How to Perform Markov Chain Analysis in R (With Example)

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Markov chain analysis is a mathematical method for studying systems that transition between states over time. It is used in fields like finance, biology, and social sciences. You can read more about the basics of Markov chains in this article. In R, this analysis is often performed using libraries like markovchain.

In this article, we show how to perform Markov chain analysis in R.

Install and Load Required Packages

First, install and load the necessary R packages. The most commonly used package for Markov chain analysis in R is “markovchain”.

# Install the markovchain package 
install.packages("markovchain")

# Load the package
library(markovchain)

Define States and Transition Matrix

In our example, the two states are “Sunny” and “Rainy.” Next, define the transition matrix, which lists the probabilities of moving from one state to another. Each row represents the current state, and each column represents the next state. Rows must sum to 1 to ensure valid probabilities.

For instance:

The probability of transitioning from “Sunny” to “Sunny” is 0.8.
The probability of transitioning from “Sunny” to “Rainy” is 0.2.
The probability of transitioning from “Rainy” to “Sunny” is 0.3.
The probability of transitioning from “Rainy” to “Rainy” is 0.7.

Let’s define the states and transition matrix in R:

# Define the states
states <- c("Sunny", "Rainy")

# Define the transition matrix
transitionMatrix <- matrix(c(0.8, 0.2, 0.3, 0.7), nrow = 2,
        byrow = TRUE, dimnames = list(c("Sunny", "Rainy"),
        c("Sunny", "Rainy")))

# View the transition matrix
transitionMatrix

Create a Markov Chain Object

To create a Markov chain object, first define the possible states and a transition matrix with the corresponding probabilities. Using the markovchain class in R, you can turn these into a Markov chain object for analysis and prediction.

# Create the Markov chain object
weatherMC <- new("markovchain", states = states, transitionMatrix = transitionMatrix)

# Display the Markov chain
weatherMC

Perform Predictions

You can predict the distribution of the next state given the current state. This is done by multiplying the current state distribution by the transition matrix.

For example, if today’s weather is “Sunny”, what is the probability that tomorrow’s weather will be “Sunny” or “Rainy”?

# Find the state distribution after 1 step 
initialState <- c(Sunny = 1, Rainy = 0)  
nextState <- initialState %*% transitionMatrix
nextState

In the above example, the state distribution after one step gives the probabilities of the weather tomorrow.

You can also simulate the weather for multiple days using the markovchain object. To simulate the weather for 10 days starting with a “Sunny” day:

# Simulate the weather for 10 days starting with a Sunny day
simulatedWeather <- rmarkovchain(n = 10, object = weatherMC, t0 = "Sunny")

# View the simulated weather
simulatedWeather

Analyzing Steady-State Probabilities

Steady-state probabilities describe the system’s long-run behavior—the probability of being in each state after many transitions. To calculate these probabilities, use the steadyStates function.

# Compute the steady-state probabilities
steadyState <- steadyStates(weatherMC)
steadyState

These steady-state probabilities tell you the long-term likelihood of the weather being “Sunny” or “Rainy” as the system evolves.

Visualizing the Markov Chain

You can visualize the Markov chain using a state transition diagram. The DiagrammeR package is helpful for this.

First, install and load the package:

# Install and load DiagrammeR
install.packages("DiagrammeR")
library(DiagrammeR)

Next, create a diagram of the transition matrix:

library(DiagrammeR)

# Build a DOT graph and render it
diagram <- grViz("
digraph {
  rankdir=LR
  node [shape = circle, fontsize = 12]

  Sunny
  Rainy

  Sunny -> Sunny [label = "0.8"]
  Sunny -> Rainy [label = "0.2"]
  Rainy -> Sunny [label = "0.3"]
  Rainy -> Rainy [label = "0.7"]
}
")

# Render the diagram
diagram

Conclusion

Markov chain analysis models systems with probabilistic state transitions. Using R, we demonstrated this with the markovchain package: we defined states, created a transition matrix, and built a Markov chain object to analyze system behavior.

We predicted future states and simulated transitions over multiple steps. We also computed steady-state probabilities to understand the system’s long-term behavior and visualized the chain with DiagrammeR to create a clear state transition diagram.