Markov Chain Transition Analysis

Markov chain transition analysis estimates the probabilities of moving between states from one period to the next, the long-run stationary distribution, and whether the next state depends on the current one.

마르코프 연쇄 전이 분석은 한 시점에서 다음 시점으로 상태가 옮겨갈 확률, 장기 정상분포, 다음 상태가 현재 상태에 의존하는지를 추정하는 방법이다.

How likely are customers to move between subscription tiers each month, and where do they end up?

고객이 매달 구독 등급 사이를 얼마나 옮겨 다니고, 결국 어느 등급에 머무는지 알고 싶어요.

Transitions are counted within each unit's time-ordered sequence and divided by row totals to give the transition matrix. A chi-square test compares the transition table with independence, and the stationary distribution shows the long-run share in each state.

When to use Markov Chain Transition Analysis

• Each unit is observed in a categorical state at repeated times.
• You want transition probabilities, persistence and long-run shares.
• Panel or longitudinal data such as employment status, tiers or health states.

When to use something else

• States are continuous measurements; use a time-series or growth model.
• Transitions depend on covariates or unobserved classes; use a multinomial logistic model or a latent transition model.

Assumptions and requirements

• First-order Markov property.
• Transition probabilities constant over time and units.
• Expected transition counts large enough for the chi-square test.

What the analysis reports

• Transition counts and probabilities
• Stationary distribution
• Chi-square and G² tests of dependence on the current state
• Persistence (diagonal probabilities)

How to report it

Across [value] units and [value] transitions, the next state depended on the current state, χ²([value]) = [value], p = [value].

Related methods

• Chi Square Test
• Markov Switching Regression Model
• Latent Transition Analysis (LTA)

Run Markov Chain Transition Analysis on Quorant