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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("lasso2-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('lasso2')
R Package to solve regression problems while imposing
	 an L1 constraint on the parameters. Based on S-plus Release 2.1
Copyright (C) 1998, 1999
Justin Lokhorst   <jlokhors@stats.adelaide.edu.au>
Berwin A. Turlach <bturlach@stats.adelaide.edu.au>
Bill Venables     <wvenable@stats.adelaide.edu.au>

Copyright (C) 2002
Martin Maechler <maechler@stat.math.ethz.ch>

> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "Iowa"
> 
> ### * Iowa
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Iowa
> ### Title: The Iowa Wheat Yield Data
> ### Aliases: Iowa
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(Iowa)
> pairs(Iowa)
> 
> 
> 
> cleanEx(); ..nameEx <- "Prostate"
> 
> ### * Prostate
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Prostate
> ### Title: Prostate Cancer Data
> ### Aliases: Prostate
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(Prostate)
> attach(Prostate)
> pairs(Prostate, col = 1+svi, pch = gleason - 5,
+       main = paste("Prostate data, n = ", nrow(Prostate)))
> detach()
> 
> l1c.P <- l1ce(lcavol ~ ., data = Prostate)
> coef(l1c.P)[coef(l1c.P) != 0] ## only age, lcp, lpsa (+ intercept)
(Intercept)         age         lcp        lpsa 
0.063731165 0.002632999 0.279970078 0.471409992 
> summary(l1c.P)

Call:
 l1ce(formula = lcavol ~ ., data = Prostate)
Residuals:
     Min       1Q   Median       3Q      Max 
-1.78581 -0.44170 -0.02532  0.54381  2.04761 

Coefficients:
            Value  Std. Error Z score Pr(>|Z|)
(Intercept) 0.0637 1.1990     0.0532  0.9576  
lweight     0.0000 0.1833     0.0000  1.0000  
age         0.0026 0.0105     0.2520  0.8011  
lbph        0.0000 0.0574     0.0000  1.0000  
svi         0.0000 0.2654     0.0000  1.0000  
lcp         0.2800 0.0835     3.3527  0.0008  
gleason     0.0000 0.1559     0.0000  1.0000  
pgg45       0.0000 0.0042     0.0000  1.0000  
lpsa        0.4714 0.0870     5.4160  0.0000  

Residual standard error: 0.739 on 88.35 degrees of freedom
The relative L1 bound was      : 0.5 
The absolute L1 bound was      : 0.9552333 
The Lagrangian for the bound is:  9.919065 

Correlation of Coefficients:
        (Intercept) lweight age     lbph    svi     lcp     gleason pgg45  
lweight -0.5537                                                            
age     -0.1881     -0.1852                                                
lbph     0.1984     -0.3899 -0.1077                                        
svi     -0.1307      0.0022 -0.0263  0.1557                                
lcp      0.2808      0.0104 -0.0268  0.1211 -0.4317                        
gleason -0.7329      0.1742 -0.2955  0.1037  0.1845 -0.1969                
pgg45    0.3650     -0.0060  0.0608 -0.2025 -0.1678 -0.2217 -0.5635        
lpsa     0.2167     -0.2903 -0.0522 -0.0288 -0.3204 -0.2623 -0.2308  0.1108
> 
> 
> 
> cleanEx(); ..nameEx <- "gl1ce"
> 
> ### * gl1ce
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: gl1ce
> ### Title: Generalized Regression With L1-constraint on the Parameters
> ### Aliases: gl1ce family.gl1ce
> ### Keywords: models optimize regression
> 
> ### ** Examples
> 
> ## example from base:
> data(esoph)
> summary(esoph)
   agegp          alcgp         tobgp        ncases         ncontrols    
 25-34:15   0-39g/day:23   0-9g/day:24   Min.   : 0.000   Min.   : 1.00  
 35-44:15   40-79    :23   10-19   :24   1st Qu.: 0.000   1st Qu.: 3.00  
 45-54:16   80-119   :21   20-29   :20   Median : 1.000   Median : 6.00  
 55-64:16   120+     :21   30+     :20   Mean   : 2.273   Mean   :11.08  
 65-74:15                                3rd Qu.: 4.000   3rd Qu.:14.00  
 75+  :11                                Max.   :17.000   Max.   :60.00  
> ## effects of alcohol, tobacco and interaction, age-adjusted
> modEso <- formula(cbind(ncases, ncontrols) ~ agegp + tobgp * alcgp)
> glm.E   <- glm(modEso, data = esoph, family = binomial())
> gl1c.E <- gl1ce(modEso, data = esoph, family = binomial())
> gl1c.E
Call:
gl1ce(formula = modEso, data = esoph, family = binomial())

Coefficients:
    (Intercept)         agegp.L         agegp.Q         agegp.C         agegp^4 
     -1.4700417       0.3681600       0.0000000       0.0000000       0.0000000 
        agegp^5         tobgp.L         tobgp.Q         tobgp.C         alcgp.L 
      0.0000000       0.0000000       0.0000000       0.0000000       0.5566889 
        alcgp.Q         alcgp.C tobgp.L:alcgp.L tobgp.Q:alcgp.L tobgp.C:alcgp.L 
      0.0000000       0.0000000       0.0000000       0.0000000       0.0000000 
tobgp.L:alcgp.Q tobgp.Q:alcgp.Q tobgp.C:alcgp.Q tobgp.L:alcgp.C tobgp.Q:alcgp.C 
      0.0000000       0.0000000       0.0000000       0.0000000       0.0000000 
tobgp.C:alcgp.C 
      0.0000000 

Family:

Family: binomial 
Link function: logit 


The absolute L1 bound was       :  0.5 
The Lagrangian for the bound is :  55.81258 
> plot(residuals(gl1c.E) ~ fitted(gl1c.E))
> 
> sg1c <- summary(gl1c.E)
> sg1c

Call:
gl1ce(formula = modEso, data = esoph, family = binomial())

Deviance Residuals:
    Min      1Q  Median      3Q     Max 
-3.9479 -1.0948  0.2076  0.8383  2.4604 

Coefficients
                Value  
(Intercept)     -1.4700
agegp.L          0.3682
agegp.Q         0      
agegp.C         0      
agegp^4         0      
agegp^5         0      
tobgp.L         0      
tobgp.Q         0      
tobgp.C         0      
alcgp.L          0.5567
alcgp.Q         0      
alcgp.C         0      
tobgp.L:alcgp.L 0      
tobgp.Q:alcgp.L 0      
tobgp.C:alcgp.L 0      
tobgp.L:alcgp.Q 0      
tobgp.Q:alcgp.Q 0      
tobgp.C:alcgp.Q 0      
tobgp.L:alcgp.C 0      
tobgp.Q:alcgp.C 0      
tobgp.C:alcgp.C 0      

Family:

Family: binomial 
Link function: logit 


The absolute L1 bound was     :  0.5 
The Lagrangian for the bound is :  55.81258 

Number of Iterations: 5 
> 
> ## Another comparison  glm() / gl1c.E:
> plot(predict(glm.E,  type="link"), predict(glm.E,  type="response"),
+      xlim = c(-3,0))
> points(predict(gl1c.E, type="link"), predict(gl1c.E, type="response"),
+        col = 2, cex = 1.5)
> 
> labels(gl1c.E)#-- oops! empty!!
character(0)
> 
> 
> 
> cleanEx(); ..nameEx <- "l1ce"
> 
> ### * l1ce
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: l1ce
> ### Title: Regression Fitting With L1-constraint on the Parameters
> ### Aliases: l1ce
> ### Keywords: models optimize regression
> 
> ### ** Examples
> 
> data(Iowa)
> l1c.I <- l1ce(Yield ~ ., Iowa, bound = 10, absolute.t=TRUE)
> l1c.I
Call:
l1ce(formula = Yield ~ ., data = Iowa, bound = 10, absolute.t = TRUE)

Coefficients:
  (Intercept)          Year         Rain0         Temp1         Rain1 
-1.223687e+03  6.665384e-01  8.895341e-03  0.000000e+00  0.000000e+00 
        Temp2         Rain2         Temp3         Rain3         Temp4 
 0.000000e+00  1.700162e+00 -1.612996e-01  0.000000e+00 -2.385012e-01 

The absolute L1 bound was      : 10 
The Lagrangian for the bound is:  69.63196 
> 
> ## The same, printing information in each step:
> l1ce(Yield ~ ., Iowa, bound = 10, trace = TRUE, absolute.t=TRUE)
******************************
  -->	Adding variable: 1
******************************

Iteration number: 0
Value of primal object function      : 2782.530000
Value of dual   object function      : -384.942354
L1 norm of current beta              : 0.000000 <= 10.000000
Maximal absolute value in t(X)%*%r   : 3.167472e+02 attained 1 time(s)
Number of parameters allowed to vary : 1
******************************

Iteration number: 1
Value of primal object function      : 1214.892326
Value of dual   object function      : 25.579582
L1 norm of current beta              : 9.898351 <= 10.000000
Maximal absolute value in t(X)%*%r   : 1.189313e+02 attained 1 time(s)
Number of parameters allowed to vary : 1
  -->	Adding variable: 9
  -->	Stepping onto the border of the L1 ball.
******************************

Iteration number: 2
Value of primal object function      : 1088.391622
Value of dual   object function      : 509.867040
L1 norm of current beta              : 10.000000 <= 10.000000
Maximal absolute value in t(X)%*%r   : 1.155562e+02 attained 1 time(s)
Number of parameters allowed to vary : 2
  -->	Adding variable: 6
******************************

Iteration number: 3
Value of primal object function      : 1015.808773
Value of dual   object function      : 925.285484
L1 norm of current beta              : 10.000000 <= 10.000000
Maximal absolute value in t(X)%*%r   : 7.728661e+01 attained 1 time(s)
Number of parameters allowed to vary : 3
  -->	Adding variable: 7
******************************

Iteration number: 4
Value of primal object function      : 1013.514687
Value of dual   object function      : 997.935649
L1 norm of current beta              : 10.000000 <= 10.000000
Maximal absolute value in t(X)%*%r   : 7.058775e+01 attained 1 time(s)
Number of parameters allowed to vary : 4
  -->	Adding variable: 2
******************************

Iteration number: 5
Value of primal object function      : 1013.485899
Value of dual   object function      : 1013.485899
L1 norm of current beta              : 10.000000 <= 10.000000
Maximal absolute value in t(X)%*%r   : 6.963196e+01 attained 5 time(s)
Number of parameters allowed to vary : 5
Call:
l1ce(formula = Yield ~ ., data = Iowa, trace = TRUE, bound = 10, 
    absolute.t = TRUE)

Coefficients:
  (Intercept)          Year         Rain0         Temp1         Rain1 
-1.223687e+03  6.665384e-01  8.895341e-03  0.000000e+00  0.000000e+00 
        Temp2         Rain2         Temp3         Rain3         Temp4 
 0.000000e+00  1.700162e+00 -1.612996e-01  0.000000e+00 -2.385012e-01 

The absolute L1 bound was      : 10 
The Lagrangian for the bound is:  69.63196 
> 
> data(Prostate)
> l1c.P <- l1ce(lpsa ~ ., Prostate, bound=(1:30)/30)
> length(l1c.P)# 30 l1ce models
[1] 30
> l1c.P # -- MM: too large; should do this in summary(.)!
Call:
l1ce(formula = lpsa ~ ., data = Prostate, bound = (1:30)/30)

Coefficients:
      (Intercept)     lcavol    lweight          age        lbph        svi
 [1,]   2.4079829 0.05215074 0.00000000  0.000000000 0.000000000 0.00000000
 [2,]   2.3375789 0.10430149 0.00000000  0.000000000 0.000000000 0.00000000
 [3,]   2.2671749 0.15645223 0.00000000  0.000000000 0.000000000 0.00000000
 [4,]   2.1967709 0.20860298 0.00000000  0.000000000 0.000000000 0.00000000
 [5,]   2.1263669 0.26075372 0.00000000  0.000000000 0.000000000 0.00000000
 [6,]   2.0559629 0.31290446 0.00000000  0.000000000 0.000000000 0.00000000
 [7,]   1.9884010 0.36118122 0.00000000  0.000000000 0.000000000 0.01102907
 [8,]   1.9371274 0.38725659 0.00000000  0.000000000 0.000000000 0.08526449
 [9,]   1.8858539 0.41333196 0.00000000  0.000000000 0.000000000 0.15949991
[10,]   1.7462431 0.43253601 0.02752108  0.000000000 0.000000000 0.22028323
[11,]   1.5266610 0.44551948 0.07995688  0.000000000 0.000000000 0.26888842
[12,]   1.3070788 0.45850294 0.13239268  0.000000000 0.000000000 0.31749362
[13,]   1.0874967 0.47148641 0.18482849  0.000000000 0.000000000 0.36609881
[14,]   0.8679146 0.48446987 0.23726429  0.000000000 0.000000000 0.41470401
[15,]   0.7284811 0.49365402 0.26818634  0.000000000 0.009282588 0.45505849
[16,]   0.6186210 0.50024970 0.29093423  0.000000000 0.021521822 0.48803364
[17,]   0.5087610 0.50684539 0.31368212  0.000000000 0.033761056 0.52100878
[18,]   0.3989010 0.51344107 0.33643002  0.000000000 0.046000291 0.55398393
[19,]   0.4140072 0.51893849 0.35553434 -0.001664361 0.056178983 0.57442325
[20,]   0.5142130 0.52368800 0.37215748 -0.004462120 0.064954486 0.58632593
[21,]   0.6144188 0.52843752 0.38878061 -0.007259879 0.073729989 0.59822860
[22,]   0.6576089 0.53207720 0.40600224 -0.010015486 0.082086242 0.61110512
[23,]   0.6687680 0.53772360 0.41600759 -0.011756627 0.086998743 0.62829926
[24,]   0.6688581 0.54476635 0.42150088 -0.012882424 0.089863829 0.64799306
[25,]   0.6689483 0.55180911 0.42699418 -0.014008221 0.092728916 0.66768687
[26,]   0.6690384 0.55885186 0.43248747 -0.015134019 0.095594003 0.68738067
[27,]   0.6691286 0.56589462 0.43798076 -0.016259816 0.098459090 0.70707447
[28,]   0.6692187 0.57293737 0.44347406 -0.017385613 0.101324177 0.72676828
[29,]   0.6693089 0.57998013 0.44896735 -0.018511410 0.104189264 0.74646208
[30,]   0.6693990 0.58702288 0.45446064 -0.019637208 0.107054351 0.76615588
               lcp     gleason        pgg45
 [1,]  0.000000000 0.000000000 0.0000000000
 [2,]  0.000000000 0.000000000 0.0000000000
 [3,]  0.000000000 0.000000000 0.0000000000
 [4,]  0.000000000 0.000000000 0.0000000000
 [5,]  0.000000000 0.000000000 0.0000000000
 [6,]  0.000000000 0.000000000 0.0000000000
 [7,]  0.000000000 0.000000000 0.0000000000
 [8,]  0.000000000 0.000000000 0.0000000000
 [9,]  0.000000000 0.000000000 0.0000000000
[10,]  0.000000000 0.000000000 0.0000000000
[11,]  0.000000000 0.000000000 0.0000000000
[12,]  0.000000000 0.000000000 0.0000000000
[13,]  0.000000000 0.000000000 0.0000000000
[14,]  0.000000000 0.000000000 0.0000000000
[15,]  0.000000000 0.000000000 0.0001812107
[16,]  0.000000000 0.000000000 0.0005707550
[17,]  0.000000000 0.000000000 0.0009602994
[18,]  0.000000000 0.000000000 0.0013498437
[19,]  0.000000000 0.000000000 0.0017000959
[20,]  0.000000000 0.000000000 0.0020235909
[21,]  0.000000000 0.000000000 0.0023470858
[22,]  0.000000000 0.008508797 0.0025069611
[23,] -0.008582305 0.015186708 0.0027130057
[24,] -0.022423914 0.019465173 0.0029719083
[25,] -0.036265523 0.023743639 0.0032308108
[26,] -0.050107133 0.028022104 0.0034897134
[27,] -0.063948742 0.032300569 0.0037486160
[28,] -0.077790351 0.036579034 0.0040075185
[29,] -0.091631960 0.040857499 0.0042664211
[30,] -0.105473570 0.045135964 0.0045253236

Relative and absolute L1 bounds and the Lagrangians:
       rel.bound  abs.bound   Lagrangian
 [1,] 0.03333333 0.06146616 7.548890e+01
 [2,] 0.06666667 0.12293233 6.958815e+01
 [3,] 0.10000000 0.18439849 6.368740e+01
 [4,] 0.13333333 0.24586466 5.778665e+01
 [5,] 0.16666667 0.30733082 5.188590e+01
 [6,] 0.20000000 0.36879698 4.598514e+01
 [7,] 0.23333333 0.43026315 4.028653e+01
 [8,] 0.26666667 0.49172931 3.574636e+01
 [9,] 0.30000000 0.55319548 3.120619e+01
[10,] 0.33333333 0.61466164 2.747686e+01
[11,] 0.36666667 0.67612780 2.448159e+01
[12,] 0.40000000 0.73759397 2.148631e+01
[13,] 0.43333333 0.79906013 1.849104e+01
[14,] 0.46666667 0.86052630 1.549576e+01
[15,] 0.50000000 0.92199246 1.305806e+01
[16,] 0.53333333 0.98345862 1.089104e+01
[17,] 0.56666667 1.04492479 8.724026e+00
[18,] 0.60000000 1.10639095 6.557010e+00
[19,] 0.63333333 1.16785712 5.138082e+00
[20,] 0.66666667 1.22932328 4.228589e+00
[21,] 0.70000000 1.29078944 3.319095e+00
[22,] 0.73333333 1.35225561 2.440644e+00
[23,] 0.76666667 1.41372177 1.938086e+00
[24,] 0.80000000 1.47518794 1.661216e+00
[25,] 0.83333333 1.53665410 1.384347e+00
[26,] 0.86666667 1.59812026 1.107478e+00
[27,] 0.90000000 1.65958643 8.306082e-01
[28,] 0.93333333 1.72105259 5.537388e-01
[29,] 0.96666667 1.78251876 2.768694e-01
[30,] 1.00000000 1.84398492 7.371335e-15
> ## Don't show:
> str(l1c.P, max.lev = 1)
List of 30
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 $ :List of 14
  ..- attr(*, "class")= chr "l1ce"
 - attr(*, "X.stds")= Named num [1:8] 1.179 0.497 7.445 1.451 0.414 ...
  ..- attr(*, "names")= chr [1:8] "lcavol" "lweight" "age" "lbph" ...
 - attr(*, "sweep.out")=List of 7
 - attr(*, "xtx")= num [1:8, 1:8] 96.00 18.64 21.60  2.63 51.73 ...
  ..- attr(*, "dimnames")=List of 2
 - attr(*, "terms")=Classes 'terms', 'formula' length 3 lpsa ~ lcavol + lweight + age + lbph + svi + lcp + gleason +      pgg45
  .. ..- attr(*, "variables")= language list(lpsa, lcavol, lweight, age, lbph, svi, lcp, gleason, pgg45)
  .. ..- attr(*, "factors")= int [1:9, 1:8] 0 1 0 0 0 0 0 0 0 0 ...
  .. .. ..- attr(*, "dimnames")=List of 2
  .. ..- attr(*, "term.labels")= chr [1:8] "lcavol" "lweight" "age" "lbph" ...
  .. ..- attr(*, "order")= int [1:8] 1 1 1 1 1 1 1 1
  .. ..- attr(*, "intercept")= int 1
  .. ..- attr(*, "response")= int 1
  .. ..- attr(*, ".Environment")=length 6 <environment> 
 - attr(*, "call")= language l1ce(formula = lpsa ~ ., data = Prostate, bound = (1:30)/30)
 - attr(*, "assign")= int [1:9] 0 1 2 3 4 5 6 7 8
 - attr(*, "class")= chr "l1celist"
> ## End Don't show
> 
> plot(resid(l1c.I) ~ fitted(l1c.I))
> abline(h = 0, lty = 3, lwd = .2)
> 
> 
> 
> cleanEx(); ..nameEx <- "merge.formula"
> 
> ### * merge.formula
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: merge.formula
> ### Title: Merge Formula With Right Hand Side of Second Formula
> ### Aliases: merge.formula
> ### Keywords: utilities
> 
> ### ** Examples
> 
> merge.formula(y ~ x1, ~ x2) ## ->  y ~ x1 + x2
y ~ x1 + x2
> 
> f2 <- merge.formula(y ~ x1*x2, z ~ (x2+x4)^3)
> f. <- merge.formula(y ~ x1*x2,   ~ (x2+x4)^3) # no LHS for 2nd term
> f2
y ~ x1 * x2 + (x2 + x4)^3
> stopifnot(f2 == f.)
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.l1celist"
> 
> ### * plot.l1celist
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.l1celist
> ### Title: Plot Method for `l1celist' Objects
> ### Aliases: plot.l1celist
> ### Keywords: hplot
> 
> ### ** Examples
> 
> data(Prostate)
> l1c.P <- l1ce(lpsa ~ ., Prostate, bound=(1:20)/20)
> length(l1c.P)# 20 l1ce models
[1] 20
> plot(l1c.P)
> 
> 
> 
> cleanEx(); ..nameEx <- "predict.gl1ce"
> 
> ### * predict.gl1ce
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: predict.gl1ce
> ### Title: Prediction Method for a `gl1ce' Object
> ### Aliases: predict.gl1ce
> ### Keywords: models
> 
> ### ** Examples
> 
>   ## start with
>   example(gl1ce)

gl1ce> data(esoph)

gl1ce> summary(esoph)
   agegp          alcgp         tobgp        ncases         ncontrols    
 25-34:15   0-39g/day:23   0-9g/day:24   Min.   : 0.000   Min.   : 1.00  
 35-44:15   40-79    :23   10-19   :24   1st Qu.: 0.000   1st Qu.: 3.00  
 45-54:16   80-119   :21   20-29   :20   Median : 1.000   Median : 6.00  
 55-64:16   120+     :21   30+     :20   Mean   : 2.273   Mean   :11.08  
 65-74:15                                3rd Qu.: 4.000   3rd Qu.:14.00  
 75+  :11                                Max.   :17.000   Max.   :60.00  

gl1ce> modEso <- formula(cbind(ncases, ncontrols) ~ agegp + 
    tobgp * alcgp)

gl1ce> glm.E <- glm(modEso, data = esoph, family = binomial())

gl1ce> gl1c.E <- gl1ce(modEso, data = esoph, family = binomial())

gl1ce> gl1c.E
Call:
gl1ce(formula = modEso, data = esoph, family = binomial())

Coefficients:
    (Intercept)         agegp.L         agegp.Q         agegp.C         agegp^4 
     -1.4700417       0.3681600       0.0000000       0.0000000       0.0000000 
        agegp^5         tobgp.L         tobgp.Q         tobgp.C         alcgp.L 
      0.0000000       0.0000000       0.0000000       0.0000000       0.5566889 
        alcgp.Q         alcgp.C tobgp.L:alcgp.L tobgp.Q:alcgp.L tobgp.C:alcgp.L 
      0.0000000       0.0000000       0.0000000       0.0000000       0.0000000 
tobgp.L:alcgp.Q tobgp.Q:alcgp.Q tobgp.C:alcgp.Q tobgp.L:alcgp.C tobgp.Q:alcgp.C 
      0.0000000       0.0000000       0.0000000       0.0000000       0.0000000 
tobgp.C:alcgp.C 
      0.0000000 

Family:

Family: binomial 
Link function: logit 


The absolute L1 bound was       :  0.5 
The Lagrangian for the bound is :  55.81258 

gl1ce> plot(residuals(gl1c.E) ~ fitted(gl1c.E))

gl1ce> sg1c <- summary(gl1c.E)

gl1ce> sg1c

Call:
gl1ce(formula = modEso, data = esoph, family = binomial())

Deviance Residuals:
    Min      1Q  Median      3Q     Max 
-3.9479 -1.0948  0.2076  0.8383  2.4604 

Coefficients
                Value  
(Intercept)     -1.4700
agegp.L          0.3682
agegp.Q         0      
agegp.C         0      
agegp^4         0      
agegp^5         0      
tobgp.L         0      
tobgp.Q         0      
tobgp.C         0      
alcgp.L          0.5567
alcgp.Q         0      
alcgp.C         0      
tobgp.L:alcgp.L 0      
tobgp.Q:alcgp.L 0      
tobgp.C:alcgp.L 0      
tobgp.L:alcgp.Q 0      
tobgp.Q:alcgp.Q 0      
tobgp.C:alcgp.Q 0      
tobgp.L:alcgp.C 0      
tobgp.Q:alcgp.C 0      
tobgp.C:alcgp.C 0      

Family:

Family: binomial 
Link function: logit 


The absolute L1 bound was     :  0.5 
The Lagrangian for the bound is :  55.81258 

Number of Iterations: 5 

gl1ce> plot(predict(glm.E, type = "link"), predict(glm.E, 
    type = "response"), xlim = c(-3, 0))

gl1ce> points(predict(gl1c.E, type = "link"), predict(gl1c.E, 
    type = "response"), col = 2, cex = 1.5)

gl1ce> labels(gl1c.E)
character(0)
>   predict(gl1c.E, new = esoph[1:7,])# type 'link'
        1         2         3         4         5         6         7 
-2.063498 -2.063498 -2.063498 -2.063498 -1.814539 -1.814539 -1.814539 
>   predict(gl1c.E, new = esoph[1:7,], type = "response")
        1         2         3         4         5         6         7 
0.1126956 0.1126956 0.1126956 0.1126956 0.1400905 0.1400905 0.1400905 
> 
>   ## identities / consistency checks :
>   stopifnot(predict(gl1c.E, type = "response") == fitted(gl1c.E),
+             all.equal(predict(gl1c.E)[1:7],
+                       predict(gl1c.E, new = esoph[1:7,])),
+             all.equal(fitted(gl1c.E)[1:7],
+                       predict(gl1c.E, new = esoph[1:7,], type = "response"))
+            )
> 
> 
> 
> cleanEx(); ..nameEx <- "predict.l1ce"
> 
> ### * predict.l1ce
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: predict.l1ce
> ### Title: Predict Method for `l1ce' Objects
> ### Aliases: predict.l1ce
> ### Keywords: models
> 
> ### ** Examples
> 
> data(Iowa)
> l1c.I <- l1ce(Yield ~ ., Iowa, bound = 10, absolute.t=TRUE)
> p10 <- predict(l1c.I, newdata =   Iowa[10:19,])
> stopifnot(all.equal(p10, fitted(l1c.I)[10:19]))
> 
> 
> 
> cleanEx(); ..nameEx <- "qr.rtr.inv"
> 
> ### * qr.rtr.inv
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: qr.rtr.inv
> ### Title: Reconstruct the Inverse of R'R from a QR Object
> ### Aliases: qr.rtr.inv
> ### Keywords: algebra array
> 
> ### ** Examples
> 
> (h3 <- 1/outer(0:5, 1:3, "+"))
          [,1]      [,2]      [,3]
[1,] 1.0000000 0.5000000 0.3333333
[2,] 0.5000000 0.3333333 0.2500000
[3,] 0.3333333 0.2500000 0.2000000
[4,] 0.2500000 0.2000000 0.1666667
[5,] 0.2000000 0.1666667 0.1428571
[6,] 0.1666667 0.1428571 0.1250000
> rtr <- qr.rtr.inv(qr(h3))
> all.equal(c(rtr %*% 1:3), solve(crossprod(h3), 1:3))
[1] TRUE
> 
> 
> 
> cleanEx(); ..nameEx <- "summary.l1ce"
> 
> ### * summary.l1ce
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.l1ce
> ### Title: Summary Method for ``l1ce'' Objects (Regression with L1
> ###   Constraint)
> ### Aliases: summary.l1ce print.summary.l1ce
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(Prostate)
> summary(l1ce(lpsa ~ .,Prostate))

Call:
 l1ce(formula = lpsa ~ ., data = Prostate)
Residuals:
    Min      1Q  Median      3Q     Max 
-1.6355 -0.4119  0.0760  0.4520  1.8299 

Coefficients:
            Value  Std. Error Z score Pr(>|Z|)
(Intercept) 0.7285 1.3898     0.5242  0.6002  
lcavol      0.4937 0.0919     5.3711  0.0000  
lweight     0.2682 0.1774     1.5115  0.1307  
age         0.0000 0.0111     0.0000  1.0000  
lbph        0.0093 0.0587     0.1581  0.8744  
svi         0.4551 0.2525     1.8023  0.0715  
lcp         0.0000 0.0947     0.0000  1.0000  
gleason     0.0000 0.1685     0.0000  1.0000  
pgg45       0.0002 0.0046     0.0391  0.9688  

Residual standard error: 0.7595 on 88.36 degrees of freedom
The relative L1 bound was      : 0.5 
The absolute L1 bound was      : 0.9219925 
The Lagrangian for the bound is:  13.05806 

Correlation of Coefficients:
        (Intercept) lcavol  lweight age     lbph    svi     lcp     gleason
lcavol   0.1988                                                            
lweight -0.4815     -0.2071                                                
age     -0.3938     -0.0603 -0.0974                                        
lbph     0.3629     -0.0201 -0.5165 -0.1303                                
svi     -0.0624     -0.2273 -0.1442  0.0635  0.0648                        
lcp      0.0457     -0.4153  0.0598  0.0665  0.0632 -0.3779                
gleason -0.7666     -0.2009  0.1163 -0.0774 -0.0617  0.1084 -0.0243        
pgg45    0.4988      0.0956 -0.0380 -0.0630 -0.1111 -0.1921 -0.2935 -0.6526
> 
> # Produces the following output:
> ## Not run: 
> ##D Call:
> ##D  l1ce(formula = lpsa ~ ., data = Prostate)
> ##D Residuals:
> ##D     Min      1Q Median    3Q  Max
> ##D  -1.636 -0.4119  0.076 0.452 1.83
> ##D 
> ##D Coefficients:
> ##D              Value Std. Error Z score Pr(>|Z|)
> ##D (Intercept) 0.7285 1.3898     0.5242  0.6002
> ##D      lcavol 0.4937 0.0919     5.3711  0.0000
> ##D     lweight 0.2682 0.1774     1.5115  0.1307
> ##D         age 0.0000 0.0111     0.0000  1.0000
> ##D        lbph 0.0093 0.0587     0.1581  0.8744
> ##D         svi 0.4551 0.2525     1.8023  0.0715
> ##D         lcp 0.0000 0.0947     0.0000  1.0000
> ##D     gleason 0.0000 0.1685     0.0000  1.0000
> ##D       pgg45 0.0002 0.0046     0.0391  0.9688
> ##D 
> ##D Residual standard error: 0.7595 on 88.36 degrees of freedom
> ##D The relative L1 bound was      : 0.5
> ##D The absolute L1 bound was      : 0.9219925
> ##D The Lagrangian for the bound is:  13.05806
> ##D 
> ##D Correlation of Coefficients:
> ##D         (Intercept)  lcavol lweight     age    lbph     svi     lcp gleason
> ##D  lcavol  0.1988
> ##D lweight -0.4815     -0.2071
> ##D     age -0.3938     -0.0603 -0.0974
> ##D    lbph  0.3629     -0.0201 -0.5165 -0.1303
> ##D     svi -0.0624     -0.2273 -0.1442  0.0635  0.0648
> ##D     lcp  0.0457     -0.4153  0.0598  0.0665  0.0632 -0.3779
> ##D gleason -0.7666     -0.2009  0.1163 -0.0774 -0.0617  0.1084 -0.0243
> ##D   pgg45  0.4988      0.0956 -0.0380 -0.0630 -0.1111 -0.1921 -0.2935 -0.6526
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "tr"
> 
> ### * tr
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: tr
> ### Title: Trace of a Matrix
> ### Aliases: tr
> ### Keywords: math
> 
> ### ** Examples
> 
> tr(cbind(1,1:3,4:2)) # 5
[1] 5
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  1.82 0.06 2.33 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')