9 Linear Regression
Now we’ll look at plain old OLS. In STATA this is done using the command reg. In R, OLS is run using the command lm(). This is part of base-R, so there are no packages to install, you just start R and you’re ready to go.
While STATA seperates each part of the regression with a space, R wraps everything in parentheses. You don’t have to include any spaces between the elements inside the pathenses, but it best to do so, for readability. You do have to add ~, +, and/or :. ~ goes between the dependent variabale, and the rest of the equation, + seperates the rest of the variables in an additive model, and : indicates a multiplitcative interation. So
gen x1x2 = x1*x2
reg y x1 x2 x1x2in STATA. Is written
lm(y ~ x1 + x2 + x1:x2, data = stata.data)
In R.
This R code could also be written:
lm(stata.data$y ~ stata.data$x1 + stata.data$x2 +
stata.data$x1:stata.data$x2)And just to add even more variety, one could also write:
attach(stata.data)
lm(y ~ x1 + x2 + x1:x2)9.1 Which way should you write your model?
Starting with attach(stata.data) is likely to be most comfortable for STATA users. This method loads a single dataframe into the environment (in this case stata.data) and now any variable you reference is assumed to belong to that dataframe. If you call a variable that doesn’t exist in the dataframe, you see the message Error in eval(predvars, data, env) : object 'variable' not found where 'variable' is that name of the non-existant variable you tried to call.
If you want to switch to another dataframe, you simply write detach(stata.data) and then attach another dataframe (i.e. attach(stata.data2)). Note that detach() will not remove the data from the environment, it only removes it from being the default for calling variables. If you want to remove the data from the environment, type rm(stata.data).
While this may be the most similar to the way you’re used to working with dataframes in STATA, one of the advantages of R is that you can work with various different dataframes at the same time. You can alsways indicate which dataframe a variable belongs to by writeing dataframe$variable. This is seen in the second example above and is quite specific, but requires specifying the dataframe for every variable. This can be tedious. Adding data = dataframe is a nice balance where you only have to specify the data once per model, but you can still access different dataframes without constantly typing detach() and attach().
9.2 Viewing the results
If you simply run the lm() command without assigning it to an object, the results will print in the console. If you do assign you model to an object, you can access the results with the summary() command. Here’s an example using the ToothGrowth dataset, which examines the role of vitimins in the rate of guinea pigs’ tooth growth.
data("ToothGrowth")
dat <- data.frame(ToothGrowth)
model <- lm(len ~ supp + dose, data = dat)
summary(model)
#>
#> Call:
#> lm(formula = len ~ supp + dose, data = dat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -6.600 -3.700 0.373 2.116 8.800
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 9.2725 1.2824 7.231 1.31e-09 ***
#> suppVC -3.7000 1.0936 -3.383 0.0013 **
#> dose 9.7636 0.8768 11.135 6.31e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 4.236 on 57 degrees of freedom
#> Multiple R-squared: 0.7038, Adjusted R-squared: 0.6934
#> F-statistic: 67.72 on 2 and 57 DF, p-value: 8.716e-16You can combine the results of numerous models into a single (publication ready) table as we’ve seen before.
library(modelsummary)
cn = c(
"suppVC" = "Supplement Type",
"dose" = "Dose (mg/day)"
)
modelsummary(models = model, coef_map = cn, stars = TRUE)
#> Warning: In version 0.8.0 of the `modelsummary` package, the default significance markers produced by the `stars=TRUE` argument were changed to be consistent with R's defaults.
#> This warning is displayed once per session.| Model 1 | |
|---|---|
| Supplement Type | −3.700** |
| (1.094) | |
| Dose (mg/day) | 9.764*** |
| (0.877) | |
| Num.Obs. | 60 |
| R2 | 0.704 |
| R2 Adj. | 0.693 |
| AIC | 348.4 |
| BIC | 356.8 |
| Log.Lik. | −170.208 |
| F | 67.718 |
| + p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001 |