Stepwise regression is a popular data-mining method to identify a useful subset of the predictors to be used in a multiple regression model. We developed an R package StepReg, which allow users to perform linear, logistic and cox proportional hazard stepwise regression with a widely used selection criteria and stop rules are available in forward selection, backward elimination, both-direcition and best subset method. User can specify effects to be included in all models and do multivariate multiple stepwise regression.
StepReg 1.4.4
Here we applied StepReg to the well-known mtcars data and lung data for clarifying how to perform linear, logistic and Cox stepwise regression.
#install.package("StepReg")
library(StepReg)formula <- mpg ~ .
sForwAIC <- stepwise(formula=formula,
data=mtcars,
selection="forward",
select="AIC")
sForwAIC## Table 1. Summary of Parameters
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Paramters Value
## —————————————————————————————————————
## Response Variable mpg
## Included Variable NULL
## Selection Method forward
## Select Criterion AIC
## Variable significance test F
## Multicollinearity Terms NULL
## Intercept 1
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 2. Variables Type
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## class variable
## ———————————————————————————————————————————————————————
## numeric mpg cyl disp hp drat wt qsec vs am gear carb
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 3. Process of Selection
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect DF NumberEffectIn NumberParmsIn AIC
## —————————————————————————————————————————————————————————————————————————————————————————
## 0 1 1 0 1 149.943449990894
## 1 wt 1 1 2 107.217362866777
## 2 cyl 1 2 3 97.1979989461637
## 3 hp 1 3 4 96.6645623851593
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 4. Selected Varaibles
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## variables1 variables2 variables3 variables4
## ————————————————————————————————————————————————
## 1 wt cyl hp
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 5. Coefficients of the Selected Variables for mpg
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate StdError t.value P.value
## ———————————————————————————————————————————————————————————————————————————————————————————————
## (Intercept) 38.7517873728655 1.78686402942753 21.6870375891336 4.7993988012846e-19
## wt -3.16697311074858 0.740575879267817 -4.27636546018709 0.000199476497472232
## cyl -0.941616811990739 0.550916381450763 -1.70918281556834 0.0984800974797216
## hp -0.0180381021431068 0.0118762499454497 -1.51883820448035 0.140015155016129
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗From the above result, we can see that stepwise() output a list with 5 tables.
‘Summary of Parameters’ tells you what parameters is used for this function, where Intercept equals to 1 showing that this stepwise regression has a intercept, otherwise 0 has not a intercept.
‘Variables Type’ is the summary of the type of all variables.
‘Process of Selection’ let you know how variables are selected, we used AIC as the criteria so the last column is value of AIC.
‘Coefficients of the Selected Variables’ is the coefficients of all selected variable.
formula <- mpg ~ .
sBidiSL <- stepwise(formula=formula,
data=mtcars,
selection="bidirection",
select="SL",
sle=0.15,
sls=0.15)
sBidiSL## Table 1. Summary of Parameters
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Paramters Value
## ————————————————————————————————————————————
## Response Variable mpg
## Included Variable NULL
## Selection Method bidirection
## Select Criterion SL
## Entry Significance Level(sle) 0.15
## Stay Significance Level(sls) 0.15
## Variable significance test F
## Multicollinearity Terms NULL
## Intercept 1
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 2. Variables Type
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## class variable
## ———————————————————————————————————————————————————————
## numeric mpg cyl disp hp drat wt qsec vs am gear carb
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 3. Process of Selection
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect DF NumberEffectIn NumberParmsIn SL
## —————————————————————————————————————————————————————————————————————————————————————————————
## 0 1 1 0 1 1
## 1 wt 1 1 2 1.29395870135053e-10
## 2 cyl 1 2 3 0.00106428178479493
## 3 hp 1 3 4 0.140015155016129
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 4. Selected Varaibles
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## variables1 variables2 variables3 variables4
## ————————————————————————————————————————————————
## 1 wt cyl hp
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 5. Coefficients of the Selected Variables for mpg
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate StdError t.value P.value
## ———————————————————————————————————————————————————————————————————————————————————————————————
## (Intercept) 38.7517873728655 1.78686402942753 21.6870375891336 4.7993988012846e-19
## wt -3.16697311074858 0.740575879267817 -4.27636546018709 0.000199476497472232
## cyl -0.941616811990739 0.550916381450763 -1.70918281556834 0.0984800974797216
## hp -0.0180381021431068 0.0118762499454497 -1.51883820448035 0.140015155016129
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗The output of this time is similar to the last time except that the last column name of ‘Process of Selection’ is SL.
#formula <- mpg ~ . -1
formula <- mpg ~ . + 0
sBackSBC <- stepwise(formula=formula,
data=mtcars,
selection="backward",
select="SBC")
sBackSBC## Table 1. Summary of Parameters
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Paramters Value
## ——————————————————————————————————————
## Response Variable mpg
## Included Variable NULL
## Selection Method backward
## Select Criterion SBC
## Variable significance test F
## Multicollinearity Terms NULL
## Intercept 0
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 2. Variables Type
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## class variable
## ———————————————————————————————————————————————————————
## numeric mpg cyl disp hp drat wt qsec vs am gear carb
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 3. Process of Selection
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect DF NumberEffectIn NumberParmsIn SBC
## —————————————————————————————————————————————————————————————————————————————————————————
## 0 10 10 84.2067855988594
## 1 vs 1 9 9 80.753286502759
## 2 carb 1 8 8 77.4481345907642
## 3 cyl 1 7 7 74.2170762315502
## 4 gear 1 6 6 71.4474257432347
## 5 hp 1 5 5 69.6121723518218
## 6 drat 1 4 4 67.2583479289403
## 7 disp 1 3 3 65.8158985591381
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 4. Selected Varaibles
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## variables1 variables2 variables3 variables4
## ————————————————————————————————————————————————
## 0 wt qsec am
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 5. Coefficients of the Selected Variables for mpg
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate StdError t.value P.value
## —————————————————————————————————————————————————————————————————————————————————————————
## wt -3.18545457405163 0.48275857401392 -6.59844225565175 3.12884395417586e-07
## qsec 1.59982255096241 0.102127563736307 15.6649438450637 1.09152213212295e-15
## am 4.29951918563878 1.02411470721657 4.19827891870082 0.000232942305441512
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗Note that 0 instead of 1 in table ‘Summary of Parameters’ and ‘Selected Varaibles’.
formula <- cbind(mpg,drat) ~ cyl+disp+hp+wt+vs+am
stepwise(formula=formula,
data=mtcars,
include='wt',
selection="score",
select="AICc")## Table 1. Summary of Parameters
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Paramters Value
## ——————————————————————————————————————————————
## Response Variable cbind(mpg, drat)
## Included Variable wt
## Selection Method score
## Select Criterion AICc
## Variable significance test Pillai
## Multicollinearity Terms NULL
## Intercept 1
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 2. Variables Type
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## class variable
## —————————————————————————————————
## nmatrix.2 cbind(mpg, drat)
## numeric cyl disp hp wt vs am
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 3. Process of Selection
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## NoVariable RankModel AICc VariablesEnteredinModel
## ——————————————————————————————————————————————————————————————————
## 1 2 195.897376923981 1 wt
## 2 3 186.904307271046 1 wt cyl
## 2 3 196.371281316355 1 wt disp
## 2 3 189.17318360105 1 wt hp
## 2 3 194.523487851372 1 wt vs
## 2 3 194.535837853377 1 wt am
## 3 4 192.457336479145 1 wt cyl disp
## 3 4 185.177463011528 1 wt cyl hp
## 3 4 190.779194002406 1 wt cyl vs
## 3 4 184.755187612804 1 wt cyl am
## 3 4 191.382214992907 1 wt disp hp
## 3 4 198.425684821612 1 wt disp vs
## 3 4 194.538955269497 1 wt disp am
## 3 4 193.829893164651 1 wt hp vs
## 3 4 186.571791388542 1 wt hp am
## 3 4 191.027956516955 1 wt vs am
## 4 5 190.104285448931 1 wt cyl disp hp
## 4 5 196.751838279683 1 wt cyl disp vs
## 4 5 190.774200697523 1 wt cyl disp am
## 4 5 190.248327011053 1 wt cyl hp vs
## 4 5 186.392004692651 1 wt cyl hp am
## 4 5 191.020708699958 1 wt cyl vs am
## 4 5 196.60614397021 1 wt disp hp vs
## 4 5 190.549673606409 1 wt disp hp am
## 4 5 196.311249386999 1 wt disp vs am
## 4 5 189.618260351885 1 wt hp vs am
## 5 6 195.586826848026 1 wt cyl disp hp vs
## 5 6 191.874880930657 1 wt cyl disp hp am
## 5 6 197.548034971133 1 wt cyl disp vs am
## 5 6 192.868991967306 1 wt cyl hp vs am
## 5 6 194.381840779641 1 wt disp hp vs am
## 6 7 198.745196549042 1 wt cyl disp hp vs am
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 4. Selected Varaibles
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## variables1 variables2 variables3 variables4
## ————————————————————————————————————————————————
## 1 wt cyl am
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 5. Coefficients of the Selected Variables for Response mpg
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate StdError t.value P.value
## ————————————————————————————————————————————————————————————————————————————————————————————
## (Intercept) 39.4179334351865 2.6414572997099 14.9227978962656 7.42499755293912e-15
## wt -3.12514220026708 0.910882701148664 -3.43089422636541 0.00188589438685631
## cyl -1.5102456624971 0.422279222208057 -3.57641480582487 0.00129160458914754
## am 0.176493157719669 1.30445145498685 0.135300671439281 0.89334214792396
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 6. Coefficients of the Selected Variables for Response drat
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate StdError t.value P.value
## ———————————————————————————————————————————————————————————————————————————————————————————————
## (Intercept) 4.31421082403332 0.332409660876704 12.9785963881282 2.29282220122696e-13
## wt -0.0579982631143607 0.114628470360106 -0.505967347659431 0.616840130742605
## cyl -0.116490969949067 0.053141004045333 -2.19211081991774 0.0368483162012922
## am 0.467038681922974 0.164156454783472 2.84508265324694 0.00821005565960176
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗formula <- am ~ .
stepwiseLogit(formula=formula,
data=mtcars,
selection="forward",
select="AIC")## Table 1. Summary of Parameters
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Paramters Value
## —————————————————————————————————————
## Response Variable am
## Included Variable NULL
## Selection Method forward
## Select Criterion AIC
## Variable significance test Rao
## Multicollinearity Terms NULL
## Intercept 1
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 2. Variables Type
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## class variable
## ———————————————————————————————————————————————————————
## numeric am mpg cyl disp hp drat wt qsec vs gear carb
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 3. Process of Selection
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect DF NumberIn AIC
## ————————————————————————————————————————————————————————————————————
## 0 1 1 1 45.2297332768578
## 1 gear 1 2 19.2763400880433
## 2 wt 1 3 6.00000000576112
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 4. Selected Varaibles
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## variables1 variables2 variables3
## ————————————————————————————————————
## 1 gear wt
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 5. Coefficients of the Selected Variables
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate StdError t.value P.value
## ———————————————————————————————————————————————————————————————————————————————————————————
## (Intercept) 24.9779264690071 211732.148224506 0.000117969456591553 0.999905873992158
## gear 105.57256202697 68256.4892424417 0.00154670366435027 0.998765909518129
## wt -148.465697432972 84415.1659816875 -0.00175875621052714 0.998596716296849
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗formula <- am ~ .
stepwiseLogit(formula=formula,
data=mtcars,
selection="score",
select="SL",
best=3)## Table 1. Summary of Parameters
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Paramters Value
## ———————————————————————————————————
## Response Variable am
## Included Variable NULL
## Selection Method score
## Select Criterion SL
## Variable significance test Rao
## Multicollinearity Terms NULL
## Intercept 1
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 2. Variables Type
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## class variable
## ———————————————————————————————————————————————————————
## numeric am mpg cyl disp hp drat wt qsec vs gear carb
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 3. Process of Selection
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## NumberOfVariables SL VariablesInModel
## ——————————————————————————————————————————————————————————————————————————————————
## 2 20.1769382094272 1 gear
## 2 16.2546289388823 1 drat
## 2 15.3455899772529 1 wt
## 3 23.024782257184 1 cyl qsec
## 3 22.7277547701151 1 wt gear
## 3 22.1620072021874 1 mpg gear
## 4 24.4804946492056 1 mpg qsec gear
## 4 24.2615455927147 1 cyl qsec gear
## 4 23.8832404475897 1 mpg cyl qsec
## 5 25.1574753593028 1 mpg cyl qsec gear
## 5 24.8193142254911 1 mpg drat qsec gear
## 5 24.725686315042 1 mpg disp qsec gear
## 6 25.4015158698094 1 mpg cyl qsec vs gear
## 6 25.2573360971424 1 mpg cyl drat qsec gear
## 6 25.1642182693208 1 mpg cyl qsec gear carb
## 7 25.5008153935662 1 mpg cyl drat qsec vs gear
## 7 25.4324233741306 1 mpg cyl hp qsec vs gear
## 7 25.4137814512785 1 mpg cyl disp qsec vs gear
## 8 25.5274280754659 1 mpg cyl hp drat qsec vs gear
## 8 25.5104718026612 1 mpg cyl disp drat qsec vs gear
## 8 25.5083472740736 1 mpg cyl drat wt qsec vs gear
## 9 25.5604248548793 1 mpg cyl disp hp drat qsec vs gear
## 9 25.5461866446911 1 mpg cyl hp drat wt qsec vs gear
## 9 25.5290367298355 1 mpg cyl hp drat qsec vs gear carb
## 10 25.5733835910141 1 mpg cyl disp hp drat qsec vs gear carb
## 10 25.5616277385224 1 mpg cyl disp hp drat wt qsec vs gear
## 10 25.5462397486206 1 mpg cyl hp drat wt qsec vs gear carb
## 11 25.57543199853 1 mpg cyl disp hp drat wt qsec vs gear carb
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 4. Selected Varaibles
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## variables1 variables2 variables3 variables4 variables5 variables6 variables7 variables8 variables9 variables10 variables11
## ——————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————————
## 1 mpg cyl disp hp drat wt qsec vs gear carb
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 5. Coefficients of the Selected Variables
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable Estimate StdError t.value P.value
## —————————————————————————————————————————————————————————————————————————————————————————————
## (Intercept) -11.6408164177017 1840046.55622753 -6.3263705900832e-06 0.99999495228658
## mpg -0.880883528085447 28843.372501277 -3.0540240328916e-05 0.999975632413762
## cyl 2.52681917330733 123556.890881509 2.04506535837855e-05 0.999983682739248
## disp -0.415506274171229 2570.02592605466 -0.000161673962102432 0.999871002842317
## hp 0.343715471343463 2194.50394230898 0.000156625588460697 0.999875030861652
## drat 23.2030530410442 215892.85221756 0.000107474855247463 0.999914247472489
## wt 7.43558654593573 310702.702473842 2.39315155186386e-05 0.999980905413253
## qsec -7.57708489509811 55096.6897542608 -0.000137523414362877 0.999890272191277
## vs -47.0120531406395 240518.468503821 -0.000195461302548135 0.999844044445455
## gear 42.855441100866 271926.299875359 0.000157599471329214 0.999874253815556
## carb -21.5677679539988 107605.517416698 -0.000200433662434599 0.999840077076349
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗lung <- survival::lung
my.data <- na.omit(lung)
my.data$status1 <- ifelse(my.data$status==2,1,0)
data <- my.data
formula = Surv(time, status1) ~ . - status
stepwiseCox(formula=formula,
data=my.data,
selection="forward",
select="IC(1)")## Table 1. Summary of Parameters
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Paramters Value
## ——————————————————————————————————————————————
## Response Variable Surv(time, status1)
## Included Variable NULL
## Selection Method forward
## Select Criterion IC(1)
## Method efron
## Multicollinearity Terms NULL
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 2. Variables Type
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## class variable
## —————————————————————————————————————————————————————————————————————
## nmatrix.2 Surv(time, status1)
## numeric inst age sex ph.ecog ph.karno pat.karno meal.cal wt.loss
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 3. Process of Selection
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Step EnteredEffect RemovedEffect DF NumberIn IC(1)
## ————————————————————————————————————————————————————————————————————
## 1 ph.ecog 1 1 1004.82485042
## 2 sex 1 2 998.751396664802
## 3 inst 1 3 996.306462601088
## 4 wt.loss 1 4 993.697932944162
## 5 ph.karno 1 5 990.792621133919
## 6 pat.karno 1 6 989.742173541071
## 7 age 1 7 989.5365169151
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 4. Selected Varaibles
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## variables1 variables2 variables3 variables4 variables5 variables6 variables7
## ————————————————————————————————————————————————————————————————————————————————————
## ph.ecog sex inst wt.loss ph.karno pat.karno age
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 5. Coefficients of the Selected Variables
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable coef exp(coef) se(coef) z Pr(>|z|)
## ————————————————————————————————————————————————————————————————————————————————————————————————————————————————
## ph.ecog 0.907317172186787 2.47766645634186 0.238503963744317 3.80420164907388 0.000142262259259765
## sex -0.5668681013351 0.56729938352366 0.200032540541155 -2.83387942682491 0.0045986679410844
## inst -0.0303746283354971 0.970082045244345 0.0131043742343093 -2.3178999464142 0.020454759369153
## wt.loss -0.0167121591832758 0.983426714247836 0.0079119389785738 -2.11227099052883 0.0346632125632794
## ph.karno 0.026580081421336 1.02693648250202 0.0116170285677177 2.28802755079718 0.02213591674028
## pat.karno -0.0108962907298638 0.98916285881416 0.00799900477152 -1.36220580448451 0.173132944510343
## age 0.0127911717927875 1.01287332875159 0.0117657197510269 1.08715591255444 0.276967911173407
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗formula = Surv(time, status1) ~ . - status
stepwiseCox(formula=formula,
data=my.data,
selection="score",
select="SL",
best=3)## Table 1. Summary of Parameters
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Paramters Value
## ——————————————————————————————————————————————
## Response Variable Surv(time, status1)
## Included Variable NULL
## Selection Method score
## Select Criterion SL
## Method efron
## Multicollinearity Terms NULL
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 2. Variables Type
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## class variable
## —————————————————————————————————————————————————————————————————————
## nmatrix.2 Surv(time, status1)
## numeric inst age sex ph.ecog ph.karno pat.karno meal.cal wt.loss
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 3. Process of Selection
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## NumberOfVariables SL VariablesInModel
## ———————————————————————————————————————————————————————————————————————————————————————————————
## 1 12.6106639278655 ph.ecog
## 1 9.40464427478488 pat.karno
## 1 6.05453549008767 sex
## 2 19.6188613806345 sex ph.ecog
## 2 16.1813654333712 inst ph.ecog
## 2 14.6996068825757 ph.ecog ph.karno
## 3 22.8462568222864 inst sex ph.ecog
## 3 22.275079322983 sex ph.ecog ph.karno
## 3 21.7185245910322 sex ph.ecog wt.loss
## 4 25.9731431898165 inst sex ph.ecog ph.karno
## 4 25.9575424705573 inst sex ph.ecog wt.loss
## 4 24.6127743544862 sex ph.ecog ph.karno wt.loss
## 5 29.489722041723 inst sex ph.ecog ph.karno wt.loss
## 5 27.6371652705792 sex ph.ecog ph.karno pat.karno wt.loss
## 5 27.4244378783933 inst sex ph.ecog pat.karno wt.loss
## 6 31.8004249527573 inst sex ph.ecog ph.karno pat.karno wt.loss
## 6 30.4167375088391 inst age sex ph.ecog ph.karno wt.loss
## 6 29.8108012992351 inst sex ph.ecog ph.karno meal.cal wt.loss
## 7 32.4668080659739 inst age sex ph.ecog ph.karno pat.karno wt.loss
## 7 31.9273069224212 inst sex ph.ecog ph.karno pat.karno meal.cal wt.loss
## 7 30.5707472827073 inst age sex ph.ecog ph.karno meal.cal wt.loss
## 8 32.5131173841979 inst age sex ph.ecog ph.karno pat.karno meal.cal wt.loss
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 4. Selected Varaibles
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## variables1 variables2 variables3 variables4 variables5 variables6 variables7 variables8
## ————————————————————————————————————————————————————————————————————————————————————————————————
## inst age sex ph.ecog ph.karno pat.karno meal.cal wt.loss
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
##
## Table 5. Coefficients of the Selected Variables
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
## Variable coef exp(coef) se(coef) z Pr(>|z|)
## ————————————————————————————————————————————————————————————————————————————————————————————————————————————————————
## inst -0.0303685592659294 0.97008793275763 0.0131188382544396 -2.31488175072607 0.0206194043459998
## age 0.0128110652843044 1.01289347853898 0.0119427514304991 1.07270634902338 0.283402890823254
## sex -0.566644726715653 0.567426117961668 0.201352245143781 -2.81419621773288 0.00488993706146962
## ph.ecog 0.907380784608605 2.4778240717187 0.238601969045798 3.80290568530237 0.000143008810713775
## ph.karno 0.0265846510127879 1.02694117519292 0.0116272658879958 2.28640604497008 0.0222305150198986
## pat.karno -0.0109109725399694 0.989148336219512 0.00814092662689389 -1.34026174660812 0.180160263382842
## meal.cal 2.60198066453765e-06 1.00000260198405 0.00026768513236283 0.00972030325916956 0.992244442233114
## wt.loss -0.0167116544277056 0.983427210638073 0.00791098319435414 -2.11246238515995 0.0346468089838536
## ‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗## R version 4.1.3 (2022-03-10)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Big Sur/Monterey 10.16
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.1/Resources/lib/libRlapack.dylib
##
## locale:
## [1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] StepReg_1.4.4 BiocStyle_2.22.0
##
## loaded via a namespace (and not attached):
## [1] bslib_0.4.1 compiler_4.1.3 pillar_1.8.1
## [4] BiocManager_1.30.19 jquerylib_0.1.4 tools_4.1.3
## [7] digest_0.6.30 jsonlite_1.8.4 evaluate_0.18
## [10] lifecycle_1.0.3 tibble_3.1.8 lattice_0.20-45
## [13] pkgconfig_2.0.3 rlang_1.0.6 Matrix_1.5-3
## [16] DBI_1.1.3 cli_3.4.1 rstudioapi_0.14
## [19] yaml_2.3.6 xfun_0.35 fastmap_1.1.0
## [22] withr_2.5.0 stringr_1.5.0 dplyr_1.0.10
## [25] knitr_1.41 generics_0.1.3 vctrs_0.5.1
## [28] sass_0.4.4 tidyselect_1.2.0 grid_4.1.3
## [31] glue_1.6.2 R6_2.5.1 fansi_1.0.3
## [34] survival_3.4-0 rmarkdown_2.18 bookdown_0.30
## [37] purrr_0.3.5 magrittr_2.0.3 htmltools_0.5.4
## [40] splines_4.1.3 assertthat_0.2.1 utf8_1.2.2
## [43] stringi_1.7.8 cachem_1.0.6China Agricultural University, junhuili@cau.edu.cn↩︎
University of Massachusset Chan medical school, junhui.li11@umassmed.edu↩︎