Creating a for loop to calculate AIC scores for different models using lm

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Im trying to create AIC scores for several different models in a for loop. I have created a for loop with the log likeliness for each model. However, I am stuck to create the lm function so that it calculates a model for each combination of my column LOGABUNDANCE with columns 4 to 11 of my dataframe. This is the code I have used so far. But that gives me a similar AIC score for every model.

# AIC score for every model 
LL <- rep(NA, 10)
AIC <- rep(NA, 10)

for(i in 1:10){
  mod <- lm(LOGABUNDANCE ~ . , data = butterfly)
  sigma = as.numeric(summary(mod)[6])
  LL[i] <- sum(log(dnorm(butterfly$LOGABUNDANCE, predict(mod), sigma)))
  AIC[i] <- -2*LL[i] + 2*(2)
}
log-likelihood lm r for-loop
1 Answers

You get the same AIC for every model, because you create 10 equal models.

To make the code work, you need some way of changing the model in each iteration.

I can see two options:

  1. Either subset the data in the start of each iteration so it only contains LOGABUNDANCE and one other variable (as suggested by @yacine-hajji in the comments), or
  2. Create a vector of the variables you want to create models with, and use as.formula() together with paste0() to create a new formula for each iteration.

I think solution 2 is easier. Here is a working example of solution 2, using mtcars:

# AIC score for every model 
LL <- rep(NA, 10)
AIC <- rep(NA, 10)

# Say I want to model all variables against `mpg`:

# Create a vector of all variable names except mpg
variables <- names(mtcars)[-1]

for(i in 1:10){

  # Note how the formula is different in each iteration
  mod <- lm(
    as.formula(paste0("mpg ~ ", variables[i])),
    data = mtcars
    )

  sigma = as.numeric(summary(mod)[6])
  LL[i] <- sum(log(dnorm(mtcars$mpg, predict(mod), sigma)))
  AIC[i] <- -2*LL[i] + 2*(2)
}

Output:

AIC
#>  [1] 167.3716 168.2746 179.3039 188.8652 164.0947 202.6534 190.2124 194.5496
#>  [9] 200.4291 197.2459
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