*! version 1.4 13mar2019

Title

acelong -- Multilevel mixed-effects ACE, AE and ADE variance decomposition models for "long" - one person per data row - formatted twin data (wrapper for gsem)

Syntax

acelong
depvar
1
2
3
[indepvars]
[if] [in]
[weight]
[, options]

aelong
depvar
1
2
3
[indepvars]
[if] [in]
[weight]
[, options]

adelong
depvar
1
2
3
[indepvars]
[if] [in]
[weight]
[, options]

Main
rsg estimate ACE, AE or ADE variance decomposition using the Rabe-Hesketh, Skrondal and Gjessing (2008)-model (the default)

mp estimate ACE, AE or ADE variance decomposition using the McArdle and Prescott (2005)-model

gw estimate ACE, AE or ADE variance decomposition using the Guo and Wang (2002)-model

dzc(#) specifies the genetic within twin pair-correlation for dizygotic twin pairs; applicable with rsg or mp

mzc(#) specifies the genetic within twin pair-correlation for monozygotic twin pairs; applicable with rsg or mp

iwc first estimate a model without parameter constraints to initialize the behavioral genetic variance decomposition; applicable with rsg or mp

tcr observed (Pearson) correlations of outcome for monozygotic (MZ) and dizygotic (DZ) twins; applicable with an uncensored linear model: family(gaussian) link(identity)

total use observed total variance as denominator for %-variance decomposition; applicable with an uncensored linear model: family(gaussian) link(identity); applicable without weights

Only one of options rsg, mp or gw is allowed.

For acelong and aelong dzc(#) has to be a real number > 0 and < 1 (the default is 0.5).

For adelong dzc(#) has to be a real number > 0.5 and < 1 (the default is 0.75).

mzc(#) has to be a real number > dzc(#) and <= 1 (the default is 1).

In addition, the options of gsem (see gsem_command) except noheader and notable are allowed.

The gsem option from() is not allowed if the option iwc is specified.

Currently, the following combinations of gsem options family() and link() are supported by acelong, aelong and adelong:

family(gaussian) link(identity): a linear behavioral genetic variance decomposition model (the default)

family(gaussian, [lcensored()] [rcensored()]) link(identity): a linear behavioral genetic variance decomposition model with left-censored and/or right-censored observations

family(bernoulli) link(probit): a (binary) probit behavioral genetic variance decomposition model

family(bernoulli) link(logit): a (binary) logit behavioral genetic variance decomposition model

family(ordinal) link(probit): an ordinal probit behavioral genetic variance decomposition model

family(ordinal) link(logit): an ordinal logit behavioral genetic variance decomposition model

Description

acelong estimates multilevel mixed-effects ACE variance decomposition models based on twin data formatted one twin per data row ("long" twin data format). An ACE variance
decomposition is a behavioral genetic analysis method which partitions the variance of an observed outcome (called phenotype) that varies within twin pairs into three latent components:

1) A component caused by additive genetic effects (A),

2) a component caused by environmental effects shared by both twins of a twin pair (C) and

3) a component caused by environmental effects which are unique to each twin (E).

aelong estimates multilevel mixed-effects AE variance decomposition models, i.e., a behavioral genetic variance decompositions without component 2) (C).

adelong estimates multilevel mixed-effects ADE variance decomposition models, i.e., a behavioral genetic variance decompositions with a component caused by dominant genetic effects (D).

CAUTION: Please verify that C is approximately 0 (using acelong) before estimating aelong or adelong!

The input data for acelong has to be a sample of monozygotic (MZ) and dizygotic (DZ) twin pairs formatted one twin (person) per data row ("long" twin data format).

depvar
is the outcome variable.

1
is a variable containing the zygosity information of the twins. It has to be coded 1 for MZ twins and 2 for DZ twins.

2
is a variable identifying the twin pairs. It has to be unique for each twin pair, i.e., it has to vary on the twin pair-level.

3
is a variable identifying the twins within each twin pair. It has to be unique to each twin, i.e., it has to vary on the twin-level.

[indepvars]
is an optional set of variables on which the mean of the outcome is conditioned or regressed on.

The ACE, ADE and AE variance decomposition methods use knowledge and assumptions about the structure of genetic correlations between twins to identify the latent variance components. A
pair of MZ twins is genetically identical, i.e., its genetic correlation is 1. First, ACE and AE variance decompositions assume that genetic effects are additive which implies that there is
no epistasis, i.e., there are no interactions between genetic influences on the phenotype analysed. In consequence, the rules of Mendelian inheritance lead to the conclusion that the genetic
correlation within a pair of DZ twins is 0.5. In contrast, ADE variance decompositions presume that there are interactions between genetic influences inducing non-additive - dominant - genetic
effects. Here, the assumed genetic correlation within a pair of DZ twins is 0.75 with an additive genetic correlation of 0.5 and a dominant genetic correlation of 0.25. Second, it is presumed
that there is no assortative (i.e., no non-random) mating of the twins parents based on the phenotype considered. Third, it is assumed that environments effect MZ and DZ twin pairs equally with
respect to the development of the phenotype (also called "equal environment(s) assumption" and abbreviated EEA). Moreover, the AE and ADE variance decomposition methods assume that there are
no environmental effects shared by both twins of a twin pair (no C). For further details on the behavioral genetic foundations of the ACE, AE and ADE variance decomposition methods see
Neale (2009).

Usually, ACE, AE and ADE variance decompositions are estimated using structural equation models (see Franić et al. 2012) based on twin data formatted one twin pair
per data row ("wide" twin data format). Outside the field of behavioral genetics using this "wide" data format is rather uncommon. In the last decade three different multilevel mixed-effects
models implementing ACE, AE and ADE variance decompositions based on twin data formatted one twin (person) per data row ("long" twin data format) have been developed (see
Guo and Wang 2002: gw, McArdle and Prescott 2005: mp, Rabe-Hesketh et al. 2008: rsg). rsg and mp
identify A and D, respectively, using random effects with equality constrains on their variances and fixed loadings mapping the assumed genetic correlation structures between twins. In Stata
these fixed loadings are implemented using weighting variables which are interacted with the respective random effects. Additionally, rsg and mp identify C using a random intercept
on the twin-pair level. In contrast, gw estimates a three-level random intercept model from which A, C and D, respectively, are derived using linear transformations. For all specifications
E is the residual variance of the model and all random effects are uncorrelated.

rsg uses 3 random effects for ACE, 2 random effects for AE and 4 random effects for ADE variance decompositions while mp uses 4 random effects for ADE, 3 random effects
for AE and 6 random effects for ADE variance decompositions. In contrast, gw uses 2 random effects for all specifications. Hence, gw is almost always the computationally most
efficient model. Moreover, gw does not place the constraint that C in ACE variance decompositions - or A and D in ADE variance decompositions - have to be > 0. In principle, this
is a disadvantage since it allows the estimation of negative, i.e., implausible variance components. But this deficiency can be used to check which behavioral genetic variance decomposition is
appropriate for the data analyzed: A negative estimate for C or an estimate of C close to zero in ACE decompositions indicates that one should try an ADE decomposition. If the estimates
for A and D in this ADE decomposition are positive this is the appropriate model. Otherwise an AE decomposition should be used instead. Furthermore, an estimate of A close to zero in ACE
decompositions indicates that a "CE variance decomposition" - a standard (two-level) random intercept model - should be used. In consequence, it is advisable to estimate an ACE and an ADE variance
decomposition using gw as a first step of an analysis in order to find the adequate behavioral genetic variance decomposition. rsg is used as the default for acelong, aelong
and adelong since it is the computationally most efficient model placing the constraint that A, C and D, respectively, have to be > 0. Moreover, calling gsem with rsg and
mp stores the estimates of A, C and D, respectively, in e(). Therefore, the estimated variance components are accessible with gsem postestimation (see gsem_postestimation)
after using rsg or mp.

acelong, aelong and adelong are wrappers for gsem facilitating the estimation of all three types of multilevel mixed-effects behavioral genetic variance decomposition
models in Stata. Furthermore, the commands calculate variance percentages of A, C, D and E, respectively, - %-variance decompositions - and enable the estimation of behavioral genetic variance
decompositions for censored continuous, binary and ordinal outcomes. acelong, aelong and adelong use gsem instead of meglm to estimate the multilevel mixed-effects
models because gsem supports a more flexible specification of random effects and related constraints. In principle, the Guo and Wang (2002)-model and the
McArdle and Prescott (2005)-model can also be estimated using meglm. For further details on acelong, aelong and adelong and the different
multilevel mixed-effects behavioral genetic variance decomposition models see Lang (2017).

Options

Main

rsg Estimate ACE, AE or ADE variance decomposition using the Rabe-Hesketh et al. (2008)-model (the default). rsg uses two random effects with variances
constraint to be equal to identify A. One of these two random effects varies on the twin pair-level and is weighted with 1 for MZ twins and with sqrt(0.5) for DZ twins. The other one varies
on the twin-level and is weighted with 0 for MZ twins and with sqrt(0.5) for DZ twins. In consequence, rsg decomposes A into a random effect varying between twin pairs and a random
effect varying within DZ twin pairs. For acelong rsg uses a random intercept on the twin pair-level to identify C. For adelong rsg uses two further random effects
with variances constrained to be equal to identify D. One of these additional random effects varies on the twin pair-level and is weighted with 1 for MZ twins and with sqrt(0.25) for DZ
twins. The other one varies on the twin-level and is weighted with 0 for MZ twins and with sqrt(0.75) for DZ twins. Hence, rsg also decomposes D into a random effect varying between
twin pairs and a random effect varying within DZ twin pairs.

mp Estimate ACE, AE or ADE variance decomposition using the McArdle and Prescott (2005)-model. mp uses three random effects with variances constraint to be
equal to identify A. All three random effects vary on the twin pair-level. The first of these three random effects is weighted with 1 for MZ twins and with sqrt(0.5) for DZ twins. The second
is weighted with sqrt(0.5) for the first twin in a DZ twin pair and with 0 for MZ twins and the second twin in a DZ twin pair. The third is weighted with sqrt(0.5) for the second twin in a DZ
twin pair and with 0 for MZ twins and the first twin in a DZ twin pair. For acelong mp uses a random intercept on the twin pair-level to identify C. For adelong mp
uses three further random effects with variances constraint to be equal to identify D. These three random effects also vary on the twin pair-level. The first of these three random effects is
weighted with 1 for MZ twins and with sqrt(0.25) for DZ twins. The second is weighted with sqrt(0.75) for the first twin in a DZ twin pair and with 0 for MZ twins and the second twin in a DZ
twin pair. The third is weighted with sqrt(0.75) for the second twin in a DZ twin pair and with 0 for MZ twins and the first twin in a DZ twin pair.

gw Estimate ACE, AE or ADE variance decomposition using the Guo and Wang (2002)-model. For gw a three level data structure is created before the
estimation. Specifically, a level varying between twin pairs for MZ twins and within twin pairs for DZ twins (called "mixture-level") is defined in addition to the twin pair-level and the
twin-level. Next, a multilevel mixed-effects model with a random intercept on the twin pair-level r1 and a random intercept on the "mixture-level" r2 is estimated. Afterwards, A, C and
D are calculated as linear transformations of r1 and r2. For acelong A is given by 2*r2 and C by r1 - r2. For aelong the variances of r1 and r2 are
constraint to be equal and in consequence, A is given by r1 + r2 or 2*r1 or 2*r2. For adelong A is given by 3*r1 - r2 and D by 2*(r2 - r1).

dzc(#) replaces the default genetic within twin pair-correlation for DZ twins with the number specified in the option. For acelong and aelong this default correlation
is 0.5 and for adelong it is 0.75. Specifically, for acelong and aelong dzc(#) replaces the additive genetic within twin pair-correlation for DZ twins with the
specified number. For adelong dzc(#) replaces the dominant genetic within twin pair-correlation for DZ twins with the specified number minus 0.5 while the additive genetic
correlation of 0.5 remains unchanged. dzc(#) can be used to asses the sensitivity of behavioral genetic variance decompositions with respect to "minor" deviations from the assumed genetic
within twin pair-correlations for DZ twins. E.g., such deviations can be due to selective sampling of twin pairs with respect to their genotype. Technically, dzc(#) can be a real
number > 0 and < 1 for acelong and aelong and a real number > 0.5 and < 1 for adelong. But substantially, dzc(#) should only be used for sensitivity analyses in a much
smaller range of values (e.g., 0.4 to 0.6 for acelong and aelong and 0.65 to 0.85 for adelong). A typical application for dzc(#) is to assess the effect of assortative
mating of parents on the behavioral genetic variance decomposition (Loehlin et al. (2009)). Here, dzc(#) is set to 0.5 + 0.5*h^2*r with h^2
the heritability (i.e., share of variance for A) estimated given the assumption of no assortative mating (i.e., given the default genetic within twin pair-correlation for DZ twins) and r the
correlation of parents on the phenotype analyzed. r needs to be observed in the sample analyzed, taken from secondary data sources or assumed. If the genetic within twin pair-correlation for
DZ twins differs substantially from the default values assumed the respective behavioral genetic variance decomposition is not appropriate for the data analyzed. A sensitivity analysis
based on such an inappropriate method will give no informative results. If the genetic within twin pair-correlation for DZ twins is expected to be much larger than 0.5 due to
non-additive genetic effects an ADE variance decomposition should be used. Since dzc(#) modifies the weighting variables interacted with the random effects for A and D it is only
applicable with options rsg or mp which use these weighting variables.

mzc(#) replaces the default genetic within twin pair-correlation for MZ twins of 1 with the number specified in the option. mzc(#) can be used like dzc(#) and has to be a
real number which is larger than the assumed genetic within twin pair-corrlation of DZ twins (> dzc(#)) as well as not larger than 1. An application are analyses in which sex-differences
within twin pairs are used as a proxy for zygosity. In such a case, it is know that opposite-sex twin pairs are dizygotic and under the assumption that same-sex and opposite-sex dizygotic
twin births are equally likely, the number of monozygotic twin pairs among same-sex twin pairs is given by the number of same-sex twin pairs (ss) minus the number of opposite-sex twins pairs
(os). This information can be just to adjust the assumed genetic within twin pair-correlation for MZ twins (Figlio et al. (2017)) which is than given by: (ss − os)/ss + dzc*(os/ss)
with dzc the assumed genetic within twin pair-correlation for DZ twins which is typically 0.5. Since mzc(#) modifies the weighting variables interacted with
the random effects for A and D it is only applicable with options rsg or mp which use these weighting variables.

iwc Informs acelong, aelong or adelong to first estimate a model without equality constraints on the variance parameters to initialize the behavioral genetic variance
decomposition. iwc is only applicable with options rsg or mp which always use equality constraints on the variances of A and D. iwc can not be combined with the gsem
option from().

tcr If tcr is specified acelong, aelong or adelong additionally calculate the observed (Pearson) correlations of the outcome for MZ and DZ twins. These
correlations can be used to derive A, C and E based on Falconer's formula (Falconer and McKay 1996) and linear transformations instead of the structural equation or
multilevel mixed-effect models typically used nowadays. Specifically, the correlation of the outcome for MZ twins (MZr) = A + C and the correlation of the outcome for DZ twins (DZr) = .5*A + C
if .5 is the assumed genetic correlation between DZ twins. In consequence, A = 2(MZr - DZr), C = MZr - A and E = 1 - MZr. Therefore, MZr and DZr can be used to assess if an ACE-model is suitable
for the data analysed: If MZr > 2*DZr it follows that C < 0. In this case an AE- or ADE-model should be used instead. Since MZr and DZr have to be observed tcr is only available for
uncensored linear models (family(gaussian) link(identity)). If tcr is specified MZr and DZr as well as the respective standard errors and confidence intervals are stored in
r(b), r(se) and r(ci).

total Instructs acelong, aelong or adelong to calculate the %-variance decomposition using the observed total variance as denominator. By default the sum of A, C, D and E,
respectively, is used as denominator for the %-variance decomposition. total is only allowed with uncensored linear models (family(gaussian) link(identity)) without weights since
this is the only type of model for which the total variance is observed, i.e., defined independent of the model specified. If no indepvars are specified the total variance equals the sum of A, C,
D and E, respectively. If indepvars are specified the total variance minus the sum of A, C, D and E, respectively, equals the variance explained by the indepvars. For the %-variance decomposition
this is the R2 of the model in %.

Stored results

acelong, aelong and adelong store the following in r():

Scalars

r(gmzc) the assumed genetic correlation for MZ twins

r(gdzc) the assumed genetic correlation for DZ twins

r(level) the confidence level for the confidence intervals of the variance decomposition

Matrices

r(b) the coefficient vector of the variance decomposition

r(se) the standard error vector of the variance decomposition

r(ci) the matrix containing the confidence intervals of the variance decomposition

In addition, all results gsem stores in e() after being called by acelong, aelong or adelong are available.

Remarks

For feedback and questions regarding acelong, aelong or adelong please contact:

Volker Lang, Bielefeld University: volker.lang@uni-bielefeld.de

If you use acelong, aelong or adelong for your research please cite it as follows:

Lang, V. 2017. ACELONG: Stata module to fit multilevel mixed-effects ACE, AE and ADE variance decomposition models. Statistical Software Components S458402, Boston College Department of
Economics. https://ideas.repec.org/c/boc/bocode/s458402.html

References

Falconer, D. S., T. F. C. McKay. 1996. Introduction to Quantitative Genetics. 4th Edition. Essex: Pearson Education. ISBN: 9780582243026

Figlio, D.N., J. Freese, K. Karbownik, and J. Roth. 2017. Socioeconomic status and genetic influences on cognitive development. Proceedings of the National Academy of Sciences of the United
States of America 114/51, pp 13441-13446. doi: http://dx.doi.org/10.1073/pnas.1708491114

Franić, S., C. V. Dolan, D. Borsboom, and D. I. Boomsma. 2012. Structural equation modeling in genetics. In: R. H. Hoyle. Handbook of Structural Equation Modeling. New York: Guilford Press, pp 617-635. ISBN: 9781606230770

Guo, G., and J. Wang. 2002. The mixed or multilevel model for behavior genetic analysis. Behavior Genetics 32/1, pp 37-49. doi: http://dx.doi.org/10.1023/A:1014455812027

Lang, V. 2017. ACELONG: Stata module to fit multilevel mixed-effects ACE, AE and ADE variance decomposition models. Statistical Software Components S458402, Boston College Department of
Economics. https://ideas.repec.org/c/boc/bocode/s458402.html

Loehlin, J.C., Harden, K.P., and Turkheimer, E. 2009. The effect of assumptions about parental assortative mating and genotype–income correlation on estimates of genotype–environment interaction in the National Merit
Twin Study. Behavior Genetics 39/2, pp 165-169. doi: http://dx.doi.org/10.1007/s10519-008-9253-9

McArdle, J. J. and C. A. Prescott. 2005. Mixed-effects variance components models for biometric family analyses. Behavior Genetics 35/5, pp 631–652. doi: http://dx.doi.org/10.1007/s10519-005-2868-1

Neale, M. C. 2009. Biometrical models in behavioral genetics. In: Y.-K. Kim. Handbook of Behavior Genetics. New York: Springer, pp 15-33. doi: http://dx.doi.org/10.1007/978-0-387-76727-7_2

Rabe-Hesketh, S., A. Skrondal, and H. K. Gjessing. 2008. Biometrical modeling of twin and family data using standard mixed model software. Biometrics 64/1, pp 280–288. doi: http://dx.doi.org/10.1111/j.1541-0420.2007.00803.x