Last data update: 2014.03.03

 R: Generate Exact Solution Path
exact.pathR Documentation

Generate Exact Solution Path

Description

exact.path generates the whole solution paths.

Usage

exact.path(X, y, max.var=20, verbose=FALSE)

Arguments

X

an n\times p design matrix for the predictors.

y

a vector of the response values.

max.var

a numerical value (default value: 20) that gives the maximum number of steps. Extra 4 steps are allowed in case the same set of predictors enter or exit the set of active predictors more than once. This value contributes to the determination of how many λ_ks are to be found.

verbose

If TRUE, the value of λ_k and the associated information will be printed at every step a new λ_k is found. The default is FALSE.

Details

Starting with a large value, this function finds recursively λ_1, λ_2, … until the desired number of steps is achieved. At each step, inactive predictors become active, active predictors become inactive, or both. The selection indicator is automatically determined. The backend engine is LASSO.exact.

It is not necessary to standardize the columns of X and the response vector y. Such standardization is conducted anyway in this function.

Value

A list object of class "path". This list contains the following components:

breaks

a length K vector of λ_ks

tau

a p\times K matrix of selection indicators.

beta

a p\times K matrix of regression coefficients. See also LASSO.exact.

score

a p\times K matrix of scores. See also LASSO.exact.

Author(s)

Kai Wang <kai-wang@uiowa.edu>

References

Wang K. (2013) Exact LASSO linear regression. Submitted.

See Also

LASSO.exact is the function for generating λ_k at each step.

Examples

library(ncvreg)
data(prostate)
exact.path(as.matrix(prostate[,-9]), prostate$lpsa, verbose=TRUE)

library(ncvreg)
data(heart)
exact.path(as.matrix(heart[,-1]), heart$sbp)

library(lars)
data(diabetes)
exact.path(diabetes$x, diabetes$y, verbose=TRUE)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(ExactPath)
Loading required package: ncvreg
Loading required package: lars
Loaded lars 1.2

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/ExactPath/exact.path.Rd_%03d_medium.png", width=480, height=480)
> ### Name: exact.path
> ### Title: Generate Exact Solution Path
> ### Aliases: exact.path
> 
> ### ** Examples
> 
> library(ncvreg)
> data(prostate)
> exact.path(as.matrix(prostate[,-9]), prostate$lpsa, verbose=TRUE)
        beta     score    breaks tau change
lcavol     0 0.7344603 0.7344603   1      +
lweight    0 0.4333194 0.4333194   0      |
age        0 0.1695928 0.1695928   0      |
lbph       0 0.1798094 0.1798094   0      |
svi        0 0.5662182 0.5662182   0      |
lcp        0 0.5488132 0.5488132   0      |
gleason    0 0.3689868 0.3689868   0      |
pgg45      0 0.4223159 0.4223159   0      |

lambda_1 = 0.7344603


             beta      score      breaks tau change
lcavol  0.3648277 0.36963266 0.734460326   1      |
lweight 0.0000000 0.33097742 0.315905924   0      |
age     0.0000000 0.08750666 0.005599166   0      |
lbph    0.0000000 0.16983148 0.164213317   0      |
svi     0.0000000 0.36963266 0.369632655   1      +
lcp     0.0000000 0.30244122 0.162692091   0      |
gleason 0.0000000 0.21122910 0.090548236   0      |
pgg45   0.0000000 0.26410752 0.183306962   0      |

lambda_2 = 0.3696327


              beta      score      breaks tau change
lcavol  0.39987516 0.31570000 0.931045893   1      |
lweight 0.00000000 0.31570000 0.315699999   1      +
age     0.00000000 0.07549736 0.006689277   0      |
lbph    0.00000000 0.17188153 0.177148069   0      |
svi     0.03504749 0.31570000 0.369632655   1      |
lcp     0.00000000 0.25518243 0.011433137   0      |
gleason 0.00000000 0.18484432 0.059513515   0      |
pgg45   0.00000000 0.23286969 0.118859665   0      |

lambda_3 = 0.3157


             beta        score      breaks tau change
lcavol  0.4829234  0.124387656 1.236864149   1      |
lweight 0.1488355  0.124387656 0.315699999   1      |
age     0.0000000 -0.009501825 0.044843100   0      |
lbph    0.0000000  0.114381619 0.110081973   0      |
svi     0.1584829  0.124387656 0.370020043   1      |
lcp     0.0000000  0.091524348 0.008021252   0      |
gleason 0.0000000  0.100916555 0.082572420   0      |
pgg45   0.0000000  0.124387656 0.124387656   1      +

lambda_4 = 0.1243877


               beta       score     breaks tau change
lcavol  0.487275262  0.10869606 1.86567157   1      |
lweight 0.161198691  0.10869606 0.31329310   1      |
age     0.000000000 -0.01816516 0.05036808   0      |
lbph    0.000000000  0.10869606 0.10869606   1      +
svi     0.165712510  0.10869606 0.46836949   1      |
lcp     0.000000000  0.07589476 0.01621793   0      |
gleason 0.000000000  0.08912116 0.02985989   0      |
pgg45   0.009168559  0.10869606 0.12438766   1      |

lambda_5 = 0.1086961


              beta       score     breaks tau change
lcavol  0.50491055  0.05558212 1.57627146   1      |
lweight 0.18200727  0.05558212 0.52015610   1      |
age     0.00000000 -0.05558212 0.05558212  -1      +
lbph    0.04431172  0.05558212 0.10869606   1      |
svi     0.19858501  0.05558212 0.37644704   1      |
lcp     0.00000000  0.02313882 0.01608855   0      |
gleason 0.00000000  0.04774973 0.02015453   0      |
pgg45   0.03388032  0.05558212 0.12840240   1      |

lambda_6 = 0.05558212


               beta        score     breaks tau change
lcavol   0.51741672  0.032103019 1.00350133   1      |
lweight  0.20157703  0.032103019 0.27394789   1      |
age     -0.05185925 -0.032103019 0.05558212  -1      |
lbph     0.07629111  0.032103019 0.08811557   1      |
svi      0.21103160  0.032103019 0.43019063   1      |
lcp      0.00000000 -0.003996983 0.01906527   0      |
gleason  0.00000000  0.032103019 0.03210302   1      +
pgg45    0.05594893  0.032103019 0.09162786   1      |

lambda_7 = 0.03210302


               beta       score     breaks tau change
lcavol   0.52231490  0.01913394 1.40208545   1      |
lweight  0.21336467  0.01913394 0.25388364   1      |
age     -0.08120861 -0.01913394 0.05501892  -1      |
lbph     0.09366845  0.01913394 0.08904069   1      |
svi      0.21890832  0.01913394 0.37956812   1      |
lcp      0.00000000 -0.01913394 0.01913394  -1      +
gleason  0.01066560  0.01913394 0.03210302   1      |
pgg45    0.06064448  0.01913394 0.18663378   1      |

lambda_8 = 0.01913394


               beta         score     breaks tau change
lcavol   0.57621928  1.214306e-16 0.20453520   1      |
lweight  0.23085294 -1.752071e-16 0.25257645   1      |
age     -0.13704517  5.551115e-17 0.04696230  -1      |
lbph     0.12155214  8.673617e-19 0.08340974   1      |
svi      0.27317070 -8.673617e-17 0.09632513   1      |
lcp     -0.12846050 -1.075529e-16 0.01913394  -1      |
gleason  0.03079639  1.630640e-16 0.02927139   1      |
pgg45    0.10891159 -4.943962e-17 0.04317448   1      |

lambda_9 = 0


               beta         score     breaks tau change
lcavol   0.57621928  1.214306e-16 0.20453520   1      |
lweight  0.23085294 -1.752071e-16 0.25257645   1      |
age     -0.13704517  5.551115e-17 0.04696230  -1      |
lbph     0.12155214  8.673617e-19 0.08340974   1      |
svi      0.27317070 -8.673617e-17 0.09632513   1      |
lcp     -0.12846050 -1.075529e-16 0.01913394  -1      |
gleason  0.03079639  1.630640e-16 0.02927139   1      |
pgg45    0.10891159 -4.943962e-17 0.04317448   1      |

lambda_10 = 0


               beta         score     breaks tau change
lcavol   0.57621928  1.214306e-16 0.20453520   1      |
lweight  0.23085294 -1.752071e-16 0.25257645   1      |
age     -0.13704517  5.551115e-17 0.04696230  -1      |
lbph     0.12155214  8.673617e-19 0.08340974   1      |
svi      0.27317070 -8.673617e-17 0.09632513   1      |
lcp     -0.12846050 -1.075529e-16 0.01913394  -1      |
gleason  0.03079639  1.630640e-16 0.02927139   1      |
pgg45    0.10891159 -4.943962e-17 0.04317448   1      |

lambda_11 = 0


               beta         score     breaks tau change
lcavol   0.57621928  1.214306e-16 0.20453520   1      |
lweight  0.23085294 -1.752071e-16 0.25257645   1      |
age     -0.13704517  5.551115e-17 0.04696230  -1      |
lbph     0.12155214  8.673617e-19 0.08340974   1      |
svi      0.27317070 -8.673617e-17 0.09632513   1      |
lcp     -0.12846050 -1.075529e-16 0.01913394  -1      |
gleason  0.03079639  1.630640e-16 0.02927139   1      |
pgg45    0.10891159 -4.943962e-17 0.04317448   1      |

lambda_12 = 0


breaks:
 [1] 0.7345 0.3696 0.3157 0.1244 0.1087 0.0556 0.0321 0.0191 0.0000 0.0000
[11] 0.0000 0.0000

Indicator matrix (parameters x breaks):
     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
[1,]    1    1    1    1    1    1    1    1    1     1     1     1
[2,]    0    0    1    1    1    1    1    1    1     1     1     1
[3,]    0    0    0    0    0   -1   -1   -1   -1    -1    -1    -1
[4,]    0    0    0    0    1    1    1    1    1     1     1     1
[5,]    0    1    1    1    1    1    1    1    1     1     1     1
[6,]    0    0    0    0    0    0    0   -1   -1    -1    -1    -1
[7,]    0    0    0    0    0    0    1    1    1     1     1     1
[8,]    0    0    0    1    1    1    1    1    1     1     1     1

Beta matrix (parameters x breaks):
     [,1]   [,2]   [,3]   [,4]   [,5]   [,6]    [,7]    [,8]    [,9]   [,10]
[1,]    0 0.3648 0.3999 0.4829 0.4873 0.5049  0.5174  0.5223  0.5762  0.5762
[2,]    0 0.0000 0.0000 0.1488 0.1612 0.1820  0.2016  0.2134  0.2309  0.2309
[3,]    0 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0519 -0.0812 -0.1370 -0.1370
[4,]    0 0.0000 0.0000 0.0000 0.0000 0.0443  0.0763  0.0937  0.1216  0.1216
[5,]    0 0.0000 0.0350 0.1585 0.1657 0.1986  0.2110  0.2189  0.2732  0.2732
[6,]    0 0.0000 0.0000 0.0000 0.0000 0.0000  0.0000  0.0000 -0.1285 -0.1285
[7,]    0 0.0000 0.0000 0.0000 0.0000 0.0000  0.0000  0.0107  0.0308  0.0308
[8,]    0 0.0000 0.0000 0.0000 0.0092 0.0339  0.0559  0.0606  0.1089  0.1089
       [,11]   [,12]
[1,]  0.5762  0.5762
[2,]  0.2309  0.2309
[3,] -0.1370 -0.1370
[4,]  0.1216  0.1216
[5,]  0.2732  0.2732
[6,] -0.1285 -0.1285
[7,]  0.0308  0.0308
[8,]  0.1089  0.1089

Score matrix (parameters x breaks):
       [,1]   [,2]   [,3]    [,4]    [,5]    [,6]    [,7]    [,8] [,9] [,10]
[1,] 0.7345 0.3696 0.3157  0.1244  0.1087  0.0556  0.0321  0.0191    0     0
[2,] 0.4333 0.3310 0.3157  0.1244  0.1087  0.0556  0.0321  0.0191    0     0
[3,] 0.1696 0.0875 0.0755 -0.0095 -0.0182 -0.0556 -0.0321 -0.0191    0     0
[4,] 0.1798 0.1698 0.1719  0.1144  0.1087  0.0556  0.0321  0.0191    0     0
[5,] 0.5662 0.3696 0.3157  0.1244  0.1087  0.0556  0.0321  0.0191    0     0
[6,] 0.5488 0.3024 0.2552  0.0915  0.0759  0.0231 -0.0040 -0.0191    0     0
[7,] 0.3690 0.2112 0.1848  0.1009  0.0891  0.0477  0.0321  0.0191    0     0
[8,] 0.4223 0.2641 0.2329  0.1244  0.1087  0.0556  0.0321  0.0191    0     0
     [,11] [,12]
[1,]     0     0
[2,]     0     0
[3,]     0     0
[4,]     0     0
[5,]     0     0
[6,]     0     0
[7,]     0     0
[8,]     0     0
> 
> library(ncvreg)
> data(heart)
> exact.path(as.matrix(heart[,-1]), heart$sbp)
breaks:
 [1] 0.3888 0.3025 0.1072 0.0695 0.0677 0.0483 0.0339 0.0189 0.0046 0.0000
[11] 0.0000 0.0000 0.0000

Indicator matrix (parameters x breaks):
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
 [1,]    0    0    0    0    0    1    1    1    1     1     1     1     1
 [2,]    0    0    0    0    0    0    0    0   -1    -1    -1    -1    -1
 [3,]    0    1    1    1    1    1    1    1    1     1     1     1     1
 [4,]    0    0    0    0    0    0    0   -1   -1    -1    -1    -1    -1
 [5,]    0    0    0    0    0    0   -1   -1   -1    -1    -1    -1    -1
 [6,]    0    0    0    0    1    1    1    1    1     1     1     1     1
 [7,]    0    0    1    1    1    1    1    1    1     1     1     1     1
 [8,]    1    1    1    1    1    1    1    1    1     1     1     1     1
 [9,]    0    0    0    1    1    1    1    1    1     1     1     1     1

Beta matrix (parameters x breaks):
      [,1]   [,2]   [,3]   [,4]   [,5]   [,6]   [,7]    [,8]    [,9]   [,10]
 [1,]    0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0062  0.0128  0.0175  0.0191
 [2,]    0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000  0.0000  0.0000 -0.0084
 [3,]    0 0.0000 0.1201 0.1412 0.1423 0.1371 0.1332  0.1265  0.1200  0.1209
 [4,]    0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000  0.0000 -0.0222 -0.0290
 [5,]    0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0180 -0.0344 -0.0393
 [6,]    0 0.0000 0.0000 0.0000 0.0000 0.0177 0.0309  0.0484  0.0661  0.0722
 [7,]    0 0.0000 0.0000 0.0334 0.0350 0.0520 0.0637  0.0768  0.0905  0.0942
 [8,]    0 0.0863 0.2064 0.2274 0.2280 0.2385 0.2440  0.2472  0.2542  0.2566
 [9,]    0 0.0000 0.0000 0.0000 0.0013 0.0152 0.0246  0.0375  0.0545  0.0613
        [,11]   [,12]   [,13]
 [1,]  0.0191  0.0191  0.0191
 [2,] -0.0084 -0.0084 -0.0084
 [3,]  0.1209  0.1209  0.1209
 [4,] -0.0290 -0.0290 -0.0290
 [5,] -0.0393 -0.0393 -0.0393
 [6,]  0.0722  0.0722  0.0722
 [7,]  0.0942  0.0942  0.0942
 [8,]  0.2566  0.2566  0.2566
 [9,]  0.0613  0.0613  0.0613

Score matrix (parameters x breaks):
         [,1]    [,2]    [,3]    [,4]    [,5]    [,6]    [,7]    [,8]    [,9]
 [1,]  0.2122  0.1734  0.0849  0.0626  0.0614  0.0483  0.0339  0.0189  0.0046
 [2,]  0.1583  0.1314  0.0410  0.0263  0.0254  0.0154  0.0080  0.0010 -0.0046
 [3,]  0.3565  0.3025  0.1072  0.0695  0.0677  0.0483  0.0339  0.0189  0.0046
 [4,]  0.0856  0.0650  0.0143  0.0028  0.0020 -0.0068 -0.0130 -0.0189 -0.0046
 [5,] -0.0575 -0.0486 -0.0311 -0.0293 -0.0294 -0.0320 -0.0339 -0.0189 -0.0046
 [6,]  0.2381  0.2129  0.0918  0.0688  0.0677  0.0483  0.0339  0.0189  0.0046
 [7,]  0.1401  0.1314  0.1072  0.0695  0.0677  0.0483  0.0339  0.0189  0.0046
 [8,]  0.3888  0.3025  0.1072  0.0695  0.0677  0.0483  0.0339  0.0189  0.0046
 [9,]  0.1924  0.1602  0.0848  0.0695  0.0677  0.0483  0.0339  0.0189  0.0046
      [,10] [,11] [,12] [,13]
 [1,]     0     0     0     0
 [2,]     0     0     0     0
 [3,]     0     0     0     0
 [4,]     0     0     0     0
 [5,]     0     0     0     0
 [6,]     0     0     0     0
 [7,]     0     0     0     0
 [8,]     0     0     0     0
 [9,]     0     0     0     0
> 
> library(lars)
> data(diabetes)
> exact.path(diabetes$x, diabetes$y, verbose=TRUE)
    beta      score     breaks tau change
age    0  0.1878888  0.1878888   0      |
sex    0  0.0430620  0.0430620   0      |
bmi    0  0.5864501  0.5864501   1      +
map    0  0.4414838  0.4414838   0      |
tc     0  0.2120225  0.2120225   0      |
ldl    0  0.1740536  0.1740536   0      |
hdl    0 -0.3947893 -0.3947893   0      |
tch    0  0.4304529  0.4304529   0      |
ltg    0  0.5658834  0.5658834   0      |
glu    0  0.3824835  0.3824835   0      |

lambda_1 = 0.5864501


          beta       score      breaks tau change
age 0.00000000  0.18101569 0.097366953   0      |
sex 0.00000000  0.03978816 0.007940243   0      |
bmi 0.03713466  0.54931548 0.586450134   1      |
map 0.00000000  0.42680024 0.346671836   0      |
tc  0.00000000  0.20274708 0.087361378   0      |
ldl 0.00000000  0.16435513 0.028275050   0      |
hdl 0.00000000 -0.38116785 0.283758715   0      |
tch 0.00000000  0.41508632 0.320331051   0      |
ltg 0.00000000  0.54931548 0.549315476   1      +
glu 0.00000000  0.36804999 0.252800576   0      |

lambda_2 = 0.5493155


         beta        score     breaks tau change
age 0.0000000  0.096042421 0.01147702   0      |
sex 0.0000000 -0.004590128 0.04348583   0      |
bmi 0.2235362  0.279749284 0.60301808   1      |
map 0.0000000  0.279749284 0.27974928   1      +
tc  0.0000000  0.060098053 0.05750773   0      |
ldl 0.0000000  0.056331097 0.03981747   0      |
hdl 0.0000000 -0.238498355 0.19212009   0      |
tch 0.0000000  0.222782566 0.08099422   0      |
ltg 0.1864015  0.279749284 0.54931548   1      |
glu 0.0000000  0.208984151 0.10711738   0      |

lambda_3 = 0.2797493


          beta       score     breaks tau change
age 0.00000000  0.05906256 0.01833811   0      |
sex 0.00000000 -0.02712679 0.06251665   0      |
bmi 0.26854265  0.19523361 0.69951820   1      |
map 0.04894302  0.19523361 0.27974928   1      |
tc  0.00000000  0.01370014 0.06034938   0      |
ldl 0.00000000  0.02111255 0.04252338   0      |
hdl 0.00000000 -0.19523361 0.19523361  -1      +
tch 0.00000000  0.16363492 0.08995998   0      |
ltg 0.23157918  0.19523361 0.62845827   1      |
glu 0.00000000  0.15138953 0.05758998   0      |

lambda_4 = 0.1952336


           beta       score     breaks tau change
age  0.00000000  0.01161673 0.01527698   0      |
sex  0.00000000 -0.08037963 0.08037963  -1      +
bmi  0.31233737  0.08037963 0.89950095   1      |
map  0.11814418  0.08037963 0.27646490   1      |
tc   0.00000000 -0.03100414 0.04483793   0      |
ldl  0.00000000 -0.02974431 0.04528435   0      |
hdl -0.07047825 -0.08037963 0.19523361  -1      |
tch  0.00000000  0.05092393 0.01410960   0      |
ltg  0.27157361  0.08037963 0.86027098   1      |
glu  0.00000000  0.06947530 0.04235850   0      |

lambda_5 = 0.08037963


           beta       score      breaks tau change
age  0.00000000  0.00569819 0.005691132   0      |
sex -0.04627467 -0.05483941 0.080379630  -1      |
bmi  0.31585107  0.05483941 2.350684568   1      |
map  0.14463335  0.05483941 0.194291389   1      |
tc   0.00000000 -0.03840588 0.042098341   0      |
ldl  0.00000000 -0.03788847 0.041986845   0      |
hdl -0.10482786 -0.05483941 0.132782843  -1      |
tch  0.00000000  0.02844749 0.010538828   0      |
ltg  0.27836968  0.05483941 1.100978007   1      |
glu  0.00000000  0.05483941 0.054839408   1      +

lambda_6 = 0.05483941


            beta        score      breaks tau change
age  0.000000000  0.002026865 0.008269386   0      |
sex -0.069167263 -0.042598653 0.079582642  -1      |
bmi  0.316280991  0.042598653 9.047830952   1      |
map  0.155981676  0.042598653 0.210846751   1      |
tc   0.000000000 -0.042598653 0.042598653  -1      +
ldl  0.000000000 -0.042544022 0.042559075   0      |
hdl -0.121093961 -0.042598653 0.133725704  -1      |
tch  0.000000000  0.017165205 0.011499160   0      |
ltg  0.279435352  0.042598653 3.252298089   1      |
glu  0.007460471  0.042598653 0.054839408   1      |

lambda_7 = 0.04259865


           beta        score      breaks tau change
age  0.00000000 -0.002166684 0.003405317   0      |
sex -0.12215085 -0.012342084 0.082096998  -1      |
bmi  0.32259418  0.012342084 1.558405741   1      |
map  0.18355055  0.012342084 0.213786990   1      |
tc  -0.06420584 -0.012342084 0.042598653  -1      |
ldl  0.00000000 -0.007487901 0.003155702   0      |
hdl -0.13831533 -0.012342084 0.255351056  -1      |
tch  0.00000000  0.012342084 0.012342084   1      +
ltg  0.31795207  0.012342084 0.262107387   1      |
glu  0.03382907  0.012342084 0.051159147   1      |

lambda_8 = 0.01234208


           beta        score       breaks tau change
age  0.00000000 -0.002995721  0.003028553   0      |
sex -0.13967895 -0.003383343  0.074774310  -1      |
bmi  0.32544826  0.003383343  1.024941235   1      |
map  0.19419295  0.003383343  0.166854508   1      |
tc  -0.12051358 -0.003383343  0.022557439  -1      |
ldl  0.00000000  0.003383343  0.003383343   1      +
hdl -0.09418263 -0.003383343 -0.015735310  -1      |
tch  0.06568616  0.003383343  0.012342084   1      |
ltg  0.32732019  0.003383343  0.316399857   1      |
glu  0.03983279  0.003383343  0.062821789   1      |

lambda_9 = 0.003383343


           beta      score       breaks tau change
age  0.00000000 -0.0031435  0.003143500  -1      +
sex -0.14032266 -0.0031435  0.055426929  -1      |
bmi  0.32514258  0.0031435 -0.251974729   1      |
map  0.19453959  0.0031435  0.137746439   1      |
tc  -0.14660151 -0.0031435  0.004491299  -1      |
ldl  0.02077162  0.0031435  0.003383343   1      |
hdl -0.08313975 -0.0031435  0.001337770  -1      |
tch  0.06880010  0.0031435  0.008442640   1      |
ltg  0.33693539  0.0031435  0.011548053   1      |
glu  0.03990645  0.0031435  0.133081872   1      |

lambda_10 = 0.0031435


             beta        score       breaks tau change
age -3.532498e-03 -0.001347939  0.003143500  -1      |
sex -1.447835e-01 -0.001347939  0.059626189  -1      |
bmi  3.228313e-01  0.001347939 -0.249452648   1      |
map  1.978702e-01  0.001347939  0.108021772   1      |
tc  -3.423610e-01 -0.001347939  0.004488170  -1      |
ldl  1.771121e-01  0.001347939  0.003382061   1      |
hdl  6.938894e-18 -0.001347939  0.001347939   0      -
tch  9.197329e-02  0.001347939  0.008474434   1      |
ltg  4.095445e-01  0.001347939  0.011475627   1      |
glu  4.097151e-02  0.001347939  0.070420793   1      |

lambda_11 = 0.001347939


            beta         score        breaks tau change
age -0.004330728 -0.0008094337  0.0037310460  -1      |
sex -0.146453153 -0.0008094337  0.0480429582  -1      |
bmi  0.321859313  0.0008094337 -0.1775025279   1      |
map  0.198615406  0.0008094337  0.1443318080   1      |
tc  -0.358527126 -0.0008094337  0.0127521927  -1      |
ldl  0.193867341  0.0008094337  0.0070402302   1      |
hdl  0.000000000  0.0008094337  0.0008094337   1      +
tch  0.086387844  0.0008094337 -0.0075194059   1      |
ltg  0.416896956  0.0008094337  0.0313434791   1      |
glu  0.041495581  0.0008094337  0.0434479835   1      |

lambda_12 = 0.0008094337


            beta         score        breaks tau change
age -0.006184366 -3.062871e-17  0.0027005460  -1      |
sex -0.148132204 -7.008147e-16  0.0714113308  -1      |
bmi  0.321096262  4.805726e-17 -0.3406144843   1      |
map  0.200370492 -1.654764e-16  0.0924095415   1      |
tc  -0.489318785  6.683564e-16  0.0030282599  -1      |
ldl  0.294477857 -1.716021e-16  0.0023691391   1      |
hdl  0.062413526 -2.586364e-16  0.0008094337   1      |
tch  0.109369553 -4.500117e-16  0.0038520811   1      |
ltg  0.464052556 -4.467506e-16  0.0079655395   1      |
glu  0.041771060 -3.242866e-16  0.1227351912   1      |

lambda_13 = 0


            beta         score        breaks tau change
age -0.006184366 -3.062871e-17  0.0027005460  -1      |
sex -0.148132204 -7.008147e-16  0.0714113308  -1      |
bmi  0.321096262  4.805726e-17 -0.3406144843   1      |
map  0.200370492 -1.654764e-16  0.0924095415   1      |
tc  -0.489318785  6.683564e-16  0.0030282599  -1      |
ldl  0.294477857 -1.716021e-16  0.0023691391   1      |
hdl  0.062413526 -2.586364e-16  0.0008094337   1      |
tch  0.109369553 -4.500117e-16  0.0038520811   1      |
ltg  0.464052556 -4.467506e-16  0.0079655395   1      |
glu  0.041771060 -3.242866e-16  0.1227351912   1      |

lambda_14 = 0


breaks:
 [1] 0.5865 0.5493 0.2797 0.1952 0.0804 0.0548 0.0426 0.0123 0.0034 0.0031
[11] 0.0013 0.0008 0.0000 0.0000

Indicator matrix (parameters x breaks):
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
 [1,]    0    0    0    0    0    0    0    0    0    -1    -1    -1    -1
 [2,]    0    0    0    0   -1   -1   -1   -1   -1    -1    -1    -1    -1
 [3,]    1    1    1    1    1    1    1    1    1     1     1     1     1
 [4,]    0    0    1    1    1    1    1    1    1     1     1     1     1
 [5,]    0    0    0    0    0    0   -1   -1   -1    -1    -1    -1    -1
 [6,]    0    0    0    0    0    0    0    0    1     1     1     1     1
 [7,]    0    0    0   -1   -1   -1   -1   -1   -1    -1     0     1     1
 [8,]    0    0    0    0    0    0    0    1    1     1     1     1     1
 [9,]    0    1    1    1    1    1    1    1    1     1     1     1     1
[10,]    0    0    0    0    0    1    1    1    1     1     1     1     1
      [,14]
 [1,]    -1
 [2,]    -1
 [3,]     1
 [4,]     1
 [5,]    -1
 [6,]     1
 [7,]     1
 [8,]     1
 [9,]     1
[10,]     1

Beta matrix (parameters x breaks):
      [,1]   [,2]   [,3]   [,4]    [,5]    [,6]    [,7]    [,8]    [,9]   [,10]
 [1,]    0 0.0000 0.0000 0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000
 [2,]    0 0.0000 0.0000 0.0000  0.0000 -0.0463 -0.0692 -0.1222 -0.1397 -0.1403
 [3,]    0 0.0371 0.2235 0.2685  0.3123  0.3159  0.3163  0.3226  0.3254  0.3251
 [4,]    0 0.0000 0.0000 0.0489  0.1181  0.1446  0.1560  0.1836  0.1942  0.1945
 [5,]    0 0.0000 0.0000 0.0000  0.0000  0.0000  0.0000 -0.0642 -0.1205 -0.1466
 [6,]    0 0.0000 0.0000 0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0208
 [7,]    0 0.0000 0.0000 0.0000 -0.0705 -0.1048 -0.1211 -0.1383 -0.0942 -0.0831
 [8,]    0 0.0000 0.0000 0.0000  0.0000  0.0000  0.0000  0.0000  0.0657  0.0688
 [9,]    0 0.0000 0.1864 0.2316  0.2716  0.2784  0.2794  0.3180  0.3273  0.3369
[10,]    0 0.0000 0.0000 0.0000  0.0000  0.0000  0.0075  0.0338  0.0398  0.0399
        [,11]   [,12]   [,13]   [,14]
 [1,] -0.0035 -0.0043 -0.0062 -0.0062
 [2,] -0.1448 -0.1465 -0.1481 -0.1481
 [3,]  0.3228  0.3219  0.3211  0.3211
 [4,]  0.1979  0.1986  0.2004  0.2004
 [5,] -0.3424 -0.3585 -0.4893 -0.4893
 [6,]  0.1771  0.1939  0.2945  0.2945
 [7,]  0.0000  0.0000  0.0624  0.0624
 [8,]  0.0920  0.0864  0.1094  0.1094
 [9,]  0.4095  0.4169  0.4641  0.4641
[10,]  0.0410  0.0415  0.0418  0.0418

Score matrix (parameters x breaks):
         [,1]    [,2]    [,3]    [,4]    [,5]    [,6]    [,7]    [,8]    [,9]
 [1,]  0.1879  0.1810  0.0960  0.0591  0.0116  0.0057  0.0020 -0.0022 -0.0030
 [2,]  0.0431  0.0398 -0.0046 -0.0271 -0.0804 -0.0548 -0.0426 -0.0123 -0.0034
 [3,]  0.5865  0.5493  0.2797  0.1952  0.0804  0.0548  0.0426  0.0123  0.0034
 [4,]  0.4415  0.4268  0.2797  0.1952  0.0804  0.0548  0.0426  0.0123  0.0034
 [5,]  0.2120  0.2027  0.0601  0.0137 -0.0310 -0.0384 -0.0426 -0.0123 -0.0034
 [6,]  0.1741  0.1644  0.0563  0.0211 -0.0297 -0.0379 -0.0425 -0.0075  0.0034
 [7,] -0.3948 -0.3812 -0.2385 -0.1952 -0.0804 -0.0548 -0.0426 -0.0123 -0.0034
 [8,]  0.4305  0.4151  0.2228  0.1636  0.0509  0.0284  0.0172  0.0123  0.0034
 [9,]  0.5659  0.5493  0.2797  0.1952  0.0804  0.0548  0.0426  0.0123  0.0034
[10,]  0.3825  0.3680  0.2090  0.1514  0.0695  0.0548  0.0426  0.0123  0.0034
        [,10]   [,11]  [,12] [,13] [,14]
 [1,] -0.0031 -0.0013 -8e-04     0     0
 [2,] -0.0031 -0.0013 -8e-04     0     0
 [3,]  0.0031  0.0013  8e-04     0     0
 [4,]  0.0031  0.0013  8e-04     0     0
 [5,] -0.0031 -0.0013 -8e-04     0     0
 [6,]  0.0031  0.0013  8e-04     0     0
 [7,] -0.0031 -0.0013  8e-04     0     0
 [8,]  0.0031  0.0013  8e-04     0     0
 [9,]  0.0031  0.0013  8e-04     0     0
[10,]  0.0031  0.0013  8e-04     0     0
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>


Created & Maintained by Osamu Ogasawara (osamu.ogasawara@gmail.com) and IMSBIO