MODEL Procedure

ERRORMODEL Statement

  • ERRORMODEL equation-name tilde distribution < CDF=CDF(options)> ;

The ERRORMODEL statement is the mechanism for specifying the distribution of the residuals. You must specify the dependent/endogenous variables or general form model name, a tilde (~), and then a distribution with its parameters. You can specify the following options:

Options to Specify the Distribution

BERNOULLI( probability )

specifies the Bernoulli distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

BETA( shape, shape <,location, location> )

specifies the beta distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

BINOMIAL( probability, counts )

specifies the binomial distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

CAUCHY( <location, scale> )

specifies the Cauchy distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

CHISQUARED ( df <, nc> )

specifies the chi squared distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

CONMAXPOI( mean, dispersion )

specifies the Conway-Maxwell-Poisson distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

EXPONENTIAL( <scale> )

specifies the exponential distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

F( ndf, ddf <, nc> )

specifies the F distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

GAMMA(shape <, scale> )

specifies the gamma distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

GENERAL(likelihood <, parm1, parm2, ellipsis parmn > )

specifies the negative of a general log-likelihood function that you construct by using SAS programming statements. This option is supported only for estimation. The procedure minimizes the negative log-likelihood function specified. The parameters sans-serif-italic parm 1 comma sans-serif-italic parm 2 comma ellipsis sans-serif-italic parmn are optional for this distribution and are used for documentation purposes only.

GENPOISSON( shape, shape )

specifies the generalized Poisson distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

GEOMETRIC( probability )

specifies the geometric distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

HYPERGEOMETRIC( population size, number of items, sample size <, odds ratio> )

specifies the hypergeometric distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

LAPLACE( <location, scale> )

specifies the Laplace distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

LOGISTIC( <location, scale> )

specifies the logistic distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

LOGNORMAL( <scale, shape> )

specifies the lognormal distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

NEGBINOMIAL( probability, counts )

specifies the negative binomial distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

NORMAL( v 1 v 2 ellipsis v Subscript n )

specifies a multivariate normal (Gaussian) distribution with mean 0 and variances v 1 through v Subscript n.

NORMALMIX( number, proportions ellipsis, means ellipsis, standard deviations ellipsis )

specifies the normal mixture distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

PARETO( shape <, scale> )

specifies the Pareto distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

POISSON( mean )

specifies the Poisson distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

T( v 1 v 2 ellipsis v Subscript n, df )

specifies a multivariate t distribution with noncentrality 0, variance v 1 through v Subscript n, and common degrees of freedom d f.

TWEEDIE( power <, mean , dispersion> )

specifies the Tweedie distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

UNIFORM( <left, right> )

specifies the uniform distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

WALD | IGAUSS( shape <, mean> )

specifies the Wald (inverse Gaussian) distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

WEIBULL( shape <, scale> )

specifies the Weibull distribution. This option is supported only for simulation. The arguments correspond to the arguments of the SAS CDF function, which computes the cumulative distribution function (ignoring the random variable argument).

Options to Specify the CDF for Simulation

CDF=( CDF(options) )

specifies the univariate distribution that is used for simulation so that the estimation can be done for one set of distributional assumptions and the simulation for another. The CDF can be any of the distributions from the previous section with the exception of the general likelihood. In addition, you can specify the empirical distribution of the residuals.

EMPIRICAL= ( <CONTINUOUS | DISCRETE | TAILS=(options)> )

uses the sorted residual data to create an empirical CDF.

CONTINUOUS

specifies that a continuous function that interpolates the residual data should be used. CONTINUOUS is the default value.

DISCRETE

specifies a discontinuous function that can take only discrete values in the residual data.

TAILS=( tail-options )

specifies how to handle the tails in computing the inverse CDF from an empirical distribution. You can specify the following tail-options:

NORMAL

specifies the normal distribution to extrapolate the tails.

PERCENT=p

specifies the percentage of the observations to use in constructing each tail. By default, PERCENT=10. A normal distribution or a t distribution is used to extrapolate the tails to infinity. The variance of the tail distribution is obtained from the data so that the empirical CDF is continuous.

T( df )

specifies the t distribution to extrapolate the tails.

Last updated: June 19, 2025