Next: 4 Application to Body
Up: 3 Restricted Models for
Previous: 1 Common Effects Sexlimitation
Index
2 Scalar Effects Sexlimitation Model
The scalar sexlimitation model is a submodel of both the general
model and the common effects model. In the scalar model, not only are
the sexspecific effects removed, but the variance components for
females are all constrained to be equal to a scalar multiple
() of the male variance components, such that =
, =
, and =
. As a result, the standardized variance components
(e.g., heritability estimates) are equal across sexes, even though the
unstandardized components differ.
Figure 9.2 shows a path diagram for DZ oppositesex under the
scalar sexlimitation model, and Appendix provides
the Mx specification. Unlike the model in Figure , the
scalar model does not include separate parameters for genetic and
environmental effects on males and females  instead, these effects
are equated across the sexes. Because of this equality, negative
estimates of malefemale genetic covariance cannot result. To
introduce a scaling factor for the male (or female) variance components, we can
pre and postmultiply the expected variances by a scalar.
Figure 9.2:
The scalar genotype sex interaction model
for twin data. Path diagram is shown for DZ oppositesex twin pairs.
The = 0.5 and = 0.25.

The full scalar sexlimitation model may be compared to the
full common effects model using a difference test with 2
degrees of freedom. Similarly, the scalar sexlimitation model may be
compared to the model with no sex differences (that is, one which
fixes k to 1.0) using a difference test with a single
degree of freedom.
The restricted sexlimitation models described in this section are not
an exhaustive list of the submodels of the general sexlimitation
model. Within either of these restricted models (as within the
general model), one can test hypotheses regarding the significance of
genetic or environmental effects. Also, within the common effects
sexlimitation model, one may test whether specific components
of variance are equal across the sexes (e.g., may be equated
to , or to ). Again, submodels may be compared
to more saturated ones through difference tests, or to
models with the same number of parameters with Akaike's Information
Criteria.
Next: 4 Application to Body
Up: 3 Restricted Models for
Previous: 1 Common Effects Sexlimitation
Index
Jeff Lessem
20020321