sddr

The complete toolkit for distribution dynamics in R — analysing how a distribution of values across units (regions, firms, markets, assets) evolves over time, and where it is heading in the long run.

sddr brings distribution-dynamics analysis into one tidy, long-format framework and pushes it beyond what any existing package offers — with continuous stochastic kernels, continuous-time transitions, and modern inference that current R (and Python) tooling simply does not provide.

What makes `sddr` different — the new ideas

These are the capabilities that set sddr apart. (Status: ✅ available now · 🔜 in active development.)

🔜 Continuous stochastic kernels — density-based distribution dynamics (Quah), estimating the full conditional density with no arbitrary class binning. The modern approach, almost absent from R.
🔜 Continuous-time & irregular-interval Markov — for panels not observed on a regular time grid.
🔜 Modern inference — bootstrap and Bayesian intervals for transition probabilities, plus formal tests for Markov order, time-stationarity, and whether space matters at all.
🔜 Change-point / non-stationarity detection in transition dynamics.
🔜 Simulation engine, animated & interactive visualisation, broom tidiers, and an optional compiled backend for large panels.

Established methods, done right

A complete, tidy, sf-friendly implementation of the classical toolkit:

✅ Classic Markov chains and ergodic (steady-state) analysis
✅ Spatial Markov — transitions conditioned on neighbourhood context
🔜 LISA / full-rank / geo-rank Markov · rank & exchange mobility (Tau family) · mobility indices (Prais, Shorrocks) · directional LISA · sequence analysis · mean first-passage & sojourn times

All from long-format id / time / value data — no transition-matrix bookkeeping.

Installation

# install.packages("pak")
pak::pak("mqfarooqi1/sddr")

Quick start

library(sddr)

df <- data.frame(
  id    = rep(1:200, each = 5),
  time  = rep(2000:2004, times = 200),
  value = rnorm(1000)
)

# Classic Markov chain over distribution quintiles.
m <- markov(df, id = "id", time = "time", value = "value", k = 5)
m
steady_state(m)              # long-run distribution

Roadmap

Release	Focus
v0.1	The complete classical toolkit in one tidy API (Markov, spatial Markov, rank mobility, ergodic, sequences)
v0.2+	The new ideas: continuous stochastic kernels, continuous-time Markov, modern inference, change-point detection
later	Compiled backend, simulation engine, animated/interactive visualisation

Validation & prior work

sddr’s methods build directly on the distribution-dynamics literature — Quah (1993) for distributional convergence and Rey (2001) for spatial Markov dynamics.

As a correctness guarantee, where methods overlap with PySAL’s giddy (the established reference implementation) sddr is checked for numerical parity: the classic and spatial Markov estimators currently reproduce giddy to machine precision. sddr extends well past giddy and the R package griddy with the continuous-kernel, continuous-time, and inference methods above.