Estimation

The estimation of a transition matrix is one of the core functionalities of transitionMatrix. Several methods and variations are available in the literature depending on aspects such as:

• The nature of the observations / data (e.g., whether temporal homogeneity is a valid assumption)
• Whether or not there are competing risk effects
• Whether or not observations have coincident values
• Treating the Right-Censorship of observations (Outcomes beyond the observation window)
• Treating the Left-Truncation of observations (Outcomes prior to the the observation window)

Estimator Types

• Cohort Based Methods that group observations in cohorts
• Duration (also Hazard Rate or Intensity) Based Methods that utilize the actual duration of each state

The main estimators currently implemented are as follows:

Implemented Estimators

• Simple Estimator
• Cohort Estimator
• Aalen-Johansen Estimator

Whichever the estimator choice, the outcome of the estimation is an Empirical Transition Matrix (or potentially a matrix set)

Implementation Notes

• All estimators derive from the highest level BaseEstimator class.
• Duration type estimators derive from the DurationEstimator class

Estimation Examples

The first example of estimating a transition matrix is covered in the Getting Started section. Here we have a few more examples:

Estimation Example 1

Example workflows using transitionMatrix to estimate an empirical transition matrix from duration type data. The datasets are produced using examples/generate_synthetic_data.py This example uses the Aalen-Johansen estimator

• Script: examples/python/empirical_transition_matrix.py

By setting the example variable the script covers a number of variations:

• Version 1: Credit Rating Migration example
• Version 2: Simple 2x2 Matrix for testing
• Version 3: Credit Rating Migration example with timestamps in raw date format

Plot of estimated transition probabilities

Estimation Example 2

Example workflows using transitionMatrix to estimate a transition matrix from data that are in duration format. The datasets are first grouped in period cohorts

• Script: examples/python/matrix_from_duration_data.py