I have a categorical independent variable (with options of "yes" or "no") that I want to add to my panel linear model. According to the answer here: After generating dummy variables?, the lm function automatically creates dummy variables for you for categorical variables.
Does this mean that creating dummy variables through i.e. dummy.data.frame is unnecessary, and I can just add in my variable in the plm function and it will automatically be treated like a dummy variable (even if the data is not numerical)? And is this the same for the plm function?
Also, I don't have much data to begin with. Would it hurt if I manually turned the data into numbers (i.e. "yes"=1, "no"=0) without creating a dummy variable?
It is unnecessary to create dummy variables (i.e., to write code to convert factor variables to dummy variables in a data frame) for use with the lm() function. To illustrate, we'll run a regression model on the mtcars data set, using am (0 = automatic, 1 = manual transmission) as a factor variable.
summary(lm(mpg ~ wt + factor(am),data=mtcars))
...and the output:
> summary(lm(mpg ~ wt + factor(am),data=mtcars))
Call:
lm(formula = mpg ~ wt + factor(am), data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-4.5295 -2.3619 -0.1317 1.4025 6.8782
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.32155 3.05464 12.218 5.84e-13 ***
wt -5.35281 0.78824 -6.791 1.87e-07 ***
factor(am)1 -0.02362 1.54565 -0.015 0.988
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.098 on 29 degrees of freedom
Multiple R-squared: 0.7528, Adjusted R-squared: 0.7358
F-statistic: 44.17 on 2 and 29 DF, p-value: 1.579e-09
We can make the answer even more obvious if we use cyl as the independent variable since it has three levels and should be modeled as factor variable, not a continuous (interval / ratio level of measurement) variable.
summary(lm(mpg ~ wt + factor(cyl),data=mtcars))
...and the output:
> summary(lm(mpg ~ wt + factor(cyl),data=mtcars))
Call:
lm(formula = mpg ~ wt + factor(cyl), data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-4.5890 -1.2357 -0.5159 1.3845 5.7915
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 33.9908 1.8878 18.006 < 2e-16 ***
wt -3.2056 0.7539 -4.252 0.000213 ***
factor(cyl)6 -4.2556 1.3861 -3.070 0.004718 **
factor(cyl)8 -6.0709 1.6523 -3.674 0.000999 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.557 on 28 degrees of freedom
Multiple R-squared: 0.8374, Adjusted R-squared: 0.82
F-statistic: 48.08 on 3 and 28 DF, p-value: 3.594e-11
We interpret the results for the factor variables as:
The original poster's question essentially asks whether this code is needed:
# alternative where you explicitly create dummy variables
mtcars$is6cyl = ifelse(mtcars$cyl == 6,1,0)
mtcars$is8cyl = ifelse(mtcars$cyl == 8,1,0)
summary(lm(mpg ~ wt + is6cyl + is8cyl,data=mtcars))
Notice that the output where we manually create factor variables for 6 or 8 cylinder cars (establishing 4 cylinders is the base value), and in particular the slope output for is6cyl and is8cyl exactly matches the output above.
> summary(lm(mpg ~ wt + is6cyl + is8cyl,data=mtcars))
Call:
lm(formula = mpg ~ wt + is6cyl + is8cyl, data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-4.5890 -1.2357 -0.5159 1.3845 5.7915
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 33.9908 1.8878 18.006 < 2e-16 ***
wt -3.2056 0.7539 -4.252 0.000213 ***
is6cyl -4.2556 1.3861 -3.070 0.004718 **
is8cyl -6.0709 1.6523 -3.674 0.000999 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.557 on 28 degrees of freedom
Multiple R-squared: 0.8374, Adjusted R-squared: 0.82
F-statistic: 48.08 on 3 and 28 DF, p-value: 3.594e-11