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 The CALIS Procedure

## 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.

• RAM and LINEQS: There are several default estimation methods available in PROC CALIS for initial values of parameters in a linear structural equation model specified by a RAM or LINEQS model statement, depending on the form of the specified model.

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two-stage least-squares estimation
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instrumental variable method (Hgglund 1982; Jennrich 1987)
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approximative factor analysis method
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ordinary least-squares estimation
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estimation method of McDonald (McDonald and Hartmann 1992)
• FACTOR: For default (exploratory) factor analysis, PROC CALIS computes initial estimates for factor loadings and unique variances by an algebraic method of approximate factor analysis. If you use a MATRIX statement together with a FACTOR model specification, initial values are computed by McDonald's (McDonald and Hartmann 1992) method if possible. McDonald's method of computing initial values works better if you scale the factors by setting the factor variances to 1 rather than setting the loadings of the reference variables equal to 1. If none of the two methods seems to be appropriate, the initial values are set by the START= option.
• COSAN: For the more general COSAN model, there is no default estimation method for the initial values. In this case, the START= or RANDOM= option can be used to set otherwise unassigned initial values.

Poor initial values can cause convergence problems, especially with maximum likelihood estimation. You should not specify a constant initial value for all parameters since this would produce a singular predicted model matrix in the first iteration. Sufficiently large positive diagonal elements in the central matrices of each model matrix term provide a nonnegative definite initial predicted model matrix. If maximum likelihood estimation fails to converge, it may 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 OUTRAM= data set, which can then be modified in accordance with the original model and used as an INRAM= 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 may be inappropriate when some variables have extremely large or small variances.

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