Editing Twin study (section)

=== 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.