Generalized Linear Models 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, binomial, or multinomial distribution. The deviance and Pearson chi-square options estimate the scale parameter from the value of those statistics. Alternatively, you can specify a fixed value for the scale parameter.
  • Initial values. The procedure will automatically compute initial values for parameters. Alternatively, you can specify initial values for the parameter estimates.
  • Covariance matrix. The model-based estimator is the negative of the generalized inverse of the Hessian matrix. The robust (also called the Huber/White/sandwich) estimator is a "corrected" model-based estimator that provides a consistent estimate of the covariance, even when the specification of the variance and link functions is incorrect.

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 Linear Models

This feature requires the Advanced Statistics option.

  1. From the menus choose:

    Analyze > Generalized Linear Models > Generalized Linear Models...

  2. In the Generalized Linear Models dialog box, click Estimation.