Dealing with nested variables in R linear regression

Question

I have a dataset which includes some nested variables. For example, I have the following variables: the speed of a car, the existence of another car following it other_car and, if there is another car, the distance between the two cars distance. Dummy dataset:

speed <- c(30,50,60,30,33,54,65,33,33,54,65,34,45,32)
other_car <- c(0,1,0,0,0,1,1,1,1,0,1,0,1,0)
distance <- c(NA,20,NA,NA,NA,21,5,15,17,NA,34,NA,13,NA)

dft <- data.frame(speed,other_car,distance)

I would like to include the variables other_car and distance in a model with the form of nested variables, i.e. if the car is present consider also the distance. Following an approach mentioned here: https://stats.stackexchange.com/questions/372257/how-do-you-deal-with-nested-variables-in-a-regression-model , I tried the following:

dft <- data.frame(speed,other_car,distance)
dft$other_car<-factor(dft$other_car)

lm_speed <- lm(speed ~ dft$other_car + dft$other_car:dft$distance)
summary(lm_speed)

Which gives the following error:

Error in contrasts<-(*tmp*, value = contr.funs[1 + isOF[nn]]) : contrasts can be applied only to factors with 2 or more levels

Any ideas?

Waldi · Accepted Answer · 2021-04-28T19:39:17.690

This is due to the fact that when other_car==0, distances are all equal to NA, see:

dft$distance[dft$other_car==0]
[1] NA NA NA NA NA NA NA

You could assign a constant distance to replace NA for other_car==0, so that the model uses the factor other_car==0 and finds out that the distance has no impact for this subset:

dft$distance[dft$other_car==0]<-0

dft$other_car<- factor(dft$other_car)

lm_speed <- lm(speed ~ other_car + other_car:distance, data = dft)
summary(lm_speed)

Call:
lm(formula = speed ~ other_car + other_car:distance, data = dft)

Residuals:
    Min      1Q  Median      3Q     Max 
-16.015  -8.500  -3.876   8.894  21.000 

Coefficients: (1 not defined because of singularities)
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)          39.0000     5.0405   7.737 8.96e-06 ***
other_car1            4.6480    13.0670   0.356    0.729    
other_car0:distance       NA         NA      NA       NA    
other_car1:distance   0.3157     0.6133   0.515    0.617    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 13.34 on 11 degrees of freedom
Multiple R-squared:  0.1758,    Adjusted R-squared:  0.026 
F-statistic: 1.174 on 2 and 11 DF,  p-value: 0.3452

Another workaround could be to convert the factor to numeric, but this isn't the same model:

speed <- c(30,50,60,30,33,54,65,33,33,54,65,34,45,32)
other_car <- c(0,1,0,0,0,1,1,1,1,0,1,0,1,0)
distance <- c(NA,20,NA,NA,NA,21,5,15,17,NA,34,NA,13,NA)

dft <- data.frame(speed,other_car,distance)



dft$other_car<- as.numeric(factor(dft$other_car))

lm_speed <- lm(speed ~ other_car + other_car:distance, data = dft)
summary(lm_speed)

Call:
lm(formula = speed ~ other_car + other_car:distance, data = dft)

Residuals:
        2         6         7         8         9        11        13 
  0.03776   3.72205  19.77341 -15.38369 -16.01511  10.61782  -2.75227 

Coefficients: (1 not defined because of singularities)
                   Estimate Std. Error t value Pr(>|t|)  
(Intercept)         43.6480    12.9010   3.383   0.0196 *
other_car                NA         NA      NA       NA  
other_car:distance   0.1579     0.3281   0.481   0.6508  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.27 on 5 degrees of freedom
  (7 observations deleted due to missingness)
Multiple R-squared:  0.04424,   Adjusted R-squared:  -0.1469 
F-statistic: 0.2314 on 1 and 5 DF,  p-value: 0.6508

Which tells that speeds increases with distance to other car (or the other way round, when the other car is too near, drivers tend to slow down).

Thank you for your answer. If I am getting this right, in the second model we can see that speed increases with distance, but we can't compare the speeds based on the variable other_car ? (i.e. include not only the interaction other_car:distance , but also consider the variable other_car as a factor variable). Would it be accurate to follow the first approach but assign 0 to all NAs? — Anna, Apr 28 '21 at 17:19
Assigning the same constant value to all `NA`s indeed works. My intuition would have been to take a high value instead of 0, because this is like having no car behind, but this makes no difference — Waldi, Apr 28 '21 at 19:29

Dealing with nested variables in R linear regression

1 Answers1