ERRORMODEL Statement

The MODEL Procedure

ERRORMODEL Statement

ERRORMODEL equation-name ${{\scriptsize{\sim}}}$ 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 ( $\sim$ ), and then a distribution with its parameters. The following options are used in the ERRORMODEL statement:

Options to Specify the Distribution

CAUCHY( <location, scale> ): specifies the Cauchy distribution. This option is only supported for simulation. The arguments correspond to the arguments of the SAS CDF function (ignoring the random variable argument).
CHISQUARED ( df < , nc> ): specifies the $\chi^2$ distribution. This option is only supported for simulation. The arguments correspond to the arguments of the SAS CDF function (ignoring the random variable argument).
GENERAL( Likelihood <, parm1, parm2, ... parmn> ): specifies a general log-likelihood function that you construct using SAS programming statements. parm1 , parm2, ... parmn are optional parameters for this distribution and are used for documentation purposes only.
F( ndf, ddf < , nc> ): specifies the F distribution. This option is only supported for simulation. The arguments correspond to the arguments of the SAS CDF function (ignoring the random variable argument).
NORMAL( v₁ v₂ ... v_n ): specifies a multivariate normal (Gaussian) distribution with mean 0 and variances v₁ through v_n.
POISSON( mean ): specifies the Poisson distribution. This option is only supported for simulation. The arguments correspond to the arguments of the SAS CDF function (ignoring the random variable argument).
T( v₁ v₂ ... v_n, df ): specifies a multivariate t-distribution with noncentrality 0, variance v₁ through v_n, and common degrees of freedom df.
UNIFORM( <left, right> ): specifies the uniform distribution. This option is only supported for simulation. The arguments correspond to the arguments of the SAS CDF 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= ( <TAILS=(options)> )

uses the sorted residual data to create an empirical CDF.

TAILS=( tail options )

specifies how to handle the tails in computing the inverse CDF from an empirical distribution, where Tail options are:


NORMAL: specifies the normal distribution to extrapolate the tails.
T( df ): specifies the t-distribution to extrapolate the tails.
PERCENT= p: specifies the percent of the observations to use in constructing each tail. The default for the PERCENT= option is 10. A normal distribution or a t-distribution is used to extrapolate the tails to infinity. The variance for the tail distributions is obtained from the data so that the empirical CDF is continuous.

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