predict.lm() in a loop. warning: prediction from a rank-deficient fit may be misleading

Question

This R code throws a warning

# Fit regression model to each cluster
y <- list() 
length(y) <- k
vars <- list() 
length(vars) <- k
f <- list()
         


        

Answer 1

You can inspect the predict function with body(predict.lm). There you will see this line:

if (p < ncol(X) && !(missing(newdata) || is.null(newdata))) 
    warning("prediction from a rank-deficient fit may be misleading")

This warning checks if the rank of your data matrix is at least equal to the number of parameters you want to fit. One way to invoke it is having some collinear covariates:

data <- data.frame(y=c(1,2,3,4), x1=c(1,1,2,3), x2=c(3,4,5,2), x3=c(4,2,6,0), x4=c(2,1,3,0))
data2 <- data.frame(x1=c(3,2,1,3), x2=c(3,2,1,4), x3=c(3,4,5,1), x4=c(0,0,2,3))
fit <- lm(y ~ ., data=data)

predict(fit, data2)
       1        2        3        4 
4.076087 2.826087 1.576087 4.065217 
Warning message:
In predict.lm(fit, data2) :
  prediction from a rank-deficient fit may be misleading

Notice that x3 and x4 have the same direction in data. One is the multiple of the other. This can be checked with length(fit$coefficients) > fit$rank

Another way is having more parameters than available variables:

fit2 <- lm(y ~ x1*x2*x3*x4, data=data)
predict(fit2, data2)
Warning message:
In predict.lm(fit2, data2) :
  prediction from a rank-deficient fit may be misleading