Testing for collinearity in a logistic regression model

[Phidelis Wamalwa]

How can i check for collinearity between variables in logistic regression. My logit regression has thrown out an important dummy variable due to collinearity but i have no idea the source variable so that i exclude it to preserve this important variable in the model?
logit Ins_covered i.uhc4##i.y2020 i.county age_ household_size wealth_asset_index LivedPoverty_index i.Residence i.education_head i.LivedPoverty_categories i.hhsize_categ i.Employment2 i.agevalid1 i.sex i.female_head i.wealth_asset_index_quantile, or

note: 25.county omitted because	of collinearity.
Iteration 0: log likelihood =	-4056.3033
Iteration 1: log likelihood =	-3443.122
Iteration 2: log likelihood =	-3398.9086
Iteration 3: log likelihood =	-3398.5775
Iteration 4: log likelihood =	-3398.5773
Logistic regression		Number of obs = 7,281
		LR chi2(78) = 1315.45
		Prob > chi2 = 0.0000
Log likelihood = -3398.5773		Pseudo R2 = 0.1621
Ins_covered	Odds ratio	Std. err.	z	P>z	[95% conf.	interval]
uhc4
UHCpilot	0.7396663	0.1810286	-1.23	0.218	0.457836	1.194984
1.y2020	1.159162	0.0806183	2.12	0.034	1.01145	1.328447
uhc4#y2020
UHCpilot#1	1.51306	0.3257683	1.92	0.054	0.992176	2.307403
county
kambitano	1.894078	0.3739938	3.23	0.001	1.286247	2.789146
mulaha	0.6486638	0.1966849	-1.43	0.153	0.358032	1.175214
Kisumundogo	1	(omitted)
nangili	0.4959938	0.1376329	-2.53	0.012	0.287923	0.854428
masaba	0.495415	0.1348137	-2.58	0.01	0.290628	0.844502
age_	1.039405	0.01216	3.3	0.001	1.015843	1.063514
household_size	0.960527	0.0266501	-1.45	0.147	0.909689	1.014207
wealth_asset_in~x	2.39613	0.3069635	6.82	0	1.86408	3.080038
LivedPoverty_in~x	0.6094347	0.0744005	-4.06	0	0.479746	0.774182
Residence
Urban	1.051032	0.0959186	0.55	0.585	0.878889	1.256891
education_head
Some primary	1.12795	0.1814564	0.75	0.454	0.822914	1.546055
Primary	1.428277	0.2232508	2.28	0.023	1.051388	1.940269
Secondary	2.534693	0.4021748	5.86	0	1.857235	3.459266

[Phidelis Wamalwa]

what can i do to have kisumundogo not ommitted from the model?

[Clyde Schechter]

Without example data and more context it is impossible to say for sure, but I imagine that the colinearity arises with the other values of county (you would expect one county to be omitted in any case as the reference category for county) and the variable uhc4. I say this because your regression looks like what one might see in a difference-in-differences analysis of the effect of some intervention on counties, where uhc4 is a dichotomous variable that distinguishes the counties that underwent the intervention from those that didn't. In that situation, the additional identifying information provided by the intervention variable (uhc4) makes the usual set of indicator ("dummy") variables for all but one county redundant, and an additional one will be omitted as a result (or Stata will omit uhc4 itself, depending on the order in which the variables are given in the regression.) The same things happens if uhc4 is not related to any intervention but simply distinguishes two groups of counties.

So, you can force Stata to include the omitted county, but only by omitting some other county, or omitting uhc4. Note that which variable you omit has no statistical consequences at all: while the coefficients among the affected variables will shift around, the predicted outcomes from the model will be the same regardless. The choice of which to retain and which to omit is purely aesthetic. It is also important to remember in this situation that neither the uhc4 coefficient (or odds ratio), should you choose to keep it, nor the coefficients and odds ratios of each of the retained county variables are meaningful: due to the colinearity, all of these effects are unidentifiable and the corresponding outputs have meaning only in terms of differences between them.