missoNet (version 1.5.1)

generateData: Generate synthetic data with missing values for missoNet

Description

Generates synthetic data from a conditional Gaussian graphical model with user-specified missing data mechanisms. This function is designed for simulation studies and testing of the missoNet package, supporting three types of missingness: Missing Completely At Random (MCAR), Missing At Random (MAR), and Missing Not At Random (MNAR).

Usage

generateData(
  n,
  p,
  q,
  rho,
  missing.type = "MCAR",
  X = NULL,
  Beta = NULL,
  E = NULL,
  Theta = NULL,
  Sigma.X = NULL,
  Beta.row.sparsity = 0.2,
  Beta.elm.sparsity = 0.2,
  seed = NULL
)

Value

A list containing:

X

n x p matrix. Predictor matrix (either user-supplied or simulated).

Y

n x q matrix. Complete response matrix without missing values.

Z

n x q matrix. Response matrix with missing values (coded as NA).

Beta

p x q matrix. Regression coefficient matrix used in generation.

Theta

q x q matrix or NULL. Precision matrix (if used in generation).

rho

Numeric vector of length q. Missing rates for each response.

missing.type

Character string. The missing mechanism used.

Arguments

n

Integer. Sample size (number of observations). Must be at least 2.

p

Integer. Number of predictor variables. Must be at least 1.

q

Integer. Number of response variables. Must be at least 2.

rho

Numeric scalar or vector of length q. Proportion of missing values for each response variable. Values must be in [0, 1). If scalar, the same missing rate is applied to all responses.

missing.type

Character string specifying the missing data mechanism. One of:

• "MCAR" (default): Missing Completely At Random

• "MAR": Missing At Random (depends on predictors)

• "MNAR": Missing Not At Random (depends on response values)

X

Optional n x p matrix. User-supplied predictor matrix. If NULL (default), predictors are simulated from a multivariate normal distribution with mean zero and covariance Sigma.X.

Beta

Optional p x q matrix. Regression coefficient matrix. If NULL (default), a sparse coefficient matrix is generated with sparsity controlled by Beta.row.sparsity and Beta.elm.sparsity.

E

Optional n x q matrix. Error/noise matrix. If NULL (default), errors are simulated from a multivariate normal distribution with mean zero and precision matrix Theta.

Theta

Optional q x q positive definite matrix. Precision matrix (inverse covariance) for the response variables. If NULL (default), a block-structured precision matrix is generated with four types of graph structures. Only used when E = NULL.

Sigma.X

Optional p x p positive definite matrix. Covariance matrix for the predictors. If NULL (default), an AR(1) covariance structure with correlation 0.7 is used. Only used when X = NULL.

Beta.row.sparsity

Numeric in [0, 1]. Proportion of rows in Beta that contain at least one non-zero element. Default is 0.2. Only used when Beta = NULL.

Beta.elm.sparsity

Numeric in [0, 1]. Proportion of non-zero elements within active rows of Beta. Default is 0.2. Only used when Beta = NULL.

seed

Optional integer. Random seed for reproducibility.

Author

Yixiao Zeng , Celia M. T. Greenwood

Details

The function generates data through the following model: $$Y = XB + E$$ where:

• \(X \in \mathbb{R}^{n \times p}\) is the predictor matrix

• \(B \in \mathbb{R}^{p \times q}\) is the coefficient matrix

• \(E \sim \mathcal{MVN}(0, \Theta^{-1})\) is the error matrix

• \(Y \in \mathbb{R}^{n \times q}\) is the complete response matrix

Missing values are then introduced to create \(Z\) (the observed response matrix with NAs) according to the specified mechanism:

MCAR: Each element has probability rho[j] of being missing, independent of all variables.

MAR: Missingness depends on the predictors through a logistic model: $$P(Z_{ij} = NA) = \mathrm{logit}^{-1}(XB)_{ij} \times c_j$$ where \(c_j\) is calibrated to achieve the target missing rate.

MNAR: The lowest rho[j] proportion of values in each column are set as missing.

See Also

missoNet for fitting models to data with missing values, cv.missoNet for cross-validation

Examples

# Example 1: Basic usage with default settings
sim.dat <- generateData(n = 300, p = 50, q = 20, rho = 0.1, seed = 857)

# Check dimensions and missing rate
dim(sim.dat$X)      # 300 x 50
dim(sim.dat$Z)      # 300 x 20
mean(is.na(sim.dat$Z))  # approximately 0.1

# Example 2: Variable missing rates with MAR mechanism
rho.vec <- seq(0.05, 0.25, length.out = 20)
sim.dat <- generateData(n = 300, p = 50, q = 20, 
                       rho = rho.vec, 
                       missing.type = "MAR")

# Example 3: High sparsity in coefficient matrix
sim.dat <- generateData(n = 500, p = 100, q = 30,
                       rho = 0.15,
                       Beta.row.sparsity = 0.1,  # 10% active predictors
                       Beta.elm.sparsity = 0.3)  # 30% active in each row

# Example 4: User-supplied matrices
n <- 300; p <- 50; q <- 20
X <- matrix(rnorm(n*p), n, p)
Beta <- matrix(rnorm(p*q) * rbinom(p*q, 1, 0.1), p, q)  # 10% non-zero
Theta <- diag(q) + 0.1  # Simple precision structure

sim.dat <- generateData(X = X, Beta = Beta, Theta = Theta,
                       n = n, p = p, q = q,
                       rho = 0.2, missing.type = "MNAR")

# \donttest{
# Example 5: Use generated data with missoNet
library(missoNet)
sim.dat <- generateData(n = 400, p = 50, q = 10, rho = 0.15)

# Split into training and test sets
train.idx <- 1:300
test.idx <- 301:400

# Fit missoNet model
fit <- missoNet(X = sim.dat$X[train.idx, ], 
               Y = sim.dat$Z[train.idx, ],
               lambda.beta = 0.1, 
               lambda.theta = 0.1)

# Evaluate on test set
pred <- predict(fit, newx = sim.dat$X[test.idx, ])
# }