Solved – Recoding a variable with three levels into a dumthe variable

categorical datacategorical-encoding

I need to recode the variable school setting (urban, sub-urban and rural settings) into a dummy variable. I know that when creating a dummy variable, there is one category less (so 2 rather than three conditions) and that the urban is the largest group and should be used as baseline (not sure if baseline is the right word, but hopefully you know what I mean). However, I don't know what to do from here.

Is the variable changed into:
1. Two dummy variables: setting 1 with urban/sub-urban and setting 2 with urban/rural?
2. One variable where urban is given the value 1, and urban and sub-urban are given the value 0?
3. Both?
4. Have I completely missed something?

Hope you can help me!!

Best Answer

Actually, there are different types of dummy variable coding. The simplest method is redundant, since it uses three dummy variables:

          V1  V2  V3
urban      1   0   0
suburban   0   1   0
rural      0   0   1

Although redundant, this is also a valid encoding. A less redundant way to encode, requiring only two dummy variables, is this:

          V1   V2
urban      0    0
suburban   1    0
rural      0    1

Note that depending on your statistical framework, chances are that you don't need to worry about the coding. In R, if you specify your variable as a factor and create a model matrix, you will not have to worry about dummy variable coding too much; you will just use your variable in the formula passed to model.matrix and that's it.

However, you will have to be confronted with the contrast coding (how to get, out of your dummy variables, the comparisons that you are interested in). You will find a thorough description here.

Question:

Can Dummy variables have overlapping categories?

Answer:

No.

Explanation:

Dummy variables arise when you try to recode Categorical variables with more than two categories into a series of binary variables. Since these categories partition your dataset (i.e. each observation can be assigned to one and only one of these 'k' categories), there is no way that there can be any "overlapping".

Now, with respect to the actual example you provide, there are two issues you should be aware of since they probably would otherwise screw up your analysis entirely:

The binary variables which you describe are based, more or less, on arbitrary distinctions (for instance, would astroturf--more or less a rug covering concrete--really qualify as "soft" ground?).
There's a good chance your model (as described in the OP) suffers from Multicollinearity (that is, that a linear combination of two or more of your independent variables are highly correlated).

Just something you should keep in mind the next time you run a regression... Anyway, hope this helps.

Solved – Dumthe Regression – Baseline Variable

From your post, it seems like you are confused about what actually constitues an effect in your model. Let's say that y stands for income (thousands od dollars), a stands for age and educ stands for education level.

For instance, the effect of the predictor variable a on the response variable y controlling for the effect of educ is estimated as 0.67439. This effect can be interpreted as follows:

Among those with the same education level, we estimate that each 1-  
year increase in age is associated with an increase in the mean income 
of 0.67439 thousands of dollars.

The effect of the predictor variable educ on the response variable y controlling for age can be described by a collection of two separate effects, estimated as 0.63322 and -0.07283. Here is the interpretation of these two effects:

The difference in mean incomes between those with a high school   
education and those with an elementary education is estimated to be 
0.63322 thousand dollars (assuming they share the same age). 

The difference in mean incomes between those with a college graduate 
education and those with an elementary education is of -0.07283 
thousand dollars (assuming they share the same age).

(It doesn't make sense that college graduates would earn less than those with an elementary education, but this example is made up.)

As you can see, effects quantify the change in the mean value of the response variable y associated with a change in the values of the predictor variables a and educ. If you don't change the value of educ, you can't really speak of an effect for it.

Best Answer

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Solved – dumthe variables with overlapping categories

Question:

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Solved – Dumthe Regression – Baseline Variable

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