offsetreg

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()

Installation

The offsetreg package can be installed from CRAN with:

install.packages("offsetreg")

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

# install.packages("devtools")
devtools::install_github("mattheaphy/offsetreg")

Basic usage

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.

us_deaths$offset <- log(us_deaths$population)

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().

glm_base <- glm(deaths ~ gender + age_group + year, offset = offset,
                data = us_deaths, family = 'poisson')

identical(extract_fit_engine(glm_off) |> coef(), coef(glm_base))
#> [1] TRUE