** Next:** Mx Output from Phenotypic
** Up:** 2 Phenotypic Factor Analysis
** Previous:** 3 Fitting a Phenotypic
** Index**

Single factor phenotypic model: 4 arithmetic computation variables
Data NGroups=1 NInput_vars=4 NObservations=42
CMatrix
259.664
209.325 259.939
209.532 220.755 245.235
221.610 221.491 221.317 249.298
Labels Time1 Time2 Time3 Time4
Begin Matrices;
B Full 1 4 Free
P Symm 1 1
E Diag 4 4 Free
End Matrices;
Value 1 P 1 1
Start 9 All
Covariances B*P*B'+E;
Option RSiduals
End

The parameters in the group type statement indicate that we have
only `NGroup=1`

group (consisting of `NObservations=42`

subjects) and there are `NInput_vars=4`

input variables. The
loadings of the four variables on the single common factor are estimated
in matrix **B** and their specific variances are estimated on the
diagonal of matrix **E**. In this phenotypic factor model, we have
sufficient information to estimate factor loadings and specific variances
for the four variables, but we cannot simultaneously estimate the variance
of the common factor because the model would then be underidentified. We
therefore fix the variance of the latent factor to an arbitrary non-zero
constant, which we choose to be unity in order to keep the factor loadings
and specific variances in the original scale of measurement (+Value 1
P 1 1+).
The Mx output (after editing) from this common factor model is shown
below. The `PARAMETER SPECIFICATIONS`

section illustrates the
assignment of parameter numbers to matrices declared `Free`

in the
matrices section. Consecutive parameter numbers are given to free
elements in matrices in the order in which they appear. It is always
advisable to check the parameter specifications for the correct assignment
of free and constrained parameters. The output depicts the single common
factor structure of the model: there are free factor loadings for each of
the four variables on the common factor, and specific variance parameters
for each of the observed variables. Thus, the model has a total of 8
parameters to explain the free statistics.
The results - from the `MX PARAMETER ESTIMATES`

section of the Mx
output - are summarized in Table 10.2.3. The chi-squared
goodness-of-fit value of 1.46 for 2 degrees of freedom suggests that this
single factor model adequately explains the observed covariances ( =
.483). This also may be seen by comparing the elements of the fitted
covariance matrix and the observed covariance matrix, which are seen to be
very similar. The fitted covariance matrix is printed by Mx when the
`RSiduals`

option is added. The fitted covariance matrix is
calculated by Mx using expression 10.2 with the final estimated
parameter values.

** Next:** Mx Output from Phenotypic
** Up:** 2 Phenotypic Factor Analysis
** Previous:** 3 Fitting a Phenotypic
** Index**
Jeff Lessem
2002-03-21