Multiple minimal models in R forward stepwise regression - r

Question

In R stepwise forward regression, I would like to specify several minimal models. I am looking for the best model whith choices between 12 variables (6 flow variables Q_ and 6 precipitation variables LE_).
Biggest model takes into account all the variables :
formule <- "Q ~ 0 + Q_minus_1h + Q_minus_2h + Q_minus_3h + Q_minus_4h + Q_minus_5h + Q_minus_6h + LE_6h + LE_12h + LE_18h + LE_24h + LE_30h + LE_36h"
biggest <- formula(lm(formule, Sub_fit))
With Sub_fit my set of data (data frame with Q and my 12 variables).
I would like to have at least one variable "LE_XX" in my model. So my minimal model could be :
formule <- "Q ~ 0 + LE_6h"
smallest <- formula(lm(formule, Sub_fit))
OR
formule <- "Q ~ 0 + LE_12h"
smallest <- formula(lm(formule, Sub_fit))
OR...
formule <- "Q ~ 0 + LE_36h"
smallest <- formula(lm(formule, Sub_fit))
With finally :
modele.res <- step(lm(as.formula("Q ~ 0"),data=Sub_fit), direction='forward', scope=list(lower=smallest, upper=biggest))
"lower", into "scope", does not allow a list but should be one unique formula. Is it possible to do what I need ?

Answer 1

To specify several minimal models in stepwise forward regression, create the smallest formulas with, for instance, lapply and then loop through them.
In the example below, built-in data set mtcars is used to fit several models having mpg as response, one per each of the 3 last variables in the data set.
data(mtcars)
biggest <- mpg ~ .
sml <- names(mtcars)[9:11]
small_list <- lapply(sml, function(x) {
fmla <- paste("mpg", x, sep = "~")
as.formula(fmla)
})
names(small_list) <- sml
fit <- lm(mpg ~ ., mtcars)
fit_list <- lapply(small_list, function(smallest){
step(fit, scope = list(lower = smallest, upper = biggest))
})
Now select with AIC as criterion
min_aic <- sapply(fit_list, AIC)
min_aic
# am gear carb
#154.1194 155.9852 154.5631
fit_list[[which.min(min_aic)]]

Answer 2

stepwise function in StepReg R package can include some variables you want in all models during the stepwise regression.
library(StepReg)
f1 <- Q ~ 0 + Q_minus_1h + Q_minus_2h + Q_minus_3h + Q_minus_4h + Q_minus_5h + Q_minus_6h + LE_6h + LE_12h + LE_18h + LE_24h + LE_30h + LE_36h
## include LE_6h in the model
stepwise(formula=f1,
data=yourdata,
include="LE_6h",
selection="forward",
select="AIC")
## include LE_6h and LE_12h in the model
stepwise(formula=f1,
data=yourdata,
include=c("LE_6h","LE_12h"),
selection="forward",
select="AIC")