TARGET_OPTIONS Subcommand (GENLINMIXED command)

The TARGET_OPTIONS subcommand specifies the reference category, distribution, and link function for the target.

• This subcommand is optional. If the TARGET_OPTIONS subcommand is not specified, then GENLINMIXED assigns a default distribution and link function based on the measurement level of the target. A continuous target has NORMAL distribution and IDENTITY link. A categorical target has MULTINOMIAL distribution and LOGIT link.

REFERENCE. For categorical targets, this is the target value to use as the reference category for parameter estimation. No model parameters are assigned to the reference category. Specify a single value. Put the value inside a pair of quotes if it is formatted (such as date or time) or if the target is of string storage type. The REFERENCE value must be found in the dataset. If REFERENCE is not specified, the last category in ascending order is used as the reference.

• If the target has ordinal measurement level, the REFERENCE keyword is ignored.

  DISTRIBUTION Keyword

  The DISTRIBUTION keyword specifies the probability distribution of the target.

  • The default probability distribution depends on the measurement level of the target. If the target is continuous, the default distribution is NORMAL. If the target is categorical, then the default is MULTINOMIAL. If an events/trials specification is used, then the default distribution is BINOMIAL.
  • Caution must be exercised when the LINK but not the DISTRIBUTION keyword is used. The discussion of the LINK keyword below gives details about proper and improper combinations of DISTRIBUTION and LINK settings.

  BINOMIAL. Binomial probability distribution. If the target is specified as a single field, then it can be numeric or string and it can have only two distinct valid data values.

  If the events and trials options are specified, then the procedure automatically computes the ratio of the events field over the trials field or number. The events field—and the trials field if specified—must be numeric. Data values for the events field must be integers greater than or equal to zero. Data values for the trials field must be integers greater than zero. For each record, the trials value must be greater than or equal to the events value. If an events value is noninteger, less than zero, or missing, then the corresponding record is not used in the analysis. If a trials value is noninteger, less than or equal to zero, less than the events value, or missing, then the corresponding record is not used in the analysis.

  If the trials option specifies a number, then it must be a positive integer, and it must be greater than or equal to the events value for each record. Records with invalid values are not used in the analysis.

  This is the default probability distribution if the target is specified using events/trials format.

  GAMMA. Gamma probability distribution. The target must be numeric, with data values greater than zero. If a data value is less than or equal to zero, or missing, then the corresponding record is not used in the analysis.

  INVERSE_GAUSSIAN. Inverse Gaussian probability distribution. The target must be numeric, with data values greater than zero. If a data value is less than or equal to zero, or missing, then the corresponding record is not used in the analysis.

  MULTINOMIAL. Multinomial probability distribution. The target can be numeric or string, and it must have at least two distinct, valid data values. This is the default probability distribution if the target is categorical. Note that the form of the model will depend on the measurement level of the target.

  • A nominal target will result in a nominal multinomial model in which a separate set of model parameters are estimated for each category of the target (except the reference category). The parameter estimates for a given predictor show the relationship between that predictor and the likelihood of each category of the target, relative to the reference category.
  • An ordinal target will result in an ordinal multinomial model in which the traditional intercept term is replaced with a set of threshold parameters that relate to the cumulative probability of the target categories.

  NEGATIVE_BINOMIAL. Negative binomial probability distribution. The target must be numeric, with data values that are integers greater than or equal to zero. If a data value is noninteger, less than zero, or missing, then the corresponding record is not used in the analysis.

  NORMAL. Normal probability distribution. The target must be numeric. This is the default probability distribution if the target is continuous.

  POISSON. Poisson probability distribution. The target must be numeric, with data values that are integers greater than or equal to zero. If a data value is noninteger, less than zero, or missing, then the corresponding record is not used in the analysis.

  LINK Keyword

  The LINK keyword specifies the link function. The following link functions are available.

  IDENTITY. Identity link function. f(x)=x. This link function is valid with any distribution except the multinomial.

  CAUCHIT. Cauchit link function. f(x) = tan(π (x − 0.5)). This is only valid with ordinal multinomial models.

  CLOGLOG. Complementary log-log link function. f(x)=ln(−ln(1−x)). This valid with binomial and ordinal multinomial models.

  LOG. Log link function. f(x)=ln(x). This link function is valid with any distribution except the multinomial.

  LOGC. Log complement link function. f(x)=ln(1−x). This is only valid with the binomial distribution.

  LOGIT. Logit link function. f(x)=ln(x / (1−x)). This is valid with the binomial and multinomial distributions.

  NLOGLOG. Negative log-log link function. f(x)=−ln(−ln(x)). This valid with binomial and ordinal multinomial models.

  POWER. Power link function. f(x)=x ^α, if α≠0. f(x)=ln(x), if α=0. α is a required number specified on the LINKPARAMETER keyword and must be a real number. If |α| < 2.2e-16, α is treated as 0. This link function is valid with any distribution except the multinomial.

  PROBIT. Probit link function. f(x)=Φ⁻¹(x), where Φ⁻¹ is the inverse standard normal cumulative distribution function. This valid with binomial and ordinal multinomial models.

• The default setting for LINK depends on the DISTRIBUTION setting, whether DISTRIBUTION is set explicitly or is the default, as shown in the following table.

  Table 1. Default link function for each distribution

  DISTRIBUTION Setting	Default LINK Setting
  NORMAL	IDENTITY
  BINOMIAL	LOGIT
  GAMMA	POWER(−1)
  INVERSE_GAUSSIAN	POWER(−2)
  MULTINOMIAL	LOGIT
  NEGATIVE_BINOMIAL	LOG
  POISSON	LOG

• The procedure will fit a model if a permissible combination of LINK and DISTRIBUTION specifications is given. The table below indicates the permissible LINK and DISTRIBUTION combinations. Specifying an improper combination will yield an error message.
• Note that the default setting for DISTRIBUTION is irrespective of the LINK specification, and that not all LINK specifications are valid for the default DISTRIBUTION. Thus, if LINK = CLOGLOG is specified for a continuous target but DISTRIBUTION is not, then the default DISTRIBUTION = NORMAL yields an improper combination of DISTRIBUTION and LINK settings.

LINKPARAMETER Keyword

The LINKPARAMETER keyword specifies the value of α for the POWER link.

• Specify a number. There is no default.