Rolling regression and prediction with lm() and predict()

Question

I need to apply lm() to an enlarging subset of my dataframe dat, while making prediction for the next observation. For example, I am doing:

Answer 1

(Efficient) solution

This is what you can do:

p <- 3  ## number of parameters in lm()
n <- nrow(dat) - 1

## a function to return what you desire for subset dat[1:x, ]
bundle <- function(x) {
  fit <- lm(log(clicks) ~ log(v1) + log(v12), data = dat, subset = 1:x, model = FALSE)
  pred <- predict(fit, newdata = dat[x+1, ], se.fit = TRUE)
  c(summary(fit)$adj.r.squared, pred$fit, pred$se.fit)
  }

## rolling regression / prediction
result <- t(sapply(p:n, bundle))
colnames(result) <- c("adj.r2", "prediction", "se")

Note I have done several things inside the bundle function:

• I have used subset argument for selecting a subset to fit
• I have used model = FALSE to not save model frame hence we save workspace

Overall, there is no obvious loop, but sapply is used.

• Fitting starts from p, the minimum number of data required to fit a model with p coefficients;
• Fitting terminates at nrow(dat) - 1, as we at least need the final column for prediction.

---

Test

Example data (with 30 "observations")

dat <- data.frame(clicks = runif(30, 1, 100), v1 = runif(30, 1, 100),
                  v12 = runif(30, 1, 100))

Applying code above gives results (27 rows in total, truncated output for 5 rows)

            adj.r2 prediction        se
 [1,]          NaN   3.881068       NaN
 [2,]  0.106592619   3.676821 0.7517040
 [3,]  0.545993989   3.892931 0.2758347
 [4,]  0.622612495   3.766101 0.1508270
 [5,]  0.180462206   3.996344 0.2059014

The first column is the adjusted-R.squared value for fitted model, while the second column is the prediction. The first value for adj.r2 is NaN, because the first model we fit has 3 coefficients for 3 data points, hence no sensible statistics is available. The same happens to se as well, as the fitted line has no 0 residuals, so prediction is done without uncertainty.