tutorialmanuscript.Xmd

---
title: "From Twins to Pedigrees: A Tutorial for Extended Family Variance Component Modeling with BGmisc"
shorttitle: "Extended Family Modeling with BGmisc"
author:
  - name: "S. Mason Garrison"
    affiliation: "1"
    corresponding: true
    email: "garrissm@wfu.edu"
abstract: |
  Twin studies remain the dominant design in behavior genetics, yet most twin half-siblings, cousins, and multi-generational relatives whose distinct kinship coefficients jointly identify a richer set of variance components than any MZ/DZ comparison alone. We demonstrate how to fit extended pedigree models using the BGmisc package and OpenMx.
  We apply the extended pedigree model to mutiple datasets
  of Youth (a large human panel study with researcher-linked kinship), the Kluane Red Squirrel Project
  (a multi-generational animal field study), and a children-of-twins dataset.
  dataset with genomic relatedness data. In each case, fitting the extended
  pedigree model on data the researcher already possesses -- but typically
  confounds become testable, and components inaccessible to twin designs emerge.
  We provide reproducible code for each application and practical guidance on
  identification, starting values, and the interpretation of results.
  registries contain far more information than researchers typically use: full siblings,
  across three empirically distinct settings: the National Longitudinal Survey
  discards -- changes the substantive conclusions: heritability estimates shift,
keywords: ["extended pedigree", "variance components", "heritability", "BGmisc", "OpenMx", "behavior genetics", "tutorial"]
output:
  rmarkdown::html_vignette:
    toc: true
    toc_depth: 3
  pdf_document:
    keep_tex: true
bibliography: references.bib
vignette: >
  %\VignetteIndexEntry{Extended Family Modeling with BGmisc}
  %\VignetteEncoding{UTF-8}
  %\VignetteEngine{knitr::rmarkdown}
editor_options:
  markdown:
    wrap: 100
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE, comment = "#>",
  echo = TRUE, message = FALSE, warning = FALSE,
  fig.width = 7, fig.height = 4.5
)

options(rmarkdown.html_vignette.check_title = FALSE)
```

# Introduction

In behavior geneticists quest to understanding the relative contributions of genetic and
environmental factors to phenotypic variation, they have long relied on the classical twin design.
By comparing the simiarly of monozygotic (MZ) twins -- who share essentially all their DNA -- to
that of dizygotic (DZ) twins -- who share on average half their segregating alleles -- researchers
can partition phenotypic variance into additive genetic ($a^2$), shared environmental ($c^2$), and
nonshared environmental ($e^2$) components [@plomin2016; @neale2004]. The twin design is elegant
precisely because it requires only two types of pairs to identify three parameters.

Its simplicity, however, is also its limitation. The classical ACE model is just identified: two
observed statistics (MZ and DZ intraclass correlations) and three unknown parameters, with zero
degrees of freedom remaining to test model fit or estimate additional components. Dominance genetic
variance ($d^2$), epistasis, and interactions between nuclear and mitochondria DNA are inestimable
from twins alone. More practically: these data are often collected in the context of larger family
studies, either intentionally (e.g., twin registries that also include siblings and parents) or as a
byproduct of large panel studies (e.g., the National Longitudinal Survey of Youth, which includes
researcher-linked kinship). In most cases, the additional relatives are excluded from analysis, and
the twin design is applied to a subset of the data, even though these relatives carry independent
information about the genetic and environmental architecture of the phenotype. For example, many of the twin registries reviewed in FOO, include triplets, sibles, children, parents. https://helda.helsinki.fi/server/api/core/bitstreams/f0b6dc08-69df-449e-a8fe-e2c78abf7f60/content

The extended pedigree model, which we have introduced elsewhere (see ETC), leverages the full range
of kinship coefficients in a pedigree to identify a richer set of variance components than the
classical twin design. By including multiple types of relatives, researchers can estimate not only
additive genetic variance but also dominance, shared environmental variance, and even more complex
interactions. This tutorial demonstrates how to fit extended pedigree models using the BGmisc
package and OpenMx, applying the model to multiple datasets across empirically distinct settings:
the National Longitudinal Survey of Youth (a large human panel study with researcher-linked
kinship), the Kluane Red Squirrel Project (a multi-generational animal field study), and a
children-of-twins dataset. In each case, fitting the extended pedigree model on data the researcher
already possesses -- but typically discards. We provide reproducible code for each application and
practical guidance on identification, starting values, and the interpretation of results.

The extended pedigree model addresses this gap directly. Rather than relying on a single MZ/DZ
contrast, it leverages the full spectrum of pairwise kinship coefficients available in a family
dataset: 1.0 for identical twins, 0.5 for parent-offspring and full siblings, 0.25 for half-siblings
and grandparent-grandchild pairs, 0.125 for first cousins, and so on. Each distinct relatedness
value provides independent leverage for disentangling genetic from environmental contributions. As
the number of distinct kinship types increases, so does the number of identifiable variance
components.

Extended pedigree designs have been used in behavior genetics since at least the 1970s [@eaves1978; @fulker_multiple_1988], but they have remained a minority practice. Partially over concerns about model identification and power (Wilson, 1982, 1989), the complexity of fitting these models, and the relative costs of collecting twin data compared to extended family data.

<! -- https://onlinelibrary.wiley.com/doi/10.1002/bimj.4710310511 -->

but also because the twin design has been so successful and widely adopted. The twin design is often seen as the "gold standard" in behavior genetics, and many researchers may be hesitant to deviate from this established approach. Additionally, many human datasets simply do not include the necessary family structure to fit extended pedigree models, which may limit their applicability in certain contexts.

<the reasosn are numerous for why this is the case, but a key factor is that many human datasets simply do not include the necessary family structure to fit these models. And the twin design is often the default analytic approach, even when more complex family data are available.



In contrast, similar
models are common in plant and animal breeding, where pedigree data is more routinely collected and
analyzed.

A persistent barrier has been the programming complexity of constructing relatedness matrices for
arbitrary family structures, checking model identification, and assembling the resulting multi-group
structural equation models. The `BGmisc` R package [@Garrison2024; @garrison_bgmisc_2025] was
extended to address these challenges, providing tools for calculating relatedness matrices from
pedigree data, checking model identification, and fitting extended pedigree models using OpenMx. The
package is designed to be user-friendly and flexible, allowing researchers to easily incorporate a
wide range of family structures into their analyses.

# References