Version: 0.2.4

Core functionality for simulating quantities of interest from generalised linear models.

Purpose

Using simulations to find quantities of interest and associated uncertainty can be an effective way of showing substantively meaningful results from generalised linear models (GLM).

This R package provides core functions that can serve as the backbone to other packages for finding and plotting simulated quantities of interest from GLMs.

coreSim currently powers pltesim, a package for simulating probabilistic long-term effects from models with temporal dependence.

Motivation

coreSim aims to solve a number of issues that arose in prior implementations of the simulation approach to showing GLM results. The main previous implementation in R is the Zelig package. This package has tried to be "Everyone's statistical software". However, paradoxically, its attempt to be everything to everyone has led to less flexibility for new use cases. Maintaining such a large project over time has led to (in my experience) frequent code breaks. The Zelig 'API' has changed considerably over time in often undocumented ways. Changes to its many dependencies also undermines its reliability.

coreSim aims to overcome these issue with a focus on simplicity. It tries to:

• Do a small set of things really well.

• Have as few dependencies as possible. Only import packages if they make significant performance improvements over base R.

• Return simple data.frame output that can be easily manipulated.

• Have informative error messages that are easy for users to understand and which guide them to solutions.

Additionally, coreSim aims for very high reliability. Simplicity helps with acheive this goal. So does aiming for 100% code test coverage.

These characteristics allow coreSim to form the backbone of many specific and unanticipated implementations of the simulation approach.

 Steps

1. Estimate your model using whatever GLM model fitting function you like (note: I've only tested lm, glm, and survival).

2. Find your quantities of interest with qi_builder.

3. Present your results, e.g. by plotting the simulated quantities of interest.

Examples

Normal linear model

Here is an example using data from the car package:

library(coreSim)
library(car)

# Normal linear model
m1 <- lm(prestige ~ education + type, data = Prestige)

# Create fitted values
fitted_df_1 <- expand.grid(education = 6:16, type = 'wc')

# Find predicted outcomes (95% central interval, by default)
linear_qi <- qi_builder(obj = m1, newdata = fitted_df_1)

## Note: FUN argument missing -> assuming b_sims is from a normal linear model.

head(linear_qi)

##   education typewc      qi_
## 1         6      1 18.26931
## 2         6      1 20.92067
## 3         6      1 20.88659
## 4         6      1 24.46231
## 5         6      1 19.15713
## 6         6      1 17.91391

Slimmed simulation data

By default qi_builder will return all of the simulations inside the central interval of the simulations for each scenario that you specify with the ci argument (this is 0.95 by default for 95% central interval).

However, you may want to only return key features of this interval so that they can be efficiently stored and plotted. Using slim = TRUE will return only the minimum, median, and maximum values of the central interval for each scenario:

linear_qi_slim <- qi_builder(m1, newdata = fitted_df_1, slim = TRUE)

head(linear_qi_slim)

##   education typewc   qi_min qi_median   qi_max
## 1         6      1 12.54993  19.33749 26.46225
## 2         7      1 18.10320  23.88602 29.90101
## 3         8      1 23.71457  28.48066 33.52652
## 4         9      1 29.04148  33.05269 36.90274
## 5        10      1 34.09772  37.64164 41.08075
## 6        11      1 38.99077  42.18919 45.31262

The slimmed simulation data set can be efficiently plotted, for example using ggplot2:

library(ggplot2)
theme_set(theme_bw())

ggplot(linear_qi_slim, aes(education, qi_median)) +
    geom_ribbon(aes(ymin = qi_min, ymax = qi_max), alpha = 0.3) +
    geom_line() +
    ylab('Prestige')

Predicted probabilities from logistic regressions

By default qi_builder simply returns the linear systematic component, which in normal linear regression is simply the predicted y, i.e. y = α + β**X.

qi_builder allows you to supply any function for creating quantities of interest that you would like. This function needs to simply be able to convert a vector of linear systematic components to your quantity of interest.

For example, to find predicted probabilities from a logistic regression model create a function to turn the systematic component into the QI:

pr_fun <- function(x) 1 / (1 + exp(-x))

Then supply the custom function to qi_builder's FUN argument:

# Load data
data(Admission)
Admission$rank <- as.factor(Admission$rank)

# Estimate model
m2 <- glm(admit ~ gre + gpa + rank, data = Admission, family = 'binomial')

# Create fitted values
m2_fitted <- expand.grid(gre = seq(220, 800, by = 10), gpa = c(1, 4), rank = '4')

# Find quantity of interest
logistic_qi <- qi_builder(m2, m2_fitted, FUN = pr_fun, slim = TRUE)

head(logistic_qi)

##   gre gpa rank4      qi_min  qi_median     qi_max
## 1 220   1     1 0.002879333 0.01431348 0.06336300
## 2 230   1     1 0.002983825 0.01471619 0.06436528
## 3 240   1     1 0.003106020 0.01501327 0.06449270
## 4 250   1     1 0.003205407 0.01537888 0.06520055
## 5 260   1     1 0.003301195 0.01566664 0.06620142
## 6 270   1     1 0.003415190 0.01588294 0.06787158

See also

Christopher Gandrud (2015). simPH: An R Package for Illustrating Estimates from Cox Proportional Hazard Models Including for Interactive and Nonlinear Effects. Journal of Statistical Software, 65(3), 1-20. http://www.jstatsoft.org/v65/i03/.

Gandrud, Christopher. Laron K. Williams and Guy D. Whitten (2015). dynsim: Dynamic Simulations of Autoregressive Relationships. R package version 1.2.1. https://CRAN.R-project.org/package=dynsim.

King, Gary, Michael Tomz, and Jason Wittenberg. 2000. "Making the Most of Statistical Analyses: Improving Interpretation and Presentation." American Journal of Political Science 44(2): 341-55.