# Dummy variables logit model: remove levels

I have the two variables with 4 different levels or categories each one (illustrative example):

A1 , A2 , A3 , A4

B1 , B2, B3, B4

I run a logistic regression model and use A1 and B1 as reference group. The point of the research I am conducting is to remove those two "worst" levels per category (remove 2 levels from A and remove 2 levels from B), that is those two levels with smaller coefficient.

Let's say I obtain this parameter estimates:

Coefficients A

A2: 0.4

A3: -0.7

A4: 1.1

Coefficients B

B2: -1.4

B3: 0.2

B4: -0.1

I don't include the standard errors as they are not necessary for the moment. So given these parameter estimates I remove A3 and B2 because they have the lowest coefficient. But how should I proceed now? A2 and A4 are larger than 0, the reference group. Does this mean that the reference group A1 is worse than the other two A2 and A4 thus it should be removed?

I would appreciate some suggestion on this point!

• You already removed A3 and B2, why do you want to remove even more? In the beginning, you state that you only want to remove the 2 worst levels. If you want to keep removing levels until you only have 1 level per group, then you can conclude from your results that only A4 and B3 should be kept. Commented May 4, 2017 at 9:19
• I meant per group. I edited the question: "remove those two "worst" levels per category (remove 2 levels from A and remove 2 levels from B". Thank you! Commented May 4, 2017 at 9:22
• Why are you wanting to remove these levels? Doing so will fundamentally change the meaning of the remaining dummy code (and it will no longer reflect dummy coding of the variable). Commented May 4, 2017 at 10:54
• @dbwilson I am coding an algorithm to find the best alternative by asking respondents. To do so I need to narrow the space of alternatives. Commented May 4, 2017 at 12:16
• I still don't understand. However, generally you keep all the dummy variables that are part of a variable in the model (at least for hypothesis testing -- you might be doing something else). By doing so, you can test the effect of the variable, that is, the block of dummy codes that make up the variable. Getting rid of alternatives changes the meaning of the variable. Commented May 4, 2017 at 12:49

## 1 Answer

Change your results into following by adding reference level A1 and B1. Then you can do what you want.

Coefficients A

A1: 0.0

A2: 0.4

A3: -0.7

A4: 1.1

Coefficients B

B1: 0.0

B2: -1.4

B3: 0.2

B4: -0.1

• Thank you for your comment. And in case I wanted to use the standard errors, which standard errors should be use for the base category? Commented May 4, 2017 at 13:25
• 0.0000000. Zero. The system does not accept one character as comment. Funny. Commented May 4, 2017 at 13:40
• When you use the estimated variance, do not forget the constant term in the model and the estimated co-variance between estimated coefficients. Commented May 4, 2017 at 13:43