Fitting higher order Markov chains in R

Question

For $n$ individuals I observe their states at fixed times. So I have $n$ observations of a data generating Markov chain.

Using the markovchain-package I then can

• fit a time-homogeneous Markov chain of order 1 to my observations by using the markovchainFit-function
• fit a time-inhomogeneous Markov chain of order 1 to my observations by using the markovchainListFit-function
• fit a time-homogeneous Markov chain of higher order to only one sequence but not to my observation of many individuals by using the fitHigherOrder-function

By using the clickstream-package I can

• fit a time-homogeneous Markov chain of higher order to my observations by using the fitMarkovChain-function

Is there a function which allows me to fit a time-inhomogeneous Markov chain of higher order to my observations (like a combination of markovchainListFit from markovchain and fitMarkovChain from clickstream)? Is there any theory on how to do such a fit?

Answer 1

What time-homogeneous Markov Chain means is basically the Markov Chain at stationary status. This is the default assumption for these functions. The time-inhomogeneous fitting function might not be readily available.

Alternatively, what you can do is to set up the sequences step-by-step and using the partial data to fit the Markov Chain model, what you will get will be several transition matrices, each of them is a transition matrix for that step, so you basically have a whole time-course of transition matrices.