[Analogue-commits] r266 - in pkg: . R inst man tests/Examples

noreply at r-forge.r-project.org noreply at r-forge.r-project.org
Fri Apr 20 16:13:14 CEST 2012


Author: gsimpson
Date: 2012-04-20 16:13:14 +0200 (Fri, 20 Apr 2012)
New Revision: 266

Modified:
   pkg/DESCRIPTION
   pkg/R/deshrink.R
   pkg/R/deshrinkPred.R
   pkg/R/wa.R
   pkg/R/wa.formula.R
   pkg/inst/ChangeLog
   pkg/man/deshrink.Rd
   pkg/man/wa.Rd
   pkg/tests/Examples/analogue-Ex.Rout.save
Log:
add monotonic deshrinking to wa()

Modified: pkg/DESCRIPTION
===================================================================
--- pkg/DESCRIPTION	2012-04-20 14:12:38 UTC (rev 265)
+++ pkg/DESCRIPTION	2012-04-20 14:13:14 UTC (rev 266)
@@ -1,10 +1,10 @@
 Package: analogue
 Type: Package
 Title: Analogue and weighted averaging methods for palaeoecology
-Version: 0.9-2
+Version: 0.9-3
 Date: $Date$
 Depends: R (>= 2.15.0), stats, graphics, vegan (>= 1.17-12), lattice, grid, 
-         MASS, princurve
+         MASS, princurve, mgcv
 Author: Gavin L. Simpson, Jari Oksanen
 Maintainer: Gavin L. Simpson <gavin.simpson at ucl.ac.uk>
 Description: Fits Modern Analogue Technique and Weighted Averaging transfer 

Modified: pkg/R/deshrink.R
===================================================================
--- pkg/R/deshrink.R	2012-04-20 14:12:38 UTC (rev 265)
+++ pkg/R/deshrink.R	2012-04-20 14:13:14 UTC (rev 266)
@@ -1,6 +1,6 @@
 `deshrink` <- function(env, wa.env,
                        type = c("inverse", "classical",
-                       "expanded", "none")) {
+                       "expanded", "none","monotonic")) {
 ### Inline Functions ############################################
     ## inverse deshrinking
     `inverse` <- function(env, wa.env) {
@@ -37,6 +37,28 @@
     `none` <- function(env, wa.env) {
         return(list(coefficients = c(0, 1), env = wa.env))
     }
+    ## Monotonic deshrinking via pcls() in mgcv
+    ## Use a spline fit to deshrink instead of the linear inverse
+    ## or classical deshrinking methods
+    ## Needs to be constrained to be monotonic so ?mono.con
+    `monotonic` <- function(env, wa.env) {
+        df <- data.frame(env = env, wa.env = drop(wa.env))
+        mod <- gam(env ~ s(wa.env, k = 10, bs = "cr"), data = df)
+        ## grab bits for setting up a monotonic spline, see ?pcls
+        sm <- smoothCon(s(wa.env, k = 10, bs = "cr"), data = df,
+                        knots = NULL)[[1]]
+        ## Fm are the constraints to enforce monotonicity
+        Fm <- mono.con(sm$xp)
+        G <- list(X = sm$X, C = matrix(0,0,0), sp = mod$sp, p = sm$xp,
+                  y = env, w = env*0+1, Ain = Fm$A, bin = Fm$b, S = sm$S,
+                  off = 0)
+        p <- pcls(G)
+        ## predict for the current data
+        pred <- Predict.matrix(sm, data = data.frame(wa.env = wa.env)) %*% p
+        pred <- drop(pred)
+        ## return
+        list(coefficients = list(sm = sm, p = p), env = pred)
+    }
 ### End Inline Functions #########################################
     if(missing(type))
         type <- "inverse"
@@ -45,7 +67,8 @@
                   inverse = inverse(env, wa.env),
                   classical = classical(env, wa.env),
                   expanded = expanded(env, wa.env),
-                  none = none(env, wa.env))
+                  none = none(env, wa.env),
+                  monotonic = monotonic(env, wa.env))
     class(res) <- c("deshrink","list")
     attr(res, "type") <- type
     return(res)

Modified: pkg/R/deshrinkPred.R
===================================================================
--- pkg/R/deshrinkPred.R	2012-04-20 14:12:38 UTC (rev 265)
+++ pkg/R/deshrinkPred.R	2012-04-20 14:13:14 UTC (rev 266)
@@ -1,6 +1,6 @@
 `deshrinkPred` <- function(x, coef,
                            type = c("inverse", "classical",
-                           "expanded", "none")) {
+                           "expanded", "none","monotonic")) {
     if(missing(type))
         type <- "inverse"
     type <- match.arg(type)
@@ -8,6 +8,8 @@
                   inverse = coef[1] + (coef[2] * x),
                   classical = (x - coef[1]) / coef[2],
                   expanded = coef[1] + (coef[2] * x),
-                  none = coef[1] + (coef[2] * x))
+                  none = coef[1] + (coef[2] * x),
+                  monotonic = drop(Predict.matrix(coef$sm,
+                  data.frame(wa.env = x)) %*% coef$p))
     return(res)
 }

Modified: pkg/R/wa.R
===================================================================
--- pkg/R/wa.R	2012-04-20 14:12:38 UTC (rev 265)
+++ pkg/R/wa.R	2012-04-20 14:13:14 UTC (rev 266)
@@ -2,7 +2,7 @@
 
 `wa.default` <-
     function(x, env,
-             deshrink = c("inverse", "classical", "expanded", "none"),
+             deshrink = c("inverse", "classical", "expanded", "none", "monotonic"),
              tol.dw = FALSE, useN2 = TRUE,
              na.tol = c("min","mean","max"),
              small.tol = c("min","mean","fraction","absolute"),

Modified: pkg/R/wa.formula.R
===================================================================
--- pkg/R/wa.formula.R	2012-04-20 14:12:38 UTC (rev 265)
+++ pkg/R/wa.formula.R	2012-04-20 14:13:14 UTC (rev 266)
@@ -1,5 +1,5 @@
 `wa.formula` <- function(formula, data, subset, na.action,
-                         deshrink = c("inverse", "classical", "expanded", "none"),
+                         deshrink = c("inverse", "classical", "expanded", "none", "monotonic"),
                          tol.dw = FALSE, useN2 = TRUE,
                          na.tol = c("min","mean","max"),
                          small.tol = c("min","mean","fraction","absolute"),

Modified: pkg/inst/ChangeLog
===================================================================
--- pkg/inst/ChangeLog	2012-04-20 14:12:38 UTC (rev 265)
+++ pkg/inst/ChangeLog	2012-04-20 14:13:14 UTC (rev 266)
@@ -1,5 +1,24 @@
 analogue Change Log
 
+Version 0.9-3
+
+	* wa: deshrinking via a monotonic cubic regression spline
+	is now available via `deshrink = "monotonic"`. This uses
+	functions from the *mgcv* package of Simon Wood and as a
+	result, *analogue* now Depends on that package too. The
+	exact nature of the dependency may change before 0.10 is
+	released.
+
+	This idea goes back to ter Braak & Juggins (1993; Hydrobiologia
+	*269/270*, 485--502) and Marchetto (1994; Journal of
+	Paleolimnology *12*, 155--162), but the implementation here
+	uses monotonic constraints after Wood (1994; SIAM Journal on
+	Scientific Computing *15*(5), 1126--1133 and follows Steve
+	Juggins' implementation borrowing code from `?pcls` in *mgcv*.
+
+	* predict.wa: example was enclosed in \dontrun{} without
+	reason. This example is now run.
+
 Version 0.9-2
 
 	* wa: small tolerances can now be replaced by the mean

Modified: pkg/man/deshrink.Rd
===================================================================
--- pkg/man/deshrink.Rd	2012-04-20 14:12:38 UTC (rev 265)
+++ pkg/man/deshrink.Rd	2012-04-20 14:13:14 UTC (rev 266)
@@ -13,11 +13,13 @@
 new samples given a set of deshrinking coefficients.
 }
 \usage{
-deshrink(env, wa.env, type = c("inverse", "classical",
-                               "expanded", "none"))
+deshrink(env, wa.env,
+         type = c("inverse", "classical", "expanded", "none",
+                  "monotonic"))
 
-deshrinkPred(x, coef, type = c("inverse", "classical",
-                               "expanded", "none"))
+deshrinkPred(x, coef,
+         type = c("inverse", "classical", "expanded", "none",
+                  "monotonic"))
 }
 \arguments{
   \item{env}{numeric; original environmental values.}

Modified: pkg/man/wa.Rd
===================================================================
--- pkg/man/wa.Rd	2012-04-20 14:12:38 UTC (rev 265)
+++ pkg/man/wa.Rd	2012-04-20 14:13:14 UTC (rev 266)
@@ -17,14 +17,14 @@
 wa(x, \dots)
 
 \method{wa}{default}(x, env,
-   deshrink = c("inverse", "classical", "expanded", "none"),
+   deshrink = c("inverse", "classical", "expanded", "none", "monotonic"),
    tol.dw = FALSE, useN2 = TRUE,
    na.tol = c("min","mean","max"),
    small.tol = c("min","mean","fraction","absolute"),
    min.tol = NULL, f = 0.1, ...)
 
 \method{wa}{formula}(formula, data, subset, na.action,
-   deshrink = c("inverse", "classical", "expanded", "none"),
+   deshrink = c("inverse", "classical", "expanded", "none", "monotonic"),
    tol.dw = FALSE, useN2 = TRUE, na.tol = c("min","mean","max"),
    small.tol = c("min","mean","fraction","absolute"), min.tol = NULL,
    f = 0.1,..., model = FALSE)
@@ -43,8 +43,8 @@
   \item{x}{The species training set data}
   \item{env, y}{The response vector}
   \item{deshrink}{Which deshrinking method to use? One of
-    \code{"inverse"} or \code{"classical"}, \code{"expanded"} or
-    \code{"none"}}
+    \code{"inverse"} or \code{"classical"}, \code{"expanded"},
+      \code{"none"}, or \code{"monotonic"}.}
   \item{tol.dw}{logical; should species with wider tolerances be given
     lower weight?}
   \item{useN2}{logical; should Hill's N2 values be used to produce
@@ -134,7 +134,12 @@
   \item{fitted.values}{The fitted values of the response for each of the
     training set samples.}
   \item{residuals}{Model residuals.}
-  \item{coefficients}{Deshrinking coefficients.}
+  \item{coefficients}{Deshrinking coefficients. Note that in the case of
+    \code{deshrink = "monotonic"} this is a list with components \code{sm}
+    (the representation of the smooth term as returned by
+    \code{\link{smoothCon}}) and \code{p} (solutions to the least squares
+    fit with monotonic constraints, the result of a call to
+    \code{\link{pcls}}).}
   \item{rmse}{The RMSE of the model.}
   \item{r.squared}{The coefficient of determination of the observed and
     fitted values of the response.}
@@ -195,6 +200,16 @@
            min.tol = 2, small.tol = "mean")
 mod3
 
+## fit a WA model with monotonic deshrinking
+mod4 <- wa(SumSST ~., data = ImbrieKipp, deshrink = "monotonic")
+mod4
+
+## extract the fitted values
+fitted(mod4)
+
+## residuals for the training set
+residuals(mod4)
+
 }
 \keyword{methods}
 \keyword{models}

Modified: pkg/tests/Examples/analogue-Ex.Rout.save
===================================================================
--- pkg/tests/Examples/analogue-Ex.Rout.save	2012-04-20 14:12:38 UTC (rev 265)
+++ pkg/tests/Examples/analogue-Ex.Rout.save	2012-04-20 14:13:14 UTC (rev 266)
@@ -1,5 +1,5 @@
 
-R version 2.15.0 Patched (2012-04-14 r59019) -- "Easter Beagle"
+R version 2.15.0 Patched (2012-04-16 r59049) -- "Easter Beagle"
 Copyright (C) 2012 The R Foundation for Statistical Computing
 ISBN 3-900051-07-0
 Platform: x86_64-unknown-linux-gnu (64-bit)
@@ -29,7 +29,9 @@
 Loading required package: grid
 Loading required package: MASS
 Loading required package: princurve
-This is analogue 0.9-2
+Loading required package: mgcv
+This is mgcv 1.7-13. For overview type 'help("mgcv-package")'.
+This is analogue 0.9-3
 > 
 > assign(".oldSearch", search(), pos = 'CheckExEnv')
 > cleanEx()
@@ -4856,6 +4858,70 @@
      RMSE  R-squared  Avg. Bias  Max. Bias  
    1.9924     0.9194     0.0000    -2.5992  
 
+
+wa> ## fit a WA model with monotonic deshrinking
+wa> mod4 <- wa(SumSST ~., data = ImbrieKipp, deshrink = "monotonic")
+
+wa> mod4
+
+	Weighted Averaging Transfer Function
+
+Call:
+wa(formula = SumSST ~ ., data = ImbrieKipp, deshrink = "monotonic") 
+
+Deshrinking  : Monotonic 
+Tolerance DW : No 
+No. samples  : 61 
+No. species  : 27 
+
+Performance:
+     RMSE  R-squared  Avg. Bias  Max. Bias  
+   1.6107     0.9474     0.0000    -3.8985  
+
+
+wa> ## extract the fitted values
+wa> fitted(mod4)
+   V14.61   V17.196   V18.110   V16.227    V14.47    V23.22     V2.12    V23.29 
+ 5.898451  5.959142  6.075776  6.163532  8.126549  8.641443  6.060926 11.563327 
+   V12.43      R9.7    A157.3    V23.81    V23.82    V12.53    V23.83    V12.56 
+11.970987 14.010916 13.276208 16.803976 16.168939 16.404646 15.002783 19.397640 
+  A152.84    V16.50   V22.122    V16.41     V4.32    V12.66   V19.245      V4.8 
+18.706537 18.292346 16.869999 22.940318 22.427838 20.008273 22.491527 22.112760 
+  A180.15    V18.34   V20.213   V19.222   A180.39   V16.189    V12.18     V7.67 
+21.211500 23.637275 23.665250 23.012758 24.659931 26.099307 25.975387 23.686165 
+  V17.165   V19.310   V16.190  A153.154   V19.308   V22.172    V10.98   V22.219 
+24.126195 23.356724 24.980999 25.862528 26.266124 26.716472 24.597292 25.941735 
+   V16.33   V22.204   V20.167    V10.89    V12.79   V19.216    V14.90   A180.72 
+26.698566 26.292611 27.127317 26.849545 26.553215 26.190434 26.330267 26.794756 
+   V16.21   A180.76   V15.164   A180.78     V14.5    V3.128   A179.13     V9.31 
+27.236962 27.145893 27.268262 26.451803 27.327863 27.351207 26.967878 26.530415 
+  V20.230     V20.7   V20.234    V18.21   V12.122 
+27.059522 27.670385 27.213081 27.390149 27.279387 
+
+wa> ## residuals for the training set
+wa> residuals(mod4)
+     V14.61     V17.196     V18.110     V16.227      V14.47      V23.22 
+-3.89845110 -0.95914237 -0.57577610  0.83646773 -1.12654866  1.85855684 
+      V2.12      V23.29      V12.43        R9.7      A157.3      V23.81 
+ 4.93907447 -1.56332718  1.02901346 -2.01091600  0.72379238 -2.30397581 
+     V23.82      V12.53      V23.83      V12.56     A152.84      V16.50 
+-1.16893885 -1.90464620  0.99721686 -1.39764003  1.29346295 -0.29234573 
+    V22.122      V16.41       V4.32      V12.66     V19.245        V4.8 
+ 2.13000056 -4.44031822 -0.92783840  0.99172654 -1.49152689  1.88724026 
+    A180.15      V18.34     V20.213     V19.222     A180.39     V16.189 
+ 2.78850048 -0.63727536  0.33475037 -0.01275751 -1.65993109 -2.09930701 
+     V12.18       V7.67     V17.165     V19.310     V16.190    A153.154 
+-0.97538682  2.31383514  1.87380535  2.64327583  0.01900071  0.13747169 
+    V19.308     V22.172      V10.98     V22.219      V16.33     V22.204 
+-0.26612390 -2.21647192  2.40270758  0.25826513 -1.69856608  0.20738893 
+    V20.167      V10.89      V12.79     V19.216      V14.90     A180.72 
+-0.92731700 -0.84954530 -0.55321548  0.80956624  0.66973330  0.70524398 
+     V16.21     A180.76     V15.164     A180.78       V14.5      V3.128 
+-0.23696237 -0.14589252 -0.26826158  0.54819699 -0.32786314  1.64879299 
+    A179.13       V9.31     V20.230       V20.7     V20.234      V18.21 
+ 1.53212230  0.96958483  0.44047759 -0.17038549 -0.21308146 -0.39014885 
+    V12.122 
+ 0.72061292 
 > 
 > ## the model performance statistics
 > performance(mod)
@@ -5927,6 +5993,70 @@
      RMSE  R-squared  Avg. Bias  Max. Bias  
    1.9924     0.9194     0.0000    -2.5992  
 
+
+wa> ## fit a WA model with monotonic deshrinking
+wa> mod4 <- wa(SumSST ~., data = ImbrieKipp, deshrink = "monotonic")
+
+wa> mod4
+
+	Weighted Averaging Transfer Function
+
+Call:
+wa(formula = SumSST ~ ., data = ImbrieKipp, deshrink = "monotonic") 
+
+Deshrinking  : Monotonic 
+Tolerance DW : No 
+No. samples  : 61 
+No. species  : 27 
+
+Performance:
+     RMSE  R-squared  Avg. Bias  Max. Bias  
+   1.6107     0.9474     0.0000    -3.8985  
+
+
+wa> ## extract the fitted values
+wa> fitted(mod4)
+   V14.61   V17.196   V18.110   V16.227    V14.47    V23.22     V2.12    V23.29 
+ 5.898451  5.959142  6.075776  6.163532  8.126549  8.641443  6.060926 11.563327 
+   V12.43      R9.7    A157.3    V23.81    V23.82    V12.53    V23.83    V12.56 
+11.970987 14.010916 13.276208 16.803976 16.168939 16.404646 15.002783 19.397640 
+  A152.84    V16.50   V22.122    V16.41     V4.32    V12.66   V19.245      V4.8 
+18.706537 18.292346 16.869999 22.940318 22.427838 20.008273 22.491527 22.112760 
+  A180.15    V18.34   V20.213   V19.222   A180.39   V16.189    V12.18     V7.67 
+21.211500 23.637275 23.665250 23.012758 24.659931 26.099307 25.975387 23.686165 
+  V17.165   V19.310   V16.190  A153.154   V19.308   V22.172    V10.98   V22.219 
+24.126195 23.356724 24.980999 25.862528 26.266124 26.716472 24.597292 25.941735 
+   V16.33   V22.204   V20.167    V10.89    V12.79   V19.216    V14.90   A180.72 
+26.698566 26.292611 27.127317 26.849545 26.553215 26.190434 26.330267 26.794756 
+   V16.21   A180.76   V15.164   A180.78     V14.5    V3.128   A179.13     V9.31 
+27.236962 27.145893 27.268262 26.451803 27.327863 27.351207 26.967878 26.530415 
+  V20.230     V20.7   V20.234    V18.21   V12.122 
+27.059522 27.670385 27.213081 27.390149 27.279387 
+
+wa> ## residuals for the training set
+wa> residuals(mod4)
+     V14.61     V17.196     V18.110     V16.227      V14.47      V23.22 
+-3.89845110 -0.95914237 -0.57577610  0.83646773 -1.12654866  1.85855684 
+      V2.12      V23.29      V12.43        R9.7      A157.3      V23.81 
+ 4.93907447 -1.56332718  1.02901346 -2.01091600  0.72379238 -2.30397581 
+     V23.82      V12.53      V23.83      V12.56     A152.84      V16.50 
+-1.16893885 -1.90464620  0.99721686 -1.39764003  1.29346295 -0.29234573 
+    V22.122      V16.41       V4.32      V12.66     V19.245        V4.8 
+ 2.13000056 -4.44031822 -0.92783840  0.99172654 -1.49152689  1.88724026 
+    A180.15      V18.34     V20.213     V19.222     A180.39     V16.189 
+ 2.78850048 -0.63727536  0.33475037 -0.01275751 -1.65993109 -2.09930701 
+     V12.18       V7.67     V17.165     V19.310     V16.190    A153.154 
+-0.97538682  2.31383514  1.87380535  2.64327583  0.01900071  0.13747169 
+    V19.308     V22.172      V10.98     V22.219      V16.33     V22.204 
+-0.26612390 -2.21647192  2.40270758  0.25826513 -1.69856608  0.20738893 
+    V20.167      V10.89      V12.79     V19.216      V14.90     A180.72 
+-0.92731700 -0.84954530 -0.55321548  0.80956624  0.66973330  0.70524398 
+     V16.21     A180.76     V15.164     A180.78       V14.5      V3.128 
+-0.23696237 -0.14589252 -0.26826158  0.54819699 -0.32786314  1.64879299 
+    A179.13       V9.31     V20.230       V20.7     V20.234      V18.21 
+ 1.53212230  0.96958483  0.44047759 -0.17038549 -0.21308146 -0.39014885 
+    V12.122 
+ 0.72061292 
 > 
 > ## diagnostics for the WA model
 > par(mfrow = c(1,2))
@@ -6123,31 +6253,49 @@
 > 
 > ### ** Examples
 > 
-> ## Not run: 
-> ##D ## Imbrie and Kipp
-> ##D data(ImbrieKipp)
-> ##D data(SumSST)
-> ##D ik.wa <- wa(SumSST ~ ., data = ImbrieKipp, tol.dw = TRUE,
-> ##D             min.tol = 2, small.tol = "min")
-> ##D ik.wa
-> ##D 
-> ##D ## load V12.122 core data
-> ##D data(V12.122)
-> ##D V12.122 <- V12.122 / 100
-> ##D 
-> ##D ## predict summer sea-surface temperature for V12.122 core
-> ##D v12.pred <- predict(ik.wa, V12.122, CV = "bootstrap", n.boot = 100)
-> ##D 
-> ##D ## draw the fitted reconstruction
-> ##D reconPlot(v12.pred, use.labels = TRUE, display = "bars")
-> ##D 
-> ##D ## extract the model performance stats
-> ##D performance(v12.pred)
-> ## End(Not run)
+> ## Imbrie and Kipp
+> data(ImbrieKipp)
+> data(SumSST)
+> ik.wa <- wa(SumSST ~ ., data = ImbrieKipp, tol.dw = TRUE,
++             min.tol = 2, small.tol = "min")
+> ik.wa
+
+	Weighted Averaging Transfer Function
+
+Call:
+wa(formula = SumSST ~ ., data = ImbrieKipp, tol.dw = TRUE, small.tol = "min",  
+
+     min.tol = 2) 
+
+Deshrinking  : Inverse 
+Tolerance DW : Yes 
+No. samples  : 61 
+No. species  : 27 
+
+Performance:
+     RMSE  R-squared  Avg. Bias  Max. Bias  
+   2.0268     0.9166     0.0000    -2.4507  
+
 > 
+> ## load V12.122 core data
+> data(V12.122)
+> V12.122 <- V12.122 / 100
 > 
+> ## predict summer sea-surface temperature for V12.122 core
+> set.seed(2)
+> v12.pred <- predict(ik.wa, V12.122, CV = "bootstrap", n.boot = 100)
 > 
+> ## draw the fitted reconstruction
+> reconPlot(v12.pred, use.labels = TRUE, display = "bars")
 > 
+> ## extract the model performance stats
+> performance(v12.pred)
+   RMSEP       R2 Avg.Bias Max.Bias 
+  2.3617   0.8989  -0.1483  -3.2158 
+> 
+> 
+> 
+> 
 > cleanEx()
 > nameEx("reconPlot")
 > ### * reconPlot
@@ -7055,9 +7203,72 @@
    1.9924     0.9194     0.0000    -2.5992  
 
 > 
+> ## fit a WA model with monotonic deshrinking
+> mod4 <- wa(SumSST ~., data = ImbrieKipp, deshrink = "monotonic")
+> mod4
+
+	Weighted Averaging Transfer Function
+
+Call:
+wa(formula = SumSST ~ ., data = ImbrieKipp, deshrink = "monotonic") 
+
+Deshrinking  : Monotonic 
+Tolerance DW : No 
+No. samples  : 61 
+No. species  : 27 
+
+Performance:
+     RMSE  R-squared  Avg. Bias  Max. Bias  
+   1.6107     0.9474     0.0000    -3.8985  
+
 > 
+> ## extract the fitted values
+> fitted(mod4)
+   V14.61   V17.196   V18.110   V16.227    V14.47    V23.22     V2.12    V23.29 
+ 5.898451  5.959142  6.075776  6.163532  8.126549  8.641443  6.060926 11.563327 
+   V12.43      R9.7    A157.3    V23.81    V23.82    V12.53    V23.83    V12.56 
+11.970987 14.010916 13.276208 16.803976 16.168939 16.404646 15.002783 19.397640 
+  A152.84    V16.50   V22.122    V16.41     V4.32    V12.66   V19.245      V4.8 
+18.706537 18.292346 16.869999 22.940318 22.427838 20.008273 22.491527 22.112760 
+  A180.15    V18.34   V20.213   V19.222   A180.39   V16.189    V12.18     V7.67 
+21.211500 23.637275 23.665250 23.012758 24.659931 26.099307 25.975387 23.686165 
+  V17.165   V19.310   V16.190  A153.154   V19.308   V22.172    V10.98   V22.219 
+24.126195 23.356724 24.980999 25.862528 26.266124 26.716472 24.597292 25.941735 
+   V16.33   V22.204   V20.167    V10.89    V12.79   V19.216    V14.90   A180.72 
+26.698566 26.292611 27.127317 26.849545 26.553215 26.190434 26.330267 26.794756 
+   V16.21   A180.76   V15.164   A180.78     V14.5    V3.128   A179.13     V9.31 
+27.236962 27.145893 27.268262 26.451803 27.327863 27.351207 26.967878 26.530415 
+  V20.230     V20.7   V20.234    V18.21   V12.122 
+27.059522 27.670385 27.213081 27.390149 27.279387 
 > 
+> ## residuals for the training set
+> residuals(mod4)
+     V14.61     V17.196     V18.110     V16.227      V14.47      V23.22 
+-3.89845110 -0.95914237 -0.57577610  0.83646773 -1.12654866  1.85855684 
+      V2.12      V23.29      V12.43        R9.7      A157.3      V23.81 
+ 4.93907447 -1.56332718  1.02901346 -2.01091600  0.72379238 -2.30397581 
+     V23.82      V12.53      V23.83      V12.56     A152.84      V16.50 
+-1.16893885 -1.90464620  0.99721686 -1.39764003  1.29346295 -0.29234573 
+    V22.122      V16.41       V4.32      V12.66     V19.245        V4.8 
+ 2.13000056 -4.44031822 -0.92783840  0.99172654 -1.49152689  1.88724026 
+    A180.15      V18.34     V20.213     V19.222     A180.39     V16.189 
+ 2.78850048 -0.63727536  0.33475037 -0.01275751 -1.65993109 -2.09930701 
+     V12.18       V7.67     V17.165     V19.310     V16.190    A153.154 
+-0.97538682  2.31383514  1.87380535  2.64327583  0.01900071  0.13747169 
+    V19.308     V22.172      V10.98     V22.219      V16.33     V22.204 
+-0.26612390 -2.21647192  2.40270758  0.25826513 -1.69856608  0.20738893 
+    V20.167      V10.89      V12.79     V19.216      V14.90     A180.72 
+-0.92731700 -0.84954530 -0.55321548  0.80956624  0.66973330  0.70524398 
+     V16.21     A180.76     V15.164     A180.78       V14.5      V3.128 
+-0.23696237 -0.14589252 -0.26826158  0.54819699 -0.32786314  1.64879299 
+    A179.13       V9.31     V20.230       V20.7     V20.234      V18.21 
+ 1.53212230  0.96958483  0.44047759 -0.17038549 -0.21308146 -0.39014885 
+    V12.122 
+ 0.72061292 
 > 
+> 
+> 
+> 
 > graphics::par(get("par.postscript", pos = 'CheckExEnv'))
 > cleanEx()
 > nameEx("weightedCor")
@@ -7201,7 +7412,7 @@
 > ### * <FOOTER>
 > ###
 > cat("Time elapsed: ", proc.time() - get("ptime", pos = 'CheckExEnv'),"\n")
-Time elapsed:  15.256 0.187 16.245 0 0 
+Time elapsed:  16.957 0.457 17.764 0 0 
 > grDevices::dev.off()
 null device 
           1 



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