Solved – dumthe variables with overlapping categories

categorical datacategorical-encodingmodelingregression

I'm quite familiar with traditional dummy variable coding – code 1 for presence of the attribute and 0 for absence. A multi-category variable is then represented by a series of dummy variables while omitting 1 category as the reference, so for a variable with n categories I would include n-1 dummy variables.

Simple.

But what happens if I have overlap in my categories?

Here's a simple (slightly contrived) example to illustrate.

Let's say I'm looking at the effect of different sports on injury (a dichotomous outcome). There are 6 sports – football, baseball, basketball, soccer, lacrosse, and hockey.

Now, I know what you're thinking, these ARE mutually exclusive, there is no overlap. True, I could represent these sports with 5 dummy variables and use one, say football, as the reference.

But instead I want to look at some facet of the sport that is related to injury. Put differently, it's not the 'sport' per se, but the actions involved in playing each sport. Some sports involve the same actions, so there is overlap.

I would like to have dummies such as the following:

'ball' is hard (baseball, hockey, lacrosse)
all players wear helmets (lacrosse, hockey, football)
floor/ground is hard (hockey, basketball)

Now, I think I can do this so long as the dummy variables are not highly collinear. That would be tantamount to the so called 'dummy variable trap'. Right? How would I check this? VIFs for the dummies? Condition number?

Is there anything else I need to look out for? Anything I'm missing?

In my actual application I'm thinking of around 5 'facets' and there are well over 50 different categories. I can collapse these categories down into 5 or so catchall categories but I'd rather not do that for theoretical reasons that we don't need to get into at this point.

I could let the machine chose the 'dimensions' or 'facets' via exploratory factor analysis, but I have a very specific set of theoretical 'facets' that I wish to test, hence the preference for dummy variables of my choosing.

Best Answer

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.

Related Solutions

Solved – SPSS dumthe variables in OLS

If you have the advanced statistics package that allows you do estimate generalized linear models (see the menus Analyze -> Generalized Linear Models or the GENLIN command), you can have SPSS on the fly generate the dummy variables. Given your data it may be good to see if some of the newer mixed model commands can estimate auto-regressive components for panel data.

Alternatively, you can use the DO REPEAT syntax to efficiently generate your dummy variables for use in regression equations. For instance, for your weekDay variable it would be;

VECTOR weekDay_Dummy(7,F1.0).
DO REPEAT weekDay_Dummy = weekDay_Dummy1 to weekDay_Dummy7 /i = 1 to 7.
    DO IF weekDay = i. 
        COMPUTE weekDay_Dummy = 1.
    ELSE IF weekDay <> i.
        COMPUTE weekDay_Dummy = 0.
    END IF.
END REPEAT.

As long as your variables are in a sequential list of integer values, the do repeat command will work (if they aren't in a sequential list see the AUTORECODE command). Then in the linear regression command you can subsequently use the TO operator to specify a list of variables that are in sequential order in your dataset (extra note it has to do with the order of the variables in the dataset, nothing to do with the names directly).

Below I have an example.

data list free / company  sector  obsDay weekDay  stockPrice.
begin data
1        15      1      3        10.40
1        15      2      4         9.42
1        15      3      5         9.66
1        15      4      1        11.00
1        15      5      2        10.21
2        10      1      3        43.55
2        10      2      4        43.50
2        10      3      5        40.31
2        10      4      1        48.43
2        10      5      2        43.00
3        20      1      3        10.00
3        20      2      4        11.00
3        20      3      5        12.00
3        20      4      1        13.00
3        20      5      2        14.00
end data.
dataset name examp.

VECTOR weekDay_Dummy(7,F1.0).
DO REPEAT weekDay_Dummy = weekDay_Dummy1 to weekDay_Dummy7 /i = 1 to 7.
    DO IF weekDay = i. 
        COMPUTE weekDay_Dummy = 1.
    ELSE IF weekDay <> i.
        COMPUTE weekDay_Dummy = 0.
    END IF.
END REPEAT.

REGRESSION
  /MISSING LISTWISE
  /STATISTICS COEFF OUTS R ANOVA
  /CRITERIA=PIN(.05) POUT(.10)
  /NOORIGIN 
  /DEPENDENT stockPrice
  /METHOD=ENTER weekDay_Dummy2 to weekDay_Dummy5.

Another extension command with more flexibility for writing dummy variables, SPSSINC_CREATE_DUMMIES (written in Python) is on the developerworks site (but I have not used it). Also one of the members here, ttnphns, has some tools to accomplish similar tasks on his site. Given your example though a few do repeat commands should be sufficient.

Solved – Multilevel: Can I include two dumthe variables of a 7-dumthe-set into a random slope

Yes, you can. A dummy variable is no different, mathematically, from any other fixed effect you might choose to include. Presumably, if some of the categories all have the same impact on the response, it would make sense to zero them out and push their effect into the intercept term.

That said, using Wald statistics to cull variables is risky. You may get the right set of variables, but this isn't necessarily the case.

When you say "random slope", are you talking about the coefficient of the categorical variable? If so, I would do some model checking. Look at the estimated random effects and see if they are trying to cover small but real differences in your categories.

To clarify that last point: suppose I have 4 categories: A,B,C and D. I decide to omit the dummies associated with C and D. The intercept in the model now corresponds to the case where categories C or D occur. It's like I'm recoding to A, B and Other. But let's suppose that C and D really are real, but just fairly small.

Now fit the random effects model. You will get random intercepts for individuals coded "Other" ... but if you plot these against the true categories (C and D), you might find that the C effects are large and the D effects are small (say), or vice versa. When you add random effects, you are giving a bunch of extra parameters to your model, which it could use to cover up for defects of the model itself.