sim_mHMM: Simulate data using a multilevel hidden Markov model
In mHMMbayes: Multilevel Hidden Markov Models Using Bayesian Estimation
sim_mHMM R Documentation
Simulate data using a multilevel hidden Markov model
Description
sim_mHMM simulates data for multiple subjects, for which the data have
either categorical or continuous (i.e., normally distributed)
observations that follow a hidden Markov model (HMM) with a
multilevel structure. The multilevel structure implies that each subject is
allowed to have its own set of parameters, and that the parameters at the
subject level (level 1) are tied together by a population distribution at
level 2 for each of the corresponding parameters. The shape of the population
distribution for each of the parameters is a normal distribution. In addition
to (natural and/or unexplained) heterogeneity between subjects, the subjects
parameters can also depend on a covariate.
Usage
sim_mHMM(
n_t,
n,
data_distr = "categorical",
gen,
gamma,
emiss_distr,
start_state = NULL,
xx_vec = NULL,
beta = NULL,
var_gamma = 0.1,
var_emiss = NULL,
return_ind_par = FALSE,
m,
n_dep,
q_emiss,
log_scale = FALSE
)
Arguments
n_t
Numeric vector with length 1 denoting the length of the observed
sequence to be simulated for each subject. To only simulate subject
specific transition probability matrices gamma and emission distributions
(and no data), set t to 0.
n
Numeric vector with length 1 denoting the number of subjects for
which data is simulated.
data_distr
A character vector of length 1 denoting the distribution
adopted for the data given the hidden states. It can take the values
'categorical', 'continuous', or 'count', standing for the for categorical
observations following a Multinomial logit, continuous observations
following a normal distribution, and count observations following a
Poisson distribution, correspondingly.
gen
List containing the following elements denoting the general model
properties:
m: numeric vector with length 1 denoting the number
of hidden states
n_dep: numeric vector with length 1 denoting the
number of dependent variables
q_emiss: only to be specified if the data represents
categorical data. Numeric vector with length n_dep denoting the
number of observed categories for the categorical emission distribution
for each of the dependent variables.
gamma
A matrix with m rows and m columns containing the
average population transition probability matrix used for simulating the
data. That is, the probability to switch from hidden state i (row
i) to hidden state j (column j).
emiss_distr
A list with n_dep elements containing the average
population emission distribution(s) of the observations given the hidden
states for each of the dependent variables. If data_distr =
'categorical', each element is a matrix with m rows and
q_emiss[k] columns for each of the k in n_dep emission
distribution(s). That is, the probability of observing category q
(column q) in state i (row i). If data_distr =
'continuous', each element is a matrix with m rows and 2 columns;
the first column denoting the mean of state i (row i) and the
second column denoting the standard deviation of state i
(row i) of the Normal distribution. If data_distr =
'count', each element is a matrix with m rows and 1 column;
the only column denoting the logmean of state i (row i)
of the lognormal distribution used as prior for the Poisson emissions
(note: by default the logmeans should be specified in the natural scale;
see argument log_scale below, unless covariates are used to predict
a count emission distribution).
start_state
Optional numeric vector with length 1 denoting in which
state the simulated state sequence should start. If left unspecified, the
simulated state for time point 1 is sampled from the initial state
distribution (which is derived from the transition probability matrix
gamma).
xx_vec
List of 1 + n_dep vectors containing the covariate(s) to
predict the transition probability matrix gamma and/or (specific)
emission distribution(s) emiss_distr using the regression parameters
specified in beta (see below). The first element in the list
xx_vec is used to predict the transition matrix. Subsequent elements
in the list are used to predict the emission distribution of (each of) the
dependent variable(s). This means that the covariate used to predict
gamma and emiss_distr can either be the same covariate,
different covariates, or a covariate for certain elements and none for the
other. At this point, it is only possible to use one covariate for both
gamma and emiss_distr. For all elements in the list,
the number of observations in the vectors should be equal to the number of
subjects to be simulated n. If xx_vec is omitted completely,
xx_vec defaults to NULL, resembling no covariates at all. Specific
elements in the list can also be left empty (i.e., set to NULL) to
signify that either the transition probability matrix or (one of) the
emission distribution(s) is not predicted by covariates.
beta
List of 1 + n_dep matrices containing the regression
parameters to predict gamma and/or emiss_distr in combination
with xx_vec using (Multinomial logistic) regression. The first
matrix is used to predict the transition probability matrix gamma.
The subsequent matrices are used to predict the emission distribution(s)
emiss_distr of the dependent variable(s). For gamma and
categorical emission distributions, one regression parameter is specified
for each element in gamma and emiss_distr, with the following
exception. The first element in each row of gamma and/or
emiss_distr is used as reference category in the Multinomial
logistic regression. As such, no regression parameters can be specified for
these parameters. Hence, the first element in the list beta to
predict gamma consist of a matrix with the number of rows equal to
m and the number of columns equal to m - 1. For categorical
emission distributions, the subsequent elements in the list beta to
predict emiss_distr consist of a matrix with the number of rows
equal to m and the number of columns equal to q_emiss[k] - 1
for each of the k in n_dep emission distribution(s). See
details for more information. For continuous and count emission
distributions, the subsequent elements in the list beta consist of
a matrix with the number of rows equal to m and 1 column.
Note that if beta is specified, xx_vec has to be specified as
well. If beta is omitted completely, beta defaults to NULL,
resembling no prediction of gamma and emiss_distr using
covariates. One of the elements in the list can also be left empty
(i.e., set to NULL) to signify that either the transition
probability matrix or a specific emission distribution is not predicted by
covariates. If covariates are used to predict a count emission
distribution (data_distr = 'count'), then the logarithmic scale
should be used for the inputs emiss_distr and var_emiss in
addition to beta, and also set log_scale = TRUE.
var_gamma
Either a numeric vector with length 1 or a matrix of
(m by m - 1) elements denoting the amount of variance
between subjects in the transition probability matrix. Note that the
value(s) correspond to the variance of the parameters of the Multinomial
distribution (i.e., the intercepts of the regression equation of the
Multinomial distribution used to sample the transition probability
matrix), see details below. Also note that if only one variance value is
provided, it will be adopted for the complete transition probability
matrix, hence the variance is assumed fixed across all components. The
default equals 0.1, which corresponds to little variation between
subjects. If one wants to simulate data from exactly the same HMM for all
subjects, var_gamma should be set to 0. Note that if data for only 1
subject is simulated (i.e., n = 1), var_gamma is set to 0.
var_emiss
Either a numeric vector with length n_dep or a
list of n_dep matrices denoting the amount of variance between
subjects in the emission distribution(s). When opting for a list of
matrices: if data_distr = 'categorical', each element of the list
is a matrix with m rows and q_emiss[k] - 1 columns for each
of the k in n_dep emission distribution(s) between subject
variances; if data_distr = 'continuous', each element is a matrix
with m rows and 1 column; the single column denoting the variance
between the subjects' means of state i (row i) of the normal
distribution used as prior for the Normal emissions. If data_distr =
'count', each element is a matrix with m rows and 1 column; the
single column denoting the logvariance between the subjects' logmeans of
state i (row i) of the lognormal distribution used as prior
for the Poisson emissions (note: by default the logvariances should be
specified in the natural scale; see argument log_scale below).
For categorical data, this value corresponds to the variance of the
parameters of the Multinomial distribution (i.e., the intercepts of the
regression equation of the Multinomial distribution used to sample the
components of the emission distribution), see details below. For
continuous data, this value corresponds to the variance in the mean of the
emission distribution(s) across subjects. For count data, it corresponds
to the variance in the logmean of the emission distribution(s) across
subjects and by should be specified in the natural scale (see argument
log_scale below). Note that if only one variance value provided for
each emission distribution, the variance is assumed fixed across states
(and, for the categorical distribution, categories within a state) within
an emission distribution. The default equals 0.1, which corresponds to
little variation between subjects given categorical observations. If one
wants to simulate data from exactly the same HMM for all subjects,
var_emiss should be set to a vector of 0's. Note that if data for only 1
subject is simulated (i.e., n = 1), var_emiss is set to a vector
of 0's.
return_ind_par
A logical scalar. Should the subject specific
transition probability matrix gamma and emission probability matrix
emiss_distr be returned by the function (return_ind_par =
TRUE) or not (return_ind_par = FALSE). The default equals
return_ind_par = FALSE.
m
The argument m is deprecated; please specify using the input
parameter gen.
n_dep
The argument n_dep is deprecated; please specify using
the input parameter gen.
q_emiss
The argument q_emiss is deprecated; please specify
using the input parameter gen (only to be specified when simulating
categorical data).
log_scale
A logical scalar. If data_distr = 'count', should
emiss_distr (i.e., the sample average logmeans) and
var_emiss (i.e., the between subject logvariances) of the lognormal
prior adopted for the count be specified in the logarithmic scale
(log_scale = TRUE) or the natural (i.e., real positive numbers)
scale (log_scale = FALSE). The default equals
log_scale = FALSE. Note that if covariates beta are used to
predict the count emission distribution, then the logarithmic scale should
be used for the inputs emiss_distr, beta, and
var_emiss, and also set log_scale = TRUE.
Details
In simulating the data, having a multilevel structure means that the
parameters for each subject are sampled from the population level
distribution of the corresponding parameter. The user specifies the
population distribution for each parameter: the average population transition
probability matrix and its variance, and the average population emission
distribution and its variance. For now, the variance of the mean population
parameters is assumed fixed for all components of the transition probability
matrix and for all components of the emission distribution.
One can simulate multivariate data. That is, the hidden states depend on more
than 1 observed variable simultaneously. The distributions of multiple
dependent variables for multivariate data are assumed to be independent, and
all distributions for one dataset have to be of the same type (either
categorical or continuous).
Note that the subject specific initial state distributions (i.e., the
probability of each of the states at the first time point) needed to simulate
the data are obtained from the stationary distributions of the subject
specific transition probability matrices gamma.
beta: As the first element in each row of gamma is used as
reference category in the Multinomial logistic regression, the first matrix
in the list beta used to predict transition probability matrix
gamma has a number of rows equal to m and the number of columns
equal to m - 1. The first element in the first row corresponds to the
probability of switching from state one to state two. The second element in
the first row corresponds to the probability of switching from state one to
state three, and so on. The last element in the first row corresponds to the
probability of switching from state one to the last state. The same principle
holds for the second matrix in the list beta used to predict
categorical emission distribution(s) emiss_distr: the first element in
the first row corresponds to the probability of observing category two in
state one. The second element in the first row corresponds to the probability
of observing category three is state one, and so on. The last element in the
first row corresponds to the probability of observing the last category in
state one.
Note that when simulating count data (data_distr = 'count'), by
default the emission distribution parameters emiss_distr and
var_emiss are specified in the natural (positive real numbers) scale
(as opposite to the logarithmic scale). If the user wants to manually
specify these values on the logarithmic scale, please set the argument
log_scale = TRUE. Also note that if covariates are used to predict a
count emission distribution, then the logarithmic scale should be used for
the inputs emiss_distr, beta, and var_emiss, and also
set log_scale = TRUE.
Value
The following components are returned by the function sim_mHMM:
statesA matrix containing the simulated hidden state
sequences, with one row per hidden state per subject. The first column
indicates subject id number. The second column contains the simulated
hidden state sequence, consecutively for all subjects. Hence, the id number
is repeated over the rows (with the number of repeats equal to the length
of the simulated hidden state sequence T for each subject).
obsA matrix containing the simulated observed outputs, with
one row per simulated observation per subject. The first column indicates
subject id number. The second column contains the simulated observation
sequence, consecutively for all subjects. Hence, the id number is repeated
over rows (with the number of repeats equal to the length of the simulated
observation sequence T for each subject).
gammaA list containing n elements with the simulated
subject specific transition probability matrices gamma. Only
returned if return_ind_par is set to TRUE.
emiss_distrA list containing n elements with the
simulated subject specific emission probability matrices
emiss_distr. Only returned if return_ind_par is set to
TRUE.
See Also
mHMM for analyzing multilevel hidden Markov data.
Examples
## Examples on univariate categorical data
# simulating data for 10 subjects with each 100 categorical observations
n_t <- 100
n <- 10
m <- 3
n_dep <- 1
q_emiss <- 4
gamma <- matrix(c(0.8, 0.1, 0.1,
0.2, 0.7, 0.1,
0.2, 0.2, 0.6), ncol = m, byrow = TRUE)
emiss_distr <- list(matrix(c(0.5, 0.5, 0.0, 0.0,
0.1, 0.1, 0.8, 0.0,
0.0, 0.0, 0.1, 0.9), nrow = m, ncol = q_emiss, byrow = TRUE))
data1 <- sim_mHMM(n_t = n_t, n = n, gen = list(m = m, n_dep = n_dep, q_emiss = q_emiss),
gamma = gamma, emiss_distr = emiss_distr, var_gamma = 1, var_emiss = 1)
head(data1$obs)
head(data1$states)
# including a covariate to predict (only) the transition probability matrix gamma
beta <- rep(list(NULL), 2)
beta[[1]] <- matrix(c(0.5, 1.0,
-0.5, 0.5,
0.0, 1.0), byrow = TRUE, ncol = 2)
xx_vec <- rep(list(NULL),2)
xx_vec[[1]] <- c(rep(0,5), rep(1,5))
data2 <- sim_mHMM(n_t = n_t, n = n, gen = list(m = m, n_dep = n_dep, q_emiss = q_emiss),
gamma = gamma, emiss_distr = emiss_distr, beta = beta, xx_vec = xx_vec,
var_gamma = 1, var_emiss = 1)
# simulating subject specific transition probability matrices and emission distributions only
n_t <- 0
n <- 5
m <- 3
n_dep <- 1
q_emiss <- 4
gamma <- matrix(c(0.8, 0.1, 0.1,
0.2, 0.7, 0.1,
0.2, 0.2, 0.6), ncol = m, byrow = TRUE)
emiss_distr <- list(matrix(c(0.5, 0.5, 0.0, 0.0,
0.1, 0.1, 0.8, 0.0,
0.0, 0.0, 0.1, 0.9), nrow = m, ncol = q_emiss, byrow = TRUE))
data3 <- sim_mHMM(n_t = n_t, n = n, gen = list(m = m, n_dep = n_dep, q_emiss = q_emiss),
gamma = gamma, emiss_distr = emiss_distr, var_gamma = 1, var_emiss = 1)
data3
data4 <- sim_mHMM(n_t = n_t, n = n, gen = list(m = m, n_dep = n_dep, q_emiss = q_emiss),
gamma = gamma, emiss_distr = emiss_distr, var_gamma = .5, var_emiss = .5)
data4
## Example on multivariate continuous data
# simulating multivariate continuous data
n_t <- 100
n <- 10
m <- 3
n_dep <- 2
gamma <- matrix(c(0.8, 0.1, 0.1,
0.2, 0.7, 0.1,
0.2, 0.2, 0.6), ncol = m, byrow = TRUE)
emiss_distr <- list(matrix(c( 50, 10,
100, 10,
150, 10), nrow = m, byrow = TRUE),
matrix(c(5, 2,
10, 5,
20, 3), nrow = m, byrow = TRUE))
data_cont <- sim_mHMM(n_t = n_t, n = n, data_distr = 'continuous',
gen = list(m = m, n_dep = n_dep),
gamma = gamma, emiss_distr = emiss_distr,
var_gamma = .5, var_emiss = c(5^2, 0.2^2))
head(data_cont$states)
head(data_cont$obs)
## Example on multivariate count data without covariates
n_t <- 200 # Number of observations on the dependent variable
m <- 3 # Number of hidden states
n_dep <- 2 # Number of dependent variables
n_subj <- 30 # Number of subjects
gamma <- matrix(c(0.9, 0.05, 0.05,
0.2, 0.7, 0.1,
0.2,0.3, 0.5), ncol = m, byrow = TRUE)
emiss_distr <- list(matrix(c(20,
10,
5), nrow = m, byrow = TRUE),
matrix(c(50,
3,
20), nrow = m, byrow = TRUE))
# Define between subject variance to use on the simulating function:
# here, the variance is varied over states within the dependent variable.
var_emiss <- list(matrix(c(5.0, 3.0, 1.5), nrow = m),
matrix(c(5.0, 5.0, 5.0), nrow = m))
# Simulate count data:
data_count <- sim_mHMM(n_t = n_t,
n = n_subj,
data_distr = "count",
gen = list(m = m, n_dep = n_dep),
gamma = gamma,
emiss_distr = emiss_distr,
var_gamma = 0.1,
var_emiss = var_emiss,
return_ind_par = TRUE)
## Example on multivariate count data with covariates
# Simulate data with one covariate for each count dependent variable
n_t <- 200 # Number of observations on the dependent variable
m <- 3 # Number of hidden states
n_dep <- 3 # Number of dependent variables
n_subj <- 30 # Number of subjects
gamma <- matrix(c(0.9, 0.05, 0.05,
0.2, 0.7, 0.1,
0.2,0.3, 0.5), ncol = m, byrow = TRUE)
emiss_distr <- list(matrix(c(20,
10,
5), nrow = m, byrow = TRUE),
matrix(c(15,
2,
5), nrow = m, byrow = TRUE),
matrix(c(50,
3,
20), nrow = m, byrow = TRUE))
# Since we have covariates, we specify inputs in the log scale:
emiss_distr_log <- lapply(emiss_distr, function(e) log(e))
# Define list of vectors of covariate values
set.seed(42)
xx_vec <- c(list(NULL),rep(list(rnorm(n_subj,mean = 0, sd = 0.1)),3))
# Define object beta with regression coefficients for the three dependent variables
beta <- rep(list(NULL), n_dep+1)
beta[[2]] <- matrix(c(1,-1,0), byrow = TRUE, ncol = 1)
beta[[3]] <- matrix(c(2,0,-2), byrow = TRUE, ncol = 1)
beta[[4]] <- matrix(c(-1,3,1), byrow = TRUE, ncol = 1)
# Calculate logvar to use on the simulating function:
logvar <- var_to_logvar(gen = list(m = m, n_dep = n_dep),
emiss_mu = emiss_distr,
var_emiss = list(rep(4, m),
rep(2, m),
rep(5, m)),
byrow = FALSE)
# Put logvar in the right format:
logvar <- lapply(logvar, function(q) matrix(q, nrow = m))
# Simulate count data:
data_count <- sim_mHMM(n_t = n_t,
n = n_subj,
data_distr = "count",
gen = list(m = m, n_dep = n_dep),
gamma = gamma,
emiss_distr = emiss_distr_log,
xx_vec = xx_vec,
beta = beta,
var_gamma = 0.1,
var_emiss = logvar,
return_ind_par = TRUE,
log_scale = TRUE)
head(data_count$states)
head(data_count$obs)
mHMMbayes documentation built on May 29, 2024, 6:41 a.m.
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| sim_mHMM | R Documentation |
Simulate data using a multilevel hidden Markov model
Description
sim_mHMM simulates data for multiple subjects, for which the data have
either categorical or continuous (i.e., normally distributed)
observations that follow a hidden Markov model (HMM) with a
multilevel structure. The multilevel structure implies that each subject is
allowed to have its own set of parameters, and that the parameters at the
subject level (level 1) are tied together by a population distribution at
level 2 for each of the corresponding parameters. The shape of the population
distribution for each of the parameters is a normal distribution. In addition
to (natural and/or unexplained) heterogeneity between subjects, the subjects
parameters can also depend on a covariate.
Usage
sim_mHMM(
n_t,
n,
data_distr = "categorical",
gen,
gamma,
emiss_distr,
start_state = NULL,
xx_vec = NULL,
beta = NULL,
var_gamma = 0.1,
var_emiss = NULL,
return_ind_par = FALSE,
m,
n_dep,
q_emiss,
log_scale = FALSE
)
Arguments
n_t |
Numeric vector with length 1 denoting the length of the observed
sequence to be simulated for each subject. To only simulate subject
specific transition probability matrices gamma and emission distributions
(and no data), set |
n |
Numeric vector with length 1 denoting the number of subjects for which data is simulated. |
data_distr |
A character vector of length 1 denoting the distribution adopted for the data given the hidden states. It can take the values 'categorical', 'continuous', or 'count', standing for the for categorical observations following a Multinomial logit, continuous observations following a normal distribution, and count observations following a Poisson distribution, correspondingly. |
gen |
List containing the following elements denoting the general model properties:
|
gamma |
A matrix with |
emiss_distr |
A list with |
start_state |
Optional numeric vector with length 1 denoting in which state the simulated state sequence should start. If left unspecified, the simulated state for time point 1 is sampled from the initial state distribution (which is derived from the transition probability matrix gamma). |
xx_vec |
List of 1 + |
beta |
List of 1 + Note that if |
var_gamma |
Either a numeric vector with length 1 or a matrix of
( |
var_emiss |
Either a numeric vector with length For categorical data, this value corresponds to the variance of the
parameters of the Multinomial distribution (i.e., the intercepts of the
regression equation of the Multinomial distribution used to sample the
components of the emission distribution), see details below. For
continuous data, this value corresponds to the variance in the mean of the
emission distribution(s) across subjects. For count data, it corresponds
to the variance in the logmean of the emission distribution(s) across
subjects and by should be specified in the natural scale (see argument
|
return_ind_par |
A logical scalar. Should the subject specific
transition probability matrix |
m |
The argument |
n_dep |
The argument |
q_emiss |
The argument |
log_scale |
A logical scalar. If |
Details
In simulating the data, having a multilevel structure means that the parameters for each subject are sampled from the population level distribution of the corresponding parameter. The user specifies the population distribution for each parameter: the average population transition probability matrix and its variance, and the average population emission distribution and its variance. For now, the variance of the mean population parameters is assumed fixed for all components of the transition probability matrix and for all components of the emission distribution.
One can simulate multivariate data. That is, the hidden states depend on more than 1 observed variable simultaneously. The distributions of multiple dependent variables for multivariate data are assumed to be independent, and all distributions for one dataset have to be of the same type (either categorical or continuous).
Note that the subject specific initial state distributions (i.e., the probability of each of the states at the first time point) needed to simulate the data are obtained from the stationary distributions of the subject specific transition probability matrices gamma.
beta: As the first element in each row of gamma is used as
reference category in the Multinomial logistic regression, the first matrix
in the list beta used to predict transition probability matrix
gamma has a number of rows equal to m and the number of columns
equal to m - 1. The first element in the first row corresponds to the
probability of switching from state one to state two. The second element in
the first row corresponds to the probability of switching from state one to
state three, and so on. The last element in the first row corresponds to the
probability of switching from state one to the last state. The same principle
holds for the second matrix in the list beta used to predict
categorical emission distribution(s) emiss_distr: the first element in
the first row corresponds to the probability of observing category two in
state one. The second element in the first row corresponds to the probability
of observing category three is state one, and so on. The last element in the
first row corresponds to the probability of observing the last category in
state one.
Note that when simulating count data (data_distr = 'count'), by
default the emission distribution parameters emiss_distr and
var_emiss are specified in the natural (positive real numbers) scale
(as opposite to the logarithmic scale). If the user wants to manually
specify these values on the logarithmic scale, please set the argument
log_scale = TRUE. Also note that if covariates are used to predict a
count emission distribution, then the logarithmic scale should be used for
the inputs emiss_distr, beta, and var_emiss, and also
set log_scale = TRUE.
Value
The following components are returned by the function sim_mHMM:
statesA matrix containing the simulated hidden state sequences, with one row per hidden state per subject. The first column indicates subject id number. The second column contains the simulated hidden state sequence, consecutively for all subjects. Hence, the id number is repeated over the rows (with the number of repeats equal to the length of the simulated hidden state sequence
Tfor each subject).obsA matrix containing the simulated observed outputs, with one row per simulated observation per subject. The first column indicates subject id number. The second column contains the simulated observation sequence, consecutively for all subjects. Hence, the id number is repeated over rows (with the number of repeats equal to the length of the simulated observation sequence
Tfor each subject).gammaA list containing
nelements with the simulated subject specific transition probability matricesgamma. Only returned ifreturn_ind_paris set toTRUE.emiss_distrA list containing
nelements with the simulated subject specific emission probability matricesemiss_distr. Only returned ifreturn_ind_paris set toTRUE.
See Also
mHMM for analyzing multilevel hidden Markov data.
Examples
## Examples on univariate categorical data
# simulating data for 10 subjects with each 100 categorical observations
n_t <- 100
n <- 10
m <- 3
n_dep <- 1
q_emiss <- 4
gamma <- matrix(c(0.8, 0.1, 0.1,
0.2, 0.7, 0.1,
0.2, 0.2, 0.6), ncol = m, byrow = TRUE)
emiss_distr <- list(matrix(c(0.5, 0.5, 0.0, 0.0,
0.1, 0.1, 0.8, 0.0,
0.0, 0.0, 0.1, 0.9), nrow = m, ncol = q_emiss, byrow = TRUE))
data1 <- sim_mHMM(n_t = n_t, n = n, gen = list(m = m, n_dep = n_dep, q_emiss = q_emiss),
gamma = gamma, emiss_distr = emiss_distr, var_gamma = 1, var_emiss = 1)
head(data1$obs)
head(data1$states)
# including a covariate to predict (only) the transition probability matrix gamma
beta <- rep(list(NULL), 2)
beta[[1]] <- matrix(c(0.5, 1.0,
-0.5, 0.5,
0.0, 1.0), byrow = TRUE, ncol = 2)
xx_vec <- rep(list(NULL),2)
xx_vec[[1]] <- c(rep(0,5), rep(1,5))
data2 <- sim_mHMM(n_t = n_t, n = n, gen = list(m = m, n_dep = n_dep, q_emiss = q_emiss),
gamma = gamma, emiss_distr = emiss_distr, beta = beta, xx_vec = xx_vec,
var_gamma = 1, var_emiss = 1)
# simulating subject specific transition probability matrices and emission distributions only
n_t <- 0
n <- 5
m <- 3
n_dep <- 1
q_emiss <- 4
gamma <- matrix(c(0.8, 0.1, 0.1,
0.2, 0.7, 0.1,
0.2, 0.2, 0.6), ncol = m, byrow = TRUE)
emiss_distr <- list(matrix(c(0.5, 0.5, 0.0, 0.0,
0.1, 0.1, 0.8, 0.0,
0.0, 0.0, 0.1, 0.9), nrow = m, ncol = q_emiss, byrow = TRUE))
data3 <- sim_mHMM(n_t = n_t, n = n, gen = list(m = m, n_dep = n_dep, q_emiss = q_emiss),
gamma = gamma, emiss_distr = emiss_distr, var_gamma = 1, var_emiss = 1)
data3
data4 <- sim_mHMM(n_t = n_t, n = n, gen = list(m = m, n_dep = n_dep, q_emiss = q_emiss),
gamma = gamma, emiss_distr = emiss_distr, var_gamma = .5, var_emiss = .5)
data4
## Example on multivariate continuous data
# simulating multivariate continuous data
n_t <- 100
n <- 10
m <- 3
n_dep <- 2
gamma <- matrix(c(0.8, 0.1, 0.1,
0.2, 0.7, 0.1,
0.2, 0.2, 0.6), ncol = m, byrow = TRUE)
emiss_distr <- list(matrix(c( 50, 10,
100, 10,
150, 10), nrow = m, byrow = TRUE),
matrix(c(5, 2,
10, 5,
20, 3), nrow = m, byrow = TRUE))
data_cont <- sim_mHMM(n_t = n_t, n = n, data_distr = 'continuous',
gen = list(m = m, n_dep = n_dep),
gamma = gamma, emiss_distr = emiss_distr,
var_gamma = .5, var_emiss = c(5^2, 0.2^2))
head(data_cont$states)
head(data_cont$obs)
## Example on multivariate count data without covariates
n_t <- 200 # Number of observations on the dependent variable
m <- 3 # Number of hidden states
n_dep <- 2 # Number of dependent variables
n_subj <- 30 # Number of subjects
gamma <- matrix(c(0.9, 0.05, 0.05,
0.2, 0.7, 0.1,
0.2,0.3, 0.5), ncol = m, byrow = TRUE)
emiss_distr <- list(matrix(c(20,
10,
5), nrow = m, byrow = TRUE),
matrix(c(50,
3,
20), nrow = m, byrow = TRUE))
# Define between subject variance to use on the simulating function:
# here, the variance is varied over states within the dependent variable.
var_emiss <- list(matrix(c(5.0, 3.0, 1.5), nrow = m),
matrix(c(5.0, 5.0, 5.0), nrow = m))
# Simulate count data:
data_count <- sim_mHMM(n_t = n_t,
n = n_subj,
data_distr = "count",
gen = list(m = m, n_dep = n_dep),
gamma = gamma,
emiss_distr = emiss_distr,
var_gamma = 0.1,
var_emiss = var_emiss,
return_ind_par = TRUE)
## Example on multivariate count data with covariates
# Simulate data with one covariate for each count dependent variable
n_t <- 200 # Number of observations on the dependent variable
m <- 3 # Number of hidden states
n_dep <- 3 # Number of dependent variables
n_subj <- 30 # Number of subjects
gamma <- matrix(c(0.9, 0.05, 0.05,
0.2, 0.7, 0.1,
0.2,0.3, 0.5), ncol = m, byrow = TRUE)
emiss_distr <- list(matrix(c(20,
10,
5), nrow = m, byrow = TRUE),
matrix(c(15,
2,
5), nrow = m, byrow = TRUE),
matrix(c(50,
3,
20), nrow = m, byrow = TRUE))
# Since we have covariates, we specify inputs in the log scale:
emiss_distr_log <- lapply(emiss_distr, function(e) log(e))
# Define list of vectors of covariate values
set.seed(42)
xx_vec <- c(list(NULL),rep(list(rnorm(n_subj,mean = 0, sd = 0.1)),3))
# Define object beta with regression coefficients for the three dependent variables
beta <- rep(list(NULL), n_dep+1)
beta[[2]] <- matrix(c(1,-1,0), byrow = TRUE, ncol = 1)
beta[[3]] <- matrix(c(2,0,-2), byrow = TRUE, ncol = 1)
beta[[4]] <- matrix(c(-1,3,1), byrow = TRUE, ncol = 1)
# Calculate logvar to use on the simulating function:
logvar <- var_to_logvar(gen = list(m = m, n_dep = n_dep),
emiss_mu = emiss_distr,
var_emiss = list(rep(4, m),
rep(2, m),
rep(5, m)),
byrow = FALSE)
# Put logvar in the right format:
logvar <- lapply(logvar, function(q) matrix(q, nrow = m))
# Simulate count data:
data_count <- sim_mHMM(n_t = n_t,
n = n_subj,
data_distr = "count",
gen = list(m = m, n_dep = n_dep),
gamma = gamma,
emiss_distr = emiss_distr_log,
xx_vec = xx_vec,
beta = beta,
var_gamma = 0.1,
var_emiss = logvar,
return_ind_par = TRUE,
log_scale = TRUE)
head(data_count$states)
head(data_count$obs)
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