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The PROBIT Procedure |

The PROBIT procedure calculates maximum likelihood estimates of regression parameters and the natural (or threshold) response rate for quantal response data from biological assays or other discrete event data. This includes probit, logit, ordinal logistic, and extreme value (or gompit) regression models. Probit analysis developed from the need to analyze qualitative (dichotomous or polytomous) dependent variables within the regression framework. Many response variables are binary by nature (yes/no), while others are measured ordinally rather than continuously (degree of severity). Ordinary least squares (OLS) regression has been shown to be inadequate when the dependent variable is discrete (Collett, 1991 and Agresti, 1990). Probit or logit analyses are more appropriate in this case.

The PROBIT procedure computes maximum likelihood
estimates of the parameters and *C* of the
probit equation using a modified Newton-Raphson algorithm.
When the response Y is binary, with values 0 and 1, the
probit equation is

where

- is a vector of parameter estimates
*F*- is a cumulative distribution function (the normal, logistic, or extreme value)
**x**- is a vector of explanatory variables
*p*- is the probability of a response
*C*- is the natural (threshold) response rate

Notice that PROC PROBIT, by default, models the probability of the

For ordinal response models, the response, Y, of an individual or an experimental unit may be restricted to one of a (usually small) number, , of ordinal values, denoted for convenience by 1, ... ,

You can set or estimate the natural (threshold) response rate
*C*.
Estimation of *C* can begin either from an initial value that you specify
or from the rate observed in a control group.
By default, the natural response rate is fixed at zero.
An observation in the data set analyzed by the PROBIT procedure
may contain the response and explanatory values for one subject.
Alternatively, it may provide the number of observed events
from a number of subjects at a particular setting of the
explanatory variables. In this case, PROC PROBIT models the probability
of an event.

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