Poisson regression via pscl

pscl::zeroinfl() uses maximum likelihood estimation to fit a model for count data that has separate model terms for predicting the counts and for predicting the probability of a zero count.

Details

For this engine, there is a single mode: regression

Tuning Parameters

This engine has no tuning parameters.

Translation from parsnip to the underlying model call (regression)

The poissonreg extension package is required to fit this model.

library(poissonreg)

poisson_reg() %>%
  set_engine("zeroinfl") %>%
  translate()

## Poisson Regression Model Specification (regression)
##
## Computational engine: zeroinfl
##
## Model fit template:
## pscl::zeroinfl(formula = missing_arg(), data = missing_arg(),
##     weights = missing_arg())

Preprocessing and special formulas for zero-inflated Poisson models

Factor/categorical predictors need to be converted to numeric values (e.g., dummy or indicator variables) for this engine. When using the formula method via fit(), parsnip will convert factor columns to indicators.

Specifying the statistical model details

For this particular model, a special formula is used to specify which columns affect the counts and which affect the model for the probability of zero counts. These sets of terms are separated by a bar. For example, y ~ x | z. This type of formula is not used by the base R infrastructure (e.g. model.matrix())

When fitting a parsnip model with this engine directly, the formula method is required and the formula is just passed through. For example:

library(tidymodels)
tidymodels_prefer()

data("bioChemists", package = "pscl")
poisson_reg() %>%
  set_engine("zeroinfl") %>%
  fit(art ~ fem + mar | ment, data = bioChemists)

## parsnip model object
##
##
## Call:
## pscl::zeroinfl(formula = art ~ fem + mar | ment, data = data)
##
## Count model coefficients (poisson with log link):
## (Intercept)     femWomen   marMarried
##     0.82840     -0.21365      0.02576
##
## Zero-inflation model coefficients (binomial with logit link):
## (Intercept)         ment
##      -0.363       -0.166

However, when using a workflow, the best approach is to avoid using workflows::add_formula() and use workflows::add_variables() in conjunction with a model formula:

data("bioChemists", package = "pscl")
spec <-
  poisson_reg() %>%
  set_engine("zeroinfl")

workflow() %>%
  add_variables(outcomes = c(art), predictors = c(fem, mar, ment)) %>%
  add_model(spec, formula = art ~ fem + mar | ment) %>%
  fit(data = bioChemists) %>%
  extract_fit_engine()

##
## Call:
## pscl::zeroinfl(formula = art ~ fem + mar | ment, data = data)
##
## Count model coefficients (poisson with log link):
## (Intercept)     femWomen   marMarried
##     0.82840     -0.21365      0.02576
##
## Zero-inflation model coefficients (binomial with logit link):
## (Intercept)         ment
##      -0.363       -0.166

The reason for this is that workflows::add_formula() will try to create the model matrix and either fail or create dummy variables prematurely.

Case weights

This model can utilize case weights during model fitting. To use them, see the documentation in case_weights and the examples on tidymodels.org.

The fit() and fit_xy() arguments have arguments called case_weights that expect vectors of case weights.