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The PROBIT Procedure |

**MODEL***response=independents < / options >***;**

<

**MODEL***events/trials=independents < / options >***;**

The MODEL statement names the variables used as the response and the independent variables. Additionally, you can specify the distribution used to model the response, as well as other options. More than one MODEL statement can be specified with the PROBIT procedure. The optional

The

Alternatively, the response can be specified as a pair of variable names separated by a slash (/). The value of the first variable,

model hits/AtBats=age;

If no independent variables are specified, PROC PROBIT fits an intercept-only model. The following options are available in the MODEL statement.

**CONVERGE=***value*-
specifies the convergence criterion.
Convergence is declared when
the maximum change in the parameter estimates between
Newton-Raphson steps is less than the value specified.
The change is a relative change if the parameter is greater than
0.01 in absolute value; otherwise, it is an absolute change.

By default, CONVERGE=0.001. **CORRB**-
displays the estimated correlation matrix of the parameter estimates.
**COVB**-
displays the estimated covariance matrix of the parameter estimates.
**DISTRIBUTION=***distribution-type***DIST=***distribution-type***D=***distribution-type*-
specifies the cumulative distribution function
used to model the response probabilities.
The distributions are described in the "Details" section.
Valid values for
*distribution-type*are- NORMAL
- the normal distribution for the probit model
- LOGISTIC
- the logistic distribution for the logit model
- EXTREMEVALUE | EXTREME | GOMPERTZ
- the extreme value, or Gompertz distribution for the gompit model

By default, DISTRIBUTION=NORMAL. **HPROB=***value*-
specifies a minimum probability level
for the Pearson chi-square
to indicate a good fit. The default value is 0.10.
The LACKFIT option must also be specified
for this option to have any effect.
For Pearson goodness of fit chi-square values with
probability greater than the HPROB= value, the fiducial
limits, if requested with the INVERSECL option,
are computed using a critical value of 1.96.
For chi-square values with probability less than the value of the
HPROB= option, the critical value is a 0.95 two-sided quantile
value taken from the
*t*distribution with degrees of freedom equal to (*k*- 1) ×*m*-*q*, where*k*is the number of levels for the response variable,*m*is the number of different sets of independent variable values, and*q*is the number of parameters fit in the model. If you specify the HPROB= option in both the PROC and MODEL statements, the MODEL statement option takes precedence. **INITIAL=***values*-
sets initial values for the parameters in the model other than the
intercept. The values must be given in the order in which the
variables are listed in the MODEL statement.
If some of the independent variables listed in the MODEL statement
are classification variables, then there must be as many values
given for that variable as there are classification levels minus 1.
The INITIAL option can be specified as follows.
**Type of List****Specification**list separated by blanks `initial=3 4 5`

list separated by commas `initial=3,4,5`

By default, all parameters have initial estimates of zero. **INTERCEPT=***value*-
initializes the intercept parameter to
*value*. By default, INTERCEPT=0. **INVERSECL**-
computes confidence limits for the values of the
first continuous independent variable (such as
dose) that yield selected response rates.
If the algorithm fails to converge (this can happen when
*C*is nonzero), missing values are reported for the confidence limits. See the section "Inverse Confidence Limits" for details. **ITPRINT**-
displays the iteration history, the final evaluation of
the gradient, and the second derivative matrix (Hessian).
**LACKFIT**-
performs two goodness-of-fit tests (a Pearson chi-square test
and a log-likelihood ratio chi-square test) for the fitted model.
**Note:**The data set must be sorted by the independent variables before the PROBIT procedure is run if you want to perform a test of fit. This test is not appropriate if the data are very sparse, with only a few values at each set of the independent variable values.

If the Pearson chi-square test statistic is significant, then the covariance estimates and standard error estimates are adjusted. See the "Lack of Fit Tests" section for a description of the tests. If you specify the LACKFIT option in both the PROC and MODEL statements, the MODEL statement option takes precedence. **MAXITER=***value*-
specifies the maximum number of iterations to
be performed in estimating the parameters.
By default, MAXITER=50.
**NOINT**-
fits a model with no intercept parameter.
If the INTERCEPT= option is also specified, the intercept
is fixed at the specified value; otherwise, it is set to zero.
This is most useful when the response is binary.
When the response has
*k*levels, then*k*-1 intercept parameters are fit. The NOINT option sets the intercept parameter corresponding to the lowest response level equal to zero. A Lagrange multiplier, or score, test for the restricted model is computed when the NOINT option is specified. **SINGULAR=***value*-
specifies the singularity criterion for determining linear
dependencies in the set of independent variables.
The sum of squares and crossproducts matrix of
the independent variables is formed and swept.
If the relative size of a pivot becomes less than
the value specified, then the variable corresponding
to the pivot is considered to be linearly dependent
on the previous set of variables considered.
By default, SINGULAR=1E-12.

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