mult.reg_1level {mult.latent.reg}

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.

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.

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.

References

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

See Also

mult.em_1level.

Examples

##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]])