mult.latent.reg (version 0.1.9)

mult.reg_1level: Selecting the best results for multivariate one level model

Description

This wrapper function runs multiple times the function mult.em_1level for fitting Zhang and Einbeck's (2024) multivariate response models with one-level random effect, and select the best results with the smallest AIC value.

Value

The best estimated result (with the smallest AIC value) in the model (Zhang and Einbeck, 2024) \(x_{i} = \alpha + \beta z_k + \Gamma v_i + \varepsilon_i\) obtained through the EM algorithm.

p

The estimates for the parameter \(\pi_k\), which is a vector of length \(K\).

alpha

The estimates for the parameter \(\alpha\), which is a vector of length \(m\).

z

The estimates for the parameter \(z_k\), which is a vector of length \(K\).

beta

The estimates for the parameter \(\beta\), which is a vector of length \(m\).

gamma

The estimates for the parameter \(\Gamma\), which is a matrix.

sigma

The estimates for the parameter \(\Sigma_k\). When var_fun = 1, \(\Sigma_k\) is a diagonal matrix and \(\Sigma_k = \Sigma\), and we obtain a vector of the diagonal elements; When var_fun = 2, \(\Sigma_k\) is a diagonal matrix, and we obtain K vectors of the diagonal elements; When var_fun = 3, \(\Sigma_k\) is a full variance-covariance matrix, \(\Sigma_k = \Sigma\), and we obtain a matrix \(\Sigma\); When var_fun = 4, \(\Sigma_k\) is a full variance-covariance matrix, and we obtain K different matrices \(\Sigma_k\).

W

The posterior probability matrix.

loglikelihood

The approximated log-likelihood of the fitted model.

disparity

The disparity (-2logL) of the fitted model.

number_parameters

The number of parameters estimated in the EM algorithm.

AIC

The AIC value (-2logL + 2number_parameters).

BIC

The BIC value (-2logL + number_parameters*log(n)), where n is the number of observations.

aic_data

All AIC values in each run.

Starting_values

Lists of starting values for parameters used in each num_runs. It allows reproduction of the best result (obtained from mult.reg_1level) in a single run using mult.em_1level by setting start equal to the list of starting values that were used to obtain the best result in mult.reg_1level.

Arguments

data

A data set object; we denote the dimension of a data set to be \(m\).

v

Covariate(s).

K

Number of mixture components, the default is K = 2.

steps

Number of iterations within each num_runs, the default is steps = 20.

num_runs

Number of function iteration runs, the default is num_runs = 10.

start

Containing parameters involved in the proposed model (p, alpha, z, beta, sigma, gamma) in a list, the starting values can be obtained through the use of start_em. More details can be found in start_em.

option

Four options for selecting the starting values for the parameters in the model. The default is option = 1. More details can be found in start_em.

var_fun

There are four types of variance specifications; var_fun = 1, the same diagonal variance specification to all K components of the mixture; var_fun = 2, different diagonal variance matrices for different components. var_fun = 3, the same full (unrestricted) variance for all components. var_fun = 4, different full (unrestricted) variance matrices for different components. The default is var_fun = 2.

References

Zhang, Y. and Einbeck J. (2024). A Versatile Model for Clustered and Highly Correlated Multivariate Data. J Stat Theory Pract 18(5).tools:::Rd_expr_doi("10.1007/s42519-023-00357-0")

See Also

mult.em_1level.

Examples

# \donttest{
##run the mult.em_1level() multiple times and select the best results with the smallest AIC value
set.seed(7)
results <- mult.reg_1level(fetal_covid_data[,c(1:5)],v=fetal_covid_data$status_bi,
K=3, num_runs = 5,steps = 20, var_fun = 2, option = 1)
##Reproduce the best result: the best result is the 5th run in the above example.
rep_best_result <- mult.em_1level(fetal_covid_data[,c(1:5)],
v=fetal_covid_data$status_bi,
K=3, steps = 20, var_fun = 2, option = 1,
start = results$Starting_values[[5]])
# }