Whenever I get email questions whose answers I think would benefit others, I like to answer them here. I leave out the asker’s name for privacy, but this is a great question about dummy coding:
First of all, thanks for all those helpful information you provided! Thanks sincerely for all your efforts!
Actually I am here to ask a technical question. See, I have 6 locations (let’s say A, B, C, D, E, and F), and I want to see the location effect on the outcome using OLS models.
I know that if I included 5 dummy location variables (6 locations in total, with A as the reference group) in 1 block of the regression analysis, the result would be based on the comparison with the reference location.
Then what if I put 6 dummies (for example, the 1st dummy would be “1” for A location, and “0” for otherwise) in 1 block? Will it be a bug? If not, how to interpret the result?
Thanks a lot!
Great question!
If you put in a 6th dummy code for Location A, your reference group, the model will actually blow up. (Yes, that’s a technical term).
This is one of those cases of pure multicollinearity, and the model can’t be estimated uniquely.
It’s the same situation you learned back in Algebra where you have two equations, one unknown. The problem isn’t that it can’t be solved–the problem is there are an infinite number of equally good solutions.
If an observation falls in Location A, the reference group, we’ve already gotten that information from the other 5 dummy variables. That observation would have a 0 on all of them. So we already know it’s location is A. We don’t need another dummy variable to tell the model that. It’s redundant information. And so perfectly redundant that the model will choke.
Dummy coding is one of the topics I get the most questions about. It can get especially tricky to interpret when the dummy variables are also used in interactions, so I’ve created some resources that really dig in deeply.
In a previous post, Interpreting Interactions in Regression, I said the following:
In our example, once we add the interaction term, our model looks like:
Height = 35 + 4.2*Bacteria + 9*Sun + 3.2*Bacteria*Sun
Adding the interaction term changed the values of B1 and B2. The effect of Bacteria on Height is now 4.2 + 3.2*Sun. For plants in partial sun, Sun = 0, so the effect of Bacteria is 4.2 + 3.2*0 = 4.2. So for two plants in partial sun, a plant with 1000 more bacteria/ml in the soil would be expected to be 4.2 cm taller than a (more…)
You’ve probably experienced this before. You’ve done a statistical analysis, you’ve figured out all the steps, you finally get results and are able to interpret them. But the statistical results just look…wrong. Backwards, or even impossible—theoretically or logically.
This happened a few times recently to a couple of my consulting clients, and once to me. So I know that feeling of panic well. There are so many possible causes of incorrect results, but there are a few steps you can take that will help you figure out which one you’ve got and how (and whether) to correct it.
Errors in Data Coding and Entry
In both of my clients’ cases, the problem was that they had coded missing data with an impossible and extreme value, like 99. But they failed to define that code as missing in SPSS. So SPSS took 99 as a real data point, which (more…)
Here’s a little quiz:
True or False?
1. When you add an interaction to a regression model, you can still evaluate the main effects of the terms that make up the interaction, just like in ANOVA.
2. The intercept is usually meaningless in a regression model. (more…)
Here’s a little tip.
When you construct Dummy Variables, make it easy on yourself to remember which code is which. Heck, if you want to be really nice, make it easy for anyone else who will analyze the data or read the results.
Make the codes inherent in the Dummy variable name.
So instead of a variable named Gender with values of 1=Female and 0=Male, call the variable Female.
Instead of a set of dummy variables named MaritalStatus1 with values of 1=Married and 0=Single, along with MaritalStatus2 with values 1=Divorced and 0=Single, name the same variables Married and Divorced.
And if you’re new to dummy coding, this has the extra bonus of making the dummy coding intuitive. It’s just a set of yes/no variables about all but one of your categories.
Someone who registered for my upcoming Interpreting (Even Tricky) Regression Models workshop asked if the content applies to logistic regression as well.
The short answer: Yes
The long-winded detailed explanation of why this is true and the one caveat:
One of the greatest things about regression models is that they all have the same set up: (more…)
