Transition Probability Matrix
The Cox Hazard model produces continuous hazard rates that will be discretized to produce piecewise constant rates.
The process is repeated for each of the transition rates (4 transitions for 3-state model, and 12 transitions for 5-state model). The rates at each age are combined into transition rate matrices for that age. Taking the matrix exponential changes that to transition probability matrices.
Note
The transition probability matrices are deterministic for each individual with the Static and Trend models, but stochastic with the Frailty model.
Get a List of Transition Probability Matrices from Initial Age to Age 110
get_trans_probs(n_states, model_type, param_file, init_age, female, year = 2012, wave_index = 8, latent = 0)
Parameters
n_states : numeric
take values 3 or 5, use 3 for 3-state model, and 5 for 5-state model
model_type : character
'S' for static model, 'T' for trend model, 'F' for frailty model
param_file : dataframe
File path, or dataframe/tibble of parameters (generally, use US_HRS or china_CLHLS for the 3-state model, and use US_HRS_5 for the 5-state-model)
init_age : numeric
integer denoting the initial age
female : numeric
0 for male, 1 for female
year : numeric
integer denoting current year, required in 3-state model and ignored in 5-state model
wave_index : numeric
integer for the wave index = (interview year - 1998)/2 + 1, required in 5-state model and ignored in 3-state model
latent : numeric
initial value of latent factor, normally take the value 0
Returns:
List of 3x3 or 5x5 transition probability matrices, from the initial age to age 110.
Usage: