Fit First-Order Vector Autoregressive Models by ID and Save Results

Fits a first-order vector autoregressive model separately for each unit ID and saves each individual fitted model object to an .Rds file. This function fits the same individual-level models as FitVARMxID(), but saves each individual fit to disk. For each unique value of id, the model is fit using the corresponding subset of data. The fitted object for that ID is saved to path with file name prefix_id.Rds, where id is replaced by the unit ID value. The value added by FitVARMxIDSave() is that the individual fits are persisted to disk while the function still returns a collated object of class varmxid, similar to the object returned by FitVARMxID().

Usage

FitVARMxIDSave(
  data,
  observed,
  id,
  time = NULL,
  ct = FALSE,
  center = TRUE,
  path = getwd(),
  prefix = "fitvarmx",
  overwrite = TRUE,
  mu_fixed = FALSE,
  mu_free = NULL,
  mu_values = NULL,
  mu_lbound = NULL,
  mu_ubound = NULL,
  alpha_fixed = FALSE,
  alpha_free = NULL,
  alpha_values = NULL,
  alpha_lbound = NULL,
  alpha_ubound = NULL,
  beta_fixed = FALSE,
  beta_free = NULL,
  beta_values = NULL,
  beta_lbound = NULL,
  beta_ubound = NULL,
  psi_diag = FALSE,
  psi_fixed = FALSE,
  psi_d_free = NULL,
  psi_d_values = NULL,
  psi_d_lbound = NULL,
  psi_d_ubound = NULL,
  psi_d_equal = FALSE,
  psi_l_free = NULL,
  psi_l_values = NULL,
  psi_l_lbound = NULL,
  psi_l_ubound = NULL,
  nu_fixed = TRUE,
  nu_free = NULL,
  nu_values = NULL,
  nu_lbound = NULL,
  nu_ubound = NULL,
  theta_diag = TRUE,
  theta_fixed = TRUE,
  theta_d_free = NULL,
  theta_d_values = NULL,
  theta_d_lbound = NULL,
  theta_d_ubound = NULL,
  theta_d_equal = FALSE,
  theta_l_free = NULL,
  theta_l_values = NULL,
  theta_l_lbound = NULL,
  theta_l_ubound = NULL,
  mu0_fixed = TRUE,
  mu0_func = TRUE,
  mu0_free = NULL,
  mu0_values = NULL,
  mu0_lbound = NULL,
  mu0_ubound = NULL,
  sigma0_fixed = TRUE,
  sigma0_func = TRUE,
  sigma0_diag = FALSE,
  sigma0_d_free = NULL,
  sigma0_d_values = NULL,
  sigma0_d_lbound = NULL,
  sigma0_d_ubound = NULL,
  sigma0_d_equal = FALSE,
  sigma0_l_free = NULL,
  sigma0_l_values = NULL,
  sigma0_l_lbound = NULL,
  sigma0_l_ubound = NULL,
  robust = FALSE,
  seed = NULL,
  tries_explore = 100,
  tries_local = 100,
  max_attempts = 10,
  silent = FALSE,
  ncores = NULL
)

Arguments

data: Data frame. A data frame object of data for potentially multiple subjects that contain a column of subject ID numbers (i.e., an ID variable), and at least one column of observed values.
observed: Character vector. A vector of character strings of the names of the observed variables in the data.
id: Character string. A character string of the name of the ID variable in the data.
time: Character string. A character string of the name of the TIME variable in the data. Used when ct = TRUE.
ct: Logical. If TRUE, fit a continuous-time vector autoregressive model. If FALSE, fit a discrete-time vector autoregressive model.
center: Logical. If TRUE, use the mean-centered (mean-reverting) state equation. When center = TRUE, alpha is implied and the set-point mu is estimated. When center = FALSE, alpha is estimated and mu is implied.
path: Character string. Path to the directory where the individual fitted model objects are saved. The directory must already exist.
prefix: Character string. Prefix used for the saved file names. Files are saved as prefix_id.Rds.
overwrite: Logical. If TRUE, existing saved fitted model objects from a previous run are overwritten. If FALSE, existing files are left unchanged and are read from disk instead.
mu_fixed: Logical. If TRUE, the set-point mean vector mu is fixed to mu_values. If mu_fixed = TRUE and mu_values = NULL, mu is fixed to a zero vector. If FALSE, mu is estimated.
mu_free: Logical vector indicating which elements of mu are freely estimated. If NULL, all elements are free. Ignored if mu_fixed = TRUE.
mu_values: Numeric vector of values for mu. If mu_fixed = TRUE, these are fixed values. If mu_fixed = FALSE, these are starting values. If NULL, defaults to a vector of zeros.
mu_lbound: Numeric vector of lower bounds for mu. Ignored if mu_fixed = TRUE.
mu_ubound: Numeric vector of upper bounds for mu. Ignored if mu_fixed = TRUE.
alpha_fixed: Logical. If TRUE, the dynamic model intercept vector alpha is fixed to alpha_values. If FALSE, alpha is estimated.
alpha_free: Logical vector indicating which elements of alpha are freely estimated. If NULL, all elements are free. Ignored if alpha_fixed = TRUE.
alpha_values: Numeric vector of values for alpha. If alpha_fixed = TRUE, these are fixed values. If alpha_fixed = FALSE, these are starting values. If NULL, defaults to a vector of zeros.
alpha_lbound: Numeric vector of lower bounds for alpha. Ignored if alpha_fixed = TRUE.
alpha_ubound: Numeric vector of upper bounds for alpha. Ignored if alpha_fixed = TRUE.
beta_fixed: Logical. If TRUE, the dynamic model coefficient matrix beta is fixed. If FALSE, beta is estimated.
beta_free: Logical matrix indicating which elements of beta are freely estimated. If NULL, all elements are free. Ignored if beta_fixed = TRUE.
beta_values: Numeric matrix. Values for beta. If beta_fixed = TRUE, these are fixed values; if beta_fixed = FALSE, these are starting values. If NULL, defaults to a diagonal matrix with -0.001 when ct = TRUE and 0.001 when ct = FALSE.
beta_lbound: Numeric matrix. Lower bounds for beta. Ignored if beta_fixed = TRUE. If NULL and ct = FALSE, defaults to -2.5. If NULL and ct = TRUE, defaults to NA.
beta_ubound: Numeric matrix. Upper bounds for beta. Ignored if beta_fixed = TRUE. If NULL and ct = FALSE, defaults to +2.5. If NULL and ct = TRUE, diagonal upper bounds are set to -1e-05 and the off-diagonals are set to NA.
psi_diag: Logical. If TRUE, psi is diagonal. If FALSE, psi is symmetric.
psi_fixed: Logical. If TRUE, the process noise covariance matrix psi is fixed using psi_d_values and psi_l_values. If psi_d_values is NULL it is fixed to a zero matrix. If FALSE, psi is estimated.
psi_d_free: Logical vector indicating free/fixed status of the elements of psi_d. If NULL, all element of psi_d are free.
psi_d_values: Numeric vector with starting values for psi_d. If psi_fixed = TRUE, these are fixed values. If psi_fixed = FALSE, these are starting values.
psi_d_lbound: Numeric vector with lower bounds for psi_d.
psi_d_ubound: Numeric vector with upper bounds for psi_d.
psi_d_equal: Logical. When TRUE, all free diagonal elements of psi_d are constrained to be equal and estimated as a single shared parameter. Ignored if no diagonal elements are free.
psi_l_free: Logical matrix indicating which strictly-lower-triangular elements of psi_l are free. If NULL, all element of psi_l are free. Ignored if psi_diag = TRUE.
psi_l_values: Numeric matrix of starting values for the strictly-lower-triangular elements of psi_l.
psi_l_lbound: Numeric matrix with lower bounds for psi_l.
psi_l_ubound: Numeric matrix with upper bounds for psi_l.
nu_fixed: Logical. If TRUE, the measurement model intercept vector nu is fixed to nu_values. If FALSE, nu is estimated.
nu_free: Logical vector indicating which elements of nu are freely estimated. If NULL, all elements are free. Ignored if nu_fixed = TRUE.
nu_values: Numeric vector of values for nu. If nu_fixed = TRUE, these are fixed values. If nu_fixed = FALSE, these are starting values. If NULL, defaults to a vector of zeros.
nu_lbound: Numeric vector of lower bounds for nu. Ignored if nu_fixed = TRUE.
nu_ubound: Numeric vector of upper bounds for nu. Ignored if nu_fixed = TRUE.
theta_diag: Logical. If TRUE, theta is diagonal. If FALSE, theta is symmetric.
theta_fixed: Logical. If TRUE, the measurement error covariance matrix theta is fixed using theta_d_values and theta_l_values. If theta_d_values is NULL it is fixed to a zero matrix. If FALSE, theta is estimated.
theta_d_free: Logical vector indicating free/fixed status of the diagonal parameters theta_d. If NULL, all element of theta_d are free.
theta_d_values: Numeric vector with starting values for theta_d. If theta_fixed = TRUE, these are fixed values. If theta_fixed = FALSE, these are starting values.
theta_d_lbound: Numeric vector with lower bounds for theta_d.
theta_d_ubound: Numeric vector with upper bounds for theta_d.
theta_d_equal: Logical. When TRUE, all free diagonal elements of theta_d are constrained to be equal and estimated as a single shared parameter. Ignored if no diagonal elements are free.
theta_l_free: Logical matrix indicating which strictly-lower-triangular elements of theta_l are free. If NULL, all element of theta_l are free. Ignored if theta_diag = TRUE.
theta_l_values: Numeric matrix of starting values for the strictly-lower-triangular elements of theta_l.
theta_l_lbound: Numeric matrix with lower bounds for theta_l.
theta_l_ubound: Numeric matrix with upper bounds for theta_l.
mu0_fixed: Logical. If TRUE, the initial mean vector mu0 is fixed. If mu0_fixed = TRUE and mu0_func = TRUE, mu0 is fixed to the implied stable mean vector. If mu0_fixed = TRUE and mu0_values = NULL, mu0 is fixed to a zero vector. If FALSE, mu0 is estimated.
mu0_func: Logical. If TRUE and mu0_fixed = TRUE, mu0 is fixed to the implied stable mean vector.
mu0_free: Logical vector indicating which elements of mu0 are free. Ignored if mu0_fixed = TRUE.
mu0_values: Numeric vector of values for mu0. If mu0_fixed = TRUE, these are fixed values. If mu0_fixed = FALSE, these are starting values. If NULL, defaults to a vector of zeros. Ignored if mu0_fixed = TRUE and mu0_func = TRUE.
mu0_lbound: Numeric vector of lower bounds for mu0. Ignored if mu0_fixed = TRUE.
mu0_ubound: Numeric vector of upper bounds for mu0. Ignored if mu0_fixed = TRUE.
sigma0_fixed: Logical. If TRUE, the initial condition covariance matrix sigma0 is fixed using sigma0_d_values and sigma0_l_values. If sigma0_fixed = TRUE and sigma0_func = TRUE, sigma0 is fixed to the implied stable covariance matrix. If sigma0_fixed = TRUE and sigma0_d_values = NULL, sigma0 is fixed to a diffused matrix.
sigma0_func: Logical. If TRUE and sigma0_fixed = TRUE, sigma0 is fixed to the implied stable covariance matrix.
sigma0_diag: Logical. If TRUE, sigma0 is diagonal. If FALSE, sigma0 is symmetric.
sigma0_d_free: Logical vector indicating free/fixed status of the elements of sigma0_d. If NULL, all element of sigma0_d are free.
sigma0_d_values: Numeric vector with starting values for sigma0_d. If sigma0_fixed = TRUE, these are fixed values. If sigma0_fixed = FALSE, these are starting values.
sigma0_d_lbound: Numeric vector with lower bounds for sigma0_d.
sigma0_d_ubound: Numeric vector with upper bounds for sigma0_d.
sigma0_d_equal: Logical. When TRUE, all free diagonal elements of sigma0_d are constrained to be equal and estimated as a single shared parameter. Ignored if no diagonal elements are free.
sigma0_l_free: Logical matrix indicating which strictly-lower-triangular elements of sigma0_l are free. If NULL, all element of sigma0_l are free. Ignored if sigma0_diag = TRUE.
sigma0_l_values: Numeric matrix of starting values for the strictly-lower-triangular elements of sigma0_l.
sigma0_l_lbound: Numeric matrix with lower bounds for sigma0_l.
sigma0_l_ubound: Numeric matrix with upper bounds for sigma0_l.
robust: Logical. If TRUE, calculate robust (sandwich) sampling variance-covariance matrix.
seed: Random seed for reproducibility.
tries_explore: Integer. Number of extra tries for the wide exploration phase.
tries_local: Integer. Number of extra tries for local polishing.
max_attempts: Integer. Maximum number of remediation attempts after the first Hessian computation fails the criteria.
silent: Logical. If TRUE, suppresses messages during the model fitting stage.
ncores: Positive integer. Number of cores to use.

Value

Returns an object of class varmxid, with the same general structure as FitVARMxID(). The object collates the individual saved fits and contains:

call: Function call.
args: List of function arguments, including path, prefix, and overwrite.
fun: Function used ("FitVARMxIDSave").
model: A list of generated OpenMx models.
output: A list of fitted OpenMx models.
converged: A named logical vector indicating converged cases.
robust: A list of output from OpenMx::imxRobustSE() with argument details = TRUE for each id if robust = TRUE; otherwise NULL.

In addition, each individual fit is saved to disk as an .Rds file. If a model fails for a given ID, an error object is saved as prefix_id_error.Rds, and that ID is omitted from the returned collated varmxid object.

References

Hunter, M. D. (2017). State space modeling in an open source, modular, structural equation modeling environment. Structural Equation Modeling: A Multidisciplinary Journal, 25(2), 307–324. doi:10.1080/10705511.2017.1369354

Neale, M. C., Hunter, M. D., Pritikin, S. M., Zahery, M., Brick, T. R., Kirkpatrick, R. M., Estabrook, R., Bates, T. C., Maes, H. H., & Boker, S. M. (2015). OpenMx 2.0: Extended structural equation and statistical modeling. Psychometrika, 81(2), 535–549. doi:10.1007/s11336-014-9435-8

Examples

# \donttest{
# Generate data using the simStateSpace package ----------------------
set.seed(42)
n <- 5
time <- 100
p <- 2
alpha <- rep(x = 0, times = p)
beta <- 0.50 * diag(p)
psi <- 0.001 * diag(p)
psi_l <- t(chol(psi))
mu0 <- simStateSpace::SSMMeanEta(
  beta = beta,
  alpha = alpha
)
sigma0 <- simStateSpace::SSMCovEta(
  beta = beta,
  psi = psi
)
sigma0_l <- t(chol(sigma0))
sim <- simStateSpace::SimSSMVARFixed(
  n = n,
  time = time,
  mu0 = mu0,
  sigma0_l = sigma0_l,
  alpha = alpha,
  beta = beta,
  psi_l = psi_l
)
data <- as.data.frame(sim)

# Save results to a temporary directory ------------------------------
path <- tempdir()

# Fit the model with person-mean centering ---------------------------
fit <- FitVARMxIDSave(
  data = data,
  observed = paste0("y", seq_len(p)),
  id = "id",
  center = TRUE,
  path = path,
  prefix = "fitvarmx_centered"
)
#> Running DTVAR_ID1 with 9 parameters
#> 
#> Beginning initial fit attempt
#> Running DTVAR_ID1 with 9 parameters
#> 
#>  Lowest minimum so far:  -822.060942313193
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-822.06094 (started at 367.82482)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> 0.331612745243841,-0.0197631400065759,0.0270181292624815,0.539260086092713,0.0057946951525851,0.007106199232002,0.0623713422440293,-6.91195717901486,-6.98806630902827
#> Running DTVAR_ID2 with 9 parameters
#> 
#> Beginning initial fit attempt
#> Running DTVAR_ID2 with 9 parameters
#> 
#>  Lowest minimum so far:  -834.035953636412
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-834.03595 (started at 367.84346)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> 0.546679030340841,-0.0201020488638611,-0.0487574618599386,0.297450290600703,-0.00284153166188121,-0.0199122101192943,0.176134255014816,-7.14253861726531,-6.87719884724769
#> Running DTVAR_ID3 with 9 parameters
#> 
#> Beginning initial fit attempt
#> Running DTVAR_ID3 with 9 parameters
#> 
#>  Lowest minimum so far:  -808.550007472268
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-808.55001 (started at 367.87017)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> 0.528105561142997,-0.332501283495961,0.0108536161301484,0.361419705300276,-0.00426229999671594,-0.00173173484843314,-0.21387789357269,-6.9657202697529,-6.80024208411447
#> Running DTVAR_ID4 with 9 parameters
#> 
#> Beginning initial fit attempt
#> Running DTVAR_ID4 with 9 parameters
#> 
#>  Lowest minimum so far:  -845.339407101868
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-845.33941 (started at 367.80199)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> 0.160844162100514,-0.121824766994102,-0.0298919550660853,0.481815653357755,-0.0130955259827441,0.00326100822229185,0.00601848006477796,-7.23151794331632,-6.89984913049538
#> Running DTVAR_ID5 with 9 parameters
#> 
#> Beginning initial fit attempt
#> Running DTVAR_ID5 with 9 parameters
#> 
#>  Lowest minimum so far:  -832.354548096018
#> 
#> Solution found
#> 


#> 
#>  Solution found!  Final fit=-832.35455 (started at 367.7976)  (1 attempt(s): 1 valid, 0 errors)
#>  Start values from best fit:
#> 0.299055985152669,0.0348621727088368,-0.0801687055865619,0.465890390856868,-0.00111115045695215,0.00331563195705935,-0.166419668597626,-6.91180267781828,-7.08999323366805
#> 
#> See /tmp/RtmpTiALvo for the saved results.
print(fit)
#> Call:
#> FitVARMxIDSave(data = data, observed = paste0("y", seq_len(p)), 
#>     id = "id", center = TRUE, path = path, prefix = "fitvarmx_centered")
#> 
#> Convergence:
#> 100.0%
#> 
#> Estimated paramaters per individual.
#>   mu[1,1] mu[2,1] beta[1,1] beta[2,1] beta[1,2] beta[2,2] psi[1,1] psi[2,1]
#> 1  0.0058  0.0071    0.3316   -0.0198    0.0270    0.5393    1e-03    1e-04
#> 2 -0.0028 -0.0199    0.5467   -0.0201   -0.0488    0.2975    8e-04    1e-04
#> 3 -0.0043 -0.0017    0.5281   -0.3325    0.0109    0.3614    9e-04   -2e-04
#> 4 -0.0131  0.0033    0.1608   -0.1218   -0.0299    0.4818    7e-04    0e+00
#> 5 -0.0011  0.0033    0.2991    0.0349   -0.0802    0.4659    1e-03   -2e-04
#>   psi[2,2]
#> 1   0.0009
#> 2   0.0011
#> 3   0.0012
#> 4   0.0010
#> 5   0.0009
summary(fit)
#> Call:
#> FitVARMxIDSave(data = data, observed = paste0("y", seq_len(p)), 
#>     id = "id", center = TRUE, path = path, prefix = "fitvarmx_centered")
#> 
#> Convergence:
#> 100.0%
#> 
#> Estimated paramaters per individual.
#>   mu[1,1] mu[2,1] beta[1,1] beta[2,1] beta[1,2] beta[2,2] psi[1,1] psi[2,1]
#> 1  0.0058  0.0071    0.3316   -0.0198    0.0270    0.5393    1e-03    1e-04
#> 2 -0.0028 -0.0199    0.5467   -0.0201   -0.0488    0.2975    8e-04    1e-04
#> 3 -0.0043 -0.0017    0.5281   -0.3325    0.0109    0.3614    9e-04   -2e-04
#> 4 -0.0131  0.0033    0.1608   -0.1218   -0.0299    0.4818    7e-04    0e+00
#> 5 -0.0011  0.0033    0.2991    0.0349   -0.0802    0.4659    1e-03   -2e-04
#>   psi[2,2]
#> 1   0.0009
#> 2   0.0011
#> 3   0.0012
#> 4   0.0010
#> 5   0.0009
coef(fit)
#> $`1`
#>       mu[1,1]       mu[2,1]     beta[1,1]     beta[2,1]     beta[1,2] 
#>  5.794695e-03  7.106199e-03  3.316127e-01 -1.976314e-02  2.701813e-02 
#>     beta[2,2]      psi[1,1]      psi[2,1]      psi[2,2] 
#>  5.392601e-01  9.953214e-04  6.207953e-05  9.262857e-04 
#> 
#> $`2`
#>       mu[1,1]       mu[2,1]     beta[1,1]     beta[2,1]     beta[1,2] 
#> -0.0028415317 -0.0199122101  0.5466790303 -0.0201020489 -0.0487574619 
#>     beta[2,2]      psi[1,1]      psi[2,1]      psi[2,2] 
#>  0.2974502906  0.0007904397  0.0001392235  0.0010550290 
#> 
#> $`3`
#>       mu[1,1]       mu[2,1]     beta[1,1]     beta[2,1]     beta[1,2] 
#> -0.0042623000 -0.0017317348  0.5281055611 -0.3325012835  0.0108536161 
#>     beta[2,2]      psi[1,1]      psi[2,1]      psi[2,2] 
#>  0.3614197053  0.0009432480 -0.0002017399  0.0011560438 
#> 
#> $`4`
#>       mu[1,1]       mu[2,1]     beta[1,1]     beta[2,1]     beta[1,2] 
#> -1.309553e-02  3.261008e-03  1.608442e-01 -1.218248e-01 -2.989196e-02 
#>     beta[2,2]      psi[1,1]      psi[2,1]      psi[2,2] 
#>  4.818157e-01  7.231704e-04  4.352386e-06  1.007466e-03 
#> 
#> $`5`
#>       mu[1,1]       mu[2,1]     beta[1,1]     beta[2,1]     beta[1,2] 
#> -0.0011111505  0.0033156320  0.2990559852  0.0348621727 -0.0801687056 
#>     beta[2,2]      psi[1,1]      psi[2,1]      psi[2,2] 
#>  0.4658903909  0.0009954751 -0.0001656666  0.0008606361 
#> 
vcov(fit)
#> $`1`
#>                 mu[1,1]       mu[2,1]     beta[1,1]     beta[2,1]     beta[1,2]
#> mu[1,1]    2.224531e-05  2.743979e-06 -5.546138e-06  5.372819e-06  1.426060e-05
#> mu[2,1]    2.743979e-06  4.246265e-05 -8.513834e-08  2.692920e-07 -6.084754e-06
#> beta[1,1] -5.546138e-06 -8.513834e-08  8.856671e-03  5.015831e-04 -6.327507e-04
#> beta[2,1]  5.372819e-06  2.692920e-07  5.015831e-04  8.222799e-03 -5.447017e-05
#> beta[1,2]  1.426060e-05 -6.084754e-06 -6.327507e-04 -5.447017e-05  7.838173e-03
#> beta[2,2]  1.561657e-06  2.505703e-05 -3.578235e-05 -5.710681e-04  4.375766e-04
#> psi[1,1]  -6.356703e-11  4.508286e-10 -6.465520e-08 -2.604991e-09 -2.201980e-09
#> psi[2,1]   1.052388e-09  1.585577e-09 -1.335929e-08 -4.590393e-08 -4.219508e-08
#> psi[2,2]   2.048862e-10 -5.688192e-10 -2.195562e-09  1.320718e-09 -6.345910e-09
#>               beta[2,2]      psi[1,1]      psi[2,1]      psi[2,2]
#> mu[1,1]    1.561657e-06 -6.356703e-11  1.052388e-09  2.048862e-10
#> mu[2,1]    2.505703e-05  4.508286e-10  1.585577e-09 -5.688192e-10
#> beta[1,1] -3.578235e-05 -6.465520e-08 -1.335929e-08 -2.195562e-09
#> beta[2,1] -5.710681e-04 -2.604991e-09 -4.590393e-08  1.320718e-09
#> beta[1,2]  4.375766e-04 -2.201980e-09 -4.219508e-08 -6.345910e-09
#> beta[2,2]  7.234812e-03  3.359103e-09  1.100977e-08 -1.024578e-07
#> psi[1,1]   3.359103e-09  1.981853e-08  1.237250e-09  7.717316e-11
#> psi[2,1]   1.100977e-08  1.237250e-09  9.257098e-09  1.150936e-09
#> psi[2,2]  -1.024578e-07  7.717316e-11  1.150936e-09  1.716564e-08
#> 
#> $`2`
#>                 mu[1,1]       mu[2,1]     beta[1,1]     beta[2,1]     beta[1,2]
#> mu[1,1]    3.711430e-05  1.028041e-06 -1.259632e-06 -1.486527e-06 -6.233540e-06
#> mu[2,1]    1.028041e-06  2.111878e-05 -5.442272e-07 -5.152523e-06  3.401863e-06
#> beta[1,1] -1.259632e-06 -5.442272e-07  7.020210e-03  1.240322e-03 -7.462724e-04
#> beta[2,1] -1.486527e-06 -5.152523e-06  1.240322e-03  9.418442e-03 -1.528294e-04
#> beta[1,2] -6.233540e-06  3.401863e-06 -7.462724e-04 -1.528294e-04  6.909651e-03
#> beta[2,2] -5.125566e-07 -6.251956e-06 -1.319441e-04 -9.994834e-04  1.212534e-03
#> psi[1,1]   1.736505e-10  4.490027e-10 -8.316323e-08 -4.757987e-09 -5.289942e-10
#> psi[2,1]   4.315405e-10  1.152683e-09 -1.582423e-09 -3.001699e-08 -4.177727e-08
#> psi[2,2]  -6.295115e-11 -1.484608e-10 -2.478939e-10 -5.296051e-10 -4.988704e-09
#>               beta[2,2]      psi[1,1]      psi[2,1]      psi[2,2]
#> mu[1,1]   -5.125566e-07  1.736505e-10  4.315405e-10 -6.295115e-11
#> mu[2,1]   -6.251956e-06  4.490027e-10  1.152683e-09 -1.484608e-10
#> beta[1,1] -1.319441e-04 -8.316323e-08 -1.582423e-09 -2.478939e-10
#> beta[2,1] -9.994834e-04 -4.757987e-09 -3.001699e-08 -5.296051e-10
#> beta[1,2]  1.212534e-03 -5.289942e-10 -4.177727e-08 -4.988704e-09
#> beta[2,2]  9.204832e-03 -6.900777e-10 -4.464222e-09 -6.176501e-08
#> psi[1,1]  -6.900777e-10  1.249914e-08  2.199571e-09  3.880986e-10
#> psi[2,1]  -4.464222e-09  2.199571e-09  8.528443e-09  2.938846e-09
#> psi[2,2]  -6.176501e-08  3.880986e-10  2.938846e-09  2.226704e-08
#> 
#> $`3`
#>                 mu[1,1]       mu[2,1]     beta[1,1]     beta[2,1]     beta[1,2]
#> mu[1,1]    4.014794e-05 -2.654775e-05 -4.975392e-06  3.545267e-08  6.952597e-06
#> mu[2,1]   -2.654775e-05  4.483621e-05 -7.485950e-06  1.159674e-05 -2.039629e-05
#> beta[1,1] -4.975392e-06 -7.485950e-06  8.624703e-03 -1.819206e-03  2.783507e-03
#> beta[2,1]  3.545267e-08  1.159674e-05 -1.819206e-03  1.025332e-02 -5.999974e-04
#> beta[1,2]  6.952597e-06 -2.039629e-05  2.783507e-03 -5.999974e-04  6.799241e-03
#> beta[2,2] -1.948947e-06  7.272828e-06 -6.216471e-04  3.312132e-03 -1.494444e-03
#> psi[1,1]  -1.436036e-09  1.121628e-09 -8.827167e-08  6.928421e-08 -1.229378e-08
#> psi[2,1]  -5.397337e-09 -2.352972e-09  1.362150e-07 -6.786872e-08  2.827157e-08
#> psi[2,2]   4.203122e-09 -3.178531e-10 -8.092158e-08  6.993384e-09 -5.252178e-09
#>               beta[2,2]      psi[1,1]      psi[2,1]      psi[2,2]
#> mu[1,1]   -1.948947e-06 -1.436036e-09 -5.397337e-09  4.203122e-09
#> mu[2,1]    7.272828e-06  1.121628e-09 -2.352972e-09 -3.178531e-10
#> beta[1,1] -6.216471e-04 -8.827167e-08  1.362150e-07 -8.092158e-08
#> beta[2,1]  3.312132e-03  6.928421e-08 -6.786872e-08  6.993384e-09
#> beta[1,2] -1.494444e-03 -1.229378e-08  2.827157e-08 -5.252178e-09
#> beta[2,2]  8.033171e-03  3.692584e-09  4.371743e-09 -7.603266e-08
#> psi[1,1]   3.692584e-09  1.776845e-08 -3.803148e-09  8.297955e-10
#> psi[2,1]   4.371743e-09 -3.803148e-09  1.136282e-08 -4.703032e-09
#> psi[2,2]  -7.603266e-08  8.297955e-10 -4.703032e-09  2.676450e-08
#> 
#> $`4`
#>                 mu[1,1]       mu[2,1]     beta[1,1]     beta[2,1]     beta[1,2]
#> mu[1,1]    1.043712e-05 -3.604418e-06  4.814324e-06 -1.628211e-06 -1.951168e-07
#> mu[2,1]   -3.604418e-06  3.796609e-05  3.531995e-07 -3.004506e-06  7.858673e-06
#> beta[1,1]  4.814324e-06  3.531995e-07  9.865757e-03  3.424691e-05  2.406062e-04
#> beta[2,1] -1.628211e-06 -3.004506e-06  3.424691e-05  1.342206e-02 -2.793637e-05
#> beta[1,2] -1.951168e-07  7.858673e-06  2.406062e-04 -2.793637e-05  5.470098e-03
#> beta[2,2]  7.280477e-08 -1.813611e-06 -3.572421e-06  3.342110e-04  1.482257e-05
#> psi[1,1]   1.858414e-10  6.042985e-10 -1.927989e-08  1.700900e-08  1.075401e-08
#> psi[2,1]   1.409379e-10 -3.190850e-09  6.911712e-09 -4.795484e-08 -6.116108e-08
#> psi[2,2]  -2.788222e-10 -8.534671e-10 -6.757041e-09  2.822853e-10 -7.525012e-09
#>               beta[2,2]      psi[1,1]      psi[2,1]      psi[2,2]
#> mu[1,1]    7.280477e-08  1.858414e-10  1.409379e-10 -2.788222e-10
#> mu[2,1]   -1.813611e-06  6.042985e-10 -3.190850e-09 -8.534671e-10
#> beta[1,1] -3.572421e-06 -1.927989e-08  6.911712e-09 -6.757041e-09
#> beta[2,1]  3.342110e-04  1.700900e-08 -4.795484e-08  2.822853e-10
#> beta[1,2]  1.482257e-05  1.075401e-08 -6.116108e-08 -7.525012e-09
#> beta[2,2]  7.419211e-03 -1.769062e-09  1.850297e-08 -9.165652e-08
#> psi[1,1]  -1.769062e-09  1.046050e-08  6.372424e-11  1.141598e-12
#> psi[2,1]   1.850297e-08  6.372424e-11  7.297033e-09  9.078742e-11
#> psi[2,2]  -9.165652e-08  1.141598e-12  9.078742e-11  2.030675e-08
#> 
#> $`5`
#>                 mu[1,1]       mu[2,1]     beta[1,1]     beta[2,1]     beta[1,2]
#> mu[1,1]    2.115776e-05 -6.312505e-06 -9.365997e-07 -7.441133e-06  2.767397e-07
#> mu[2,1]   -6.312505e-06  2.876505e-05  3.661845e-08  8.679316e-08 -8.396412e-07
#> beta[1,1] -9.365997e-07  3.661845e-08  9.209205e-03 -1.527788e-03  1.910733e-03
#> beta[2,1] -7.441133e-06  8.679316e-08 -1.527788e-03  8.067790e-03 -3.233289e-04
#> beta[1,2]  2.767397e-07 -8.396412e-07  1.910733e-03 -3.233289e-04  9.374810e-03
#> beta[2,2] -6.090495e-08 -7.854492e-06 -3.163124e-04  1.665073e-03 -1.546388e-03
#> psi[1,1]  -1.799574e-10 -2.759494e-11 -6.116907e-08  1.073268e-08 -2.432120e-09
#> psi[2,1]  -1.077773e-09 -4.450186e-10  1.327054e-08 -2.513345e-08 -2.731715e-08
#> psi[2,2]   5.203866e-10  2.457130e-10 -6.550906e-10 -7.755098e-09  2.272470e-08
#>               beta[2,2]      psi[1,1]      psi[2,1]      psi[2,2]
#> mu[1,1]   -6.090495e-08 -1.799574e-10 -1.077773e-09  5.203866e-10
#> mu[2,1]   -7.854492e-06 -2.759494e-11 -4.450186e-10  2.457130e-10
#> beta[1,1] -3.163124e-04 -6.116907e-08  1.327054e-08 -6.550906e-10
#> beta[2,1]  1.665073e-03  1.073268e-08 -2.513345e-08 -7.755098e-09
#> beta[1,2] -1.546388e-03 -2.432120e-09 -2.731715e-08  2.272470e-08
#> beta[2,2]  8.178308e-03  1.594600e-09  1.057114e-08 -8.224086e-08
#> psi[1,1]   1.594600e-09  1.982445e-08 -3.299155e-09  5.501745e-10
#> psi[2,1]   1.057114e-08 -3.299155e-09  8.842776e-09 -2.854392e-09
#> psi[2,2]  -8.224086e-08  5.501745e-10 -2.854392e-09  1.481772e-08
#> 
converged(fit)
#>    1    2    3    4    5 
#> TRUE TRUE TRUE TRUE TRUE 
confint(fit)
#> $`1`
#>                     est           se          z            p          2.5%
#> mu[1,1]    5.794695e-03 4.716494e-03  1.2286023 2.192209e-01 -0.0034494626
#> mu[2,1]    7.106199e-03 6.516337e-03  1.0905206 2.754839e-01 -0.0056655862
#> beta[1,1]  3.316127e-01 9.410989e-02  3.5236760 4.256043e-04  0.1471607586
#> beta[2,1] -1.976314e-02 9.067965e-02 -0.2179446 8.274723e-01 -0.1974919839
#> beta[1,2]  2.701813e-02 8.853346e-02  0.3051742 7.602335e-01 -0.1465042608
#> beta[2,2]  5.392601e-01 8.505770e-02  6.3399328 2.298653e-10  0.3725500634
#> psi[1,1]   9.953214e-04 1.407783e-04  7.0701331 1.547852e-12  0.0007194010
#> psi[2,1]   6.207953e-05 9.621382e-05  0.6452247 5.187816e-01 -0.0001264961
#> psi[2,2]   9.262857e-04 1.310177e-04  7.0699276 1.550145e-12  0.0006694957
#>                  97.5%
#> mu[1,1]   0.0150388529
#> mu[2,1]   0.0198779847
#> beta[1,1] 0.5160647319
#> beta[2,1] 0.1579657039
#> beta[1,2] 0.2005405193
#> beta[2,2] 0.7059701088
#> psi[1,1]  0.0012712419
#> psi[2,1]  0.0002506551
#> psi[2,2]  0.0011830757
#> 
#> $`2`
#>                     est           se          z            p          2.5%
#> mu[1,1]   -0.0028415317 6.092150e-03 -0.4664251 6.409113e-01 -1.478193e-02
#> mu[2,1]   -0.0199122101 4.595517e-03 -4.3329637 1.471154e-05 -2.891926e-02
#> beta[1,1]  0.5466790303 8.378669e-02  6.5246521 6.815955e-11  3.824601e-01
#> beta[2,1] -0.0201020489 9.704866e-02 -0.2071337 8.359054e-01 -2.103139e-01
#> beta[1,2] -0.0487574619 8.312431e-02 -0.5865608 5.574987e-01 -2.116781e-01
#> beta[2,2]  0.2974502906 9.594182e-02  3.1003196 1.933119e-03  1.094078e-01
#> psi[1,1]   0.0007904397 1.117995e-04  7.0701511 1.547651e-12  5.713166e-04
#> psi[2,1]   0.0001392235 9.234957e-05  1.5075707 1.316644e-01 -4.177832e-05
#> psi[2,2]   0.0010550290 1.492214e-04  7.0702241 1.546837e-12  7.625603e-04
#>                   97.5%
#> mu[1,1]    0.0090988639
#> mu[2,1]   -0.0109051615
#> beta[1,1]  0.7108979333
#> beta[2,1]  0.1701098267
#> beta[1,2]  0.1141631945
#> beta[2,2]  0.4854927942
#> psi[1,1]   0.0010095628
#> psi[2,1]   0.0003202253
#> psi[2,2]   0.0013474976
#> 
#> $`3`
#>                     est           se          z            p          2.5%
#> mu[1,1]   -0.0042623000 0.0063362402 -0.6726860 5.011471e-01 -0.0166811025
#> mu[2,1]   -0.0017317348 0.0066959846 -0.2586229 7.959262e-01 -0.0148556235
#> beta[1,1]  0.5281055611 0.0928692778  5.6865475 1.296333e-08  0.3460851215
#> beta[2,1] -0.3325012835 0.1012586808 -3.2836818 1.024605e-03 -0.5309646510
#> beta[1,2]  0.0108536161 0.0824575110  0.1316268 8.952795e-01 -0.1507601357
#> beta[2,2]  0.3614197053 0.0896279579  4.0324438 5.519981e-05  0.1857521358
#> psi[1,1]   0.0009432480 0.0001332983  7.0762167 1.481432e-12  0.0006819880
#> psi[2,1]  -0.0002017399 0.0001065965 -1.8925564 5.841689e-02 -0.0004106652
#> psi[2,2]   0.0011560438 0.0001635986  7.0663433 1.590696e-12  0.0008353964
#>                   97.5%
#> mu[1,1]    8.156503e-03
#> mu[2,1]    1.139215e-02
#> beta[1,1]  7.101260e-01
#> beta[2,1] -1.340379e-01
#> beta[1,2]  1.724674e-01
#> beta[2,2]  5.370873e-01
#> psi[1,1]   1.204508e-03
#> psi[2,1]   7.185418e-06
#> psi[2,2]   1.476691e-03
#> 
#> $`4`
#>                     est           se           z            p          2.5%
#> mu[1,1]   -1.309553e-02 3.230653e-03 -4.05352239 5.045217e-05 -0.0194274903
#> mu[2,1]    3.261008e-03 6.161663e-03  0.52924156 5.966379e-01 -0.0088156295
#> beta[1,1]  1.608442e-01 9.932652e-02  1.61934768 1.053725e-01 -0.0338322305
#> beta[2,1] -1.218248e-01 1.158536e-01 -1.05154040 2.930105e-01 -0.3488936994
#> beta[1,2] -2.989196e-02 7.396011e-02 -0.40416319 6.860927e-01 -0.1748511120
#> beta[2,2]  4.818157e-01 8.613484e-02  5.59373709 2.222334e-08  0.3129944678
#> psi[1,1]   7.231704e-04 1.022766e-04  7.07073379 1.541165e-12  0.0005227120
#> psi[2,1]   4.352386e-06 8.542267e-05  0.05095119 9.593644e-01 -0.0001630730
#> psi[2,2]   1.007466e-03 1.425018e-04  7.06984995 1.551013e-12  0.0007281677
#>                   97.5%
#> mu[1,1]   -0.0067635616
#> mu[2,1]    0.0153376460
#> beta[1,1]  0.3555205547
#> beta[2,1]  0.1052441654
#> beta[1,2]  0.1150672019
#> beta[2,2]  0.6506368389
#> psi[1,1]   0.0009236288
#> psi[2,1]   0.0001717777
#> psi[2,2]   0.0012867644
#> 
#> $`5`
#>                     est           se          z            p          2.5%
#> mu[1,1]   -0.0011111505 4.599757e-03 -0.2415672 8.091155e-01 -0.0101265080
#> mu[2,1]    0.0033156320 5.363306e-03  0.6182068 5.364391e-01 -0.0071962544
#> beta[1,1]  0.2990559852 9.596461e-02  3.1163155 1.831262e-03  0.1109688153
#> beta[2,1]  0.0348621727 8.982088e-02  0.3881300 6.979199e-01 -0.1411835079
#> beta[1,2] -0.0801687056 9.682360e-02 -0.8279872 4.076777e-01 -0.2699394786
#> beta[2,2]  0.4658903909 9.043400e-02  5.1517173 2.581119e-07  0.2886430126
#> psi[1,1]   0.0009954751 1.407993e-04  7.0701700 1.547440e-12  0.0007195135
#> psi[2,1]  -0.0001656666 9.403604e-05 -1.7617357 7.811397e-02 -0.0003499739
#> psi[2,2]   0.0008606361 1.217281e-04  7.0701532 1.547627e-12  0.0006220535
#>                  97.5%
#> mu[1,1]   0.0079042071
#> mu[2,1]   0.0138275183
#> beta[1,1] 0.4871431550
#> beta[2,1] 0.2109078533
#> beta[1,2] 0.1096020674
#> beta[2,2] 0.6431377691
#> psi[1,1]  0.0012714367
#> psi[2,1]  0.0000186406
#> psi[2,2]  0.0010992187
#> 
plot(fit)









# }