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Building a logistic regression model with three categorical features and one continuous. For simplicity, let's say I have the following features and variables:

      Feature    |        Variable
 ========================================
      Gender     |         Male
 ----------------------------------------
      Weight     |  Weight (continuous)
 ----------------------------------------
   Income Bucket |        0 - 50k 
   Income Bucket |       51k - 75k 
   Income Bucket |       76k - 100k 
   Income Bucket |       101k - 150k 
 ----------------------------------------
     Continent   |      North America 
     Continent   |      South America
     Continent   |         Europe
     Continent   |          Asia
     Continent   |         Africa
     Continent   |        Australia

Recall that I am using (n - 1) for the number of variables so there is no variable for Gender = Female, Income Bucket = 100k+, or Continent = Antarctica.

  1. if I run this through a multicollinearity check and get VIFs for one categorical variable being higher than 10, does it make sense to remove it?

For example:

      Feature    |        Variable       |  VIF  |
 =================================================
      Gender     |         Male          |   2
 -------------------------------------------------
      Weight     |  Weight (continuous)  |   1
 -------------------------------------------------
   Income Bucket |        0 - 50k        |   3
   Income Bucket |       51k - 75k       |   4
   Income Bucket |       76k - 100k      |   11 <--
   Income Bucket |       101k - 150k     |   1
 -------------------------------------------------
     Continent   |      North America    |   2
     Continent   |      South America    |   3
     Continent   |         Europe        |   4
     Continent   |          Asia         |   1
     Continent   |         Africa        |   1
     Continent   |        Australia      |   2

Should I drop the categorical variable for Income Bucket = 76k- 100k and then proceed to further model selection?

  1. Furthermore, does it make sense if one or more (but not all) have p-values are not significant?

For example:

      Feature    |        Variable       |  P-Value  |
 =====================================================
      Gender     |         Male          |   0.002
 -----------------------------------------------------
      Weight     |  Weight (continuous)  |   0.001
 -----------------------------------------------------
   Income Bucket |        0 - 50k        |    0.05
   Income Bucket |       51k - 75k       |    1.65 <--
   Income Bucket |       76k - 100k      |    0.03
   Income Bucket |       101k - 150k     |   0.002
 -----------------------------------------------------
     Continent   |      North America    |    0.05
     Continent   |      South America    |   0.001
     Continent   |         Europe        |    11.2 <--
     Continent   |          Asia         |    0.01
     Continent   |         Africa        |    0.09
     Continent   |        Australia      |    0.1

Here, does it make sense to drop Income Bucket = 51k - 75k and Continent = Europe based on the P-values?

  1. How does the "missing" categorical variable (the one removed due to the (n - 1) rule) become interpreted once you drop a few of the ones that are included?

Remember that this is for a logistic regression but I am okay with knowing how it would work for linear as well. And would another method be more suited for this?

Thank you!

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