The HPCOUNTREG Procedure

ZEROMODEL Statement

ZEROMODEL dependent-variable $\sim$ zero-inflated-regressors < / options >;

The ZEROMODEL statement is required if either ZIP or ZINB is specified in the DIST= option in the MODEL statement. If ZIP or ZINB is specified, then the ZEROMODEL statement must follow the MODEL statement. The dependent variable in the ZEROMODEL statement must be the same as the dependent variable in the MODEL statement.

The zero-inflated (ZI) regressors appear in the equation that determines the probability ( $\varphi _ i$ ) of a zero count. Each of these q variables has a parameter to be estimated in the regression. For example, let $\mathbf{z}_{i}’$ be the ith observation’s $1 \times (q+1)$ vector of values of the q ZI explanatory variables ( $w_0$ is set to 1 for the intercept term). Then $\varphi _ i$ is a function of $\mathbf{z}_{i}’\bgamma$ , where $\bgamma$ is the $(q+1) \times 1$ vector of parameters to be estimated. (The zero-inflated intercept is $\gamma _0$ ; the coefficients for the q zero-inflated covariates are $\gamma _1, \ldots , \gamma _ q$ .) If q is equal to 0 (no ZI explanatory variables are provided), then only the intercept term $\gamma _0$ is estimated. The "Parameter Estimates" table in the displayed output shows the estimates for the ZI intercept and ZI explanatory variables; they are labeled with the prefix "Inf_". For example, the ZI intercept is labeled "Inf_intercept". If you specify Age (a variable in your data set) as a ZI explanatory variable, then the "Parameter Estimates" table labels the corresponding parameter estimate "Inf_Age".

You can specify the following options in the ZEROMODEL statement after a slash (/):

LINK=LOGISTIC | NORMAL

specifies the distribution function used to compute probability of zeros. The supported distribution functions are as follows:

LOGISTIC: specifies logistic distribution.
NORMAL: specifies standard normal distribution.

If this option is omitted, then the default ZI link function is logistic.

OFFSET=zero-inflated-offset-variable

specifies a variable in the input data set to be used as a zero-inflated (ZI) offset variable. The ZI offset variable zero-inflated-offset-variable is included as a term, with coefficient restricted to 1, in the equation that determines the probability ( $\varphi _ i$ ) of a zero count and represents an adjustment to a common observational unit. The ZI offset variable cannot be the response variable, the offset variable (if any), or any of the explanatory variables. The name of the data set variable that is used as the ZI offset variable is displayed in the "Model Fit Summary" table, where it is labeled as "Inf_offset".