2 Mx Specification

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 or by taking the square root of the variance components (as is done in this example). 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.

The full Mx specification for the general sex-limitation model is provided in Appendix . 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 9.3, in the discussion of the model-fitting results.