如何让R中的Forward Selection逐步回归返回非仅截距的模型？

我正在对比新型自动化最优模型选择技术与LASSO、向后逐步回归两种基准方法的特性。此前已在蒙特卡洛模拟所用的47501个合成数据集上成功迭代运行LASSO和向后逐步回归，出于好奇尝试运行向前逐步回归，但每个数据集拟合的模型都仅包含截距。

成功运行的向后逐步回归代码 #

directory_path <- "~/DAEN_698/other datasets/sample_obs2"
filepath_list <- list.files(path = directory_path, full.names = TRUE, 
                        recursive = TRUE)

# reformat the names of each of the csv file formatted datasets
DS_names_list <- basename(filepath_list)
DS_names_list <- tools::file_path_sans_ext(DS_names_list)

## This line reads all of the data in each of the csv files 
## using the name of each store in the list we just created.
datasets <- lapply(list.files(path = "~/DAEN_698/other datasets/sample_obs2", 
                              full.names = TRUE, recursive = TRUE), read.csv)

### Step 3: Run a Backward Elimination Stepwise Regression
### function on each of the 47,500 datasets.
set.seed(11)      # for reproducibility
full_model <- vector("list", length = length(datasets))
BE_fits <- vector("list", length = length(datasets))
BE_fits   # returns a list with 15 elements, all of which are NULL

set.seed(11)      # for reproducibility
for(i in seq_along(datasets)) {
  full_model[[i]] <- lm(formula = Y ~ ., data = datasets[[i]])
  BE_fits[[i]] <- step(object = full_model[[i]], scope = formula(full_model[[i]]),
                       direction = 'backward', trace = 0) }

尝试的向前逐步回归代码 #

### Step 4/5 (optional): Run a Forward Selection Stepwise Regression
### function on each of the 47,500 datasets.
### Assign the null models to their corresponding datasets and
### store these in the object "null_models"
set.seed(11)      # for reproducibility
#datasets[[1]]$
# try this line below if the line of code after it does not run/work
#null_model = lm(datasets[[1]]$Y ~ 1, data = datasets)
null_models <- vector("list", length = length(datasets))
FS_fits <- vector("list", length = length(datasets))
FS_fits   # returns a list with 15 elements, all of which are NULL

set.seed(11)      # for reproducibility
for(j in seq_along(datasets)) {
  null_models[[j]] <- lm(formula = Y ~ 1, data = datasets[[j]])
  FS_fits[[j]] <- step(object = null_models[[j]], 
                       scope = formula(null_models[[j]]),
                       direction = 'forward',
                       trace = 0) }

运行结果 #

> head(null_models, n = 1)
[[1]]
Call:
lm(formula = Y ~ 1, data = datasets[[j]])
Coefficients:
(Intercept)  
      1.017 
> head(FS_fits, n = 1)
[[1]]
Call:
lm(formula = Y ~ 1, data = datasets[[j]])
Coefficients:
(Intercept)  
      1.017  

> names(coef(FS_fits[[1]]))
[1] "(Intercept)"
> names(coef(FS_fits[[2]]))
[1] "(Intercept)"
> names(coef(FS_fits[[3]]))
[1] "(Intercept)"

内容的提问来源于stack exchange，提问作者Marlen