Orthogonalization and CATE estimation for binomial outcome with continous treatment

[quinn-ca]

I have observational data for a binary outcome variable (dispersed, not dispersed). My treatment is a continuous variable (breeding success, a proportion). I created a DAG to identify confounding variables and need to control for diet (proportion) and predator abundance (average counts). I want to estimate the effect of breeding success (BS) on dispersal (DP), acknowledging that there are heterogenous effects across islands (HI).

From reading the grf documentation and other issues on github, I understand that I need to orthogonalize my data prior to running the causal forest. My preliminary code is below and I had several questions:

1. Is my setup to adjust for confounding and input the orthogonalized data into causal forest correct? Should I be inputting the residuals as Y and W (as below) or should I be adjusting Y.hat and W.hat?
2. Does this code give me my desired results: effect of breeding success on dispersal for each island after adjusting for confounding (diet, predators)?

Thanks for developing such an amazing package!

#-------------------------
# STEP 1 — Adjust for confounding
#-------------------------

# Outcome model: DP ~ confounders
m_y <- ranger(DP ~ Diet + Predation,
              data = ATPU_ExtProspOth_BS_Summary_Complete, probability = TRUE)

# Treatment model: BS ~ confounders
m_t <- ranger(BS ~ Diet + Predation,
              data = ATPU_ExtProspOth_BS_Summary_Complete)

# Predicted nuisance components
e_hat <- predict(m_y, 
                 ATPU_ExtProspOth_BS_Summary_Complete)$predictions[,2] 
                  # P(DP=1 | confounders)
p_hat <- predict(m_t, 
                 ATPU_ExtProspOth_BS_Summary_Complete)$predictions      
                 # E[BS | confounders]

# Orthogonalized residuals
res_y <- ATPU_ExtProspOth_BS_Summary_Complete$DP - e_hat
  # resid_Y represents variation in DP that is not explained by diet or predation
  # aka orthogonalized outcome
res_t <- ATPU_ExtProspOth_BS_Summary_Complete$BS - p_hat
  # resid_T represents variation in BS that is not explained by diet or predation
  # aka orthogonalized treatment

#-------------------------
# STEP 2 — Causal Forest on residuals
#-------------------------

# Use moderators (HI) for heterogeneity
X_mat <- model.matrix(~ HI, ATPU_ExtProspOth_BS_Summary_Complete)[, -1]   # removes intercept

# Estimates how BS affects DP, free from confounding
cf <- causal_forest(
  X = X_mat,
  Y = res_y,
  W = res_t
)

#-------------------------
# STEP 3 — CATE
#-------------------------

# CATE predictions
ATPU_ExtProspOth_BS_Summary_Complete$CATE_HI <- predict(cf)$predictions

[erikcs]

Hi @quinn-ca, by default, causal forests does orthogonalization. If you do not supply Y.hat and W.hat, these are estimated using separate regression forests along with the covariates you supply. Unless you wish to use different variables for HTE and propensity/regression adjustments, it's fine to just let grf do it for you. This vignette might be useful: it is the same (orthogonalized) partially linear model that is fit when W is continuous, so you can interpret it as a conditional average partial effect.

[quinn-ca]

Ahh, I didn't realize the orthogonalization was automatic! I am, however, interested in using a different variable for HTE than I am using as covariates. I hypothesize that the hatch island will lead to heterogenous treatment effects, however, I do not think this is confounding the relationship between the effect of breeding success on dispersal (based on the structure of my DAG). In other words, I am hypothesizing that hatch island is a competing exposure and could be a source of heterogeneity. Is there a way for me to analyze the heterogeneous effect of Hatch Island (a factor variable) outside the confounding variables provided?

From the vignette, my understanding is that I get individual CATEs, which I can interrogate for additional information about heterogeneity. But I am also interested in getting group average treatment effects: the effect of breeding success on dispersal for each island.

Thanks for your help!

[quinn-ca]

Also, one additional question, I evaluated the propensity score distribution as recommended in the tutorial. I get negative scores and scores around 0, in some cases peaking close to zero. I saw your response to another user (#1334) and suggested trimming scores <0.1 and >0.9. Does this apply if I have a continuous treatment? Do I still need to worry about scores outside the 0, 1 boundary? When I ran average_treatment_effect, I didn't get any warnings.