A brief introduction to the mathematical theory involved in model fitting is provided. The properties of maximum-likelihood estimates are described, and their advantages in fitting structural models are given. Identification of models is considered. Standard errors of parameter estimates are compared with the use of likelihood-ratio (L-R) statistics. For structural modeling, L-R tests are invariant to parameter transformation and give robust tests of significance. Some guidelines for fitting models to data collected from twins are given, with discussion of the relative merits of parsimony and data description.