Using a dichotomous categorical variable that has an underlying continuous dichotomy in a multiple regression?

Question

FINAL EDIT

I just found a good answer to this question in another thread in the forum here, therefore, I think this question could be closed. Thanks so much for your help and the clarification about the underlying continuous.

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I know that the biserial correlation coefficient (rb) is used when we want to correlate a continuous variables (say, number of activities identified) with a dichotomous categorical variable that has an underlying a continuous dichotomy. By this I mean, for instance, the education level of parents divided in two categories (low / high), each of which contains the following "subcategories":

1) LOW educational level: 6 categories ranging from 1 (never attended school) to 6 (vocational school not finished).

2) HIGH educational level: 4 categories ranging from 7 (vocational school finished) to 10 (graduate degree).

I know I can dummy code these categories, but if I were to, I would end up with 9 new predictors (to be added to the other 10 predictors of the regression). Though I have a large sample (n = 2,643), I am not sure using all the many dummies would be good.

So, the bottom line is: can I use a dichotomous categorical variable that has an underlying continuous dichotomy in a multiple regression?

I want to discover if the educational level of parents (high/low) is a good predictor of the number of activities identified by their children.

Thank you very much.

EDITION TO THE ORIGINAL QUESTION

I guess I should have given a better example. I have dichotomized a continuous variable (a test score) into:

• high (scores between 100 and 50)
• low (scores between 49 and 0)

The reason why I am not using the actual scores is because more than half the sample did not provide their test score results. Based on another category (the type of higher education institution attended), I can estimate their test score to be high or low: a high is a requirement to enter one specific type of institution, so if the student attends that institution, he must have had a high score (above 50) in the test. I hope here the "underlying continuous" is clearer.

Answer 1

You can dummy code with these two categories just like you could with 10. However, this is nearly always a bad idea as it can obscure important information and lowers power. If you had a small sample, you might have to recode, but you have a reasonable sample.

For example, I saw one study of depression that found that the relationship with educational level was non-monotonic: People who had completed any level of education (whether grade school, high school, college or grad school) had lower levels of education than those who stopped in the middle of any level.

Also, you don't have an underlying continuous distribution here. You are proposing lumping a 10 category scale into an ordinal one.

Answer 2

"Continuous dichotomy" is somewhat of a contradiction in terms.

But to your point I find that for variables such as yours a quadratic effect is often sufficient, i.e., model edu. level + its square. If your dependent variable is continuous, you have a fairly high effective sample size and are likely to be able to afford modeling using all 9 indicator variables for edu.