`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

### 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()
```

### 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.