Editing Heritability (section)

===Linear mixed models===
A wide variety of approaches using linear mixed models have been reported in literature. Via these methods, phenotypic variance is partitioned into genetic, environmental and experimental design variances to estimate heritability. Environmental variance can be explicitly modeled by studying individuals across a broad range of environments, although inference of genetic variance from phenotypic and environmental variance may lead to underestimation of heritability due to the challenge of capturing the full range of environmental influence affecting a trait. Other methods for calculating heritability use data from [[genome-wide association studies]] to estimate the influence on a trait by genetic factors, which is reflected by the rate and influence of putatively associated genetic loci (usually [[single-nucleotide polymorphisms]]) on the trait. This can lead to underestimation of heritability, however. This discrepancy is referred to as "missing heritability" and reflects the challenge of accurately modeling both genetic and environmental variance in heritability models.<ref name="pmid27382152">{{cite journal | vauthors = Heckerman D, Gurdasani D, Kadie C, Pomilla C, Carstensen T, Martin H, Ekoru K, Nsubuga RN, Ssenyomo G, Kamali A, Kaleebu P, Widmer C, Sandhu MS | title = Linear mixed model for heritability estimation that explicitly addresses environmental variation | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 113 | issue = 27 | pages = 7377–82 | date = July 2016 | pmid = 27382152 | pmc = 4941438 | doi = 10.1073/pnas.1510497113 | bibcode = 2016PNAS..113.7377H | doi-access = free }}</ref>

When a large, complex pedigree or another aforementioned type of data is available, heritability and other quantitative genetic parameters can be estimated by [[restricted maximum likelihood]] (REML) or [[Bayesian statistics|Bayesian methods]]. The [[raw data]] will usually have three or more data points for each individual: a code for the sire, a code for the dam and one or several trait values. Different trait values may be for different traits or for different time points of measurement.

The currently popular methodology relies on high degrees of certainty over the identities of the sire and dam; it is not common to treat the sire identity probabilistically. This is not usually a problem, since the methodology is rarely applied to wild populations (although it has been used for several wild ungulate and bird populations), and sires are invariably known with a very high degree of certainty in breeding programmes. There are also algorithms that account for uncertain paternity.

The pedigrees can be viewed using programs such as Pedigree Viewer [http://www-personal.une.edu.au/~bkinghor/pedigree.htm], and analyzed with programs such as [[ASReml]], VCE [https://web.archive.org/web/20070312053650/http://vce.tzv.fal.de/index.pl], WOMBAT [https://web.archive.org/web/20061128123632/http://agbu.une.edu.au/~kmeyer/wombat.html], MCMCglmm within the R environment [https://www.rdocumentation.org/packages/MCMCglmm/versions/2.29/topics/MCMCglmm-package] or the [[BLUPF90]] family of programs [http://nce.ads.uga.edu/~ignacy/programs.html].

Pedigree models are helpful for untangling confounds such as [[reverse causality]], [[maternal effects]] such as the [[prenatal environment]], and confounding of [[genetic dominance]], shared environment, and maternal gene effects.<ref>{{cite journal | vauthors = Hill WG, Goddard ME, Visscher PM | title = Data and theory point to mainly additive genetic variance for complex traits | journal = PLOS Genetics | volume = 4 | issue = 2 | pages = e1000008 | date = February 2008 | pmid = 18454194 | pmc = 2265475 | doi = 10.1371/journal.pgen.1000008 | veditors = MacKay TF, Goddard ME | doi-access = free }} {{open access}}</ref><ref name=VisscherHillWray>{{cite journal | vauthors = Visscher PM, Hill WG, Wray NR | title = Heritability in the genomics era--concepts and misconceptions | journal = Nature Reviews. Genetics | volume = 9 | issue = 4 | pages = 255–66 | date = April 2008 | pmid = 18319743 | doi = 10.1038/nrg2322 | s2cid = 690431 | url = http://genepi.qimr.edu.au/contents/p/staff/visscher_hill_wray_nrg2.pdf | author-link2 = William G. Hill | access-date = 2015-08-28 | archive-date = 2016-03-24 | archive-url = https://web.archive.org/web/20160324154308/https://genepi.qimr.edu.au/contents/p/staff/visscher_hill_wray_nrg2.pdf | url-status = live }}</ref>