exact.path: Generate Exact Solution Path
In ExactPath: Exact solution paths for regularized LASSO regressions with L_1 penalty
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
exact.path generates the whole solution paths.
Usage
1
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
1
2
3
4
5
6
7
8
9
10
11
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)
Example output
Loading required package: ncvreg
Loading required package: lars
Loaded lars 1.2
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
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
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
ExactPath documentation built on May 30, 2017, 5:15 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
exact.path generates the whole solution paths.
Usage
1 | 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 |
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 |
score |
a p\times K matrix of scores. See also |
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
1 2 3 4 5 6 7 8 9 10 11 | 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)
|
Example output
Loading required package: ncvreg
Loading required package: lars
Loaded lars 1.2
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
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
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
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