I am using Stata 16.

I am trying to determine whether the effect of crime type (either coded as dummies or as a single categorical measure) has an effect on my dichotomous outcome and whether this effect varies between locations (n=5 counties in New York). I have been reading on the subject, including Allison's work, and Williams' work on heterogeneous choice models with OGLM, but I am wondering whether it is appropriate to compare coefficients when there are more than two groups? All of the published examples use a difference between males and females, or otherwise, but I would like to compare across a total of 5 areas.

In an attempt to do this, I specified an equation with a large number of interaction terms between each crime type (leaving one out as a reference cat) and each of the boroughs (again leaving one out). Below is the code used. The OGLM model provides a variance parameter for each of the included boroughs and estimates for each interaction. I am just curious whether this is the best way to test for equality across more than 2 groups, when I also have a categorical (not ordinal) predictor variable and a dichotomous outcome.

Thanks for any input.

Code:
//Generate Dummies from categorical variable//
tab offtype2, gen(offtype_)

//Create Interaction Terms for each crimeXborough
gen weap_bx=offtype_1*Bronx
gen weap_bk=offtype_1*Brooklyn
gen weap_qn=offtype_1*Queens
gen weap_si=offtype_1*Staten

gen sexc_bx=offtype_2*Bronx
gen sexc_bk=offtype_2*Brooklyn
gen sexc_qn=offtype_2*Queens
gen sexc_si=offtype_2*Staten

gen drug_bx=offtype_3*Bronx
gen drug_bk=offtype_3*Brooklyn
gen drug_qn=offtype_3*Queens
gen drug_si=offtype_3*Staten

gen vio_bx=offtype_4*Bronx
gen vio_bk=offtype_4*Brooklyn
gen vio_qn=offtype_4*Queens
gen vio_si=offtype_4*Staten

//Property (offtpe_5) is Baseline

gen dwi_bx=offtype_6*Bronx
gen dwi_bk=offtype_6*Brooklyn
gen dwi_qn=offtype_6*Queens
gen dwi_si=offtype_6*Staten

gen other_bx=offtype_7*Bronx
gen other_bk=offtype_7*Brooklyn
gen other_qn=offtype_7*Queens
gen other_si=offtype_7*Staten

//Heterogeneous Choice Models//
estimates clear
oglm detained2 offtype_1 offtype_2 offtype_3 offtype_5 offtype_6 offtype_7 Bronx Brooklyn Queens Staten ///
weap_bx weap_bk weap_qn weap_si sexc_bx sexc_bk sexc_qn sexc_si vio_bx vio_bk vio_qn vio_si drug_bx drug_bk ///
drug_qn drug_si dwi_bx dwi_bk dwi_qn dwi_si other_bx other_bk other_qn other_si  ///
sex age age2 black other priorfel priormisd offsever_2 offsever_3 offsever_5 offsever_6 offsever_7 offsever_8 offsever_9 offsever_10 ///
arrmonth_2-arrmonth_12 arryear_2-arryear_3, hetero(Bronx Brooklyn Queens Staten) store(oglm1) link(logit)