SimSSMLinGrowthIVary {simStateSpace} | R Documentation |
Simulate Data from the Linear Growth Curve Model (Individual-Varying Parameters)
Description
This function simulates data from the linear growth curve model. It assumes that the parameters can vary across individuals.
Usage
SimSSMLinGrowthIVary(
n,
time,
mu0,
sigma0_l,
theta_l,
type = 0,
x = NULL,
gamma = NULL,
kappa = NULL
)
Arguments
n |
Positive integer. Number of individuals. |
time |
Positive integer. Number of time points. |
mu0 |
A list of numeric vectors. Each element of the list is a vector of length two. The first element is the mean of the intercept, and the second element is the mean of the slope. |
sigma0_l |
A list of numeric matrices.
Each element of the list is the
Cholesky factorization ( |
theta_l |
A list numeric values. Each element of the list is the square root of the common measurement error variance. |
type |
Integer.
State space model type.
See Details in |
x |
List.
Each element of the list is a matrix of covariates
for each individual |
gamma |
List of numeric matrices.
Each element of the list
is the matrix linking the covariates to the latent variables
at current time point
( |
kappa |
List of numeric matrices.
Each element of the list
is the matrix linking the covariates to the observed variables
at current time point
( |
Details
Parameters can vary across individuals
by providing a list of parameter values.
If the length of any of the parameters
(mu0
,
sigma0
,
mu
,
theta_l
,
gamma
, or
kappa
)
is less the n
,
the function will cycle through the available values.
Value
Returns an object of class simstatespace
which is a list with the following elements:
-
call
: Function call. -
args
: Function arguments. -
data
: Generated data which is a list of lengthn
. Each element ofdata
is a list with the following elements:-
id
: A vector of ID numbers with lengthl
, wherel
is the value of the function argumenttime
. -
time
: A vector time points of lengthl
. -
y
: Al
byk
matrix of values for the manifest variables. -
eta
: Al
byp
matrix of values for the latent variables. -
x
: Al
byj
matrix of values for the covariates (when covariates are included).
-
-
fun
: Function used.
Author(s)
Ivan Jacob Agaloos Pesigan
References
Chow, S.-M., Ho, M. R., Hamaker, E. L., & Dolan, C. V. (2010). Equivalence and differences between structural equation modeling and state-space modeling techniques. Structural Equation Modeling: A Multidisciplinary Journal, 17(2), 303–332. doi:10.1080/10705511003661553
See Also
Other Simulation of State Space Models Data Functions:
LinSDE2SSM()
,
SimBetaN()
,
SimPhiN()
,
SimSSMFixed()
,
SimSSMIVary()
,
SimSSMLinGrowth()
,
SimSSMLinSDEFixed()
,
SimSSMLinSDEIVary()
,
SimSSMOUFixed()
,
SimSSMOUIVary()
,
SimSSMVARFixed()
,
SimSSMVARIVary()
,
TestPhi()
,
TestStability()
,
TestStationarity()
Other Simulation of State Space Models Data Functions:
LinSDE2SSM()
,
SimBetaN()
,
SimPhiN()
,
SimSSMFixed()
,
SimSSMIVary()
,
SimSSMLinGrowth()
,
SimSSMLinSDEFixed()
,
SimSSMLinSDEIVary()
,
SimSSMOUFixed()
,
SimSSMOUIVary()
,
SimSSMVARFixed()
,
SimSSMVARIVary()
,
TestPhi()
,
TestStability()
,
TestStationarity()
Examples
# prepare parameters
# In this example, the mean vector of the intercept and slope vary.
# Specifically,
# there are two sets of values representing two latent classes.
set.seed(42)
## number of individuals
n <- 10
## time points
time <- 5
## dynamic structure
p <- 2
mu0_1 <- c(0.615, 1.006) # lower starting point, higher growth
mu0_2 <- c(1.000, 0.500) # higher starting point, lower growth
mu0 <- list(mu0_1, mu0_2)
sigma0 <- matrix(
data = c(
1.932,
0.618,
0.618,
0.587
),
nrow = p
)
sigma0_l <- list(t(chol(sigma0)))
## measurement model
k <- 1
theta <- 0.50
theta_l <- list(sqrt(theta))
## covariates
j <- 2
x <- lapply(
X = seq_len(n),
FUN = function(i) {
matrix(
data = stats::rnorm(n = time * j),
nrow = j,
ncol = time
)
}
)
gamma <- list(
diag(x = 0.10, nrow = p, ncol = j)
)
kappa <- list(
diag(x = 0.10, nrow = k, ncol = j)
)
# Type 0
ssm <- SimSSMLinGrowthIVary(
n = n,
time = time,
mu0 = mu0,
sigma0_l = sigma0_l,
theta_l = theta_l,
type = 0
)
plot(ssm)
# Type 1
ssm <- SimSSMLinGrowthIVary(
n = n,
time = time,
mu0 = mu0,
sigma0_l = sigma0_l,
theta_l = theta_l,
type = 1,
x = x,
gamma = gamma
)
plot(ssm)
# Type 2
ssm <- SimSSMLinGrowthIVary(
n = n,
time = time,
mu0 = mu0,
sigma0_l = sigma0_l,
theta_l = theta_l,
type = 2,
x = x,
gamma = gamma,
kappa = kappa
)
plot(ssm)