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I have the following result of a logistic regression:

                                  Estimate Std. Error z value Pr(>|z|)    
(Intercept)                        3.34260    0.41116   8.130 4.30e-16 ***
AgeGr18-22                        -0.61845    0.28974  -2.135 0.032799 *  
AgeGr28-30                        -0.46384    0.27474  -1.688 0.091361 .  
AgeGr31-35                         0.38351    0.28102   1.365 0.172352    
AgeGr36-40                        -0.24538    0.25113  -0.977 0.328525    
AgeGr41-50                         0.11316    0.23918   0.473 0.636140    
AgeGr51-high                       0.49277    0.29597   1.665 0.095924 .  
AutomobileGr1                      0.61832    0.17570   3.519 0.000433 ***
AutomobileGr2-high                -0.07095    0.37665  -0.188 0.850590    

The dummy "AutomobileGr2-high" (having 2 or more automobiles) have a P-value 0.85 and I would like to drop it from the model.

Would it make a difference if I just drop the dummy (i.e. create a regression formula without this group) or if I put it into the reference group (our reference group in the example above is AutomobileGr0 - ppl that do not have a car, hence the combined reference group will be AutombileGr0 & AutombileGr>=2 -> ppl either without a car or with at least 2).

From what I read so far (http://www.ats.ucla.edu/stat/mult_pkg/faq/general/dummy.htm) it should make a difference on the intercept hence on the whole resulting target log odds.

What approach is suggested as best practice (or what are the pros and cons of the two approaches)?

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