MODEL Subcommand (PROBIT command)

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 T (p) = 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 T (p) = 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

You can request one or both of the models on the MODEL subcommand. The default is PROBIT if the subcommand is not specified or is specified with no keyword.

PROBIT. Probit response model. This is the default.

LOGIT. Logit response model.

BOTH. Both probit and logit response models. PROBIT displays all the output for the logit model followed by the output for the probit model.

• If subgroups and multiple-predictor variables are defined, PROBIT estimates a separate intercept, a_j, for each subgroup and a regression coefficient, b_i, for each predictor.