Mx Output from Reduced Common Factor Model (No C)

MX PARAMETER ESTIMATES
MATRIX F
             1         2         3         4
   1    59.502      .000      .000      .000
   2      .000    39.433      .000      .000
   3      .000      .000    30.843      .000
   4      .000      .000      .000    36.057
MATRIX X
             1
   1    14.756
   2    14.274
   3    14.081
   4    14.405
MATRIX Y
             1
   1      .000
   2      .000
   3      .000
   4      .000
MATRIX Z
             1
   1     3.559
   2     6.331
   3     7.047
   4     5.845

 Chi-squared fit of model >>>>>>>    51.08
 Degrees of freedom >>>>>>>>>>>>>       60
 Probability >>>>>>>>>>>>>>>>>>>>     .787
 Akaike's Information Criterion >

The estimates for the genetic and non-shared environment parameters differ somewhat between the reduced model and those estimated in the full common factor model. Such differences often appear when fitting nested models, and are not necessarily indicative of misspecification (of course, one would not expect the estimates to change in the case where parameters to be omitted are estimated as 0.0 in the full model). The fitting functions used in Mx (see Chapter ) are designed to produce parameter estimates that yield the closest match between the observed and estimated covariance matrices. Omission of selected parameters, for example, the $C$ loadings in the present model, generates a different model $\Sigma$ and thus may be expected to yield slightly different parameter estimates in order to best approximate the observed matrix.