Twin study
Twin studies are one of a family of designs in behavior genetics which aid the study of individual differences by highlighting the role of environmental and genetic causes on behavior. Twins are invaluable for studying these important questions because they disentangle the sharing of genes and environments. If we observe that children in a family are more similar than might be expected by chance, this may reflect shared environmental influences common to members of family class, parenting styles, education etc. but they will also reflect shared genes, inherited from parents. The twin design compares the similarity of  identical twins who share 100% of their genes, to that of dizygotic or fraternal twins, who share only 50% of their genes. By studying many hundreds of families of twins, researchers can then understand more about the role of genetic effects, and the effects of shared and unique environment effects.
Modern twin studies have shown that almost all traits are in part influenced by genetic differences, with some characteristics showing a strong influence (e.g., height), others an intermediate level (i.e. IQ) and some more complex heritabilities, with evidence for different genes affecting different elements of the trait - for instance Autism.

## History
While twins have been of interest to scholars since early civilization, such as the early physician Hippocrates (5th c. BCE), who attributed similar diseases in twins to shared material circumstances, and the stoic philosopher Posidonius (1rst c. BCE), who attributed such similarities to shared astrological sex circumstances, the modern history of the twin study derives from  Sir Francis Galton's pioneering use of twins to study the role of genes and environment on human development and behavior.

# Methods
The power of twin designs arises from the fact that twins may be either monozygotic (MZ: developing from a single fertilized egg and therefore sharing all of their genes)  or dizygotic (DZ: developing from two fertilized eggs and therefore sharing on average 50% of their genes, the same level of genetic similarity as found in non-twin siblings). These known differences in genetic similarity, together with a testable assumption of equal environments for MZ and DZ twins (Bouchard & Propping, 1993) creates the basis for the twin design for exploring the effects of genetic and environmental variance on a phenotype (Neale & Cardon, 1992).
The basic logic of the twin study can be understood with very little mathematics beyond an understanding of correlation and the concept of variance.
Like all behavior genetic research, the classic twin study begins from assessing the variance of a behavior (called a phenotype by geneticists) in a large group, and attempts to estimate how much of this is due to genetic effects (heritability), how much appears to be due to shared environmental effects, and how much is due to unique environmental effects - events occurring to one twin but not another.
Typically these three components are called A (additive genetics) C (common environment) and E (unique environment). the so-called ACE Model. It is also possible to examine non-additive genetics effects (often denoted D for dominance (see below for more complex twin designs).
Given the ACE model, researchers can determine what proportion of variance in a trait is heritable, versus the proportions which are due to shared environment or unshared environment. While nearly all research is carried out using SEM programs such as the freeware Mx, the essential logic of the twin design is as follows:
MZ twins raised in a family share both 100% of their genes, and all of the shared environment. All differences between them in this framework are unique. The correlation we observe between MZ twins provides an estimate of A+C. DZ twins have a common shared environment, and share 50% of their genes: so the correlation between DZ twins is a direct estimate of 1/2A + C.
rMZ = A+C
rDZ = .5*A+C
These two equations allow us to derive A C and E:
A = 2*(rmz- rdz)
C = rmz-A
E= 1-rmz
Where rmz and rdz are simply the correlations of the trait in MZ and DZ twins respectively. Twice difference between MZ and DZ twins gives us A: the additive genetic effect. C is simply the MZ correlation - our estimate of A, and E is estimated directly by how much the MZ twin correlation deviates from 1. (Jinks & Fulker, 1970; Plomin, DeFries , McClearn, & McGuffin, 2001).

### Modern Modeling
Beginning in the 1970s, research transitioned to explicitly modeling the values of A, C, and E within a maximum likelihood framework (Martin & Eaves, 1977). While computationally much more complex, benefits of this approach are manifold, and modeling tools such as Mx (Neale, Boker, Xie, & Maes, 2002) have made the new techniques relatively accessible.

## Assumptions
Equal environments.
It can be seen from the modelling above, that the main assumption of the twin study is that of equal environments. At an intuitive level, this seems reasonable - why would parents note that two children shared their hair and eye color, and then contrive to make their IQs identical? Indeed, how could they? This assumption, however, has been directly tested. An interesting case occurs where parents believe their twins to be non-identical when in fact they are genetically MZ. Studies of a range of psychological traits indicate that these children remain as concordant as MZs raised by parents who treated them as identical (Kendler, Neale, Kessler, Heath, & Eaves, 1993).

## Measured similarity: A direct test of assumptions in twin designs
A particularly powerful technique for testing the twin method has recently been reported by Visscher et al. 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 in the domains of cognition, personality, and psychopathology.

## Extended twin designs and more complex genetic models
The basic or classical twin-design contains only MZ and DZ 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 covariance and 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 is 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 GE correlation is not detectable as a distinct effect. Addressing this limit requires incorporating adoption models, or children-of-twins designs, to assess family influences uncorrelated with shared genetic effects.

# Criticism
The Twin Method has been subject to criticism from Statistical Genetics, Statistics and Psychology, with some argueing that conclusions reached via this method are ambiguous or meaningless. Core elements of these criticisms and their rejoinders are listed below:

## Criticisms of Statistical Methods
It has been argued that that the Statistical underpinnings of twin research are invalid. Such statistical critiques argue that heritability estimates used for most twin studies rest on restrictive assumptions which are usually not tested, and if they are, are often found to be violated by the data.
For example, Peter Schonemann has criticized methods for estimating heritability developed in the 1970s. He has also argued that the heritability estimate from a twin study may reflect factors other than shared genes. Using the statistical models published in Loehlin and Nichols (1976), the narrow heritabilitys of HR of responses to the question did you have your back rubbed  has been shown to work out to .92 heritable for males and .21 heritable for females, and the question Did you wear sunglasses after dark? is 130% heritable for males and 103% for females
In the days before the computer, statisticians were forced to use methods which were computationally tractable, at the cost of known limitations. Since the 1980s these approximate statistical methods have been discarded: Modern twin methods based on Structural Equation Modeling are not subject to the limitations and heritability estimates such as those noted above are impossible. Critically, the newer methods allow for explicit testing of the role of different pathways and incorporation and testing of complex effects.

## Sampling: Twins as representative members of the population
The results of twin studies cannot be automatically generalised beyond the population in which they have been derived. It is therefore important to understand the particular sample studied, and the nature of twins themselves.
Twins are not a random sample of the population, and they differ in their developmental environment. In this sense they are not representative
For example: Dizygotic (DZ) twin births are affected by many factors. Some women frequently produce more than one egg at each menstrual period and, therefore, are more likely to have twins. This tendency may run in the family either in the mother's or father's side of the family, and often runs through both. Women over the age of 35 are more likely to produce two eggs. Women who have three or more children are also likely to have dizygotic twins. Artificial induction of ovulation and in vitro fertilization-embryo replacement can also give rise to DZ and MZ twins 
Twins differ very little from non-twin siblings. Measured studies on the personality and intelligence of twins suggest that they have scores on these traits very similar to those of non-twins (for instance Deary et al. 2006).

## Observational nature of twin studies
For very obvious reasons, studies of twins are with almost no exceptions observational. This contrasts with, for instance, studies in plants or in animal breeding where the effects of experimentally randomized genotypes and environment combinations are measured. In human studies, we observe rather than control the exposure of individuals to different environments.
The observational study and it inherent confounding of causes is common in psychology. Twin studies are 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. This, 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 argued to be a considerable advance over the alternative: which is no knowledge of the different roles of genes and families whatsoever.

# Advanced Methodology

## Interactions
The effects of genes depend on the environment they are in. Possible complex genetic effects include G*E interactions, in which the effects of a gene allele differ across different environments. Simple examples would include situations where a gene multiples the effect of an environment (in this case the slope of response to an environment would differ between genotypes). A second effect is "GE correlation", in which certain allelles occur more frequently than others in certain environments. If a gene causes a person to enjoy reading, then children with this allele are likely to be raised in households with books in them (due to GE correlation: one or both of their parents has the allele and therefore both accumulates a book collection and passes on the book-reading allele). Such effects can be assessed 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 (Byrne etal 2006) as well as intelligence (Deary et al, 2006). 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 (Plomin et al., 1987).

## Continuous variable or Correlational studies
While concordance studies compare traits which are either present or absent in each twin, correlational studies compare the agreement in continuously varying traits across twins.

# Terminology
Pairwise concordance
Probandwise concordance

## Pairwise concordance
For a group of twins, pairwise concordance is defined as C/(C+D), where C is the number of concordant pairs and D is the number of discordant pairs.
For example, a group of 10 twins have been pre-selected to have one affected member (of the pair). During the course of the study four other previously non-affected members become affected, giving a pairwise concordance of 4/(4+6) or 4/10 or 40%.

## Probandwise concordance
For a group of twins in which at least one member of each pair is affected, probandwise concordance is a measure of the proportion of twins who have the illness who have an affected twin and can be calculated with the formula of 2C/(2C+D), in which C is the number of concordant pairs and D is the number of discordant pairs.
For example, consider a group of 10 twins that have been pre-selected to have one affected member. During the course of the study, four other previously non-affected members become affected, giving a probandwise concordance of 8/(8+6) or 8/14 or 57%.

# Further reading
- Textbook, software, and example scripts for twin research
- Jang, K.L., McCrae, R.R., Angleitner, A. Riemann, R. & Livesley, W.J. (1998). Heritability of facet-level traits in a cross-cultural twin sample: support for a hierarchical model of personality. Journal of Personality and Social Psychology 74:1556-1565.
- Plomin, DeFries, McClearn & McGuffin (2000). Behavioral Genetics: A Primer 4th edition. W.H.Freeman & Co Ltd.
- Nancy L. Segal (2005) Indivisible by Two: Lives of Extraordinary Twins. New York, Harvard University Press.

### Critical Accounts
- Peter Schonemann (1997). Models and muddles of heritability. Genetica, 99, 97-108: 
- Peter Schonemann and Roberta D. Schonemann (1994). Environmental versus genetic models for Osbornes personality data on identical and fraternal twins. CPC, 1994, 13 (2), 141-167 
- Kamin, L. J. (1974). The Science and Politics of I.Q. Potomac, MD: Lawrence Erlbaum Associates.
- Kempthorne O. (1997). Heritability: uses and abuses. Genetica, Volume 99, Numbers 2-3, 1997 , pp. 109-112(4)
- Joseph, J. (2003).  The Gene Illusion: Genetic Research in Psychiatry and Psychology Under the Microscope. PCCS Books.
- Christiane Capron, Adrian R. Vetta, Michel Duyme and Atam Vetta (1999). Misconceptions of biometrical IQists. Cahiers de Psychologie Cognitive/Current Psychology of Cognition 1999, 18 (2), 115-160
- Horwitz AV, Videon TM, Schmitz MF, Davis D. Rethinking twins and environments: possible social sources for assumed genetic influences in twin research. J Health Soc Behav. 2003 Jun;44(2):111-129.
And in reply to this article see:
- Freese J and Powell B Tilting at Twindmills: rethinking sociological responses to behavioral genetics. J Health Soc Behav. 2003 Jun;44(2):130-135.