4 Interpreting the Mx Output

We can run the example of Appendix  on a personal computer with Mx installed by typing:

Mx univar.mx univar.mxo

where univar.mx is the name of the script file, and univar.mxo is the name of the output file. We recommend mx and mxo as file extensions to make Mx input and output distinct from input and output of other programs. This example fits a model allowing for random environmental effects, additive genetic effects, and dominance genetic effects, to the young female like-sex MZ and DZ covariance matrices for log-transformed BMI. The Mx output includes:

1. Listing of the Mx script.
2. Parameter Specifications for each group, indicating the parameters to be estimated. Matrices are ordered alphabetically.

    MATRIX W
   This is a LOWER matrix of order    1 by    1
         1
     1   3
   
    MATRIX X
   This is a LOWER matrix of order    1 by    1
         1
     1   1
   
    MATRIX Y
   This is a LOWER matrix of order    1 by    1
    It has no free parameters specified
   
    MATRIX Z
   This is a LOWER matrix of order    1 by    1
         1
     1   2
   

   If no labels are specified in the input script, Mx will use consecutive numbers for the rows and columns of each matrix. The matrix element 1 identifies the first free parameter to be estimated ($a$), referring to the first matrix element that was declared free (Free) in the matrices declaration section. Similarly, 2 identifies parameter $e$, and 3 identifies parameter $d$. It is important to check these to confirm that parameters have been correctly specified and that the total number of estimated parameters corresponds to the number of free parameters in the model to be fitted.
3. Mx Parameter Estimates for each group, obtained at the solution. In the case of Appendix , for example, we obtain

    MATRIX W
   This is a LOWER matrix of order    1 by    1
             1
     1   .5441
   
    MATRIX X
   This is a LOWER matrix of order    1 by    1
             1
     1   .5621
   
    MATRIX Y
   This is a LOWER matrix of order    1 by    1
    It has no free parameters specified
   
    MATRIX Z
   This is a LOWER matrix of order    1 by    1
             1
     1   .4119
   

   In other words, our maximum-likelihood parameter estimates are $a=0.56$, $d=0.54$, and $e=0.41$ for these data.
4. If we include the option RSiduals in a group, the observed, and expected (`fitted') covariance matrix and residuals for that group are printed; Comparison of models should normally be based on likelihood-ratio chi-squared tests, since significance tests based on standard errors may be misleading for this example (Neale et al., 1989b).
5. The goodness-of-fit chi-squared is reported. In this example, $\chi^{2}_{3}=3.71, p=0.29$, indicating that the model gives a good fit to the data. A small p value (e.g. $<.05$) would indicate a lack of agreement between the data and the predictions of the model.
6. Finally, standardized parameter estimates can be calculated for each group. In this univariate case, we may standardize $a^2$ by computing $a^2/(a^2+c^2+e^2+d^2)$ to give the proportion of the total variance in BMI which is accounted for by additive genetic effects (40.4%). Similarly, we can calculate the proportion of variance accounted for by random environmental effects (21.7%), and by dominance genetic effects (37.9%). These analyses suggest that in young women age 30 and under, additive and non-additive genetic factors account for approximately 78% of the variance in BMI.

Discussion of these results continues in Section 6.2.6.