Package 'heteromixgm'

data_sim

Description

Simulate mixed multi-group data.

Usage

data_sim(network, n, p, K, ncat, rho, gamma_g = NULL, gamma_o, gamma_b = NULL,
gamma_p = NULL, prob = NULL, nclass = NULL)

Arguments

network	Type of network, either "circle", "Random", "Cluster", "Scale-free", "AR1" or "AR2".
n	Number of observations.
p	Number of variables.
K	Number of groups.
ncat	Number of categories for ordinal variables.
rho	Dissimilarity parameter inducing dissimilarity between the K datasets.
gamma_g	Proportion of Gaussian variables in the data.
gamma_o	Proportion of ordinal variables in the data.
gamma_b	Proportion of binomial variables in the data.
gamma_p	Proportion of Poisson variables in the data..
prob	Edge occurency probability in random graph.
nclass	Number of clusters in cluster graph.

Value

z	A list of $K$ $n$ by $p$ matrices representing the latent Gaussian transformed (observed) data.
theta	A list of $K$ $n$ by $p$ matrices representing the precision matrices corresponding to the latent Gaussian (unobserved) data.

Author(s)

Sjoerd Hermes, Joost van Heerwaarden and Pariya Behrouzi
Maintainer: Sjoerd Hermes [email protected]

References

1. Hermes, S., van Heerwaarden, J., & Behrouzi, P. (2024). Copula graphical models for heterogeneous mixed data. Journal of Computational and Graphical Statistics, 1-15.

Examples

data_sim(network = "Random", n = 10, p = 50, K = 3, ncat = 6, rho = 0.25,
gamma_o = 0.5, gamma_b = 0.1, gamma_p = 0.2, prob = 0.05)

---

heteromixgm

Description

This function implements either the Gibbs or approximation method within the Gaussian copula graphical model to estimate the conditional expectation for the data that not follow Gaussianity assumption (e.g. ordinal, discrete, continuous non-Gaussian, or mixed dataset).

Usage

heteromixgm(X, method, lambda1, lambda2, ncores)

Arguments

X	A list containing $K$ $n_k \times p$ matrices ($K$ is the number of groups, $n_k$ is the sample size for group $k$ and $p$ is the number of variables
method	Choice between "Gibbs" and "Approximate" indicating which method to use.
lambda1	Vector containing values (in [0,1]) for the sparsity penalization of each $\Theta^k$.
lambda2	Vector containing values (in [0,1]) for the similarity penalization between the $\Theta^k$.
ncores	Number of cores to be used during parallel computing.

Value

Z	New transformation of the data based on given or default Sigma.
ES	Expectation of covariance matrix( diagonal scaled to 1) of the Gaussian copula graphical model.
Sigma	The covariance matrix of the latent variable given the data.
Theta	The inverse covariance matrix of the latent variable given the data.
loglik	Value of the Log likelihood under the estimated parameters.

Author(s)

Sjoerd Hermes, Joost van Heerwaarden and Pariya Behrouzi
Maintainer: Sjoerd Hermes [email protected]

References

1. Hermes, S., van Heerwaarden, J., & Behrouzi, P. (2024). Copula graphical models for heterogeneous mixed data. Journal of Computational and Graphical Statistics, 1-15.

Examples

data(maize)
l1 <- c(0.4)
l2 <- c(0,0.1)
ncores <- 1
est <- heteromixgm(maize, "Approximate", l1, l2, ncores)

---

initialize

Description

Initializes parameters to be used in the approximate method algorithm.

Usage

initialize(y, ncores)

Arguments

y	Data.
ncores	Number of cores to be used during parallel computing.

Value

ES	Expectation of covariance matrices ( diagonal scaled to 1) of the Gaussian copula graphical model.
Z	New transformation of the data based on given or default Sigma.
lower_upper	Lower and upper truncation points for the truncated normal distribution.

Author(s)

Sjoerd Hermes, Joost van Heerwaarden and Pariya Behrouzi
Maintainer: Sjoerd Hermes [email protected]

References

1. Hermes, S., van Heerwaarden, J., & Behrouzi, P. (2024). Copula graphical models for heterogeneous mixed data. Journal of Computational and Graphical Statistics, 1-15.

Examples

y <- list(matrix(runif(25), 5, 5),matrix(runif(25), 5, 5),matrix(runif(25),
5, 5))
ncores <- 1
initialize(y, ncores)

---

lower.upper

Description

Calculates lower and upper bands for each data point, using a set of cut-points which is obtained from the Gaussian copula.

Usage

lower.upper(y)

Arguments

y	An ($n_k \times p$) matrix corresponding to the data matrix ($n_k$ is the sample size for group $k$ and $p$ is the number of variables).

Value

lower	A $n_k$ by $p$ matrix representing the lower band for each data point.
upper	A $n_k$ by $p$ matrix representing the upper band for each data point.

Author(s)

Sjoerd Hermes, Joost van Heerwaarden and Pariya Behrouzi
Maintainer: Sjoerd Hermes [email protected]

References

1. Hermes, S., van Heerwaarden, J., & Behrouzi, P. (2024). Copula graphical models for heterogeneous mixed data. Journal of Computational and Graphical Statistics, 1-15.

Examples

y <- list(matrix(runif(25), 5, 5),matrix(runif(25), 5, 5),matrix(runif(25),
5, 5))
lower.upper(y[[1]])

---

Maize data

Description

This is a dataset consisting of maize yields, environmental and management variables measured across 2 groups. The groups pertain to different seasons (2010 and 2013) for farms in Pawe Ethiopia.

Usage

data("maize")

Format

The format is: List of 2

Details

Contains a subset of data used in the Hermes et al. (2024) paper, which is a subset of data used in the Vasco Silva et al. (forthcoming) paper.

Source

1. Hermes, S., van Heerwaarden, J., & Behrouzi, P. (2024). Copula graphical models for heterogeneous mixed data. Journal of Computational and Graphical Statistics, 1-15.

References

1. Hermes, S., van Heerwaarden, J., & Behrouzi, P. (2024). Copula graphical models for heterogeneous mixed data. Journal of Computational and Graphical Statistics, 1-15.
2. Vasco Silva, J., J. van Heerwaarden, R. Pytrik, A. G. Laborte, K. Tesfaye, and M. K. van Ittersum (forthcoming). Big data, small explanatory power? lessons learnt with random forest predictive modeling of crop yield in contrasting farming systems.

Examples

data(maize)

---

modselect

Description

Model selection using the AIC, BIC and eBIC.

Usage

modselect(est, X, l1, l2, gamma)

Arguments

est	Estimates of model obtained from cgmmd() function
X	A list of $K$ $n_k$ by $p$ data matrices.
l1	Vector containing l1 penalty values.
l2	Vector containing l2 penalty values.
gamma	EBIC gamma parameter.

Value

selectmat	Matrix containing the "optimal" l1 and l2 values for each information criterion.
theta_aic	Estimated precision matrices using the AIC for model selection.
theta_bic	Estimated precision matrices using the BIC for model selection.
theta_ebic	Estimated precision matrices using the EBIC for model selection.

Author(s)

Sjoerd Hermes, Joost van Heerwaarden and Pariya Behrouzi
Maintainer: Sjoerd Hermes [email protected]

References

1. Hermes, S., van Heerwaarden, J., & Behrouzi, P. (2024). Copula graphical models for heterogeneous mixed data. Journal of Computational and Graphical Statistics, 1-15.

Examples

X <- list(matrix(runif(25), 5, 5),matrix(runif(25), 5, 5),matrix(runif(25),
5, 5))
l1 <- c(0.4)
l2 <- c(0,0.1)
gamma <- 0.5
ncores <- 1
est <- heteromixgm(X, "Approximate", l1, l2, ncores)
modselect(est, X, l1, l2, gamma)

---

Plot partial correlation graphs

Description

Plots all $K$ partial correlation graphs based on the $\Theta$ selected using one of the information criteria.

Usage

plot_pcorgraph(Theta, pos_clr, neg_clr, plot_layout, label_cex)

Arguments

Theta	List of $K$ selected $\Theta$
pos_clr	Color, hexadecimal color allowed, representing the positive partial correlations in the plotted graphs.
neg_clr	Color, hexadecimal color allowed, representing the negative partial correlations in the plotted graphs.
plot_layout	Number of rows and columns for the plot layout.
label_cex	Size of the vertex labels in the plotted graphs.

Value

There is no return value. The function only shows plots in the graphics output device.

Author(s)

Sjoerd Hermes, Joost van Heerwaarden and Pariya Behrouzi
Maintainer: Sjoerd Hermes [email protected]

References

1. Hermes, S., van Heerwaarden, J., & Behrouzi, P. (2024). Copula graphical models for heterogeneous mixed data. Journal of Computational and Graphical Statistics, 1-15.

Examples

temp <- data_sim(network = "Random", n = 100, p = 20, K = 4, ncat = 6, rho = 0.25,
         gamma_o = 0.5, gamma_b = 0.1, gamma_p = 0.2, prob = 0.05)
X <- temp$z
l1 <- c(0.1)
l2 <- c(0,0.1)
gamma <- 0.5
ncores <- 1
est <- heteromixgm(X, "Approximate", l1, l2, ncores)
temp = modselect(est, X, l1, l2, gamma)
plot_pcorgraph(temp$theta_aic, "green", "red", c(2,2), 4.5)

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