How to report a standardized model in stargazer package?

Question

I made the following simple regression model and used stargazer to output a table that plots the standardized vs non-standardized regression model coefficients, standard errors and p-values.

library(lm.beta)

mod <- lm(mpg ~ cyl + disp, mtcars)
summary(mod)
mod_std <- lm.beta(mod)
summary(mod_std)$coe[, 2]


library(stargazer)
stargazer(mod, mod_std, 
          coef = list(mod$coefficients, 
                      mod_std$standardized.coefficients),
          type='text')

And this is the output:

==========================================================
                                  Dependent variable:     
                              ----------------------------
                                          mpg             
                                   (1)            (2)     
----------------------------------------------------------
cyl                              -1.587**       -0.470    
                                 (0.712)        (0.712)   
                                                          
disp                             -0.021**      -0.423***  
                                 (0.010)        (0.010)   
                                                          
Constant                        34.661***        0.000    
                                 (2.547)        (2.547)   
                                                          
----------------------------------------------------------
Observations                        32            32      
R2                                0.760          0.760    
Adjusted R2                       0.743          0.743    
Residual Std. Error (df = 29)     3.055          3.055    
F Statistic (df = 2; 29)        45.808***      45.808***  
==========================================================
Note:                          *p<0.1; **p<0.05; ***p<0.01

As can be observed here, the standard errors that are reported by the stargazer (for the coefficients) are the same for the standardized model and the non-standardized one. This is not correct as standard errors should change with the standardization of coefficients. Is there a way to report the correct standard errors? Or if not, simply remove them?

Lastly, what also changes from the standardized to the non-standardized models are the significance levels (of the coefficients). These should not change as they are not affected by standardization. Is there a way to prevent stargazer from modifying them? p or p.auto arguments maybe would work but I have no idea how to use them.

Reference for lm.beta: Stefan Behrendt (2014). lm.beta: Add Standardized Regression Coefficients to lm-Objects. R package version 1.5-1. https://CRAN.R-project.org/package=lm.beta

Answer 1

You would need to enter the additional values by hand, list-wise for each model, as you started with the coefficients. Standardized se=, the p= values (for the stars), ... as well as the the GOFs (R², R²_adj., ...), read options in help page: ?stargazer.

However, lm.beta appears to add nothing but the standardized coefficients, and none are yet calculated to report them.

Standardized standard errors are calculated using the formula SE*beta_star/beta.

So you could wrap a function, and calculate them, in order to fill them in the stargazer table:

std_se <- \(x) x[, 'Std. Error']*x[, 'Standardized']/x[, 'Estimate']

std_se(summary(mod_std)$coefficients)
# (Intercept)         cyl        disp 
#   0.0000000   0.2109356   0.2109356 

However, it might definitely be easier to calculate a actual standardized model

mod_std2 <- lm(mpg ~ cyl + disp, as.data.frame(scale(mtcars)))
summary(mod_std2) |> getElement('coefficients')
#                Estimate Std. Error   t value     Pr(>|t|)
# (Intercept) 34.66099474 2.54700388 13.608536 4.022869e-14
# cyl         -1.58727681 0.71184427 -2.229809 3.366495e-02
# disp        -0.02058363 0.01025748 -2.006696 5.418572e-02

and put that in:

stargazer(mod, mod_std2, type='text')
# ==========================================================
#                                   Dependent variable:     
#                               ----------------------------
#                                           mpg             
#                                    (1)            (2)     
# ----------------------------------------------------------
# cyl                              -1.587**      -0.470**   
#                                  (0.712)        (0.211)   
                                                          
# disp                             -0.021*        -0.423*   
#                                  (0.010)        (0.211)   
                                                          
# Constant                        34.661***       -0.000    
#                                  (2.547)        (0.090)   
                                                          
# ----------------------------------------------------------
# Observations                        32            32      
# R2                                0.760          0.760    
# Adjusted R2                       0.743          0.743    
# Residual Std. Error (df = 29)     3.055          0.507    
# F Statistic (df = 2; 29)        45.808***      45.808***  
# ==========================================================
# Note:                          *p<0.1; **p<0.05; ***p<0.01

Answer 2

I managed to make the following script:

stargazer(mod_std, 
          coef=list(mod_std$standardized.coefficients),
          se=list(summary(mod_std)$coe[, 2]),
          p=list(summary(mod)$coe[, 4]),
          type='text',
          omit.stat = c("all"),
          keep = c("cyl","disp"),
          report = c('vcp'), notes.append = FALSE,
          notes = "Coefficients are standardized")

With the following output:

===================================
           Dependent variable:     
      -----------------------------
                   mpg             
-----------------------------------
cyl              -0.470            
                p = 0.034          
                                   
disp             -0.423            
                p = 0.055          
                                   
===================================
===================================
Note: Coefficients are standardized

Here, the standardized coefficients are reported, together with the p-values from the original model (which should be unchanged across standardization).