
COVPRIOR=IWISHART<(options)>

specifies an inverse Wishart prior distribution, IWISHART(a,b), for the covariance matrix of the random effects.
You can specify the following options, enclosed in parentheses:

DF=a

specifies the degrees of freedom of the inverse Wishart distribution. The default is the dimension of the covariance matrix
of the random effects plus 3.

SCALE=b

specifies for the scale parameter of the inverse Wishart distribution, where is the identity matrix. The default is the dimension of the covariance matrix of the random effects plus 3.

MONITOR
MONITOR=(numericlist)
MONITOR=RANDOM (number)

outputs results for the individuallevel randomeffects parameters. (By default, PROC BCHOICE does not output results for individuallevel randomeffects parameters.) You can monitor a subset
of the randomeffects parameters. You can provide a numeric list of the SUBJECT indexes, or PROC BCHOICE can randomly choose
a subset of all subjects for you.
To monitor a list of randomeffects parameters for certain subjects, you can provide their indexes as follows:
random x / subject=index monitor=(1 to 5 by 2 23 57);
PROC BCHOICE outputs results of random effects for subjects 1, 3, 5, 23, and 57. PROC BCHOICE can also randomly choose a subset
of all the subjects to monitor, if you submit a statement such as the following:
random x / subject=index monitor=(random(12));
PROC BCHOICE outputs results of random effects for 12 randomly selected subjects. You control the sequence of the random indexes
by specifying the SEED
= option in the PROC BCHOICE statement.
When you specify the MONITOR option, it uses the specification of the STATISTICS=
and PLOTS=
options in the PROC BCHOICE statement. By default, PROC BCHOICE outputs all the posterior samples of all randomeffects parameters
to the OUTPOST=
output data set. You can use the NOOUTPOST
option to suppress the saving of the randomeffects parameters.

NOOUTPOST

suppresses the output of the posterior samples of randomeffects parameters to the OUTPOST=
data set. In models that have a large number of randomeffects parameters (for example, tens of thousands), PROC BCHOICE
can run faster if it does not save the posterior samples of the randomeffects parameters.
When you specify both the NOOUTPOST option and the MONITOR
option, PROC BCHOICE outputs the list of variables that are monitored.
The maximum number of variables that can be saved to an OUTPOST=
data set is 32,767. If you run a largescale randomeffects model in which the number of parameters exceeds this limit, the
NOOUTPOST option is invoked automatically and PROC BCHOICE does not save the randomeffects draws to the posterior output
data set. You can use the MONITOR
option to select a subset of the parameters to store in the OUTPOST=
data set.

REMEAN

models the mean of the random effects, so that is estimated. You can also model the prior mean of the random effects as a function of individual demographic variables.
Rossi, McCulloch, and Allenby (1996) and Rossi, Allenby, and McCulloch (2005) propose adding another layer of flexibility to the randomeffectsonly model by allowing heterogeneity that is driven by
observable (demographic) characteristics of the individuals. The following REMEAN=(AGE GENDER) option in the RANDOM statement
estimates the mean of the random effect, X
, and models the mean as a function of Age
and Gender
:
random X / subject=Index remean=(Age Gender);

SUBJECT=effect
SUB=effect

identifies the subjects in the model. PROC BCHOICE assumes complete independence across subjects; thus, for the RANDOM statement, the SUBJECT= option produces a blockdiagonal structure that has identical
blocks. Specifying a subject effect is equivalent to nesting all other effects in the RANDOM statement within the subject
effect.
The effect can be continuous variables. PROC BCHOICE does not sort by the values of the continuous variable; rather, it considers the data to be from a new subject
or group whenever the value of the continuous variable changes from the previous observation.

TYPE=UN  VC

specifies the covariance structure. Although a variety of structures are available, most applications call for either TYPE=VC or TYPE=UN. The TYPE=VC (variance
components) option, which is the default structure, models a different variance component for each random effect. The TYPE=UN
(unstructured) specifies a full structured covariance matrix for the random effects. The unstructured form accommodates any
pattern of correlation between the random effects in addition to fitting a different variance component for each random effect.