# Sabre

Model constants

### Sabre manual

There are a number of constants which SABRE uses when fitting models. These constants all have default settings, but can be changed within a SABRE run.

For the numerical fitting of models, SABRE needs to know

• the initial estimate of the scale parameter(s) (default = 1.0, or 0.5 for Poisson models)
• the initial estimate of the intrinsic scale parameter(s) in linear models (default = 1.0)
• the initial estimate of the correlation parameter(s) in multivariate models (default = 0.0)
• the number of mass points used in the Gaussian quadrature (default = 12)
• the convergence criterion (default = 1e-4)
• the orthogonality criterion (default = 0.01)
• whether end-points are needed, and, if so, values for their initial estimates (default = no end-points used)
• the tolerance for use in the matrix inversion routine (default = 1e-6)

The initial estimate of the scale parameter(s) is specified by

SCALE real

The initial estimate of the intrinsic scale parameter(s) in linear models is specified by

SIGMA real

where the argument must be a positive real number.

The initial estimate of the correlation parameter(s) is specified by

RHO real

where the argument must be a real number between -1 and +1. where the argument must be a positive real number.

The number of quadrature points is set using

MASS integer

where the argument must be 1,2,4,6,8,10,12,14,16,20,24,32,48, or 64. This restriction to even numbers stops the scale parameter becoming large for models in which no end-points are fitted. For binary data, the value of one is a special case which, when used with end-points, specifies the conventional mover-stayer model, and without end-points specifies the standard logistic model.

The convergence criterion for both the standard and the mixture models is set using

CONVERGENCE real

where, clearly, the argument should be a fairly small positive real number.

Note that convergence is based on the likelihood rather than the deviance.

An orthogonality criterion is calculated at each iteration and is used to establish whether the Hessian matrix can be used to give a good search direction for an improved set of parameter estimates. A small value indicates that the search direction is almost orthogonal to the slope at the current location. If the orthogonality criterion is less than a tolerance level alpha, the diagonal of the estimated Hessian is multiplied by two, and the orthogonality criterion re-estimated. The process continues until the orthogonality criterion is above the tolerance level. To reset the tolerance, type

ALPHA real

where the argument must be a positive real number.

To determine if end-points are to be included in subsequent fitting, type

ENDPOINTS arg

where the argument is BOTH for both end-points, LEFT for just the left end-point, RIGHT for just the right end-point and NONE if neither are required. By default, no end-points are used.

The user can specify initial estimates by typing

ENDPOINTS arg est0 est1

where est0 and est1 refer to the end-points associated with probabilities zero and one respectively.

Note that Poisson models contain only the left end-point and so the argument must be either LEFT or NONE.

Note that end-points cannnot be used in linear or ordered response models, or in any multivariate models.

The parameter set by the command TOLERANCE is used to detect extrinsic aliasing and whether the Hessian is non-positive semi-definite. The syntax is

TOLERANCE real

where the argument must be a positive real number.

At any time, the current settings of constants used in the numerical fitting can be found using

DISPLAY SETTINGS

and can be reset to their default values by typing

DEFAULT