How to run multiple linear regressions with different independent variables and dependent variables adding standardized coefficients in R?

Question

I'm currently trying to run a loop performing linear regression for multiple independent variables (n = 6) with multiple dependent variables (n=1000).

Here is some example data, with age, sex, and education representing my independent variables of interest and testscore_* being my dependent variables.

df = data.frame(ID = c(1001, 1002, 1003, 1004, 1005, 1006,1007, 1008, 1009,   1010, 1011),
                    age = as.numeric(c('56', '43','59','74','61','62','69','80','40','55','58')),
                    sex = as.numeric(c('0','1','0','0','1','1','0','1','0','1','0')),
                    testscore_1 = as.numeric(c('23','28','30','15','7','18','29','27','14','22','24')),
                    testscore_2 = as.numeric(c('1','3','2','5','8','2','5','6','7','8','2')),
                    testscore_3 = as.numeric(c('18','20','19','15','20','23','19','25','10','14','12')),
                    education =  as.numeric(c('5','4','3','5','2', '1','4','4','3','5','2')))

I have working code that allows me to run a regression model for multiple DVs (which I'm sure more experienced R users will dislike for its lack of efficiency):

y <- as.matrix(df[4:6])
#model for age
lm_results <- lm(y ~ age, data = df)

write.csv((broom::tidy(lm_results)), "lm_results_age.csv")

regression_results <-broom::tidy(lm_results)
standardized_coefficients <- lm.beta(lm_results)
age_standardize_results <- coef(standardized_coefficients)

write.csv(age_standardize_results, "lm_results_age_standardized_coefficients.csv")

I would then repeat this all by manually replacing age with sex and education

Does anyone have a more elegant way of running this - for example, by way of a loop for all IVs of interest (i.e. age, sex and education)?

Also would greatly appreciate anyone who would suggest a quick way of combining broom::tidy(lm_results) with standardized coefficients from lm.beta::lm.beta, i.e. combining the standardized regression coefficients with the main model output.

Answer 1

This is an adaptation for a similar workflow I had to use in the past. Remember to really penalize yourself for running a crazy number of models. I added a couple predictor columns to your dataframe. Good luck!!

Solution:

# Creating pedictor and outcome vectors
ivs_vec <- names(df)[c(2:6, 10)]
dvs_vec <- names(df)[7:9]

# Creating formulas and running the models
ivs <- paste0(" ~ ", ivs_vec)
dvs_ivs <- unlist(lapply(ivs, function(x) paste0(dvs_vec, x)))
formulas <- lapply(dvs_ivs, formula)

lm_results <- lapply(formulas, function(x) {
  lm(x, data = df)
})

# Creating / combining results
tidy_results <- lapply(lm_results, broom::tidy)
dv_list <- lapply(as.list(stringi::stri_extract_first_words(dvs_ivs)), rep, 2)
tidy_results <- Map(cbind, dv_list, tidy_results)

standardized_results <- lapply(lm_results, function(x) coef(lm.beta::lm.beta(x)))
combined_results <- Map(cbind, tidy_results, standardized_results)

# Cleaning up final results
names(combined_results) <- dvs_ivs
combined_results <- lapply(combined_results, function(x) {row.names(x) <- c(NULL); x})

new_names <- c("Outcome", "Term", "Estimate", "Std. Error", "Statistic", "P-value", "Standardized Estimate")
combined_results <- lapply(combined_results, setNames, new_names)

Results:

combined_results[1:5]

$`testscore_1 ~ age`
  Outcome        Term    Estimate Std. Error Statistic   P-value 
Standardized Estimate
1 testscore_1 (Intercept) 18.06027731 12.3493569 1.4624468 0.1776424            0.00000000
2 testscore_1         age  0.05835152  0.2031295 0.2872627 0.7804155            0.09531823

$`testscore_2 ~ age`
      Outcome        Term   Estimate Std. Error Statistic   P-value Standardized Estimate
1 testscore_2 (Intercept) 3.63788676 4.39014570 0.8286483 0.4287311             0.0000000
2 testscore_2         age 0.01367313 0.07221171 0.1893478 0.8540216             0.0629906

$`testscore_3 ~ age`
      Outcome        Term  Estimate Std. Error Statistic   P-value Standardized Estimate
1 testscore_3 (Intercept) 6.1215175   6.698083 0.9139208 0.3845886             0.0000000
2 testscore_3         age 0.1943125   0.110174 1.7636870 0.1116119             0.5068026

$`testscore_1 ~ sex`
      Outcome        Term Estimate Std. Error  Statistic      P-value Standardized Estimate
1 testscore_1 (Intercept)     22.5   3.099283  7.2597435 4.766069e-05             0.0000000
2 testscore_1         sex     -2.1   4.596980 -0.4568217 6.586248e-01            -0.1505386

$`testscore_2 ~ sex`
      Outcome        Term Estimate Std. Error Statistic     P-value Standardized Estimate
1 testscore_2 (Intercept) 3.666667   1.041129  3.521816 0.006496884             0.0000000
2 testscore_2         sex 1.733333   1.544245  1.122447 0.290723029             0.3504247

Data:

df <- data.frame(ID = c(1001, 1002, 1003, 1004, 1005, 1006,1007, 1008, 1009,   1010, 1011),
                     age = as.numeric(c('56', '43','59','74','61','62','69','80','40','55','58')),
                     sex = as.numeric(c('0','1','0','0','1','1','0','1','0','1','0')),
                     pred1 = sample(1:11, 11),
                     pred2 = sample(1:11, 11),
                     pred3 = sample(1:11, 11),
                     testscore_1 = as.numeric(c('23','28','30','15','7','18','29','27','14','22','24')),
                     testscore_2 = as.numeric(c('1','3','2','5','8','2','5','6','7','8','2')),
                     testscore_3 = as.numeric(c('18','20','19','15','20','23','19','25','10','14','12')),
                     education =  as.numeric(c('5','4','3','5','2', '1','4','4','3','5','2')))

Answer 2

Stumbled upon this a year later and documenting a tidyverse solution same data as @Andrew.

library(dplyr)
library(purrr)
library(tidyr)
library(stringi)

# Creating pedictor and outcome vectors
ivs_vec <- names(df)[c(2:6, 10)]
dvs_vec <- names(df)[7:9]

# Creating formulas and running the models
ivs <- paste0(" ~ ", ivs_vec)
dvs_ivs <- unlist(map(ivs, ~paste0(dvs_vec, .x)))

models <- map(setNames(dvs_ivs, dvs_ivs),
              ~ lm(formula = as.formula(.x),
                   data = df))

basics <-
   map(models, ~ broom::tidy(.)) %>%
   map2_df(.,
           names(.),
           ~ mutate(.x, which_dependent = .y)) %>%
   select(which_dependent, everything()) %>%
   mutate(term = gsub("\\(Intercept\\)", "Intercept", term),
          which_dependent = stringi::stri_extract_first_words(which_dependent))

basics$std_estimate <-
   map_dfr(models, ~ coef(lm.beta::lm.beta(.)), .id = "which_dependent") %>%
   pivot_longer(.,
                cols = -which_dependent,
                names_to = "term",
                values_to = "std_estimate",
                values_drop_na = TRUE) %>%
   pull(std_estimate)

basics
#> # A tibble: 36 x 7
#>    which_dependent term      estimate std.error statistic   p.value std_estimate
#>    <chr>           <chr>        <dbl>     <dbl>     <dbl>     <dbl>        <dbl>
#>  1 testscore_1     Intercept  18.1      12.3        1.46  0.178           0     
#>  2 testscore_1     age         0.0584    0.203      0.287 0.780           0.0953
#>  3 testscore_2     Intercept   3.64      4.39       0.829 0.429           0     
#>  4 testscore_2     age         0.0137    0.0722     0.189 0.854           0.0630
#>  5 testscore_3     Intercept   6.12      6.70       0.914 0.385           0     
#>  6 testscore_3     age         0.194     0.110      1.76  0.112           0.507 
#>  7 testscore_1     Intercept  22.5       3.10       7.26  0.0000477       0     
#>  8 testscore_1     sex        -2.10      4.60      -0.457 0.659          -0.151 
#>  9 testscore_2     Intercept   3.67      1.04       3.52  0.00650         0     
#> 10 testscore_2     sex         1.73      1.54       1.12  0.291           0.350 
#> # … with 26 more rows