You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
Extend the zero-truncated families to handle right-censored (top-coded) counts, where the count y is observed only in grouped form such as 1, 2, 3+ (the top category lumps all y ≥ c) rather than the full 1, 2, 3, 4, … .
This is the concrete, count-specific version of the "right-censored models" line in #10.
Motivation
Capture–recapture / unseen-species data are frequently reported in top-coded form — e.g. "identified once, twice, or three-or-more times". The Chao-type estimators (chao, oichao) use only the low counts (f₁,f₂ or f₂,f₃) and are therefore already robust to top-coding, but the full-likelihood parametric families (ztpoisson, ztgeom, ztnegbin, the OI/ZT and Hurdle variants, …) currently assume every count is observed exactly and cannot be fit to top-coded data.
What's needed
Allow the response to encode a censoring threshold c, so the data are (f₁, …, f_{c−1}, f_{c+}) with f_{c+} = #{units with y ≥ c}.
In the (zero-truncated) likelihood, use the exact pmf p₊(y) for the fully-observed cells y < c and the tail / survival probability P(Y ≥ c | Y ≥ 1) = 1 − Σ_{y=1}^{c−1} p₊(y) for the censored top cell. (The families already carry the pmf and a CDF — used internally in their simulate methods — so the survival term is readily available.)
Propagate to deviance / residuals and confirm the Horvitz–Thompson / popSizeEst() machinery works once parameters are estimated from censored data.
Scope / notes
Primarily benefits the parametric ZT families; chao/oichao are unaffected (they ignore high counts by construction).
Likely a controlModel / response-encoding option plus a family survival/tail hook, rather than new families.
Acceptance
Fit a ZT family to top-coded data (e.g. {1, 2, 3+}) and recover sensible parameter + population-size estimates; unit tests on a synthetic top-coded sample; documentation.
Extend the zero-truncated families to handle right-censored (top-coded) counts, where the count y is observed only in grouped form such as 1, 2, 3+ (the top category lumps all y ≥ c) rather than the full 1, 2, 3, 4, … .
This is the concrete, count-specific version of the "right-censored models" line in #10.
Motivation
Capture–recapture / unseen-species data are frequently reported in top-coded form — e.g. "identified once, twice, or three-or-more times". The Chao-type estimators (
chao,oichao) use only the low counts (f₁,f₂ or f₂,f₃) and are therefore already robust to top-coding, but the full-likelihood parametric families (ztpoisson,ztgeom,ztnegbin, the OI/ZT and Hurdle variants, …) currently assume every count is observed exactly and cannot be fit to top-coded data.What's needed
simulatemethods — so the survival term is readily available.)popSizeEst()machinery works once parameters are estimated from censored data.Scope / notes
chao/oichaoare unaffected (they ignore high counts by construction).controlModel/ response-encoding option plus a familysurvival/tail hook, rather than new families.Acceptance