Linear Regression prediction in R using Leave One out Approach

Question

I have 3 linear regression models built using the mtcars and would like to use those models to generate predictions for each rows of the mtcars tables. Those predictions should be added as additional columns (3 additional columns) of the mtcars dataframe and should be generated in a for loop using the leave one out approach. Furthermore predictions for model1 and model2 should be performed by "grouping" the cyl numbers whiles predictions made with the model 3 should be accomplished without doing any grouping.

So far I've been able to somewhat get something with a single model in the loop:

model1 =lm(hp ~ mpg, data = mtcars)

model2 =lm(hp ~ mpg + hp, data = mtcars)

model3 =lm(hp ~ mpg + hp + wt, data = mtcars)

fitted_value <- NULL

for(i in 1:nrow(mtcars)){
  

  validation<-mtcars[i,]

  training<-mtcars[-i,]

  model1<-lm(mpg ~ hp, data = training)

  fitted_value[i] <-predict(model1, newdata = validation)

   }```


I would like to be able to generate all the model predictions by first putting all the models in a list or vector and attaching the result to the mtcars dataframe. Somthing lke thislike this:

```model1 =lm(hp ~ mpg, data = mtcars)

model2 =lm(hp ~ mpg + hp, data = mtcars)

model3 =lm(hp ~ mpg + hp + wt, data = mtcars)

models <- list(model1, model2, model3)

fitted_value <- NULL

for(i in 1:nrow(mtcars)){
  

  validation<-mtcars[i,]

  training<-mtcars[-i,]

  fitted_value[i] <-predict(models, newdata = validation)

   }```

Thank you for you help

andrew_reece · Accepted Answer · 2020-11-20T03:17:49.347

You can use a nested map to fit each of the three formulas for each row i. Then just bind_cols with mtcars to attach the predictions.

library(tidyverse)

frml_1 <- as.formula("hp ~ mpg")
frml_2 <- as.formula("hp ~ mpg + drat")
frml_3 <- as.formula("hp ~ mpg + drat + wt")
frmls <- list(frml_1 = frml_1, frml_2 = frml_2, frml_3 = frml_3)

mtcars %>%
  bind_cols(
    map(1:nrow(mtcars), function(i) {
      map_dfc(frmls, function(frml) {
        training <- mtcars[-i, ]
        fit <- lm(frml, data = training)
        
        validation <- mtcars[i, ]
        predict(fit, newdata = validation)
      })
    }) %>%
    bind_rows()
  )

                     mpg cyl  disp  hp drat    wt  qsec vs am gear carb    frml_1    frml_2    frml_3
Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4 138.65796 138.65796 140.61340
Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4 138.65796 138.65796 139.55056
Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1 122.76445 122.76445 124.91348
Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1 135.12607 135.12607 134.36670
Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2 158.96634 158.96634 158.85438
Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1 164.26418 164.26418 164.42112
Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4 197.81716 197.81716 199.74665
...

Note that the formulas have hp removed from RHS, as hp is also the response. I used drat instead for demonstration purposes.

This is great! However I'm trying to avoid using the tidyverse and purr/map package in this particular case. How can I transform that to a loop with 2 variables? — user3670179, Nov 20 '20 at 03:04
Should it be fit <- lm(j, data = training) instead of fit <- lm(j, data = mtcars) — user3670179, Nov 20 '20 at 03:12
good correction on `data = training`, i've added to my answer. i will have to come back to add a for-loop version, but i imagine someone else might provide a translation too. — andrew_reece, Nov 20 '20 at 03:19
Could you help me solve this problem?: https://stackoverflow.com/questions/65440030/leave-one-out-regression-model-evaluation-by-group-subset-in-r It's a slight variation of the problem above — user3670179, Dec 24 '20 at 15:07
How can use this solution by using nest_by(cyl)? In other words I would to do this evaluation a cyl perspective. — user3670179, Dec 26 '20 at 17:45

score 0 · Answer 2 · edited Dec 24 '20 at 17:34

I been able to accomplish that by doing the following script:

fitted_value1 <- NULL
fitted_value2 <- NULL
fitted_value3 <- NULL

for(i in 1:nrow(mtcars)){
  validation<-mtcars[i,] 
  training<-mtcars[-i,]
  model1 =lm(hp ~ mpg, data = training)
  model2 =lm(hp ~ mpg + hp, data = training)
  model3 =lm(hp ~ mpg + hp + wt, data = training)
  fitted_value1[i] <-predict(model1, newdata = validation)
  fitted_value2[i] <-predict(model2, newdata = validation)
  fitted_value3[i] <-predict(model3, newdata = validation)
  res<- as.data.frame(cbind(mtcars,fitted_value1,fitted_value2,fitted_value3))
}

How can I improve this code? I would like to take the models out of the loop, save them as a list and only refer to the list inside the loop. This is more or less what I would ideally want (but it's not working):

model1 =lm(hp ~ mpg, data = mtcars)
model2 =lm(hp ~ mpg + hp, data = mtcars)
model3 =lm(hp ~ mpg + hp + wt, data = mtcars)
models <- list(model1, model2, model3)

fitted_value <- NULL

for(i in 1:nrow(mtcars)){
  for (j in models){

    validation<-mtcars[i,]
    training<-mtcars[-i,]
    fitted_value[i] <-predict(models[j], newdata = validation)

    # this should save the predictions for all the models and append it to the original dataframe
    df <- cbind(mtcars,fitted_value) 
  }
}

Thank you for your help

Linear Regression prediction in R using Leave One out Approach

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