Latent Hidden Markov Models for Response Process Data.

proclhmm: Latent Hidden Markov Model for Process Data

This package provides functions for simulating from and fitting the latent hidden Markov models for response process data (Tang, 2024). It also includes functions for simulating from and fitting ordinary hidden Markov models.

Installation

You can install the development version of proclhmm from GitHub with

devtools::install_github("xytangtang/proclhmm")

Basic Usage

Simulate Parameters and Data

library(proclhmm)
N <- 10 # number of actions
K <- 3 # number of hidden states

# generate parameters
set.seed(12345)
paras_true <- sim_lhmm_paras(N, K)

n <- 100 # sample size
# generate data
data0 <- sim_lhmm(n, paras_true, min_len = 4, mean_len = 25)
action_seqs <- data0$seqs # action sequences

Estimating parameters and latent traits

# generate initial values of parameters
paras_init <- sim_lhmm_paras(N, K)
# model fitting
lhmm_res <- lhmm(action_seqs, K, paras_init)
#> Optimizing obj fun...
#> Computing theta...
# estimated discrimation parameters for state transition probability matrix
lhmm_res$paras_est$para_a
#>            state2       state3
#> state1 -0.6088158 -15.52584332
#> state2 -2.3456255  -2.83225548
#> state3 -4.5802817   0.08433227
# estimated location parameters for state-action probability matrix
lhmm_res$paras_est$para_beta
#>                 4          0          5         9         6         7
#> state1 -0.9987221  4.4206005  2.3740381 -1.472788 -6.503268  4.059780
#> state2  0.5821316 -1.4579551  0.5479029  1.214155  1.044911  0.736849
#> state3 -3.2111616 -0.5614971 -0.3598079 -6.618605 -4.027255 -1.426849
#>                  1          2         8
#> state1  3.24121223  4.1195709 -5.666249
#> state2 -0.32826612  0.2443809 -8.464710
#> state3 -0.05355758 -1.0904959 -9.719579

Most likely hidden state sequences

# compute state-transition and state-action probability matrix for the first action sequnece
paras_est <- lhmm_res$paras_est
paras_PQ <- compute_PQ_lhmm(lhmm_res$theta_est[1], paras_est$para_a, paras_est$para_b, paras_est$para_alpha, paras_est$para_beta)
P <- paras_PQ$P
Q <- paras_PQ$Q
# compute initial state probability
P1 <- compute_P1_lhmm(paras_est$para_P1)
# find the most likely hidden state sequences for the first action sequence
find_state_seq(action_seqs[[1]], P1, P, Q)
#>  [1] 2 1 2 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 1 2 1 2 1 1 2 1