during this process.
At level 0 the existing ridge terms are not refitted. At level 1
the projection directions are not refitted, but the ridge
functions and the regression coefficients are.
Levels 2 and 3 refit all the terms and are equivalent for one
response; level 3 is more careful to re-balance the contributions
from each regressor at each step and so is a little less likely to
converge to a saddle point of the sum of squares criterion.

##### Value

A list with the following components, many of which are for use by the method functions.

the matched call

the number of explanatory variables (after any coding)

the number of response variables

the argument `nterms`

the argument `max.terms`

the overall residual (weighted) sum of squares for the selected model

the overall residual (weighted) sum of squares against the
number of terms, up to `max.terms`

. Will be invalid (and zero)
for less than `nterms`

.

the argument `df`

if `sm.method`

is `"spline"`

or `"gcvspline"`

the equivalent number of degrees of freedom for each ridge term used.

the names of the explanatory variables

the names of the response variables

a matrix of the projection directions, with a column for each ridge term

a matrix of the coefficients applied for each response to the ridge terms: the rows are the responses and the columns the ridge terms

the weighted means of each response

the overall scale factor used: internally the responses are
divided by `ys`

to have unit total weighted sum of squares.

the fitted values, as a matrix if `q > 1`

.

the residuals, as a matrix if `q > 1`

.

internal work array, which includes the ridge functions evaluated at the training set points.

(only if `model = TRUE`

) the model frame.

##### References

Friedman, J. H. and Stuetzle, W. (1981).
Projection pursuit regression.
*Journal of the American Statistical Association*,
**76**, 817--823.
10.2307/2287576.

Friedman, J. H. (1984). SMART User's Guide. Laboratory for Computational Statistics, Stanford University Technical Report No.1.

Venables, W. N. and Ripley, B. D. (2002).
*Modern Applied Statistics with S*.
Springer.

##### See Also

##### Examples

`library(stats)`

```
# NOT RUN {
require(graphics)
# Note: your numerical values may differ
attach(rock)
area1 <- area/10000; peri1 <- peri/10000
rock.ppr <- ppr(log(perm) ~ area1 + peri1 + shape,
data = rock, nterms = 2, max.terms = 5)
rock.ppr
# Call:
# ppr.formula(formula = log(perm) ~ area1 + peri1 + shape, data = rock,
# nterms = 2, max.terms = 5)
#
# Goodness of fit:
# 2 terms 3 terms 4 terms 5 terms
# 8.737806 5.289517 4.745799 4.490378
summary(rock.ppr)
# ..... (same as above)
# .....
#
# Projection direction vectors ('alpha'):
# term 1 term 2
# area1 0.34357179 0.37071027
# peri1 -0.93781471 -0.61923542
# shape 0.04961846 0.69218595
#
# Coefficients of ridge terms:
# term 1 term 2
# 1.6079271 0.5460971
par(mfrow = c(3,2)) # maybe: , pty = "s")
plot(rock.ppr, main = "ppr(log(perm)~ ., nterms=2, max.terms=5)")
plot(update(rock.ppr, bass = 5), main = "update(..., bass = 5)")
plot(update(rock.ppr, sm.method = "gcv", gcvpen = 2),
main = "update(..., sm.method=\"gcv\", gcvpen=2)")
cbind(perm = rock$perm, prediction = round(exp(predict(rock.ppr)), 1))
detach()
# }
```

*Documentation reproduced from package stats, version 3.6.1, License: Part of R 3.6.1*