The MODEL statement defines the statistical model in terms of a response variable (the target) or an events/trials specification. You can also specify model effects that are constructed from variables in the input data set, and you can
specify options. An intercept is included in the model by default. You can remove the intercept by specifying the NOINT option.
You can specify a single response variable that contains your interval, binary, ordinal, or nominal response values. When you have binomial data, you can specify
the events/trials form of the response, where one variable contains the number of positive responses (or events) and another variable contains
the number of trials. The values of both events and (trials – events) must be nonnegative, and the value of trials must be positive. If you specify a single response variable that is in a CLASS
statement, then the response is assumed to be either binary or multinomial, depending on the number of levels.
For information about constructing the model effects, see the section Specification and Parameterization of Model Effects.
There are two sets of options in the MODEL statement. The responseoptions
determine how the HPGENSELECT procedure models probabilities for binary and multinomial data. The modeloptions
control other aspects of model formation and inference. Table 8.3 summarizes these options.
Table 8.3: MODEL Statement Options
Option

Description

Response Variable Options for Binary and Multinomial Models

DESCENDING

Reverses the response categories

EVENT=

Specifies the event category

ORDER=

Specifies the sort order

REF=

Specifies the reference category

Model Options

ALPHA=

Specifies the confidence level for confidence limits

CL

Requests confidence limits

DISPERSION  PHI=

Specifies a fixed dispersion parameter

DISTRIBUTION  DIST=

Specifies the response distribution

INCLUDE=

Includes effects in all models for model selection

INITIALPHI=

Specifies a starting value of the dispersion parameter

LINK=

Specifies the link function

NOCENTER

Requests that continuous main effects not be centered and scaled

NOINT

Suppresses the intercept

OFFSET=

Specifies the offset variable

SAMPLEFRAC=

Specifies the fraction of the data to be used to compute starting


values for the Tweedie distribution

START=

Includes effects in the initial model for model selection

Response Variable Options
Response variable options determine how the HPGENSELECT procedure models probabilities for binary and multinomial data.
You can specify the following responseoptions by enclosing them in parentheses after the response or trials variable.

DESCENDING
DESC

reverses the order of the response categories.
If both the DESCENDING and ORDER=
options are specified, PROC HPGENSELECT orders the response categories according to the ORDER=
option and then reverses that order.

EVENT=’category’  FIRST  LAST

specifies the event category for the binary response model. PROC HPGENSELECT models the probability of the event category.
The EVENT= option has no effect when there are more than two response categories.
You can specify the event category (formatted, if a format is applied) in quotes, or you can specify one of the following:

FIRST

designates the first ordered category as the event. This is the default.

LAST

designates the last ordered category as the event.
For example, the following statements specify that observations that have a formatted value of '1' represent events in the
data. The probability modeled by the HPGENSELECT procedure is thus the probability that the variable def
takes on the (formatted) value '1'.
proc hpgenselect data=MyData;
class A B C;
model def(event ='1') = A B C x1 x2 x3;
run;

ORDER=DATA  FORMATTED  INTERNAL
ORDER=FREQ  FREQDATA  FREQFORMATTED  FREQINTERNAL

specifies the sort order for the levels of the response variable. When ORDER=FORMATTED (the default) for numeric variables for which you have supplied no explicit format (that is,
for which there is no corresponding FORMAT statement in the current PROC HPGENSELECT run or in the DATA step that created
the data set), the levels are ordered by their internal (numeric) value. Table 8.4 shows the interpretation of the ORDER= option.
Table 8.4: Sort Order
ORDER=

Levels Sorted By

DATA

Order of appearance in the input data set

FORMATTED

External formatted value, except for numeric variables that have no explicit format, which are sorted by their unformatted
(internal) value

FREQ

Descending frequency count (levels that have the most observations come first in the order)

FREQDATA

Order of descending frequency count; within counts by order of appearance in the input data set when counts are tied

FREQFORMATTED

Order of descending frequency count; within counts by formatted value when counts are tied

FREQINTERNAL

Order of descending frequency count; within counts by unformatted value when counts are tied

INTERNAL

Unformatted value

By default, ORDER=FORMATTED. For the FORMATTED and INTERNAL orders, the sort order is machinedependent.
For more information about sort order, see the chapter about the SORT procedure in Base SAS Procedures Guide and the discussion of BYgroup processing in SAS Language Reference: Concepts.

REF=’category’  FIRST  LAST

specifies the reference category for the generalized logit model and the binary response model. For the generalized logit
model, each logit contrasts a nonreference category with the reference category. For the binary response model, specifying
one response category as the reference is the same as specifying the other response category as the event category. You can
specify the reference category (formatted if a format is applied) in quotes, or you can specify one of the following:

FIRST

designates the first ordered category as the reference

LAST

designates the last ordered category as the reference. This is the default.

ALPHA=number

requests that confidence intervals for each of the parameters that are requested by the CL
option be constructed with confidence level 1–number. The value of number must be between 0 and 1; the default is 0.05.

CL

requests that confidence limits be constructed for each of the parameter estimates. The confidence level is 0.95 by default;
this can be changed by specifying the ALPHA=
option.

DISPERSION=number

specifies a fixed dispersion parameter for those distributions that have a dispersion parameter. The dispersion parameter
used in all computations is fixed at number, and not estimated.

DISTRIBUTION=keyword

specifies the response distribution
for the model. The keywords and the associated distributions are shown in Table 8.5.
Table 8.5: BuiltIn Distribution Functions

Distribution

DISTRIBUTION=

Function

BINARY

Binary

BINOMIAL

Binary or binomial

GAMMA

Gamma

INVERSEGAUSSIAN  IG

Inverse Gaussian

MULTINOMIAL  MULT

Multinomial

NEGATIVEBINOMIAL  NB

Negative binomial

NORMAL  GAUSSIAN

Normal

POISSON

Poisson

TWEEDIE<(Tweedieoptions)>

Tweedie

ZINB

Zeroinflated negative binomial

ZIP

Zeroinflated Poisson

When DISTRIBUTION=TWEEDIE, you can specify the following Tweedieoptions:

INITIALP=

specifies a starting value for iterative estimation of the Tweedie power parameter.

OPTMETHOD=Tweedieoptimizationoption

requests an optimization method for iterative estimation of the Tweedie model parameters. You can specify the following Tweedieoptimizationoptions:

EQL

requests that extended quasilikelihood be used for a sample of the data, followed by extended quasilikelihood for the full
data. This is equivalent to the TWEEDIEEQL Tweedieoption.

EQLLHOOD

requests that extended quasilikelihood be used for a sample of the data, followed by Tweedie log likelihood for the full
data. This is the default method.

FINALLHOOD

requests a fourstage approach to estimating the Tweedie model parameters. The four stages are as follows:

extended quasilikelihood for a sample of the data

Tweedie log likelihood for a sample of the data

extended quasilikelihood for the full data

Tweedie log likelihood for the full data

LHOOD

requests that Tweedie log likelihood be used for a sample of the data, followed by Tweedie log likelihood for the full data.

P=

requests a fixed Tweedie power parameter.

TWEEDIEEQL  EQL

requests that extended quasilikelihood be used instead of Tweedie log likelihood in parameter estimation.
If you do not specify a link function with the LINK=
option, a default link function is used. The default link function for each distribution is shown in Table 8.6. For the binary and multinomial distributions, only the link functions shown in Table 8.6 are available. For the other distributions, you can use any link function shown in Table 8.7 by specifying the LINK=
option. Other commonly used link functions for each distribution are shown in Table 8.6.
Table 8.6: Default and Commonly Used Link Functions

Default

Other Commonly Used

DISTRIBUTION=

Link Function

Link Functions

BINARY

Logit

Probit, complementary loglog, loglog

BINOMIAL

Logit

Probit, complementary loglog, loglog

GAMMA

Reciprocal

Log

INVERSEGAUSSIAN  IG

Reciprocal square

Log

MULTINOMIAL  MULT

Logit (ordinal)

Probit, complementary loglog, loglog

MULTINOMIAL  MULT

Generalized logit (nominal)


NEGATIVEBINOMIAL  NB

Log


NORMAL  GAUSSIAN

Identity

Log

POISSON

Log


TWEEDIE

Log


ZINB

Log


ZIP

Log



INCLUDE=n
INCLUDE=singleeffect
INCLUDE=(effects)

forces effects to be included in all models. If you specify INCLUDE=n, then the first n effects that are listed in the MODEL
statement are included in all models. If you specify INCLUDE=singleeffect or if you specify a list of effects within parentheses, then the specified effects are forced into all models. The effects
that you specify in this option must be explanatory effects that are specified in the MODEL
statement before the slash (/).

INITIALPHI=number

specifies a starting value for iterative maximum likelihood estimation of the dispersion parameter for distributions that
have a dispersion parameter.

LINK=keyword

specifies the link function
for the model. The keywords and the associated link functions are shown in Table 8.7. Default and commonly used link functions for the available distributions are shown in Table 8.6.
Table 8.7: BuiltIn Link Functions

Link


LINK=

Function


CLOGLOG  CLL

Complementary loglog


GLOGIT  GENLOGIT

Generalized logit


IDENTITY  ID

Identity


INV  RECIP

Reciprocal


INV2

Reciprocal square


LOG

Logarithm


LOGIT

Logit


LOGLOG

Loglog


PROBIT

Probit


denotes the quantile function of the standard normal distribution.
If a multinomial response variable has more than two categories, the HPGENSELECT procedure fits a model by using a cumulative
link function that is based on the specified link. However, if you specify LINK=GLOGIT, the procedure assumes a generalized
logit model for nominal (unordered) data, regardless of the number of response categories.

NOCENTER

requests that continuous main effects not be centered and scaled internally. (Continuous main effects are centered and scaled
by default to aid in computing maximum likelihood estimates.) Parameter estimates and related statistics are always reported
on the original scale.

NOINT

requests that no intercept be included in the model. (An intercept is included by default.) The NOINT option is not available
in multinomial models.

OFFSET=variable

specifies a variable to be used as an offset to the linear predictor. An offset plays the role of an effect whose coefficient is known to be 1.
The offset variable cannot appear in the CLASS
statement or elsewhere in the MODEL
statement. Observations that have missing values for the offset variable are excluded from the analysis.

SAMPLEFRAC=number

specifies a fraction of the data to be used to determine starting values for iterative estimation of the parameters of a Tweedie
model. The sampled data are used in an extended quasilikelihood estimation of the model parameters. The estimated parameters
are then used as starting values in a full maximum likelihood estimation of the model parameters that uses all of the data.

START=n
START=singleeffect
START=(effects)

begins the selection process from the designated initial model for the FORWARD and STEPWISE selection methods. If you specify
START=n, then the starting model includes the first n effects that are listed in the MODEL
statement. If you specify START=singleeffect or if you specify a list of effects within parentheses, then the starting model includes those specified effects. The effects
that you specify in the START= option must be explanatory effects that are specified in the MODEL
statement before the slash (/). The START= option is not available when you specify METHOD=BACKWARD in the SELECTION
statement.