Poisson hurdle effects

The task

Task statement

Fit a Poisson hurdle model on all supplied rows. Model Pr(y>0|x,d) by logit with an intercept, x, and d. Conditional on y>0, fit a zero-truncated Poisson with log lambda=b0+b_x*x+b_d*d, using only positive observations. Its likelihood is the Poisson mass divided by 1-exp(-lambda). The unconditional mean is Pr(y>0)*lambda/(1-exp(-lambda)). Report mean_y, the equally weighted average unconditional fitted mean over all rows. Report ame_x, the average derivative of this unconditional mean with respect to continuous x, accounting for x in both fitted equations. Report effect_d, the average difference in this unconditional mean when d changes from zero to one in both equations. Keep x at its observed value. Also report prob_at_least_three, the equally weighted average fitted unconditional probability Pr(y>=3|x,d) over all supplied rows. This probability includes the hurdle probability and the zero-truncation adjustment. For all results, n_obs is the full dataset row count, including zeros.

Data

Simulated CSV. Columns: y, x, d

Files

input.csv

Seed

2026091703

Required output

Scored estimates: mean_y, ame_x, effect_d, prob_at_least_three.

Reference output

A run succeeds when every scored estimate lies within 1 percent or 0.005 of its reference value, whichever is larger. Sample sizes are not scored.