`X, W`

and `Z`

represent the additive and dominance genetic and
specific environmental loadings on the latent phenotype. The
factor loadings on the observed variables are estimated in matrix `S`

. The residual variances are decomposed
in genetic and environmental diagonal matrices `G`

and `F`

.
The data groups are identical to those of the independent pathway
model.
One final feature of the model is that since ATOPY is a latent
variable whose scale (and hence variance) is not indexed to any
measured variable, we must fix its residual variance term (EATOPY) to
unity to make the model identified. This
inevitably means that the estimates for the loadings contributing
to ATOPY are arbitrary and hence so are the paths leading from
ATOPY to the symptoms. It is thus particularly important to
standardize the solution so that the total variance explained for each
symptom is unity. The fixing of the loading on
EATOPY clearly has implications for the calculation of degrees of
freedom, as we shall see below.
The condensed output for this model is presented below, showing the
completely standardized estimates which give unit variance for each
variable.
Asthma | .671 | .531 | .517 | |||

Hayfever | .814 | .456 | .358 | |||

Dust Allergy | .941 | -.059 | .334 | |||

Eczema | .301 | .735 | .608 | |||

Atopy | .686 | .397 | .610 | |||

, 46 df, p=.238 |

Note that here

`NInput_vars=8`

so there are 56 (
) unique correlations. From
the above table it appears that 15 parameters have been estimated, but
in fact EATOPY was fixed and the four specifics are obtained by
difference, so there are only 10 free parameters in the model, hence
46 degrees of freedom.
The latent variable ATOPY has a broad heritability of over 0.6
(
) of which approximately a quarter is due to
dominance, and this factor has an important phenotypic influence
on all symptoms, particularly dust allergy (0.941) and
hayfever (0.814). There are still sizeable specific genetic
influences not accounted for by the ATOPY factor on all symptoms
except dust allergy (). However, despite the appeal of this
model, it does not fit as well as the independent pathway model and
the imposition of constraints that covariation between symptoms arises
purely from their phenotypic relation with the latent variable ATOPY
has worsened fit by for 6 degrees of freedom, which is
significant at the 5% level.
We conclude that while there are common environmental, additive, and
nonadditive genetic factors which influence all four symptoms of
atopy, these have