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Dummy Coding: The how and why

Nominal variables, or variables that describe a characteristic using 2 or more categories, are commonplace in quantitative research, but are not always useable in their categorical course. A common workaround for using these variables in a regression analysis is dummy coding, but there is oft a lot of confusion (sometimes even amidst dissertation committees!) near what dummy variables are, how they work, and why we use them. With this in mind, it is important that the researcher knows how and why to use dummy coding and so they can defend their right (and in many cases, necessary) use.

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Dummy coding is a way of incorporating nominal variables into regression assay, and the reason why is pretty intuitive one time yous sympathise the regression model. Regressions are nearly commonly known for their use in using continuous variables (for instance, hours spent studying) to predict an outcome value (such equally form point average, or GPA). In this example, we might find that increased study time corresponds with increased GPAs.

At present, what if we wanted to also know if favorite grade (due east.g., scientific discipline, math, and linguistic communication) corresponded with an increased GPA. Let'southward say we coded this so that science = 1, math = 2, and language = 3. Looking at the nominal favorite grade variable, nosotros tin run into that there is no such thing equally an increase in favorite class – math is not higher than science, and is not lower than language either. This is sometimes referred to as directionality, and knowing that a loftier versus low score means something is an integral role of regression analysis. Luckily, there is a manner around this! Enter: dummy coding.

Dummy coding allows the states to turn categories into something a regression can care for as having a high (ane) and low (0) score. Whatsoever binary variable can be thought of as having directionality, because if it is college, it is category 1, but if it is lower, it is category 0. This allows the regression await at directionality by comparison ii sides, rather than expecting each unit to correspond with some kind of increase. Let'south become back to the favorite grade variable. Remember, we originally coded this as scientific discipline = 1, math = 2, and language = iii. To give the regression something to work with, we can make a carve up column, or variable, for each category. These columns will each show whether each category was a pupil'southward favorite; if a student has a (1), the loftier (or yes) score, in the science column, scientific discipline is their favorite, merely if they take a (0), the low (or no) score, science did not make the cut. The aforementioned goes for each of the dummy variables, as they are called. Beneath is an example of how this ends upwardly working out:
Dummy variables
Pupil Favorite class Science Math Linguistic communication

		Dummy variables
Educatee	Favorite class	Science	Math	Language
ane	Science	one	0	0
2	Scientific discipline	i	0	0
three	Language	0	0	one
iv	Math	0	i	0
5	Language	0	0	i
6	Math	0	1	0

Now, looking at this you can meet that knowing the values for ii of the variables tell the states what value the final variable has to exist. Allow's look at student 1; we know they can only have ane favorite class. If we know scientific discipline = 1 and math = 0, we know that language has to exist 0 likewise. The same goes for student 5; we know that science is not their favorite, nor is math, so linguistic communication has to have a yep (or 1).

For this reason, we do not use all three categories in a regression. Doing then would requite the regression redundant information, result in multicollinearity, and intermission the model. This ways we have to leave one category out, and we call this missing category the reference category. Using the reference category makes all interpretation in reference to that category. For case, if you included the dummy variable of science and used language as the reference, results for that variable tell you those students' results in comparison to students with language as their favorite course. The reference category is ordinarily chosen based on how you want to interpret the results, then if you would rather talk about students in comparing to those with math equally their favorite class, simply include the other ii instead.

Now that we have covered the basics of i of the most common data transformations washed for regression, next time nosotros will embrace a piffling more of a general interpretation of the linear regression. You tin can also larn more than about interpreting binary logistic regression here!

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