Using glmnet for many regression formulas

I have a code that creates formulas for many possible combinations of my independent variables then fits a linear model for each of these formulas.

I want to use ridge and lasso regression now, however I am having trouble adapting the code.

Here is my code for the linear model case (sample data is given at the end):

variables <- colnames(dat)[2:ncol(dat)]
    formulas <- list()
    for (i in 4:5) {
      tmp <- combn(variables, i)
      tmp <- apply(tmp, 2, paste, collapse="+")
      tmp <- paste0("Y~", tmp)
      formulas[[i]] <- tmp
    }
    formulas <- unlist(formulas)
    formulas <- sapply(formulas, as.formula)    
    
    models <- lapply(formulas, lm, data=dat)

This was created using some combination of answers from stackoverflow, however I couldn't find the source for credit.

Now I want to addapt this for ridge regression, for instance. I tried the code below which does not work.

set.seed(123)
cv.ridge <- lapply(formulas,cv.glmnet,data=dat,alpha=0)
model.ridge <- lapply(formulas,glmnet,data=dat,alpha=0,lambda = cv.ridge$lambda.min)

Is there any way to do the lasso and ridge regressions in a similar way to my linear model solution?

Here is some sample data:

dat=structure(list(Y = c(0.400771450594052, 0.11068271594512, -0.555841134754075, 
1.78691313680308, 0.497850478229239, -1.96661715662964, 0.701355901563686, 
-0.472791407727934, -1.06782370598685, -0.217974914658295, -1.02600444830724, 
-0.72889122929114, -0.625039267849257, -1.68669331074241, 0.837787044494525, 
0.153373117836515, -1.13813693701195, 1.25381492106993, 0.426464221476814, 
-0.295071482992271, 0.895125661045022, 0.878133487533042), X1 = c(0.821581081637487, 
0.688640254100091, 0.553917653537589, -0.0619117105767217, -0.305962663739917, 
-0.380471001012383, -0.694706978920513, -0.207917278019599, -1.26539635156826, 
2.16895596533851, 1.20796199830499, -1.12310858320335, -0.402884835299076, 
-0.466655353623219, 0.779965118336318, -0.0833690664718293, 0.253318513994755, 
-0.028546755348703, -0.0428704572913161, 1.36860228401446, -0.225770985659268, 
1.51647060442954), X2 = c(-1.54875280423022, 0.584613749636069, 
0.123854243844614, 0.215941568743973, 0.379639482759882, -0.502323453109302, 
-0.33320738366942, -1.01857538310709, -1.07179122647558, 0.303528641404258, 
0.448209778629426, 0.0530042267305041, 0.922267467879738, 2.05008468562714, 
-0.491031166056535, -2.30916887564081, 1.00573852446226, -0.709200762582393, 
-0.688008616467358, 1.0255713696967, -0.284773007051009, -1.22071771225454
), X3 = c(0.18130347974915, -0.138891362439045, 0.00576418589988693, 
0.38528040112633, -0.370660031792409, 0.644376548518833, -0.220486561818751, 
0.331781963915697, 1.09683901314935, 0.435181490833803, -0.325931585531227, 
1.14880761845109, 0.993503855962119, 0.54839695950807, 0.238731735111441, 
-0.627906076039371, 1.36065244853001, -0.600259587147127, 2.18733299301658, 
1.53261062618519, -0.235700359100477, -1.02642090030678), X4 = c(-0.710406563699301, 
0.25688370915653, -0.246691878462374, -0.347542599397733, -0.951618567265016, 
-0.0450277248089203, -0.784904469457076, -1.66794193658814, -0.380226520287762, 
0.918996609060766, -0.575346962608392, 0.607964322225033, -1.61788270828916, 
-0.0555619655245394, 0.519407203943462, 0.301153362166714, 0.105676194148943, 
-0.640706008305376, -0.849704346033582, -1.02412879060491, 0.117646597100126, 
-0.947474614184802), X5 = c(-0.490557443700668, -0.256092192198247, 
1.84386200523221, -0.651949901695459, 0.235386572284857, 0.0779608495637108, 
-0.961856634130129, -0.0713080861235987, 1.44455085842335, 0.451504053079215, 
0.0412329219929399, -0.422496832339625, -2.05324722154052, 1.13133721341418, 
-1.46064007092482, 0.739947510877334, 1.90910356921748, -1.4438931609718, 
0.701784335374711, -0.262197489402468, -1.57214415914549, -1.51466765378175
), X6 = c(-1.60153617357459, -0.530906522170303, -1.4617555849959, 
0.687916772975828, 2.10010894052567, -1.28703047603518, 0.787738847475178, 
0.76904224100091, 0.332202578950118, -1.00837660827701, -0.119452606630659, 
-0.280395335170247, 0.56298953322048, -0.372438756103829, 0.976973386685621, 
-0.374580857767014, 1.05271146557933, -1.04917700666607, -1.26015524475811, 
3.2410399349424, -0.416857588160432, 0.298227591540715), X7 = c(0.636569674033849, 
-0.483780625708744, 0.516862044313609, 0.368964527385086, -0.215380507641693, 
0.0652930335253153, -0.034067253738464, 2.12845189901618, -0.741336096272828, 
-1.09599626707466, 0.0377883991710788, 0.310480749443137, 0.436523478910183, 
-0.458365332711106, -1.06332613397119, 1.26318517608949, -0.349650387953555, 
-0.865512862653374, -0.236279568941097, -0.197175894348552, 1.10992028971364, 
0.0847372921971965)), row.names = 75:96, class = "data.frame")

It doesn't appear that cv.glmnet or glmnet accept the formula syntax. You need to convert those formulas into vectors/matries and pass in the x and y values. Here's one method

frames <- lapply(formulas, model.frame, dat)
Xs <- lapply(frames, function(val) as.matrix(subset(val, select=-Y)))
Ys <- lapply(frames, function(val) val$Y)

cv.ridge <- Map(function(x, y) cv.glmnet(x, y, alpha=0), Xs, Ys)
lambdas <- sapply(cv.ridge, function(x) x$lambda.min)
model.ridge <- Map(function(x, y, lambda) glmnet(x, y, alpha=0,lambda = lambda),
                   Xs, Ys, lambdas)

We use model.frame to create a data.frame for the formula, then we have a separate step to split the x and y values we will use in the models. Then you pass these inputs into the modeling functions using Map to pass multiple parameters at once.