### Initial Estimates

Each optimization technique requires a set of initial values for the parameters. To avoid local optima, the initial values should be as close as possible to the globally optimal solution. You can check for local optima by running the analysis with several different sets of initial values; the RANDOM= option in the PROC CALIS statement is useful in this regard.

Except for the case of exploratory FACTOR model, you can specify initial estimates manually for all different types of models. If you do not specify some of the initial estimates and the RANDOM= option is not used, PROC CALIS will use a combination of good strategic methods to compute initial estimates for your model.

These initial estimation methods are used in PROC CALIS:

• two-stage least squares estimation

• instrumental variable method (Hägglund 1982; Jennrich 1987)

• approximate factor analysis method

• ordinary least squares estimation

• estimation method of McDonald (McDonald and Hartmann, 1992)

• observed moments of manifest exogenous variables

The choice of initial estimation methods is dependent on the data and on the model. In general, it is difficult to tell in advance which initial estimation methods will be used for a given analysis. However, PROC CALIS displays the methods used to obtain initial estimates in the output. Notice that none of these initial estimation methods can be applied to the COSAN model because of the general formulation of the COSAN model. If you do not provide initial parameter estimates for the COSAN model, the default values or random values are used (see the START= and the RANDOM= options).

Poor initial values can cause convergence problems, especially with maximum likelihood estimation. Sufficiently large positive initial values for variance estimates (as compared with the covariance estimates) might help prevent a nonnegative definite initial predicted covariance model matrix from happening. If maximum likelihood estimation fails to converge, it might help to use METHOD=LSML, which uses the final estimates from an unweighted least squares analysis as initial estimates for maximum likelihood. Or you can fit a slightly different but better-behaved model and produce an OUTMODEL= data set, which can then be modified in accordance with the original model and used as an INMODEL= data set to provide initial values for another analysis.

If you are analyzing a covariance or scalar product matrix, be sure to take into account the scales of the variables. The default initial values might be inappropriate when some variables have extremely large or small variances.