Build a Latent Class Model
Function build_lcm is a shortcut for constructing a latent class model
as a restricted case of an mhmm object.
build_lcm(observations, n_clusters, emission_probs, formula, data, coefficients, cluster_names = NULL, channel_names = NULL)
observations |
An |
n_clusters |
A scalar giving the number of clusters/submodels
(not used if starting values for model parameters are given with |
emission_probs |
A matrix containing emission probabilities for each class by rows,
or in case of multichannel data a list of such matrices.
Note that the matrices must have dimensions k x s where k is the number of
latent classes and s is the number of unique symbols (observed states) in the
data. Emission probabilities should follow the ordering of the alphabet of
observations ( |
formula |
Covariates as an object of class |
data |
An optional data frame, list or environment containing the variables
in the model. If not found in data, the variables are taken from
|
coefficients |
An optional k x l matrix of regression coefficients for time-constant covariates for mixture probabilities, where l is the number of clusters and k is the number of covariates. A logit-link is used for mixture probabilities. The first column is set to zero. |
cluster_names |
A vector of optional names for the classes/clusters. |
channel_names |
A vector of optional names for the channels. |
Object of class mhmm with the following elements:
observationsState sequence object or a list of such containing the data.
transition_probsA matrix of transition probabilities.
emission_probsA matrix or a list of matrices of emission probabilities.
initial_probsA vector of initial probabilities.
coefficientsA matrix of parameter coefficients for covariates (covariates in rows, clusters in columns).
XCovariate values for each subject.
cluster_namesNames for clusters.
state_namesNames for hidden states.
symbol_namesNames for observed states.
channel_namesNames for channels of sequence data
length_of_sequences(Maximum) length of sequences.
n_sequencesNumber of sequences.
n_symbolsNumber of observed states (in each channel).
n_statesNumber of hidden states.
n_channelsNumber of channels.
n_covariatesNumber of covariates.
n_clustersNumber of clusters.
fit_model for estimating model parameters;
summary.mhmm for a summary of a mixture model;
separate_mhmm for organizing an mhmm object into a list of
separate hmm objects; and plot.mhmm for plotting
mixture models.
# Simulate observations from two classes
set.seed(123)
obs <- seqdef(rbind(
matrix(sample(letters[1:3], 500, TRUE, prob = c(0.1, 0.6, 0.3)), 50, 10),
matrix(sample(letters[1:3], 200, TRUE, prob = c(0.4, 0.4, 0.2)), 20, 10)))
# Initialize the model
set.seed(9087)
model <- build_lcm(obs, n_clusters = 2)
# Estimate model parameters
fit <- fit_model(model)
# How many of the observations were correctly classified:
sum(summary(fit$model)$most_probable_cluster == rep(c("Class 2", "Class 1"), times = c(500, 200)))
############################################################
## Not run:
# LCM for longitudinal data
# Define sequence data
data("mvad", package = "TraMineR")
mvad_alphabet <- c("employment", "FE", "HE", "joblessness", "school",
"training")
mvad_labels <- c("employment", "further education", "higher education",
"joblessness", "school", "training")
mvad_scodes <- c("EM", "FE", "HE", "JL", "SC", "TR")
mvad_seq <- seqdef(mvad, 17:86, alphabet = mvad_alphabet, states = mvad_scodes,
labels = mvad_labels, xtstep = 6)
# Initialize the LCM with random starting values
set.seed(7654)
init_lcm_mvad1 <- build_lcm(observations = mvad_seq,
n_clusters = 2, formula = ~male, data = mvad)
# Own starting values for emission probabilities
emiss <- rbind(rep(1/6, 6), rep(1/6, 6))
# LCM with own starting values
init_lcm_mvad2 <- build_lcm(observations = mvad_seq,
emission_probs = emiss, formula = ~male, data = mvad)
# Estimate model parameters (EM algorithm with random restarts)
lcm_mvad <- fit_model(init_lcm_mvad1,
control_em = list(restart = list(times = 5)))$model
# Plot the LCM
plot(lcm_mvad, interactive = FALSE, ncol = 2)
###################################################################
# Binomial regression (comparison to glm)
require("MASS")
data("birthwt")
model <- build_lcm(
observations = seqdef(birthwt$low), emission_probs = diag(2),
formula = ~age + lwt + smoke + ht, data = birthwt)
fit <- fit_model(model)
summary(fit$model)
summary(glm(low ~ age + lwt + smoke + ht, binomial, data = birthwt))
# Multinomial regression (comparison to multinom)
require("nnet")
set.seed(123)
n <- 100
X <- cbind(1, x1 = runif(n, 0, 1), x2 = runif(n, 0, 1))
coefs <- cbind(0,c(-2, 5, -2), c(0, -2, 2))
pr <- exp(X %*% coefs) + rnorm(n*3)
pr <- pr/rowSums(pr)
y <- apply(pr, 1, which.max)
table(y)
model <- build_lcm(
observations = seqdef(y), emission_probs = diag(3),
formula = ~x1 + x2, data = data.frame(X[, -1]))
fit <- fit_model(model)
summary(fit$model)
summary(multinom(y ~ x1 + x2, data = data.frame(X[,-1])))
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