Linear Regression and storing results in data frame

Question

I am running a linear regression on some variables in a data frame. I'd like to be able to subset the linear regressions by a categorical variable, run the linear regression for each categorical variable, and then store the t-stats in a data frame. I'd like to do this without a loop if possible.

Here's a sample of what I'm trying to do:

  a<-  c("a","a","a","a","a",
         "b","b","b","b","b",
         "c","c","c","c","c")     
  b<-  c(0.1,0.2,0.3,0.2,0.3,
         0.1,0.2,0.3,0.2,0.3,
         0.1,0.2,0.3,0.2,0.3)
  c<-  c(0.2,0.1,0.3,0.2,0.4,
         0.2,0.5,0.2,0.1,0.2,
         0.4,0.2,0.4,0.6,0.8)
      cbind(a,b,c)

I can begin by running the following linear regression and pulling the t-statistic out very easily:

  summary(lm(b~c))$coefficients[2,3]

However, I'd like to be able to run the regression for when column a is a, b, or c. I'd like to then store the t-stats in a table that looks like this:

variable t-stat
a        0.9
b        2.4
c        1.1

Hope that makes sense. Please let me know if you have any suggestions!

All of the answers will have loops (lapply, and sapply are loops). You might look at http://stackoverflow.com/q/27434101/321622 — John, Jan 19 '15 at 17:22

alex23lemm · Answer 1 · 2015-01-21T14:45:00.863

Here is a solution using dplyr and tidy() from the broom package. tidy() converts various statistical model outputs (e.g. lm, glm, anova, etc.) into a tidy data frame.

library(broom)
library(dplyr)

data <- data_frame(a, b, c)

data %>% 
  group_by(a) %>% 
  do(tidy(lm(b ~ c, data = .))) %>% 
  select(variable = a, t_stat = statistic) %>% 
  slice(2)

#   variable     t_stat
# 1        a  1.6124515
# 2        b -0.1369306
# 3        c  0.8000000

Or extracting both, the t-statistic for the intercept and the slope term:

data %>% 
  group_by(a) %>% 
  do(tidy(lm(b ~ c, data = .))) %>% 
  select(variable = a, term, t_stat = statistic)

#   variable        term     t_stat
# 1        a (Intercept)  1.2366939
# 2        a           c  1.6124515
# 3        b (Intercept)  2.6325081
# 4        b           c -0.1369306
# 5        c (Intercept)  1.4572335
# 6        c           c  0.8000000

The select-command does not work for me (variable, term and t_stat is unused). — Ben, Apr 30 '20 at 12:54
@Ben: The code is still fully reproducible for me and everything works as outlined above. — alex23lemm, May 04 '20 at 12:02

Sven Hohenstein · Answer 2 · 2015-01-19T18:27:56.957

You can use the lmList function from the nlme package to apply lm to subsets of data:

# the data
df <- data.frame(a, b, c)

library(nlme)
res <- lmList(b ~ c | a, df, pool = FALSE)
coef(summary(res))

The output:

, , (Intercept)

   Estimate Std. Error  t value   Pr(>|t|)
a 0.1000000 0.08086075 1.236694 0.30418942
b 0.2304348 0.08753431 2.632508 0.07815663
c 0.1461538 0.10029542 1.457233 0.24110393

, , c

     Estimate Std. Error    t value  Pr(>|t|)
a  0.50000000  0.3100868  1.6124515 0.2052590
b -0.04347826  0.3175203 -0.1369306 0.8997586
c  0.15384615  0.1923077  0.8000000 0.4821990

If you want the t values only, you can use this command:

coef(summary(res))[, "t value", -1]
#          a          b          c 
#  1.6124515 -0.1369306  0.8000000

Steven · Accepted Answer · 2015-01-19T18:08:20.197

5

Here's a vote for the plyr package and ddply().

plyrFunc <- function(x){
  mod <- lm(b~c, data = x)
  return(summary(mod)$coefficients[2,3])
  }

tStats <- ddply(dF, .(a), plyrFunc)
tStats
  a         V1
1 a  1.6124515
2 b -0.1369306
3 c  0.6852483

edited Jan 19 '15 at 18:08

answered Jan 19 '15 at 17:48

Steven

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1

Thank you, this was incredibly straight forward and simple. – Trexion Kameha Jan 20 '15 at 16:00
No problem. The `plyr` package is pretty handy. I only learned about it fairly recently but it's been incredibly useful. – Steven Jan 20 '15 at 17:07

score 3 · Answer 4 · answered Jan 19 '15 at 17:17

Use split to subset the data and do the looping by lapply

dat <- data.frame(b,c)
dat_split <- split(x = dat, f = a)
res <- sapply(dat_split, function(x){
  summary(lm(b~c, data = x))$coefficients[2,3]
})

Reshape the result to your needs:

data.frame(variable = names(res), "t-stat" = res) 

  variable     t.stat
a        a  1.6124515
b        b -0.1369306
c        c  0.8000000

LyzandeR · Answer 5 · 2015-01-19T17:44:58.333

You could do this:

a<-  c("a","a","a","a","a",
       "b","b","b","b","b",
       "c","c","c","c","c")     
b<-  c(0.1,0.2,0.3,0.2,0.3,
       0.1,0.2,0.3,0.2,0.3,
       0.1,0.2,0.3,0.2,0.3)
c<-  c(0.2,0.1,0.3,0.2,0.4,
       0.2,0.5,0.2,0.1,0.2,
       0.4,0.2,0.4,0.6,0.8)
df <- data.frame(a,b,c)


t.stats <- t(data.frame(lapply(c('a','b','c'), 
             function(x) summary(lm(b~c,data=df[df$a==x,]))$coefficients[2,3])))
colnames(t.stats) <- 't-stat'
rownames(t.stats) <- c('a','b','c')

Output:

> t.stats
      t-stat
a  1.6124515
b -0.1369306
c  0.8000000

Unless I am mistaken the values you give in your output are not the correct ones.

Or:

t.stats <- data.frame(t.stats)
t.stats$variable <- rownames(t.stats)

> t.stats[,c(2,1)]
  variable     t.stat
a        a  1.6124515
b        b -0.1369306
c        c  0.8000000

If you want a data.frame and a separate column.

Linear Regression and storing results in data frame

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