This package extends the tidymodels ecosystem to enable usage of predictive models with offset terms. Offset terms are predictors in a linear model that with a known *a priori* value. In other words, these terms do not have an associated coefficient (\(\beta_i\)) that needs to be determined. In a generalized linear model (GLM), an offset specification looks like:

\[ \hat{Y} = g^{-1}(offset + \beta_0 + \beta_1X_1 + \beta_2X_2 + \ldots + \beta_pX_p) \]

Models with offsets are most useful when working with count data or when fitting an adjustment model on top of an existing model with a prior expectation. The former situation is common in insurance where data is often aggregated or weighted by exposures. The latter is common in life insurance where industry mortality tables are often used as a starting point for setting assumptions on a particular block of business.

In general, offsetreg functions are named after existing functions from tidymodels or other modeling packages suffixed by `_offset`

(or `_exposure`

). The modeling engines in this package are wrappers around existing, well-known modeling functions. These engines all include the argument `offset_col`

(or `exposure_col`

) which is used to specify which column in the data passed to the engine contains offsets.

Currently, the following model specifications and engines are available:

`poisson_reg_offset()`

- create a Poisson GLM spec. Engines:`glm_offset`

- a wrapper around`stats::glm()`

`glmnet_offset`

- a wrapper around`glmnet::glmnet()`

`boost_tree_offset()`

- create an ensemble of boosted Poisson decision trees. Engines:`xgboost_offset`

- a wrapper around`xgboost::xgb.train()`

`decision_tree_exposure()`

- create a Poisson decision tree with weighted exposures. Engines:`rpart_exposure`

- a wrapper around`rpart::rpart()`

The offsetreg package can be installed from CRAN with:

You can install the development version of offsetreg from GitHub with:

The `us_deaths`

data set contains United States deaths, population estimates, and crude mortality rates for ages 25+ from the CDC Multiple Causes of Death Files for the years 2011-2020.

```
library(offsetreg)
library(parsnip)
us_deaths
#> # A tibble: 140 × 6
#> gender age_group year deaths population qx
#> <fct> <fct> <int> <dbl> <dbl> <dbl>
#> 1 Female 25-34 2011 13663 20746335 0.000659
#> 2 Female 25-34 2012 13808 20970529 0.000658
#> 3 Female 25-34 2013 14001 21203096 0.000660
#> 4 Female 25-34 2014 14480 21546290 0.000672
#> 5 Female 25-34 2015 15736 21838064 0.000721
#> 6 Female 25-34 2016 17359 22077505 0.000786
#> 7 Female 25-34 2017 18066 22351311 0.000808
#> 8 Female 25-34 2018 17980 22487065 0.000800
#> 9 Female 25-34 2019 17827 22581141 0.000789
#> 10 Female 25-34 2020 21654 22625267 0.000957
#> # ℹ 130 more rows
```

Assume we want to create a poisson model for the number of deaths. First, an offset term is created by taking the natural log of population, which is our exposure basis. A natural log is used because the link function in poisson regression is the exponential function.

Create a poisson regression model with an offset, and set the engine to “glm_offset”. The engine-specific argument `offset_col`

must refer to the name of the column in `us_deaths`

that contains offsets.

**Note**: The offset term should always be included in model formulas.

```
glm_off <- poisson_reg_offset() |>
# set the modeling engine and specify the offset column
set_engine("glm_offset", offset_col = "offset") |>
# always include the offset term in the model formula
fit(deaths ~ gender + age_group + year + offset, data = us_deaths)
glm_off
#> parsnip model object
#>
#>
#> Call: stats::glm(formula = formula, family = family, data = data, weights = weights,
#> offset = offset)
#>
#> Coefficients:
#> (Intercept) genderMale age_group35-44 age_group45-54 age_group55-64
#> -18.337940 0.327632 0.442935 1.212463 1.990698
#> age_group65-74 age_group75-84 age_group85+ year
#> 2.713410 3.645763 4.770408 0.005683
#>
#> Degrees of Freedom: 139 Total (i.e. Null); 131 Residual
#> Null Deviance: 51700000
#> Residual Deviance: 237800 AIC: 239800
```

Verify that coefficients match `stats::glm()`

.