When using multi dummy variables, the constant term gets bigger in absolute value, and significant in pvalue.... and most importantly, you just can't make sense out of it, to have a clear interpretation of the whole regression formula.
I don’t think there is a fixed answer and sample size has much to do with it. At a certain point, though, one risks over controlling of course.
If you are doing a traditional regression, then the number of predictors needs to be smaller than the sample size, To get precise and meaningful estimates it is often useful to have the number of predictors much smaller (this is what people use techniques like the lasso to search for more sparse solutions). However, the number will depend on more situations so rules of thumb may now apply. (
Daniel Wright)
DUMMY VARIABLE should not cause any problems if they are treated or handled properly. Generally, these variables are qualitative and would take the values of 1 and 0. These 1 and 0 should not be incorporated as values and mixed with other quantitative data in the regression model and should be treated separated under discrete probability. These are generally handled as non-parametric. In parametric analysis, these dummy variables are treated separately under logistic function to answer questions specifically dealing with, say DV and gender or age, etc.
For general predictive function under regression, no many how many dummy variables you used, there should not be any problem because they are not treated as "measurable" quantitative values.
LINKS:
https://en.wikipedia.org/wiki/Dummy_variable_(statistics)
If you are modeling time series there is a risk of creating a model only capable of explaining to itself by inflating R2
As a rule of thumb there are three aspects you should worry about:
- total number of regression parameters (including the intercept) should be smaller than number of observations (this was already mentioned)
- collinearity in matrix X (of explanatory variables). If you inflate the number of dummies in X then your X'X may be singular or close to it (to a working precision). This happens when dummies have similar 0-1 patterns over observations. The more dummies there are the bigger the chances are you have this.
- common sense. Theoretically you can have only dummies in your matrix X. But I would be very sceptical about such a model.
As others have explained, there is no fixed number of dummy variables, the rule of them is n>k, where n is total number of observations, and k is the total number of parameters being estimated... Hope this helps!
1. I do not see why one should get higher and more significant constants, if one uses dummies in a regression.
2. Dummies should never be used only for statistical reasons (to get a better fit and a higher R2 by eliminating data outsiders). They should always be well-justified. In this case, it is no problem to interpret the estimated coefficients.
3. Dummies need not have the values 0 and 1, one can also set -1 and 1 and sometimes even more than two numbers (for example: good, medium, bad quality; very high, high, medium, low, very low and no income). One can, of course, take dummies for each of these categories, but this could lead to unduly low degrees of freedom. By simple one-by-one regressions, one could try to find out what categories are relevant and what (rough) numbers should be used as dummies for the different categories.
4. Of course, it is true that n>k, but n should be much greater than k. I would say n>2k.
Suppose that you have a regression with no dummy variables and an estimate of b for the constant. Now add a dummy variable say 1 for male and 0 for female. Suppose that you now get a constant of b0 and a coefficient of b1 on the dummy variable. This is equivalent to doing a regression for males and females separately but holding slope beta coefficients the same for both male and female. The slope on the male equation is b0+b1 and on the female equation b0. The relative sizes of b b0 and b1 are determined by the data and b can be greater or less than b0 depending on the data set,
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