SPSS® 12.0 Command Syntax Reference

1268 PROBIT
• Keywords BY and WITH can appear in either order. However, both must follow the
response-and-observation-count variables.
Example
PROBIT R OF N WITH X.
• The number of observations having the measured response appears in variable R, and the
total number of observations is in N. The predictor is X.
Example
PROBIT R OF N BY ROOT(1,2) WITH X.
PROBIT R OF N WITH X BY ROOT(1,2).
• Because keywords BY and WITH can be used in either order, these two commands are
equivalent. Each command specifies X as a continuous predictor and ROOT as a categorical
grouping variable.
• Groups are identified by the levels of variable ROOT, which may be 1 or 2.
• For each combination of predictor and grouping variables, the variable R contains the
number of observations with the response of interest, and N contains the total number of
observations.
MODEL Subcommand
MODEL specifies the form of the dichotomous-response model. Response models can be
thought of as transformations (T) of response rates, which are proportions or probabilities
(p). Note the difference in the transformations between the current version and the previous
versions.
• A probit is the inverse of the cumulative standard normal distribution function. Thus, for
any proportion, the probit transformation returns the value below which that proportion
of standard normal deviates is found. For the probit response model, the program uses
Tp ( ) = PROBIT( p)
. Hence:
T( 0.025)
= PROBIT( 0.025)
= – 1.96
T( 0.400)
= PROBIT( 0.400)
= – 0.25
T( 0.500)
= PROBIT( 0.500)
= 0.00
T( 0.950)
= PROBIT( 0.950)
= 1.64
• A logit is simply the natural log of the odds ratio, p ⁄ ( 1 – p)
. In the Probit procedure, the
response function is given as Tp ( ) = log e(
p ⁄ ( 1 – p)
) . Hence:
T( 0.025)
= LOGIT( 0.025)
= – 3.66
T( 0.400)
= LOGIT( 0.400)
= – 0.40
T( 0.500)
= LOGIT( 0.500)
= 0.00
T( 0.950)
= LOGIT( 0.950)
=
2.94