Description Usage Arguments Details Value Note Author(s) References Examples
Calculates the PRESS statistic, a leave-one-out refitting and prediction method, as described in Allen (1971).
Works for any regression model with a call
slot, an update
and a predict
function, hence all models of class lm
, glm
, nls
and drc
(and maybe more...).
The function also returns the PRESS analog to R-square, the P-square.
1 |
object |
a fitted model. |
verbose |
logical. If |
From a fitted model, each of the predictors x_i, i = 1 …{n} is removed and the model is refitted to the n-1 points. The predicted value \hat{y}_{i, -i} is calculated at the excluded point x_i and the PRESS statistic is given by:
∑_{i=1}^n (y_i - \hat{y}_{i, -i})^2
The PRESS statistic is a surrogate measure of crossvalidation of small sample sizes and a measure for internal validity. Small values indicate that the model is not overly sensitive to any single data point. The P-square value, the PRESS equivalent to R-square, is given by
P^2 = \frac{∑_{i=1}^n \hat{\varepsilon}^2_{-i}}{∑_{i=1}^n (y_i - \bar{y})^2}
with \hat\varepsilon_{-i} = y_i - \hat{y}_{-i}.
A list with the following components:
stat |
The PRESS statistic. |
residuals |
a vector containing the PRESS residuals for each x_i. |
P.square |
the P-square value. See 'Details'. |
There is also a PRESS
function in library 'MPV' that works solely for lm
models using the hat matrix.
Andrej-Nikolai Spiess
The relationship between variable selection and data augmentation and a method for prediction.
Allen DM.
Technometrics (1974), 16: 25-127.
The Prediction Sum of Squares as a Criterion for Selecting Predictor Variables.
Allen DM.
Technical Report Number 23 (1971), Department of Statistics, University of Kentucky.
Classical and Modern Regression with Applications.
Myers RH.
Second Edition (1990), Duxbury Press (PWS-KENT Publishing Company), 299-304.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ## Example for PCR analysis.
m1 <- pcrfit(reps, 1, 2, l7)
PRESS(m1)
## Compare PRESS statistic in models
## with fewer parameters.
m2 <- pcrfit(reps, 1, 2, l5)
PRESS(m2)
m3 <- pcrfit(reps, 1, 2, l4)
PRESS(m3)
## Example for linear regression.
x <- 1:10
y <- rnorm(10, x, 0.1)
mod <- lm(y ~ x)
PRESS(mod)
## Example for NLS fitting.
DNase1 <- subset(DNase, Run == 1)
fm1DNase1 <- nls(density ~ SSlogis(log(conc), Asym, xmid, scal), DNase1)
res <- PRESS(fm1DNase1)
## PRESS residuals plot.
barplot(res$residuals)
|
Loading required package: MASS
Loading required package: minpack.lm
Loading required package: rgl
Loading required package: robustbase
Loading required package: Matrix
Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE
3: .onUnload failed in unloadNamespace() for 'rgl', details:
call: fun(...)
error: object 'rgl_quit' not found
.........10.........20.........30.........40.........
$stat
[1] 0.1707453
$residuals
[1] 0.0699912011 0.0492530168 0.0336378205 0.0140590934 0.0059468637
[6] -0.0152327406 -0.0243766115 -0.0426399156 -0.0501553346 -0.0482169526
[11] -0.0366446095 -0.0036441082 0.0373464997 0.0573424976 0.0522079969
[16] -0.0273484899 -0.1055046107 -0.0758678030 0.1430477620 0.1444815092
[21] -0.0389319241 -0.0531211747 -0.0925170482 -0.1211925186 -0.0689272016
[26] -0.0894964170 -0.0373461368 -0.0010994085 0.0876387288 0.0341216634
[31] 0.0411379038 0.0339644121 -0.0007373321 0.0896910509 0.0585704515
[36] 0.0754036046 0.0474721358 -0.0042283054 0.0293228863 0.0346239127
[41] 0.0119107545 0.0155387052 -0.0308005207 -0.0467234448 -0.0267803826
[46] -0.0365759500 -0.0778858256 -0.0113176165 0.0120983719
$P.square
[1] 0.9998614
.........10.........20.........30.........40.........
$stat
[1] 0.3268035
$residuals
[1] -0.106118454 -0.081593284 -0.057837927 -0.041580309 -0.016816340
[6] -0.006930450 0.013450991 0.022785352 0.038748617 0.055243604
[11] 0.066340758 0.078839608 0.080558464 0.040298420 -0.020051138
[16] -0.078591715 -0.085985589 -0.021335394 0.161313557 0.118811611
[21] -0.079458234 -0.084876337 -0.106059001 -0.116170742 -0.051263943
[26] -0.058884450 -0.000323674 0.040957433 0.130516252 0.083106588
[31] 0.091850841 0.085472438 0.050791569 0.137114478 0.103272589
[36] 0.115322965 0.081801592 0.023285051 0.048233674 0.043882281
[41] 0.010554768 0.002151746 -0.056229156 -0.085428283 -0.081179422
[46] -0.106273794 -0.160373431 -0.118745576 -0.118750543
$P.square
[1] 0.9997347
.........10.........20.........30.........40.........
$stat
[1] 0.4309723
$residuals
[1] -0.137979577 -0.113829850 -0.090439453 -0.074429395 -0.050020906
[6] -0.040134803 -0.019433513 -0.008210846 0.012964285 0.041420877
[11] 0.074913451 0.121080019 0.162461276 0.162884497 0.111075713
[16] -0.053469110 -0.182877980 -0.133366255 0.129065194 0.175136046
[21] 0.025454779 0.009426146 -0.034599262 -0.067603271 -0.021445994
[26] -0.042099717 0.006962126 0.041520911 0.126253717 0.075519524
[31] 0.081881330 0.073842883 0.038047779 0.123366768 0.088994207
[36] 0.100591043 0.066831593 0.008217351 0.032949217 0.028487557
[41] -0.004855648 -0.013305953 -0.071607114 -0.100778227 -0.096566825
[46] -0.121626423 -0.175620672 -0.134099097 -0.134113759
$P.square
[1] 0.9996502
.........10
$stat
[1] 0.1115235
$residuals
[1] 0.152527590 0.027823320 -0.109059747 -0.085491313 -0.009560023
[6] 0.010612568 0.103179965 -0.103810472 -0.110594330 0.185537340
$P.square
[1] 0.9986148
.........10......
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