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I have in my model two dummy's, for a categorical variable with 3 categories (native, EU-immigrant and non-EU-immigrant). The reference category is 'native'. These are merely control variables.

Now I find a significant coefficient for one dummy, and not for the other. See last 2 rows here. Note these are log odds.

    L1PRED  S.E.
Response    R   

Fixed Part      
cons    -1.775  0.080
female  0.431   0.042
age 0.016   0.001
FA  1.053   0.052
TV  1.778   0.112
second  -0.277  0.052
third   -0.269  0.070
fourth  -0.298  0.093
fifth   -0.163  0.102
EU_imm  -0.011  0.092
nEU_imm 0.953   0.439

I was wondering what the right thing to do here is? Because any control variable that has no effect is usually left out of the model. But I cannot do that here, I think?

Would it be most common to recode 'native' and 'EU-immigrants' into one category, since there is no significant effect on the outcome?

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You seem to be taking for granted that "any control variable that has no effect is usually left out of the model" - why is that? Unless you have a specific reason for doing so, it seems that any variables that must be "controlled for" (based on substantive knowledge) should be left in the model regardless of their significance. –  Macro Jan 4 '13 at 13:34
    
Oh, ok, thats easy. And it does make sense, because it's not about the effect on the outcome, but rather the correlation with the predictors. Is that right? –  Marloes Jan 4 '13 at 13:41
1  
I'm not sure what you mean. What I meant was that, if you included the variable in the model because you believe, for substantive reasons, that it should be controlled for, an insignificant $p$-value shouldn't change that. –  Macro Jan 4 '13 at 14:25
    
+1 to @Macro for this reminder and for fighting against the cult of significance. –  Peter Flom Jan 4 '13 at 15:33
2  
@Marlo, usually when one talks about "controlling" for a variable, they mean that, if that variable is left out of the model (or not entered into the model correctly), then the effects of interest will not be estimated correctly. Thus, controlling is done to prevent confounding. A typical toy example of confounding is a drug efficacy trial where baseline characteristics (e.g. what if young people tend to slightly improve regardless of treatment?) are not accounted for. In that case you wouldn't want to delete age based only on its $p$-value. –  Macro Jan 4 '13 at 16:07
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2 Answers

up vote 9 down vote accepted

It is not one of your control variables that is not significant but rather one level of that variable that is not significantly different from your baseline, as you point out. In this situation, I would not change anything and report coefficients for both levels. Recoding is an option, but unless there is a good reason to do it, I would not.

You state that "any control variable that has no effect is usually left out of the model", this is not standard practice in every (any?) field and if there is a good theoretical reason to think that the variable might have an impact on the outcome I would keep it in the model for this reason, whether it is significant or not. For more on variable selection, this question is helpful.

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+1 for the same reasons I gave @Macro +1. –  Peter Flom Jan 4 '13 at 15:34
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Adding to the good comments and answers so far, here are some reasons to include control variables even if not significant:

1) If you expected a large effect and you get a small one, that is important to know 2) Adding the control variable may affect the relationship between the other independent variables and the dependent variable

And here is a reason not to combine "native" and "EU immigrant": it loses information. As is you have evidence that non-EU immigrants are different from EU immigrants and natives. Part of that is lost if you combine the levels.

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Can you make conclusions about the difference between EU immigrants and non-EU immigrants, if you don't use any of these two as a reference category? –  Marloes Jan 4 '13 at 15:49
2  
Impressionistically, yes, based on the magnitude of the difference of their coefficients or odds ratios (and probably considering those differences in light of the standard errors for each variable). But if you want to formally test the stat. sig. of their difference, you do need to use one as the reference category. –  rolando2 Jan 4 '13 at 16:31
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