About
1 Project Description
This project studies how fertility distributions shape sibling and broader kin-count distributions. Using statistical models of fertility and family structure, we estimate empirical fertility patterns, derive sibling distributions, and simulate relative counts across relationship categories.
2 Methods
2.1 Fertility Modeling
We use a zero-inflated negative binomial (ZINB) distribution to model fertility patterns:
\[P(X = k) = \begin{cases} \pi + (1 - \pi) \cdot NB(0; \mu, \theta) & \text{if } k = 0 \\ (1 - \pi) \cdot NB(k; \mu, \theta) & \text{if } k > 0 \end{cases}\]
where: - \(\pi\) is the zero-inflation probability (excess childlessness) - \(\mu\) is the mean of the negative binomial component - \(\theta\) is the dispersion parameter
2.2 Sibling Distribution
The sibling distribution is derived from the fertility distribution, using the relationship: \[P(num_{sib}=k) \propto (k+1)P(num_{child}=k+1).\]
3 Software
This project uses:
- R for statistical computing, with
psclfor zero-inflated models andggplot2for visualization - Quarto for the methods and analysis website
- React, Vite, and Recharts for the interactive Kincounts simulator (deployed on Vercel)
5 Contact
For questions or collaborations, please visit our GitHub repository.