Generalized Estimating Equations Estimation

Parameter Estimation. The controls in this group allow you to specify estimation methods and to provide initial values for the parameter estimates.

• Method. You can select a parameter estimation method; choose between Newton-Raphson, Fisher scoring, or a hybrid method in which Fisher scoring iterations are performed before switching to the Newton-Raphson method. If convergence is achieved during the Fisher scoring phase of the hybrid method before the maximum number of Fisher iterations is reached, the algorithm continues with the Newton-Raphson method.
• Scale Parameter Method. You can select the scale parameter estimation method.

  Maximum-likelihood jointly estimates the scale parameter with the model effects; note that this option is not valid if the response has a negative binomial, Poisson, or binomial distribution. Since the concept of likelihood does not enter into generalized estimating equations, this specification applies only to the initial generalized linear model; this scale parameter estimate is then passed to the generalized estimating equations, which update the scale parameter by the Pearson chi-square divided by its degrees of freedom.

  The deviance and Pearson chi-square options estimate the scale parameter from the value of those statistics in the initial generalized linear model; this scale parameter estimate is then passed to the generalized estimating equations, which treat it as fixed.

  Alternatively, specify a fixed value for the scale parameter. It will be treated as fixed in estimating the initial generalized linear model and the generalized estimating equations.

• Initial values. The procedure will automatically compute initial values for parameters. Alternatively, you can specify initial values for the parameter estimates.

The iterations and convergence criteria specified on this tab are applicable only to the initial generalized linear model. For estimation criteria used in fitting the generalized estimating equations, see the Repeated tab.

Iterations. The following options are available:

• Maximum iterations. The maximum number of iterations the algorithm will execute. Specify a non-negative integer.
• Maximum step-halving. At each iteration, the step size is reduced by a factor of 0.5 until the log-likelihood increases or maximum step-halving is reached. Specify a positive integer.
• Check for separation of data points. When selected, the algorithm performs tests to ensure that the parameter estimates have unique values. Separation occurs when the procedure can produce a model that correctly classifies every case. This option is available for multinomial responses and binomial responses with binary format.

Convergence Criteria. The following options are available

• Parameter convergence. When selected, the algorithm stops after an iteration in which the absolute or relative change in the parameter estimates is less than the value specified, which must be positive.
• Log-likelihood convergence. When selected, the algorithm stops after an iteration in which the absolute or relative change in the log-likelihood function is less than the value specified, which must be positive.
• Hessian convergence. For the Absolute specification, convergence is assumed if a statistic based on the Hessian convergence is less than the positive value specified. For the Relative specification, convergence is assumed if the statistic is less than the product of the positive value specified and the absolute value of the log-likelihood.

Singularity tolerance. Singular (or non-invertible) matrices have linearly dependent columns, which can cause serious problems for the estimation algorithm. Even near-singular matrices can lead to poor results, so the procedure will treat a matrix whose determinant is less than the tolerance as singular. Specify a positive value.

How To Specify Estimation Settings for Generalized Estimating Equations

This feature requires SPSS® Statistics Standard Edition or the Advanced Statistics Option.

1. From the menus choose:

   Analyze > Generalized Linear Models > Generalized Estimating Equations...

2. In the Generalized Estimating Equations dialog box, click Estimation.