Two-step fractioal logitstic regression model

[Luis Mijares Castaneda]

Hello, I am trying to fit a two-step model where the first equation is a binary logit and the second equation is a fractional logit. I don't think the command -twopm- has the option for a fractional logit in the second stage, so I was wondering if the commands below would properly implement the model. I have also included the -dataex- output for the variables. For more background, I am interested in modeling the variable avrg_prop_dental_cost, which represents the proportion of out-of-pocket dental costs to household income.

****creating a proportion variable and estimating using fractional logit model**** 
gen oopdental_proportion_wave1 = oopdental_costs_wave1/HouseholdIncome_wave1 
replace oopdental_proportion_wave1=0 if oopdental_costs_wave1==0 & HouseholdIncome_wave1==0 
drop if oopdental_proportion_wave1 >1  

gen oopdental_proportion_wave2 = oopdental_costs_wave2/HouseholdIncome_wave2 
replace oopdental_proportion_wave2 = 0 if oopdental_costs_wave2 ==0 & HouseholdIncome_wave2==0 
drop if oopdental_proportion_wave2>1 

***generating an average variable**** 
egen avrg_prop_dental_cost = rowmean(oopdental_proportion_wave1 oopdental_proportion_wave2) 


**first step logit model**** 
logit r11dentst inc_d i.endentulism i.race i.age_cat i.male i.education i.veteran i.mothered i.dentalinsurance_w1 i.QuantHI_wave1 i.Quant_wealth_wave1 /// 
i.smoke_now c.chronicdisease i.r11dentst

**second fractional logit*** 
fracreg logit avrg_prop_dental_cost r11dentst inc_d i.endentulism i.race i.age_cat i.male i.education i.veteran i.mothered i.dentalinsurance_w1 i.QuantHI_wave1 i.Quant_wealth_wave1 if avrg_prop_dental_cost >0

* Example generated by -dataex-. For more info, type help dataex
clear
input float avrg_prop_dental_cost byte r11dentst float(inc_d endentulism race age_cat) byte(male education veteran) float(mothered dentalinsurance_w1) byte(QuantHI_wave1 Quant_wealth_wave1)
  .003784648 1 0 0 1 3 0 5 0 1 0 3 4
           0 1 0 0 1 1 0 5 0 1 1 1 3
  .021537896 1 0 0 1 2 0 3 0 0 1 4 4
   .09236358 1 0 0 1 2 0 4 0 1 0 1 4
 .0046232087 1 0 0 1 3 1 5 1 1 1 4 4
   .04624664 1 0 0 1 2 0 5 0 0 1 4 4
 .0019889215 1 0 0 4 3 0 5 0 1 1 4 4
           0 0 0 0 3 3 0 1 0 . 1 1 1
   .16542825 1 0 0 3 3 0 1 0 0 1 1 1
  .033333335 1 0 0 1 2 0 1 0 1 1 1 4
   .02422194 1 0 0 1 4 1 5 1 0 0 3 4
           0 1 0 0 3 3 0 1 0 0 1 1 1
           0 0 0 1 4 3 1 1 0 0 1 1 1
           0 1 0 1 2 3 0 3 0 0 1 1 1
           0 0 0 0 2 3 1 1 0 . 0 1 1
   .01634702 1 0 0 1 3 0 4 0 1 1 4 1
           0 0 1 1 2 3 0 1 0 . 1 2 1
   .04144562 1 0 0 1 3 0 4 0 1 1 3 4
 .0035514846 1 0 0 1 3 1 5 1 1 1 4 4
   .14424561 1 0 0 1 3 0 1 0 1 0 2 4
           0 0 0 0 1 3 0 3 0 1 0 1 3
  .002596046 1 0 1 4 3 0 5 0 0 1 4 3
  .002776852 0 0 0 4 3 1 5 1 0 1 4 3
 .0032806755 1 0 0 1 3 0 3 0 0 1 3 4
           0 0 0 1 1 3 1 4 1 . 1 3 3
  .020654306 1 0 0 1 2 0 5 0 1 1 3 3
    .3813447 1 0 0 1 4 0 5 0 1 0 4 4
  .016246201 1 0 0 1 3 1 5 1 1 0 1 4
   .10871864 1 0 0 1 3 0 3 0 1 0 1 4
   .01777209 1 0 0 1 3 1 5 0 0 1 4 3
   .00951611 1 0 0 1 3 0 5 0 1 1 4 3
           0 1 0 0 2 3 0 1 0 0 1 2 3
           0 0 0 0 2 3 0 5 0 1 0 2 1
           0 0 0 1 2 3 0 1 0 0 0 1 3
           0 0 0 1 2 2 0 3 0 0 0 3 1
   .02071823 1 0 0 2 3 1 3 1 1 1 2 3
           0 1 0 0 2 3 0 3 0 1 1 2 3
   .10893247 0 0 0 2 3 1 3 0 0 0 1 1
   .00540276 1 0 0 3 1 0 3 0 1 1 2 4
  .001699293 1 0 0 4 3 0 1 0 0 1 3 3
 .0029537205 1 0 0 4 4 1 5 0 0 1 3 3
   .05338598 1 0 0 3 3 1 4 1 1 1 1 3
  .001384535 1 0 0 1 2 0 4 0 1 1 1 3
  .012099246 1 0 0 1 2 0 4 0 0 0 4 4
    .8439155 1 0 0 2 3 0 5 0 0 1 1 1
           0 0 0 1 4 3 0 4 0 0 1 2 1
  .004110477 1 1 0 1 3 1 1 0 1 1 2 4
   .01130746 1 0 0 1 3 0 5 0 1 1 2 4
  .004008539 1 0 0 1 3 1 3 1 0 1 3 4
           0 0 0 0 2 3 0 4 0 0 0 2 3
  .004610162 1 0 0 1 4 1 5 1 1 1 4 4
   .05020221 1 0 0 3 3 0 3 0 0 0 2 2
           0 0 0 1 3 3 1 2 1 0 0 2 2
 .0020562997 1 0 0 4 3 0 5 0 0 0 2 2
           0 0 0 0 2 3 0 1 0 0 0 1 1
  .017711425 1 0 0 2 3 0 3 0 0 0 1 1
           0 0 0 0 2 3 0 1 0 . 0 1 1
  .013680274 1 0 0 1 3 1 4 1 0 0 3 1
    .0292491 1 1 0 4 2 0 1 0 1 1 3 1
    .0445552 1 0 0 1 4 1 3 1 1 0 3 4
  .007221488 1 0 0 1 3 0 1 0 1 0 3 4
  .014167874 1 0 0 1 3 0 5 0 1 1 3 4
           0 0 0 0 1 3 0 3 0 1 0 2 2
   .04431479 1 0 0 1 4 0 4 0 0 0 3 4
  .016026935 1 0 0 1 4 1 5 1 . 1 3 4
   .02799761 1 0 0 1 4 1 4 1 1 0 2 3
   .01935859 1 0 0 1 3 0 3 0 0 0 2 3
           0 1 0 0 1 2 0 3 0 1 1 2 2
           0 1 0 0 1 3 0 2 0 0 1 1 4
.00057418464 1 0 0 3 3 0 3 0 . 0 1 1
           0 0 0 1 2 3 0 4 0 1 0 1 2
           0 0 0 0 1 3 0 1 0 0 0 1 1
  .018763967 1 0 0 1 3 1 4 1 1 1 3 3
   .00919189 1 0 0 1 3 1 3 0 . 0 2 3
           0 0 0 0 1 3 0 3 0 1 0 1 4
 .0022878346 1 0 0 1 4 1 1 1 0 1 3 3
 .0089355465 1 0 0 1 3 1 5 1 1 0 4 4
  .002441883 0 0 0 1 3 1 5 0 0 1 2 4
   .01016793 1 0 0 1 1 0 5 0 1 1 2 4
           0 0 0 1 1 3 1 2 0 0 0 2 2
  .017079419 1 0 0 3 2 0 1 0 0 0 2 2
           0 0 0 0 1 4 1 1 0 0 1 2 3
  .015497336 1 0 0 1 4 0 4 0 0 0 1 2
           0 0 0 1 2 3 0 3 0 0 0 1 1
           0 0 0 0 2 3 1 2 0 1 0 1 1
           0 0 1 1 2 3 1 3 0 1 0 1 2
           0 0 0 0 2 3 0 4 0 0 0 1 1
 .0003999116 1 0 0 2 3 1 4 1 0 1 4 2
 .0004577078 1 1 0 2 1 0 4 0 0 1 4 2
  .007543103 1 0 0 2 3 1 1 0 1 0 2 2
           0 0 0 1 1 3 1 1 1 0 0 3 4
   .03690508 1 0 0 1 3 0 1 0 0 0 3 4
           0 0 0 1 2 3 1 1 1 . 0 1 2
           0 0 0 0 2 2 0 3 0 1 0 2 3
           0 0 0 1 1 2 0 3 0 . 0 2 1
           0 0 1 1 1 3 1 4 0 1 0 3 3
           0 0 0 0 1 2 0 3 0 1 0 3 3
  .010373444 1 0 0 1 3 0 4 0 1 1 1 1
           0 0 0 0 1 3 0 3 0 0 0 2 3
           0 0 0 0 1 3 0 1 0 1 0 1 1
end
label values r11dentst YESNO
label def YESNO 0 "0.no", modify
label def YESNO 1 "1.yes", modify
label values inc_d inc_d
label def inc_d 0 "No", modify
label def inc_d 1 "Yes", modify
label values endentulism endentulism
label def endentulism 0 "No", modify
label def endentulism 1 "Yes", modify
label values race race
label def race 1 "White", modify
label def race 2 "Black", modify
label def race 3 "Hispanic", modify
label def race 4 "Other", modify
label values age_cat age_cat
label def age_cat 1 "50-59", modify
label def age_cat 2 "60-69", modify
label def age_cat 3 "70-79", modify
label def age_cat 4 "80+", modify
label values male male
label def male 0 "Female", modify
label def male 1 "Male", modify
label values education EDUC
label def EDUC 1 "1.lt high-school", modify
label def EDUC 2 "2.ged", modify
label def EDUC 3 "3.high-school graduate", modify
label def EDUC 4 "4.some college", modify
label def EDUC 5 "5.college and above", modify
label values veteran veteran
label def veteran 0 "No", modify
label def veteran 1 "Yes", modify
label values mothered mothered
label def mothered 0 "Less than High School", modify
label def mothered 1 "High School or Higher", modify
label values dentalinsurance_w1 dentalinsurance_w1
label def dentalinsurance_w1 0 "No", modify
label def dentalinsurance_w1 1 "Yes", modify

[Richard Williams]

When I try to run your code I get the error "oopdental_costs_wave1 not found". When you use dataex, make sure that the data and code provided actually work.

Roodman's cmp command (available from SSC) seems to be able to estimate 98% of all the statistical models known to humankind as well as several that aren't. ;-) Perhaps it could handle your task? It lets you specify probit and fractional probit models in one command, but I am not sure if that is the same as a 2 step model.

[Richard Williams]

Ok, check this article:

https://journals.sagepub.com/doi/10....36867X19854017

Generalized two-part fractional regression with cmp

Abstract

Researchers who model fractional dependent variables often need to consider whether their data were generated by a two-part process. Two-part models are ideal for modeling two-part processes because they allow us to model the participation and magnitude decisions separately. While community-contributed commands currently facilitate estimation of two-part models, no specialized command exists for fitting two-part models with process dependency. In this article, I describe generalized two-part fractional regression, which allows for dependency between models’ parts. I show how this model can be fit using the community-contributed cmp command (Roodman, 2011, Stata Journal 11: 159–206). I use a data example on the financial leverage of firms to illustrate how cmp can be used to fit generalized two-part fractional regression. Furthermore, I show how to obtain predicted values of the fractional dependent variable and marginal effects that are useful for model interpretation. Finally, I show how to compute model fit statistics and perform the RESET test, which are useful for model evaluation.