Normally, me and you(assuming you're not a bot) are easily able to identify whether a predictor is categorical or quantitative. Like, for example, gender is obviously categorical. Your last vote can be classified categorically.
Basically, we can identify categorical predictors easily. But what happens when we input some data in R
, and it's lm
function makes dummy variables for a predictor? How does it do that?
Somewhat related Question on StackOverflow.
Categorical Variable: A categorical variable is a variable that is not numerical - instead it is based on a qualitative property, such as color, breed, or gender, among others. Categorical variables do not have a particular ordering, since they are not numerical, and take on values from a limited set of possibilities.
Categorical variables require special attention in regression analysis because, unlike dichotomous or continuous variables, they cannot by entered into the regression equation just as they are. Instead, they need to be recoded into a series of variables which can then be entered into the regression model.
In linear regression the independent variables can be categorical and/or continuous. But, when you fit the model if you have more than two category in the categorical independent variable make sure you are creating dummy variables.
Predictor variables in statistical models can be treated as either continuous or categorical.
Search R factor
function. Here is a small demo, first model uses number of cylinder as a numerical valuable. Second model uses it as a categorical variable.
> summary(lm(mpg~cyl,mtcars))
Call:
lm(formula = mpg ~ cyl, data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-4.9814 -2.1185 0.2217 1.0717 7.5186
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.8846 2.0738 18.27 < 2e-16 ***
cyl -2.8758 0.3224 -8.92 6.11e-10 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.206 on 30 degrees of freedom
Multiple R-squared: 0.7262, Adjusted R-squared: 0.7171
F-statistic: 79.56 on 1 and 30 DF, p-value: 6.113e-10
> summary(lm(mpg~factor(cyl),mtcars))
Call:
lm(formula = mpg ~ factor(cyl), data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-5.2636 -1.8357 0.0286 1.3893 7.2364
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 26.6636 0.9718 27.437 < 2e-16 ***
factor(cyl)6 -6.9208 1.5583 -4.441 0.000119 ***
factor(cyl)8 -11.5636 1.2986 -8.905 8.57e-10 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.223 on 29 degrees of freedom
Multiple R-squared: 0.7325, Adjusted R-squared: 0.714
F-statistic: 39.7 on 2 and 29 DF, p-value: 4.979e-09
Hxd1011 adressed the more difficult case, when a categorical variable is stored as a number and therefore R understands by default that it is a numerical value - and if this is not the desired behaviour we must use factor
function.
Your example with predictor ShelveLoc
in dataset Carseats
is easier because it's a text (character) variable, and therefore it can only be a categorical variable.
> head(Carseats$ShelveLoc)
[1] Bad Good Medium Medium Bad Bad
Levels: Bad Good Medium
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