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Get residuals for model diagnostics (Cox-Snell Residuals)

Source: R/gof.R
get_residuals.Rd

Computes Cox-Snell residuals for a fitted model to diagnose goodness-of-fit and calibration.

Usage

get_residuals(object, get_0_1 = TRUE, get_1_0 = TRUE, raw = FALSE)

Arguments

object

A redeem object (either rem or dem).

get_0_1

Logical; if `TRUE`, computes residuals for the formation (0 -> 1) process. Defaults to TRUE.

get_1_0

Logical; if `TRUE`, computes residuals for the dissolution (1 -> 0) process. Defaults to TRUE.

raw

Logical; if `TRUE`, returns the raw Cox-Snell residuals. Defaults to FALSE.

Value

If `raw = TRUE`, a list containing the raw residuals for the selected process(es). If `raw = FALSE`, a list of data frames containing the Kaplan-Meier coordinates (`time`, `surv`) and the corresponding `theoretical` standard exponential survival values.

Details

Cox-Snell residuals are a standard diagnostic tool for continuous-time survival models and counting processes. Under the true model specification, the integrated cumulative intensity computed up to the exact time of an observed event is distributed as a standard exponential random variable, i.e., \(\Lambda_{ij}(t_k) \sim Exp(1)\).

Consequently, if the model is correctly specified:

  • The empirical survival function of these residuals should closely match the theoretical survival function of a standard exponential distribution, \(S(r) = \exp(-r)\).

  • Deviations between the empirical Kaplan-Meier curve of the residuals and the theoretical exponential curve signal model misspecification, unmodeled dyadic heterogeneity, or non-stationarity.

The function can compute residuals for both the formation/incidence (\(0 \rightarrow 1\)) process and the dissolution/duration (\(1 \rightarrow 0\)) process.

References

Cox, D. R., & Snell, E. J. (1968). A general definition of residuals. Journal of the Royal Statistical Society: Series B (Methodological), 30(2), 248-265.