Extract the coefficients for the best tuning parameters of a glmnet model in caret

Question

I am running elastic net regularization in caret using glmnet.

I pass sequence of values to trainControl for alpha and lambda, then I perform repeatedcv to get the optimal tunings of alpha and lambda.

Here is an example where the optimal tunings for alpha and lambda are 0.7 and 0.5 respectively:

age     <- c(4, 8, 7, 12, 6, 9, 10, 14, 7, 6, 8, 11, 11, 6, 2, 10, 14, 7, 12, 6, 9, 10, 14, 7) 
gender  <-  make.names(as.factor(c(1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1)))
bmi_p   <- c(0.86, 0.45, 0.99, 0.84, 0.85, 0.67, 0.91, 0.29, 0.88, 0.83, 0.48, 0.99, 0.80, 0.85,
         0.50, 0.91, 0.29, 0.88, 0.99, 0.84, 0.80, 0.85, 0.88, 0.99) 
m_edu   <- make.names(as.factor(c(0, 1, 1, 2, 2, 3, 2, 0, 1, 1, 0, 1, 2, 2, 1, 2, 0, 1, 1, 2, 2, 0 , 1, 0)))
p_edu   <-  make.names(as.factor(c(0, 2, 2, 2, 2, 3, 2, 0, 0, 0, 1, 2, 2, 1, 3, 2, 3, 0, 0, 2, 0, 1, 0, 1)))
f_color <-  make.names(as.factor(c("blue", "blue", "yellow", "red", "red", "yellow", 
                   "yellow", "red", "yellow","blue", "blue", "yellow", "red", "red", "yellow", 
                   "yellow", "red", "yellow", "yellow", "red", "blue", "yellow", "yellow", "red")))
asthma <-  make.names(as.factor(c(1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1)))
x <- data.frame(age, gender, bmi_p, m_edu, p_edu, f_color, asthma)

tuneGrid <- expand.grid(alpha = seq(0, 1, 0.05), lambda = seq(0, 0.5, 0.05))
fitControl <- trainControl(method = 'repeatedcv', number = 3, repeats = 5, classProbs = TRUE, summaryFunction = twoClassSummary) 

set.seed(1352)
model.test <- caret::train(asthma ~ age + gender + bmi_p + m_edu + p_edu + f_color, data = x, method = "glmnet", 
                       family = "binomial", trControl = fitControl, tuneGrid = tuneGrid, 
                       metric = "ROC")

model.test$bestTune

My question?

When I run as.matrix(coef(model.test$finalModel)) which I would assume give me the coefficients corresponding to the best model, I get 100 different sets of coefficients.

So how do I get the coefficients corresponding to the best tuning?

I've seen this recommendation to get the best model coef(model.test$finalModel, model.test$bestTune$lambda) However, this returns NULL coefficients, and In any case, would only be returning the best tunings related to lambda, and not to alpha in addition.

EDIT:

After searching everywhere on the internet, all I can find now which points me in the direction of the correct answer is this blog post, which says that model.test$finalModel returns the model corresponding to the best alpha tuning, and coef(model.test$finalModel, model.caret$bestTune$lambda) returns the set of coefficients corresponding to the best values of lambda. If this is true then this is the answer to my question. However, as this is a single blog post, and I can't find anything else to back up this claim, I am still skeptical. Can anyone validate this claim that model.test$finalModel returns the model corresponding to the best alpha?? If so then this question would be solved. Thanks!

Answer 1

After a bit of playing with your code I find it very odd that glmnet train chooses different lambda ranges depending on the seed. Here is an example:

library(caret)
library(glmnet)
set.seed(13)
model.test <- caret::train(asthma ~ age + gender + bmi_p + m_edu + p_edu + f_color, data = x, method = "glmnet", 
                           family = "binomial", trControl = fitControl, tuneGrid = tuneGrid, 
                           metric = "ROC")

c(head(model.test$finalModel$lambda, 5), tail(model.test$finalModel$lambda, 5))
#output
 [1] 3.7796447301 3.4438715094 3.1379274562 2.8591626295 2.6051625017 0.0005483617 0.0004996468 0.0004552595 0.0004148155
[10] 0.0003779645

optimum lambda is:

model.test$finalModel$lambdaOpt
#output
#[1] 0.05

and this works:

coef(model.test$finalModel, model.test$finalModel$lambdaOpt)
#12 x 1 sparse Matrix of class "dgCMatrix"
                        1
(Intercept)   -0.03158974
age            0.03329806
genderX1      -1.24093677
bmi_p          1.65156913
m_eduX1        0.45314106
m_eduX2       -0.09934991
m_eduX3       -0.72360297
p_eduX1       -0.51949828
p_eduX2       -0.80063642
p_eduX3       -2.18231433
f_colorred     0.87618211
f_coloryellow -1.52699254

giving the coefficients at best alpha and lambda

when using this model to predict some y are predicted as X1 and some as X2

 [1] X1 X1 X0 X1 X1 X0 X0 X1 X1 X1 X0 X1 X1 X1 X0 X0 X0 X1 X1 X1 X1 X0 X1 X1
Levels: X0 X1

now with the seed you used

set.seed(1352)
model.test <- caret::train(asthma ~ age + gender + bmi_p + m_edu + p_edu + f_color, data = x, method = "glmnet", 
                           family = "binomial", trControl = fitControl, tuneGrid = tuneGrid, 
                           metric = "ROC")

c(head(model.test$finalModel$lambda, 5), tail(model.test$finalModel$lambda, 5))
#output
 [1] 2.699746e-01 2.459908e-01 2.241377e-01 2.042259e-01 1.860830e-01 3.916870e-05 3.568906e-05 3.251854e-05 2.962968e-05
[10] 2.699746e-05

lambda values are 10 times smaller and this gives empty coefficients since lambdaOpt is not in the range of tested lambda:

coef(model.test$finalModel, model.test$finalModel$lambdaOpt)
#output
12 x 1 sparse Matrix of class "dgCMatrix"
              1
(Intercept)   .
age           .
genderX1      .
bmi_p         .
m_eduX1       .
m_eduX2       .
m_eduX3       .
p_eduX1       .
p_eduX2       .
p_eduX3       .
f_colorred    .
f_coloryellow .

model.test$finalModel$lambdaOpt
#output
0.5

now when predicting upon this model only X0 is predicted (the first level):

predict(model.test, x)
#output
 [1] X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0 X0
Levels: X0 X1

quite odd behavior, probably worth reporting