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The full Mx specification for the general sex-limitation model is
provided in Appendix .
In theory, the same approach that was used to specify the simple
univariate ACE model (Chapter 6) in Mx could be used for
the general sex-limitation model. That is, genetic and environmental
parameters can be specified in calculation groups and the matrices can
be included in the data groups to specify the expected covariance
matrices. The female and male parameters are declared in separate groups
which simplifies the data groups. The only differences between the male
and female data groups are the details about the data and the number of
the group from which matrices are being imported. Note that for the
general sex limitation model, one extra matrix (`N`

) is declared in
the male group to account for the male-specific additive genetic effects.
While the specification of the same-sex groups is a straightforward
extension of the univariate model, the opposite-sex group requires some
special attention. First, the matrices for both male and female *variance
components* are read in to formulate the expected variance for females
(twin 1) and males (twin 2). Second, the expected covariance between male
and female twins can be specified by multiplying the male and female *path
coefficient matrices*. Although not a problem in
the univariate analysis, note that the male-female expected covariance
matrix is not necessarily symmetric.
Without boundary constraints on the parameters, this
specification may lead to *negative* parameter estimates for
one sex, especially when the DZ opposite-sex correlation is low, as
compared to DZ like-sex correlations. Such negative parameter
estimates result in a negative genetic (or common environmental)
covariation between the sexes. Although a negative covariation is
plausible, it seems quite unlikely that the *same* genes or common
environmental influences would have *opposite* effects across the
sexes. With the availability of linear and non-linear constraints in
Mx, we can parameterize the general sex-limitation model so that
the male-female covariance components are constrained to be non-negative
by using a boundary statement:
Bound .000 10 X 1 1 1 Z 1 1 1 W 1 1 1
Bound .000 10 X 2 1 1 Z 2 1 1 W 2 1 1 N 2 1 1

where `.000`

is the lower boundary, `10`

is the upper
boundary followed by matrix elements.
In this example, we estimate
sex-specific additive genetic effects (and fix the sex-specific
dominance effects to zero). The data are log-transformed indices of
body mass index (BMI) obtained from twins belonging to the Virginia
and American Association of Retired Persons twin registries. A
detailed description of these data will be provided in
section 9.2.4, in the discussion of the model-fitting
results.

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Jeff Lessem
2002-03-21