A flexible ratio regression approach for zero-truncated capture-recapture counts.

Area of Science:

• Statistics
• Ecology
• Biometry

Background:

• Capture-recapture methods are crucial for estimating population sizes when direct observation is impossible.
• Real-world data often present truncated count distributions, where zero counts are unobserved, complicating estimation.
• Existing methods struggle to accurately model these zero-truncated distributions.

Purpose of the Study:

• To validate a regression-based approach for analyzing truncated count distributions in capture-recapture studies.
• To demonstrate that regression models can effectively estimate unobserved zero counts.
• To extend the applicability of regression modeling to a wider class of count distributions.

Main Methods:

• Utilizing ratios of neighboring count probabilities, estimated from observed frequencies.
• Modeling these ratios using a regression approach, previously applied to Katz family densities and beta-binomial distributions.
• Extending the regression framework to include fractional polynomial models for broader applicability.

Main Results:

• The regression model approach is shown to yield a valid count distribution under general conditions.
• The method successfully estimates the unobserved frequency of zero counts.
• The approach is robust across various empirical applications and simulation studies.

Conclusions:

• The regression modeling of count probabilities provides a reliable method for estimating population sizes from truncated data.
• This approach simplifies the estimation of unobserved units by focusing on regression model fitting.
• The study bridges the gap between regression models and their associated count distributions, offering a more complete analysis.