R: repeat linear regression for all variables and save results in a new data frame

Question

I have a data frame named “dat” with 10 numeric variables (var1, var2,var3,var4, var5,…var 10), each with several observations…

dat

   var1 var2 var3 var4 var5 var6 var7 var8 var9 var10 
1    12    5   18   19   12 17   11   16   18   10
2     3    2   10    6   13 17   11   16   18   10
3    13   15   14   13    1 17   11   16   18   10
4    17   11   16   18   10 17   11   16   18   10
5     9   13    8    8    7 17   11   16   18   10
6    15    6   20   17    3 17   11   16   18   10
7    12    5   18   19   12 17   11   16   18   10
8     3    2   10    6   13 17   11   16   18   10
9    13   15   14   13    1 17   11   16   18   10

...

I would like to write a code to repeat the same function for all the variables (except the first) in a data frame. The function should analyse the linear regression between var 1 and all the other variables (var2, var3, var4, var5) each at time, using the lm() function

eg cycle 1: linear regression between var 1 and var 2

lm(var1~var2, data=dat)

cycle 2: linear regression between var 1 and var 3,

lm(var1~var3, data=dat)

cycle 3: linear regression between var 1 and var 4

lm(var1~var4, data=dat)

and so on…

I would also like that the results from each cycle will be saved in a new data frame named “results”, having the following structure

Var_tested  Correlation_coefficient         P_value_correlation     R_squared
Var2        corr_coeff_var2                 p_value_var2            R_sq_var2
Var3        corr_coeff_var3                 p_value_var3            R_sq_var3
Var4        corr_coeff_var4                 p_value_var4            R_sq_var4

With each rows reporting data the results of each correlation. Is it possible?

Thank you so much for your help!

Answer 1

You can try the following code to have the desired output

data <- structure(list(var1 = c(12L, 3L, 13L, 17L, 9L, 15L, 12L, 3L, 
13L), var2 = c(5L, 2L, 15L, 11L, 13L, 6L, 5L, 2L, 15L), var3 = c(18L, 
10L, 14L, 16L, 8L, 20L, 18L, 10L, 14L), var4 = c(19L, 6L, 13L, 
18L, 8L, 17L, 19L, 6L, 13L), var5 = c(12L, 13L, 1L, 10L, 7L, 
3L, 12L, 13L, 1L), var6 = c(17L, 17L, 17L, 17L, 17L, 17L, 17L, 
17L, 17L), var7 = c(11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L
), var8 = c(16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L), var9 = c(18L, 
18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L), var10 = c(10L, 10L, 
10L, 10L, 10L, 10L, 10L, 10L, 10L)), class = "data.frame", row.names = c(NA, 
-9L))

head(data,2)
#>   var1 var2 var3 var4 var5 var6 var7 var8 var9 var10
#> 1   12    5   18   19   12   17   11   16   18    10
#> 2    3    2   10    6   13   17   11   16   18    10

x = names(data[,-1])
out <- unlist(lapply(1, function(n) combn(x, 1, FUN=function(row) paste0("var1 ~ ", paste0(row, collapse = "+")))))
out
#> [1] "var1 ~ var2"  "var1 ~ var3"  "var1 ~ var4"  "var1 ~ var5" 
#> [5] "var1 ~ var6"  "var1 ~ var7"  "var1 ~ var8"  "var1 ~ var9" 
#> [9] "var1 ~ var10"

library(broom)
#> Warning: package 'broom' was built under R version 3.5.3

library(dplyr)
#> Warning: package 'dplyr' was built under R version 3.5.3
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union

#To have the regression coefficients
tmp1 = bind_rows(lapply(out, function(frml) {
 a = tidy(lm(frml, data=data))
 a$frml = frml
 return(a)
}))
head(tmp1)
#> # A tibble: 6 x 6
#>   term        estimate std.error statistic p.value frml       
#>   <chr>          <dbl>     <dbl>     <dbl>   <dbl> <chr>      
#> 1 (Intercept)    6.46      2.78      2.33  0.0529  var1 ~ var2
#> 2 var2           0.525     0.288     1.82  0.111   var1 ~ var2
#> 3 (Intercept)   -1.50      4.47     -0.335 0.748   var1 ~ var3
#> 4 var3           0.863     0.303     2.85  0.0247  var1 ~ var3
#> 5 (Intercept)    0.649     2.60      0.250 0.810   var1 ~ var4
#> 6 var4           0.766     0.183     4.18  0.00413 var1 ~ var4

#To have the regression results i.e. R2, AIC, BIC
tmp2 = bind_rows(lapply(out, function(frml) {
 a = glance(lm(frml, data=data))
 a$frml = frml
 return(a)
}))
head(tmp2)
#> # A tibble: 6 x 12
#>   r.squared adj.r.squared sigma statistic  p.value    df logLik   AIC   BIC
#>       <dbl>         <dbl> <dbl>     <dbl>    <dbl> <int>  <dbl> <dbl> <dbl>
#> 1     0.321         0.224  4.33      3.31  0.111       2  -24.8  55.7  56.3
#> 2     0.537         0.471  3.58      8.12  0.0247      2  -23.1  52.2  52.8
#> 3     0.714         0.673  2.81     17.5   0.00413     2  -20.9  47.9  48.5
#> 4     0.276         0.173  4.47      2.67  0.146       2  -25.1  56.2  56.8
#> 5     0             0      4.92     NA    NA           1  -26.6  57.2  57.6
#> 6     0             0      4.92     NA    NA           1  -26.6  57.2  57.6
#> # ... with 3 more variables: deviance <dbl>, df.residual <int>, frml <chr>

write.csv(tmp1, "Try_lm_coefficients.csv")
write.csv(tmp2, "Try_lm_results.csv")

^{Created on 2019-11-20 by the reprex package (v0.3.0)}

Answer 2

dat <- structure(list(var1 = c(12L, 3L, 13L, 17L, 9L, 15L, 12L, 3L, 
13L), var2 = c(5L, 2L, 15L, 11L, 13L, 6L, 5L, 2L, 15L), var3 = c(18L, 
10L, 14L, 16L, 8L, 20L, 18L, 10L, 14L), var4 = c(19L, 6L, 13L, 
18L, 8L, 17L, 19L, 6L, 13L), var5 = c(12L, 13L, 1L, 10L, 7L, 
3L, 12L, 13L, 1L), var6 = c(17L, 17L, 17L, 17L, 17L, 17L, 17L, 
17L, 17L), var7 = c(11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L
), var8 = c(16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L), var9 = c(18L, 
18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L), var10 = c(10L, 10L, 
10L, 10L, 10L, 10L, 10L, 10L, 10L)), class = "data.frame", row.names = c("1", 
"2", "3", "4", "5", "6", "7", "8", "9"))

We first write a function to obtain all the statistics you need. Note, rsq is the square of the correlation coefficient. So you don't need the linear model. The coefficient you get from the model is the slope.

STATS = function(x,y,DATA){
 COR = cor.test(DATA[,y],DATA[,x])
 MODEL = summary(lm(DATA[,y]~DATA[,x]))
 data.frame(
 VAR=x,
 PEARSON_COR=as.numeric(COR$estimate),
 PVAL=COR$p.value,
 RSQ=as.numeric(COR$estimate^2),
 SLOPE = MODEL$coefficients[2,1],
 stringsAsFactors=FALSE
 )
}

We test it on var2

STATS("var2","var1",dat)

     VAR PEARSON_COR      PVAL      RSQ     SLOPE
1 var2   0.5668721 0.1114741 0.321344 0.5251232

We do it for example on var2,var3,var4 and combine them into a data frame. Note I did not try var 6 to 10 because it's only 1 value

results = do.call(rbind,
lapply(c("var2","var3","var4"),function(i)STATS(i,"var1",dat)))
results

    VAR PEARSON_COR        PVAL       RSQ     SLOPE
1 var2   0.5668721 0.111474101 0.3213440 0.5251232
2 var3   0.7328421 0.024699805 0.5370575 0.8630573
3 var4   0.8450726 0.004127542 0.7141477 0.7660377

If you are familiar with tidyverse and purrr, you can do the following:

library(dplyr)
library(purrr)
c("var2","var3","var4") %>% map_dfr(STATS,"var1",dat)

Answer 3

There a several ways to do what you want in R. I suggest sapply which is a simple way to apply a function other a list of variables. Here is an example to get the coefficients of each linear regression between var1 and all other variables.

# define a function to get coefficients from linear regression
do_lm <- function(var){ # var is the name of the column
  res <- lm(as.formula(paste0("var1~",var)), data = dat) # compute linear regression
  coefs <- c(intercept = res$coefficient[2], slope = res$coefficient[1]) # get coefficients
  return(coefs)
}

t(
  sapply(colnames(dat)[2:10], do_lm)
 )
# t transposes the result 
# sapply : applies on "var2" ... "var10" the function do_lm

It returns:

      intercept.var2 slope.(Intercept)
var2       0.5251232         6.4600985
var3       0.8630573        -1.4968153
var4       0.7660377         0.6490566
var5      -0.5047619        14.8158730
var6              NA        10.7777778
var7              NA        10.7777778
var8              NA        10.7777778
var9              NA        10.7777778
var10             NA        10.7777778

You can adapt the function do_lm in sapply to compute other things, like correlations...