Heterogeneity Analysis

A skill for conducting subgroup and heterogeneity analyses in Stata, testing whether treatment effects differ across population subgroups.

Quick Start

stata

* Interaction model
svy: regress outcome controls c.treatment##i.group
margins group, dydx(treatment)

* Stratified analysis
levelsof group, local(groups)
foreach g of local groups {
    svy: regress outcome controls treatment if group == `g'
    estimates store model_g`g'
}

Key Patterns

1. Interaction Model Approach

Test whether treatment effects vary by group using interactions:

stata

* Define controls
local control_var i.batch leukocytes age i.race i.gender i.education

* Interaction model: treatment × age group
svy: regress outcome `control_var' c.treatment##i.age_group
estimates store interaction_model

* Get treatment effect at each level of age_group
margins age_group, dydx(treatment) post
estimates store margins_by_age

2. Stratified Regression

Run separate models for each subgroup:

stata

local control_var i.batch leukocytes i.race i.gender i.education

* Get unique values of grouping variable
levelsof age_group, local(age_groups)

* Loop through groups
foreach g of local age_groups {
    * Run model for this subgroup
    quietly svy: regress outcome `control_var' c.treatment if age_group == `g'
    estimates store reg_age`g'

    * Get marginal effect
    quietly margins, dydx(treatment) post
    estimates store margins_age`g'

    * Get group label for export
    local lbl: label (age_group) `g'
    if "`lbl'" == "" {
        local lbl "Group `g'"
    }
}

3. Complete Heterogeneity Template

stata

*------------------------------------------------------------
* Heterogeneity Analysis by Age Group
*------------------------------------------------------------
version 17
clear all

use "analysis_data.dta", clear
svyset cluster [pweight = weight]

* Create age groups if needed
cap drop age_group
gen age_cap = min(age, 85)
egen age_group = cut(age_cap), at(18 30 40 50 60 70 85) icodes
label define agegrp 0 "18-29" 1 "30-39" 2 "40-49" 3 "50-59" 4 "60-69" 5 "70-85"
label values age_group agegrp

* Controls (exclude age since we're stratifying by it)
local control_var i.batch leukocytes i.race i.gender i.education i.marital

estimates clear

*--- Interaction model ---
svy: regress outcome `control_var' c.treatment##i.age_group
estimates store interaction

* Marginal effects by age group
margins age_group, dydx(treatment) post
estimates store interaction_margins

*--- Stratified models ---
local margin_models "interaction_margins"
local reg_models "interaction"

levelsof age_group, local(age_groups)
foreach g of local age_groups {
    * Regression
    quietly svy: regress outcome `control_var' c.treatment ///
        if age_group == `g' & !missing(treatment)
    estimates store reg_age`g'

    * Margins
    quietly margins, dydx(treatment) post
    estimates store margins_age`g'

    * Add to lists
    local margin_models "`margin_models' margins_age`g'"
    local reg_models "`reg_models' reg_age`g'"
}

*--- Export ---
esttab `margin_models' using "heterogeneity_age_margins.csv", csv se ///
    nogap label replace star(+ 0.1 * 0.05 ** 0.01)

esttab `reg_models' using "heterogeneity_age_coeffs.csv", csv se ///
    nogap label replace star(+ 0.1 * 0.05 ** 0.01)

4. Test for Heterogeneity

stata

* Fit interaction model
svy: regress outcome controls c.treatment##i.group

* Test if interaction terms are jointly significant
testparm i.group#c.treatment

* Store p-value for reporting
local p_interaction = r(p)
display "Interaction p-value: `p_interaction'"

* Test specific contrasts
contrast i.group#c.treatment, effects

5. Multiple Moderators

stata

estimates clear

* By age
svy: regress outcome `control_var' c.treatment##i.age_group
margins age_group, dydx(treatment) post
estimates store by_age

* By gender
svy: regress outcome `control_var' c.treatment##i.gender
margins gender, dydx(treatment) post
estimates store by_gender

* By race
svy: regress outcome `control_var' c.treatment##i.race
margins race, dydx(treatment) post
estimates store by_race

* By education
svy: regress outcome `control_var' c.treatment##i.education
margins education, dydx(treatment) post
estimates store by_education

* Export all
esttab by_age by_gender by_race by_education using "all_moderators.csv", ///
    csv se nogap label replace star(+ 0.1 * 0.05 ** 0.01)

6. Continuous Moderator

stata

* Interaction with continuous moderator
svy: regress outcome `control_var' c.treatment##c.age

* Marginal effects at representative values
margins, dydx(treatment) at(age=(30 40 50 60 70))

* Plot (in Stata 17+)
marginsplot, recast(line) recastci(rarea)

7. Triple Interaction

stata

* Three-way interaction
svy: regress outcome `control_var' c.treatment##i.gender##i.age_group

* Marginal effects for each combination
margins gender#age_group, dydx(treatment)

* Or specific contrasts
margins, dydx(treatment) at(gender=(1 2) age_group=(0 1 2 3 4 5))

Complete Example

stata

*------------------------------------------------------------
* Heterogeneity Analysis: Hasslers × Age/Gender/Spouse Status
*------------------------------------------------------------
version 17
clear all
set more off

use "analysis_data.dta", clear
svyset fips [pweight = wt_final2]

* Create age groups
cap drop age_group
gen age_cap = min(age, 85)
egen age_group = cut(age_cap), at(18 30 40 50 60 70 85) icodes
label define agegrp 0 "18-29" 1 "30-39" 2 "40-49" 3 "50-59" 4 "60-69" 5 "70-85"
label values age_group agegrp

* Controls
local control_var i.batch_int leukocytes i.race3 i.gender_birth i.educ3

*============================================================
* PART 1: Heterogeneity by Age
*============================================================
estimates clear

* Interaction model
svy: regress pace `control_var' c.n_size_hassler##i.age_group
estimates store pace_age_inter
margins age_group, dydx(n_size_hassler) post
estimates store pace_age_margins

* Stratified models
levelsof age_group, local(age_groups)
foreach g of local age_groups {
    quietly svy: regress pace `control_var' c.n_size_hassler if age_group == `g'
    estimates store pace_strat`g'
    quietly margins, dydx(n_size_hassler) post
    estimates store pace_strat`g'_m
}

*============================================================
* PART 2: Heterogeneity by Gender
*============================================================
svy: regress pace `control_var' c.n_size_hassler##i.gender_birth
estimates store pace_gender_inter
margins gender_birth, dydx(n_size_hassler) post
estimates store pace_gender_margins

*============================================================
* PART 3: Heterogeneity by Marital Status
*============================================================
svy: regress pace `control_var' c.n_size_hassler##i.marital3
estimates store pace_marital_inter
margins marital3, dydx(n_size_hassler) post
estimates store pace_marital_margins

*============================================================
* Export Results
*============================================================
esttab pace_age_margins pace_gender_margins pace_marital_margins ///
    using "heterogeneity_summary.csv", csv se ///
    mtitle("By Age" "By Gender" "By Marital") ///
    nogap label replace star(+ 0.1 * 0.05 ** 0.01)

* Completion flag
file open fh using "heterogeneity.ok", write replace
file close fh

Interpretation

Pattern	Interpretation
Non-significant interaction	Effect is similar across groups
Significant interaction	Effect varies by group
Effect in one group only	Targeted intervention potential
Opposing effects	Complex mechanism

Tips

•Always report both interaction models AND stratified models
•Test interaction terms formally with testparm
•Consider multiple testing corrections when testing many moderators
•Plot marginal effects for continuous moderators
•Be cautious about power in small subgroups
•Pre-register heterogeneity analyses to avoid p-hacking