Editing Twin study (section)

== Methods ==
The power of twin designs arises from the fact that twins may be either identical ([[Twins#Monozygotic twins|monozygotic]] (MZ), i.e. developing from a single fertilized egg and therefore sharing all of their [[polymorphism (biology)|polymorphic]] [[allele]]s) or fraternal ([[Twins#Dizygotic twins|dizygotic]] (DZ), i.e. developing from two fertilized eggs and therefore sharing on average 50% of their alleles, the same level of genetic similarity found in non-twin siblings). These known differences in genetic similarity, together with a testable assumption of equal environments for identical and fraternal twins,<ref>{{cite book | editor1-last = Propping | editor1-first = Peter | editor2-last = Bouchard | editor2-first = Thomas J. | title = Twins as a tool of behavioral genetics | publisher = J. Wiley | location = London | year = 1993 | page = 326 | isbn = 978-0-471-94174-3 }}</ref> creates the basis for the design of twin studies aimed at estimating the overall effects of genes and environment on a phenotype.<ref>{{cite book | last1 = Cardon | first1 = Lon R. | last2 = Neale | first2 = Michael C. | title = Methodology for genetic studies of twins and families | publisher = Kluwer Academic Publishers | location = Boston | year = 1992 | isbn = 978-0-7923-1874-3 }}</ref><ref name=ATK />

The basic logic of the twin study can be understood with very little mathematical knowledge beyond an understanding of the concepts of [[variance]] and thence derived [[correlation]].

=== Classical twin method ===
Like all behavior genetic research, the '''classical twin study''' begins by assessing the variance of behavior (called a [[phenotype]] by geneticists) in a large group, and attempts to estimate how much of this is due to:
* genetic effects ([[heritability]])
* shared environment – events that happen to both twins, affecting them in the same way
* unshared, or unique, or nonshared environment – events that occur to one twin but not the other, or events that affect either twin in a different way.
Typically these three components are called '''A''' (additive genetics) '''C''' (common environment) and '''E''' (unique environment); hence the acronym ''ACE''. It is also possible to examine non-additive genetics effects (often denoted '''D''' for dominance ([[ADE model]]); see below for more complex twin designs).

The [[ACE model]] indicates what proportion of variance in a trait is heritable, versus the proportion due to a shared environment or unshared environment. Research is typically carried out using [[Structural equation modeling]] (SEM) programs such as  [[OpenMx]] capable in principle of handling all sorts of complex pedigrees. However the core logic underlying such programs is the same as the one underlying the twin design described here.

Monozygotic (identical – MZ) twins raised in a family share 100% of their genes, and all of their shared environment. Any differences arising between them in these circumstances are random (i.e. due to environmental effects unique to each twin). The correlation between identical twins provides an estimate of ''A'' + ''C''. Dizygotic (DZ) twins also share C, but share, on average only 50% of their genes: so the correlation between fraternal twins is a direct estimate of ½''A''+''C''. If we denote with ''r'' the [[correlation]], we can define ''r''<sub>mz</sub> and ''r''<sub>dz</sub> as the correlations of a trait among identical and fraternal twins, respectively. For any particular trait, then:

:''r''<sub>mz</sub> = ''A'' + ''C''

:''r''<sub>dz</sub> = ½''A'' + ''C''

Stated again, the difference between these two sums then allows us to solve for ''A'' and ''C'' (and as a consequence, for ''E''). As the difference between the identical and fraternal correlations is due entirely to a halving of the genetic similarity, the additive genetic effect ''A'' is twice the difference between the identical and fraternal correlations:

:''A'' = 2&nbsp;(''r''<sub>mz</sub> − ''r''<sub>dz</sub>)

given the estimate for ''A'', the one for ''C'' can be derived, for instance, from the first equation:

:''C'' = ''r''<sub>mz</sub> − ''A''

Finally, since the trait correlation among identical twins reflects the full contribution of ''A'' and ''C'', the residual variation ''E'' can be estimated by subtracting this correlation from 1

:''E'' = 1 − ''r''<sub>mz</sub>.

To summarize therefore, the additive genetic factor ''A'' is twice the difference between MZ and DZ twin correlations (this is known as [[Falconer's formula]]), ''C'' is the MZ twin correlation minus this estimate of ''A'', and the random (unique) factor ''E'' is (1 - ''r''<sub>mz</sub>), i.e. MZ twins differ due to unique environments only (Jinks & Fulker, 1970; Plomin, DeFries, McClearn, & McGuffin, 2001).

=== Modern modeling ===

Beginning in the 1970s, research transitioned to [[Structural equation modeling|modeling]]  genetic, environmental effects using [[maximum likelihood]] methods (Martin & Eaves, 1977). While computationally much more complex, this approach has numerous benefits rendering it almost universal in current research.

An example structural model (for the heritability of height among Danish males)<ref>{{Cite journal | last1 = Silventoinen | first1 = K.| last2 = Sammalisto | first2 = S.| last3 = Perola | first3 = M.| last4 = Boomsma | first4 = D. I.| last5 = Cornes | first5 = B. K.| last6 = Davis | first6 = C.| last7 = Dunkel | first7 = L.| last8 = De Lange | first8 = M.| last9 = Harris | first9 = J. R.| last10 = Hjelmborg | first10 = J. V. B.| last11 = Luciano | first11 = M.| last12 = Martin | first12 = N. G.| last13 = Mortensen | first13 = J.| last14 = Nisticò | first14 = L.| last15 = Pedersen | first15 = N. L.| last16 = Skytthe | first16 = A.| last17 = Spector | first17 = T. D.| last18 = Stazi | first18 = M. A.| last19 = Willemsen | first19 = G.| last20 = Kaprio | first20 = J.| doi = 10.1375/136905203770326402 | title = Heritability of Adult Body Height: A Comparative Study of Twin Cohorts in Eight Countries | journal = [[Twin Research and Human Genetics|Twin Research]] | volume = 6 | issue = 5 | pages = 399–408 | date=October 2003 | pmid =  14624724| citeseerx = 10.1.1.81.3898| s2cid = 2235255}}</ref> is shown:

{|
| [[File:Twin Study Structural ACE model.png|thumb|upright=1.3|'''A''': ACE model showing raw (non-standardised) variance coefficients]]
| [[File:Twin Study Structural ACE model STD.png|thumb|upright=1.3|'''B''': ACE model showing standardised variance coefficients]]
|}

Model A on the left shows the raw variance in height. This is useful as it preserves the absolute effects of genes and environments, and expresses these in natural units, such as mm of height change. Sometimes it is helpful to standardize the parameters, so each is expressed as percentage of total variance. Because we have decomposed variance into A, C, and E, the total variance is simply A + C + E. We can then scale each of the single parameters as a proportion of this total, i.e., Standardised–A = A/(A + C + E). Heritability is the standardised genetic effect.

==== Model comparison ====
A principal benefit of modeling is the ability to explicitly compare models: Rather than simply returning a value for each component, the modeler can compute [[confidence intervals]] on parameters, but, crucially, can drop and add paths and test the effect via statistics such as the [[Akaike's Information Criterion|AIC]]. Thus, for instance to test for predicted effects of family or shared environment on behavior, an AE model can be objectively compared to a full ACE model. For example, we can ask of the figure above for height: Can C (shared environment) be dropped without significant loss of fit? Alternatively, [[confidence intervals]] can be calculated for each path.

==== Multi-group and multivariate modeling ====
Multivariate modeling can give answers to questions about the genetic relationship between variables that appear independent. For instance: do IQ and long-term memory share genes? Do they share environmental causes? Additional benefits include the ability to deal with interval, threshold, and continuous data, retaining full information from data with missing values, integrating the latent modeling with measured variables, be they measured environments, or, now, measured molecular genetic markers such as [[Single-nucleotide polymorphism|SNPs]]. In addition, models avoid constraint problems in the crude correlation method: all parameters will lie, as they should, between 0–1 (standardized).

Multivariate, and multiple-time wave studies, with measured environment and repeated measures of potentially causal behaviours are now the norm. Examples of these models include extended twin designs,<ref>{{Cite journal | last1 = Keller | first1 = M. C.| last2 = Medland | first2 = S. E. |author-link2=Sarah Medland |last3 = Duncan | first3 = L. E.| doi = 10.1007/s10519-009-9320-x | title = Are Extended Twin Family Designs Worth the Trouble? A Comparison of the Bias, Precision, and Accuracy of Parameters Estimated in Four Twin Family Models | journal = [[Behavior Genetics (journal)|Behavior Genetics]] | volume = 40 | issue = 3 | pages = 377–393 | date=May 2010 | pmid =  20013306| pmc = 3228846 }}</ref><ref>{{Cite journal | last1 = Coventry | first1 = W. L. | last2 = Keller | first2 = M. C. | doi = 10.1375/1832427054253121 | title = Estimating the Extent of Parameter Bias in the Classical Twin Design: A Comparison of Parameter Estimates from Extended Twin-Family and Classical Twin Designs | journal = [[Twin Research and Human Genetics]] | volume = 8 | issue = 3 | pages = 214–223 | date = June 2005 | pmid = 15989749 | url = http://e-publications.une.edu.au/1959.11/6460 | doi-access = free }}{{Dead link|date=October 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> simplex models,<ref>{{Cite journal | last1 = Gillespie | first1 = Nathan A. | last2 = Evans | first2 = David E. | last3 = Wright | first3 = Margie. M. | last4 = Martin | first4 = Nicholas G. | title = Genetic Simplex Modeling of Eysenck's Dimensions of Personality in a Sample of Young Australian Twins | doi = 10.1375/1369052042663814 | journal = [[Twin Research and Human Genetics|Twin Research]] | volume = 7 | issue = 6 | pages = 637–648 | year = 2004 | pmid = 15607015 | url = http://www.vipbg.vcu.edu/~nathan/publications/Gillespie2005b.pdf | access-date = 2010-11-05 | archive-url = https://web.archive.org/web/20100624040406/http://www.vipbg.vcu.edu/~nathan/publications/Gillespie2005b.pdf | archive-date = 2010-06-24 | url-status = dead }}</ref> and growth-curve models.<ref>{{Cite journal | last1 = Neale | first1 = M. C.| last2 = McArdle | first2 = J. J.| doi = 10.1375/136905200320565454 | title = Structured latent growth curves for twin data | journal = [[Twin Research and Human Genetics|Twin Research]]| volume = 3 | issue = 3 | pages = 165–177| date=September 2000 | pmid = 11035490| url = http://www.vipbg.vcu.edu/vipbg/Articles/TwinRes-structured-2000.pdf| citeseerx = 10.1.1.336.1002}}</ref>

[[Structural equation modeling|SEM]] programs such as [[OpenMx]]<ref>{{Cite journal | last1 = Boker | first1 = Steven| last2 = Neale | first2 = Michael| last3 = Maes | first3 = Hermine| last4 = Wilde | first4 = Michael| last5 = Spiegel | first5 = Michael| last6 = Brick | first6 = Timothy| last7 = Spies | first7 = Jeffrey| last8 = Estabrook | first8 = Ryne| last9 = Kenny | first9 = Sarah| last10 = Bates | first10 = Timothy| last11 = Mehta | first11 = Paras| last12 = Fox | first12 = John| doi = 10.1007/s11336-010-9200-6 | title = OpenMx: An Open Source Extended Structural Equation Modeling Framework | journal = [[Psychometrika]] | volume = 76 | issue = 2 | pages = 306–317| year = 2011 | pmid =  23258944| pmc = 3525063}}</ref> and other applications suited to constraints and multiple groups have made the new techniques accessible to reasonably skilled users.

==== Modeling the environment: MZ discordant designs ====
As MZ twins share both their genes and their family-level environmental factors, any differences between MZ twins reflect E: the unique environment. Researchers can use this information to understand the environment in powerful ways, allowing [[epidemiology|epidemiological]] tests of causality that are otherwise typically confounded by factors such as gene–environment covariance, [[reverse causation]] and [[confounding]].

An example of a positive MZ discordant effect is shown below on the left. The twin who scores higher on trait 1 also scores higher on trait 2. This is compatible with a "dose" of trait 1 causing an increase in trait 2. Of course, trait 2 might also be affecting trait 1. Disentangling these two possibilities requires a different design (see below for an example). A null result is incompatible with a causal hypothesis.

{|
| [[File:Twin Study MZ discordant positive example.png|thumb|left|A depiction of MZ-discordance data]]
| [[File:Twin Study MZ discordant test of hypothesis that exercise protects against depression.png|thumb|MZ discordant test of hypothesis that exercise protects against depression]]
|}

Take for instance the case of an observed link between depression and exercise (See Figure above on right). People who are depressed also reporting doing little physical activity. One might ''hypothesise'' that this is a [[causal]] link: that "dosing" patients with exercise would raise their mood and protect against depression. The next figure shows what empirical tests of this hypothesis have found: a null result.<ref name="DeMoor2008">{{cite journal | last1 = De Moor | first1 = M. H. | last2 = Boomsma | first2 = D. I. | last3 = Stubbe | first3 = J. H. | last4 = Willemsen | first4 = G. | last5 = de Geus | first5 = E. J. | year = 2008 | title = Testing causality in the association between regular exercise and symptoms of anxiety and depression | doi = 10.1001/archpsyc.65.8.897 | journal = Archives of General Psychiatry | volume = 65 | issue = 8| pages = 897–905 | pmid=18678794| doi-access = free }}</ref>

'''Longitudinal discordance designs'''

[[File:Twin Study MZ discordant design.png|thumb|A cross-lagged longitudinal MZ discordant twin design. This model can take account of relationships among differences across traits at time one, and then examine the distinct hypotheses that increments in trait1 drive subsequent change in that trait in the future, or, importantly, in other traits.]]
As may be seen in the next Figure, this design can be extended to multiple measurements, with consequent increase in the kinds of information that one can learn. This is called a cross-lagged model (multiple traits measured over more than one time).<ref name="Burt2009">{{cite journal | last1 = Burt | first1 = S. A. | last2 = McGue | first2 = M. | last3 = Iacono | first3 = W. G. | year = 2009 | title = Nonshared environmental mediation of the association between deviant peer affiliation and adolescent externalizing behaviors over time: results from a cross-lagged monozygotic twin differences design | doi = 10.1037/a0016687 | pmid = 19899929 | journal = Dev Psychol | volume = 45 | issue = 6| pages = 1752–60 | pmc = 2778800 }}</ref>

In the longitudinal discordance model, differences between identical twins can be used to take account of relationships among differences across traits at time one (path A), and then examine the distinct hypotheses that increments in trait1 drive subsequent change in that trait in the future (paths B and  E), or, importantly, in other traits (paths C & D). In the example, the hypothesis that the observed [[correlation]] where [[Depression (mood)|depressed]] persons often also [[exercise]] less than average is causal, can be tested. If exercise is protective against depression, then path D should be significant, with a twin who exercises more showing less depression as a consequence.

=== Assumptions ===

It can be seen from the modeling above, the main assumption of the twin study is that of equal family environments, also known as the '''equal environments assumption'''.<ref>{{Cite journal |title=The equal environments assumption of classical twin studies may not hold |journal = British Journal of Educational Psychology|volume = 75|issue = 3|last1=Richardson |first1=Ken |last2=Norgate |first2=Sarah |date=2005-09-01 |pages=339–350 |language=en |doi=10.1348/000709904x24690 |pmid = 16238870|url = http://usir.salford.ac.uk/93/5/EP200506revised.pdf}}</ref><ref>{{Cite journal |last1=Plomin |first1=Robert |last2=Willerman |first2=Lee |last3=Loehlin |first3=John C. |date=1976-03-01 |title=Resemblance in appearance and the equal environments assumption in twin studies of personality traits |journal=Behavior Genetics |language=en |volume=6 |issue=1 |pages=43–52 |doi=10.1007/bf01065677 |pmid=943160 |s2cid=30732913 |issn=0001-8244}}</ref><ref>{{Cite web |url=http://www.apa.org/monitor/apr04/second.aspx |title=Behavioral Genetics--A second look at twin studies |last=Winerman |first=Lea |date=2004-04-01 |website=Monitor on Psychology |language=en |access-date=2017-08-23}}</ref> A special ability to test this assumption occurs where parents believe their twins to be non-identical when in fact they are genetically identical. Studies of a range of psychological traits indicate that these children remain as concordant as MZ twins raised by parents who treated them as identical.<ref>{{cite journal | last1 = Kendler | first1 = K.S. | last2 = Neale | first2 = M.C. | last3 = Kessler | first3 = R.C. | last4 = Heath | first4 = A.C. | last5 = Eaves | first5 = L.J. | year = 1993 | title = Panic disorder in women: A population-based twin study | journal = Psychological Medicine | volume = 23 | issue = 2| pages = 397–406 | doi=10.1017/s003329170002849x| pmid = 8332656 | s2cid = 30324607 }}</ref>

Molecular genetic methods of heritability estimation have tended to produce lower estimates than classical twin studies due to modern SNP arrays not capturing the influence of certain types of variants (e.g., rare variants or repeat polymorphsisms), though some have suggested it is because twin studies overestimate heritability.<ref>{{Cite journal |last=Felson |first=Jacob |date=January 2014 |title=What can we learn from twin studies? A comprehensive evaluation of the equal environments assumption |journal=[[Social Science Research]] |volume=43 |pages=184–199 |doi=10.1016/j.ssresearch.2013.10.004 |pmid=24267761 |issn=0049-089X|quote=...estimates of cumulative genetic influence using molecular-level data have tended to be substantially lower than the corresponding estimates from twin studies.}}</ref> A 2016 study determined that the assumption that the prenatal environment of twins was equal was largely tenable.<ref>{{cite journal|last1=Van Beijsterveldt|first1=C. E. M.|last2=Overbeek|first2=L. I. H.|last3=Rozendaal|first3=L.|last4=McMaster|first4=M. T. B.|last5=Glasner|first5=T. J. |last6=Bartels|first6=M. |last7=Vink|first7=J. M. |last8=Martin|first8= N. G. |last9=Dolan|first9=C. V.| last10=Boomsma|first10=D. I.|title=Chorionicity and heritability estimates from twin studies: The prenatal environment of twins and their resemblance across a large number of traits.|journal=Behavior Genetics|volume=46|number=3|year=2016|pages=304–314|doi=10.1007/s10519-015-9745-3|pmid=26410687|pmc=4858554}}.</ref> Researchers continue to debate whether or not the equal environment assumption is valid.<ref>{{cite journal | last1 = Conley | first1 = Dalton | last2 = Rauscher | first2 = Emily | last3 = Dawes | first3 = Christopher | last4 = Magnusson | first4 = Patrik KE | last5 = Siegal | first5 = Mark L. | year = 2013 | title = Heritability and the equal environments assumption: Evidence from multiple samples of misclassified twins | journal = Behavior Genetics | volume = 43 | issue = 5| pages = 415–426 | doi=10.1007/s10519-013-9602-1| pmid = 23903437 | hdl = 1808/24764 | s2cid = 2083213 | hdl-access = free }}</ref><ref>Fosse, Roar, Jay Joseph, and Ken Richardson. "A critical assessment of the equal-environment assumption of the twin method for schizophrenia." Frontiers in psychiatry 6 (2015): 62.</ref><ref>{{cite journal | last1 = Barnes | first1 = J. C. | last2 = Paul Wright | first2 = John | last3 = Boutwell | first3 = Brian B. | last4 = Schwartz | first4 = Joseph A. | last5 = Connolly | first5 = Eric J. | last6 = Nedelec | first6 = Joseph L. | last7 = Beaver | first7 = Kevin M. | year = 2014 | title = Demonstrating the validity of twin research in criminology | journal = Criminology | volume = 52 | issue = 4| pages = 588–626 | doi=10.1111/1745-9125.12049}}</ref><ref>Joseph, Jay. The trouble with twin studies: A reassessment of twin research in the social and behavioral sciences. Routledge, 2014.</ref><ref>{{cite journal | last1 = Felson | first1 = Jacob | year = 2014 | title = What can we learn from twin studies? A comprehensive evaluation of the equal environments assumption | journal = Social Science Research | volume = 43 | pages = 184–199 | doi=10.1016/j.ssresearch.2013.10.004 | pmid=24267761}}</ref>

==== Measured similarity: A direct test of assumptions in twin designs ====
A particularly powerful technique for testing the twin method was reported by Visscher ''et al.''<ref>{{Cite journal | last1 = Visscher | first1 = Peter M.| last2 = Medland | first2 = Sarah E.| last3 = Ferreira | first3 = Manuel A. R.| last4 = Morley | first4 = Katherine I.| last5 = Zhu | first5 = Gu| last6 = Cornes | first6 = Belinda K.| last7 = Montgomery | first7 = Grant W.| last8 = Martin | first8 = Nicholas G.| doi = 10.1371/journal.pgen.0020041 | title = Assumption-Free Estimation of Heritability from Genome-Wide Identity-by-Descent Sharing between Full Siblings | journal = [[PLOS Genetics]] | volume = 2 | issue = 3 | pages = e41 | year = 2006 | pmid =  16565746| pmc =1413498 | doi-access = free}}</ref> Instead of using twins, this group took advantage of the fact that while siblings on average share 50% of their genes, the actual gene-sharing for individual sibling pairs varies around this value, essentially creating a continuum of genetic similarity or "twinness" within families. Estimates of heritability based on direct estimates of gene sharing confirm those from the twin method, providing support for the assumptions of the method.

=== Sex differences ===
Genetic factors, including both gene expression and the range of gene × environment interactions, may differ between the sexes. Fraternal opposite sex twin pairs are invaluable in explicating these effects.

In an extreme case, a gene may only be expressed in one sex (qualitative sex limitation).{{clarify|date=September 2022}}<!-- does this refer only to genes that can't be expressed in one sex, e.g. in the genitals, or does it also refer to genes expressed only in one of the twins, e.g. an X-linked recessive trait? --> More commonly, the effects of particular alleles may depend on the sex of the individual. A gene might cause a change of 100&nbsp;g in weight in males, but perhaps 150&nbsp;g in females – a quantitative gene effect.

Environments may impact on the ability of genes to express themselves and may do this via sex differences. For instance, genes affecting voting behavior would have no effect in females if females are excluded from the vote. More generally, the logic of sex-difference testing can extend to any defined sub-group of individuals. In cases such as these, the correlation for same and opposite sex DZ twins will differ, betraying the effect of the sex difference.

For this reason, it is normal to distinguish three types of fraternal twins.  A standard analytic workflow would involve testing for sex-limitation by fitting models to five groups, identical male, identical female, fraternal male, fraternal female, and fraternal opposite sex. Twin modeling thus goes beyond correlation to test causal models involving potential causal variables, such as sex.

=== Gene × environment interactions ===

Gene effects may often be dependent on the environment. Such interactions are known as ''G×E interactions'', in which the effects of a gene allele differ across different environments. Simple examples would include situations where a gene multiplies the effect of an environment: perhaps adding 1&nbsp;inch to height in high nutrient environments, but only half an inch to height in low-nutrient environments. This is seen in different slopes of response to an environment for different genotypes.

Often researchers are interested in changes in [[heritability]] under different conditions: In environments where [[alleles]] can drive large phenotypic effects (as above), the relative role of genes will increase, corresponding to higher heritability in these environments.

A second effect is ''G × E correlation'', in which certain alleles tend to accompany certain environments. If a gene causes a parent to enjoy reading, then children inheriting this allele are likely to be raised in households with books due to GE correlation: one or both of their parents has the allele and therefore will accumulate a book collection ''and'' pass on the book-reading allele. Such effects can be tested by measuring the purported environmental correlate (in this case books in the home) directly.

Often the role of environment seems maximal very early in life, and decreases rapidly after [[compulsory education]] begins. This is observed for instance in reading<ref>{{Cite journal | last1 = Byrne | first1 = Brian | last2 = Wadsworth | first2 = Sally | last3 = Corley | first3 = Robin | last4 = Samuelsson | first4 = Stefan | last5 = Quain | first5 = Peter | last6 = Defries | first6 = John C. | last7 = Willcutt | first7 = Erik | last8 = Olson | first8 = Richard K. | doi = 10.1207/s1532799xssr0903_3 | title = Longitudinal Twin Study of Early Literacy Development: Preschool and Kindergarten Phases | journal = [[Scientific Studies of Reading]] | volume = 9 | issue = 3 | pages = 219–235 | year = 2005 | url = http://psych.colorado.edu/~willcutt/pdfs/Byrne_2007.pdf | access-date = 2015-08-28 | archive-url = https://web.archive.org/web/20160304111352/http://psych.colorado.edu/~willcutt/pdfs/Byrne_2007.pdf | archive-date = 2016-03-04 | url-status = dead | citeseerx = 10.1.1.530.7555 | s2cid = 144069119 }}</ref>
as well as intelligence.<ref>{{Cite journal | last1 = Deary | first1 = Ian J.| last2 = Spinath | first2 = Frank M.| last3 = Bates | first3 = Timothy C.| doi = 10.1038/Sj.Ejhg.5201588 | title = Genetics of intelligence | journal = [[European Journal of Human Genetics]]| volume = 14 | issue = 6 | pages = 690–700 | year = 2006 | pmid =  16721405| doi-access = free }}</ref> This is an example of a G*Age effect and allows an examination of both GE correlations due to parental environments (these are broken up with time), and of G*E correlations caused by individuals actively seeking certain environments.<ref>{{Cite journal | last1 = Plomin | first1 = Robert| last2 = Daniels | first2 = Denise| doi = 10.1017/S0140525X00055941 | title = Why are children in the same family so different from one another? | journal = [[Behavioral and Brain Sciences]] | volume = 10 | issue = 3| pages = 1–16| year = 1987| pmc = <!--none-->}}<br />''revisited in: <!-- or possibly republished as-->'' {{Cite journal | last1 = Plomin | first1 = R.| last2 = Daniels | first2 = D.| doi = 10.1093/ije/dyq148 | title = Why are children in the same family so different from one another? | journal = [[International Journal of Epidemiology]] | volume = 40 | issue = 3 | pages = 563–582 | date=June 2011 | pmid = 21807642| pmc = 3147063 }}</ref>

==== Norms of reaction ====
Studies in plants or in [[animal breeding]] allow the effects of experimentally randomized [[genotypes]] and environment combinations to be measured. By contrast, human studies are typically observational.<ref>{{Cite journal | last1 = Kempthorne | first1 = Oscar| title = Heritability: uses and abuses| journal = [[Genetica]]| volume = 99 | issue = 2–3| pages = 109–112 | doi = 10.1007/bf02259514 | year = 1997 | pmid = 9463066| s2cid = 23266944}}</ref><ref>{{Cite journal | last1 = Kendler | first1 = K. S.| last2 = Gruenberg | first2 = A. M.| doi = 10.1001/archpsyc.1984.01790170029004 | title = An Independent Analysis of the Danish Adoption Study of Schizophrenia: VI. The Relationship Between Psychiatric Disorders as Defined by DSM-III in the Relatives and Adoptees | journal = [[Archives of General Psychiatry]]| volume = 41 | issue = 6 | pages = 555–564 |date=June 1984 | pmid =  6732417}}</ref> This may suggest that [[norms of reaction]] cannot be evaluated.<ref>{{cite book | last1 = Kamin | first1 = Leon J. | last2 = Rose | first2 = Steven R. | last3 = Lewontin | first3 = Richard C. | title = Not in Our Genes: Biology, Ideology and Human Nature | publisher = Penguin Books | location = New York | year = 1984 | isbn = 978-0-14-022605-8 | title-link = Not in Our Genes }}</ref><ref>{{Cite journal | last1 = Rose | first1 = Richard J.| title = Separated Twins: Data and Their Limits | doi = 10.1126/science.215.4535.959 | journal = [[Science (journal)|Science]] | volume = 215 | issue = 4535 | pages = 959–960 | year = 1982 | pmid =  17821364| bibcode = 1982Sci...215..959F}}</ref>

As in other fields such as [[instrumental variable|economics]] and [[Mendelian randomization|epidemiology]], several designs have been developed to capitalise on the ability to use differential gene-sharing, repeated exposures, and measured exposure to environments (such as children social status, chaos in the family, availability and quality of education, nutrition, toxins etc.) to combat this confounding of causes. An inherent appeal of the classic twin design is that it begins to untangle these confounds. For example, in identical and fraternal twins shared environment and genetic effects are  not confounded, as they are in non-twin familial studies.<ref name=ATK>{{Cite journal | last1 = Martin | first1 = Nicholas| last2 = Boomsma | first2 = Dorret| last3 = Machin | first3 = Geoffrey| doi = 10.1038/ng1297-387 | title = A twin-pronged attack on complex traits | url = http://genepi.qimr.edu.au/contents/p/staff/CV190Martin_UQ_Copy.pdf| journal = [[Nature Genetics]] | volume = 17 | issue = 4 | pages = 387–392 | year = 1997 | pmid =  9398838| hdl = 1871/2733| s2cid = 2028886}}</ref> Twin studies are thus in part motivated by an attempt to take advantage of the random assortment of genes between members of a family to help understand these correlations.

While the twin study tells us only how genes and families affect behavior within the observed range of environments, and with the caveat that often genes and environments will covary, this is a considerable advance over the alternative, which is no knowledge of the different roles of genes and environment whatsoever.<ref name=Neale1996>M. C. Neale and H. H. Maes. (1996). Methodology for genetics studies of twins and families. ''Journal''.</ref> Twin studies are therefore often used as a method of controlling at least one part of this observed variance: Partitioning, for instance, what might previously  have been assumed to be family environment into shared environment and additive genetics using the experiment of fully and partly shared genomes in twins.<ref name=Neale1996 /> Additional information is available outside the classic twin design. [[Adoption Study|Adoption designs]] are a form of natural experiment that tests norms of reaction by placing the same genotype in different environments.<ref>{{Cite journal | last1 = Petrill | first1 = S. A.| last2 = Deater-Deckard | first2 = K.| title = The heritability of general cognitive ability: A within-family adoption design | doi = 10.1016/j.intell.2004.05.001 | journal = [[Intelligence (journal)|Intelligence]] | volume = 32 | issue = 4 | pages = 403–409| date=July–August 2004 }}</ref> Association studies, e.g.,<ref>{{Cite journal | last1 = Steer | first1 = C. D.| last2 = Davey Smith | first2 = G.| author-link2=George Davey Smith| last3 = Emmett | first3 = P. M.| last4 = Hibbeln | first4 = J. R.| last5 = Golding | first5 = J.| editor1-last = Penha-Goncalves | editor1-first = Carlos | title = FADS2 Polymorphisms Modify the Effect of Breastfeeding on Child IQ | doi = 10.1371/journal.pone.0011570 | journal = [[PLoS ONE]] | volume = 5 | issue = 7 | pages = e11570 | date=July 2010 | pmid =  20644632| pmc = 2903485 | bibcode = 2010PLoSO...511570S| doi-access = free}}</ref> allow direct study of allelic effects.  [[Mendelian randomization]] of alleles also provides opportunities to study the effects of alleles at random with respect to their associated environments and other genes.<ref>e.g. {{Cite journal | last1 = Davey Smith | first1 = G.| author-link1=George Davey Smith| title = Capitalizing on Mendelian randomization to assess the effects of treatments | doi = 10.1177/014107680710000923 | journal = [[Journal of the Royal Society of Medicine]]| volume = 100 | issue = 9 | pages = 432–435 | date=September 2007 | pmid =  17766918| pmc = 1963388 }}</ref>

=== Extended twin designs and more complex genetic models ===
The basic or classical twin-design contains only identical and fraternal twins raised in their biological family. This represents only a sub-set of the possible genetic and environmental relationships. It is fair to say, therefore, that the heritability estimates from twin designs represent a first step in understanding the genetics of behavior.

The variance partitioning of the twin study into additive genetic, shared, and unshared environment is a first approximation to a complete analysis taking into account [[gene–environment correlation|gene–environment covariance]] and [[gene–environment interaction|interaction]], as well as other non-additive effects on behavior. The revolution in [[molecular genetics]] has provided more effective tools for describing the genome, and many researchers are pursuing molecular genetics in order to directly assess the influence of [[alleles]] and environments on traits.

An initial limitation of the twin design is that it does not afford an opportunity to consider both Shared Environment and Non-additive genetic effects simultaneously. This limit can be addressed by including additional siblings to the design.

A second limitation is that gene–environment correlation is not detectable as a distinct effect unless it is added to the model. Addressing this limit requires incorporating adoption models, or children-of-twins designs, to assess family influences uncorrelated with shared genetic effects.

==== Continuous variables and ordinal variables ====

While concordance studies compare traits either present or absent in each twin, [[correlation]]al studies compare the agreement in continuously varying traits across twins.