How to perform stepwise regression without intercept?

Question

I have to implement a regression model and I have about 30 variables in the model. Some of the variables do not have much influence on the model, but I need to use a formalized method for eliminating variables. I ended up with the AIC and BIC methods and I have been using the step function in R. The problem is that I need to do a regression model that goes through the origin. In R I use the following statement for regression through the origin,

g <- lm(Pcubes ~ 0 + ., data)

and a regression with intercept

g <- lm(Pcubes ~ ., data)

I then use the step function as

l <- step(g)

and the summary for the new the regression model l, summary(l). Whenever I use the regression through the origin, I get a summary from summary(l) where some variables are not significant to the model and I also get a new regression model that looks as follows,

lm(formula = Pcubes ~ X1 + X4 + X6 + X7 + X8 + X13 + X14 + X17 + 
    X18 + X23 + X24 + X25 + X29 + X30 + X40 + X41 + X44 + X45 + 
    X46 + X48 + X52 + X53 + X54 + X55 + X71 + X82 + X91 + X96 - 1, data = data)

The new model subtracts a 1. And the step function also results in different variables for regression through the origin and regression with intercept. So my questions are, can I use the step function in R for regression through the origin or can I just ignore the -1 in the model or should I use the regression with intercept to choose the best variables and implement the regression through the origin with those variables?

Answer 1

For the lm model with intercept lm(y~.), the simplest model to consider by step function is lm(y~1). So it will try to drop the intercept at all.

For the lm model without intercept lm(y~-1+.), step function will compare the model family all without intercept but different predictor x.