The PLM Procedure

Scoring Data Sets for Zero-Inflated Models

The PLM procedure can score new observations for zero-inflated models with the SCORE statement. If you specify the ILINK option, the computed statistics are for estimated counts.

In the following formula, is the design row for covariates that correspond to the Poisson or negative binomial component, is the column vector of the fitted regression parameters; is the design row for covariates that correspond to the zero inflation component, is the column vector of the fitted regression parameters; g and g are the link and inverse link functions for the Poisson or negative binomial component, and are the link and inverse link functions for the zero inflation component; is the standard normal cumulative distribution function and is the nominal significance level. Let

StartLayout 1st Row 1st Column mu 2nd Column equals 3rd Column g Superscript negative 1 Baseline left-parenthesis eta right-parenthesis 4th Column equals 5th Column g Superscript negative 1 Baseline left-parenthesis bold x ModifyingAbove bold-italic beta With caret right-parenthesis 2nd Row 1st Column mu Subscript z 2nd Column equals 3rd Column g Subscript z Superscript negative 1 Baseline left-parenthesis eta Subscript z Baseline right-parenthesis 4th Column equals 5th Column g Subscript z Superscript negative 1 Baseline left-parenthesis bold z ModifyingAbove bold-italic gamma With caret right-parenthesis 3rd Row 1st Column v 1 2nd Column equals 3rd Column left-parenthesis StartFraction normal d mu Over normal d eta EndFraction right-parenthesis squared bold x ModifyingAbove bold upper V With caret Subscript bold-italic beta comma bold-italic beta Baseline bold x prime 4th Row 1st Column v 2 2nd Column equals 3rd Column left-parenthesis StartFraction normal d mu Subscript z Baseline Over normal d eta Subscript z Baseline EndFraction right-parenthesis squared bold z ModifyingAbove bold upper V With caret Subscript bold-italic gamma comma bold-italic gamma Baseline bold z prime 5th Row 1st Column v 12 2nd Column equals 3rd Column minus left-parenthesis StartFraction normal d mu Over normal d eta EndFraction right-parenthesis left-parenthesis StartFraction normal d mu Subscript z Baseline Over normal d eta Subscript z Baseline EndFraction right-parenthesis bold x ModifyingAbove bold upper V With caret Subscript bold-italic beta comma bold-italic gamma Baseline bold z prime EndLayout

The formula for statistics in the SCORE statement for zero-inflated models are listed as follows.

StartLayout 1st Row 1st Column normal upper P normal upper Z normal upper E normal upper R normal upper O 2nd Column equals 3rd Column omega 4th Column equals 5th Column mu Subscript z 2nd Row 1st Column normal upper P normal upper R normal upper E normal upper D slash normal upper I normal upper L normal upper I normal upper N normal upper K 2nd Column equals 3rd Column p Subscript c 4th Column equals 5th Column mu left-parenthesis 1 minus omega right-parenthesis 3rd Row 1st Column normal upper S normal upper T normal upper D slash normal upper I normal upper L normal upper I normal upper N normal upper K 2nd Column equals 3rd Column s Subscript c 4th Column equals 5th Column StartRoot p Subscript c Superscript 2 Baseline v 2 plus left-parenthesis 1 minus omega right-parenthesis squared v 1 plus v 1 v 2 plus 2 p Subscript c Baseline left-parenthesis 1 minus omega right-parenthesis v 12 plus v 12 squared EndRoot 4th Row 1st Column normal upper U normal upper C normal upper L normal upper M slash normal upper I normal upper L normal upper I normal upper N normal upper K 2nd Column equals 3rd Column u Subscript c 4th Column equals 5th Column p Subscript c Baseline exp left-parenthesis normal upper Phi Superscript negative 1 Baseline left-parenthesis 1 minus alpha slash 2 right-parenthesis s Subscript c Baseline slash p Subscript c Baseline right-parenthesis 5th Row 1st Column normal upper L normal upper C normal upper L normal upper M slash normal upper I normal upper L normal upper I normal upper N normal upper K 2nd Column equals 3rd Column l Subscript c 4th Column equals 5th Column p Subscript c Baseline slash exp left-parenthesis normal upper Phi Superscript negative 1 Baseline left-parenthesis 1 minus alpha slash 2 right-parenthesis s Subscript c Baseline slash p Subscript c Baseline right-parenthesis 6th Row 1st Column normal upper P normal upper R normal upper E normal upper D 2nd Column equals 3rd Column p Subscript l 4th Column equals 5th Column g left-parenthesis p Subscript c Baseline right-parenthesis 7th Row 1st Column normal upper S normal upper T normal upper D 2nd Column equals 3rd Column s Subscript l 4th Column equals 5th Column g left-parenthesis s Subscript c Baseline right-parenthesis slash left-parenthesis StartFraction normal d mu Over normal d eta EndFraction right-parenthesis 8th Row 1st Column normal upper U normal upper C normal upper L normal upper M 2nd Column equals 3rd Column u Subscript l 4th Column equals 5th Column g left-parenthesis u Subscript c Baseline right-parenthesis 9th Row 1st Column normal upper L normal upper C normal upper L normal upper M 2nd Column equals 3rd Column l Subscript l 4th Column equals 5th Column g left-parenthesis l Subscript c Baseline right-parenthesis EndLayout

Last updated: December 09, 2022