How are parameters actually estimated?
Estimation is usually done with simple iterative numerical methods. Basically, one wishes to find the set of parameter values that optimize some mathematical criterion–usually the criterion of maximum likelihood. The oldest forms of LCA used complicated estimation methods based on matrix manipulation and simultaneous linear equations. A breakthrough came when Goodman (1974) showed how simple iterative proportional fitting could be used to find ML parameter values; this method is type of EM algorithm. Haberman, working within a loglinear modeling framework, successfully used Newton-Raphson estimation for estimation. More generally, estimation can be approached as a problem of multivariate nonlinear optimization. The simplex method, gradient methods, the Davidon-Fletcher-Powell method, and many other algorithms (see Press et al., 1989), as implemented, for example, by subroutines in the IMSL or NAG subroutine libraries, can be used for parameter estimation. The advantage of approaching
