calibrate_vm: Calibrate the VM (Vale-Maurelli) model

In covsim: VITA, IG, PLSIM and VM Simulation for Given Covariance and Marginals

Calibrate the VM (Vale-Maurelli) model

Description

Performs the calibration step of the Vale-Maurelli algorithm: for each variable the Fleishman polynomial a + bZ + cZ^2 + dZ^3 (with a = -c) matching the target skewness and excess kurtosis is found, and for each pair of variables the intermediate normal correlation that yields the target correlation after transformation is solved from the Vale-Maurelli cubic. Calibration is decoupled from simulation so the same calibration object can be reused to draw many samples without recomputation.

Usage

calibrate_vm(sigma.target, skewness, excesskurtosis)

Arguments

sigma.target	Target population covariance matrix.
skewness	Target skewness vector.
excesskurtosis	Target excess kurtosis vector.

Details

When the Fleishman equations have several solutions, a monotone increasing polynomial is preferred. For many common skewness/kurtosis combinations (e.g. skewness 1 and excess kurtosis 1.5) only polynomials that turn down in the far tails exist; these are used, and flagged in monotone.

Value

An object of class c("covsim_calib_vm", "covsim_calib") that can be passed to simulate to draw samples. The element coef holds the Fleishman coefficients (one row per variable), monotone whether each polynomial is monotone increasing, and z.corr the intermediate correlation matrix.

References

Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43(4), 521-532.

Vale, C. D. and Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48(3), 465-471.

See Also

rVM, simulate

Examples

sigma.target <- matrix(c(1, 0.5, 0.5, 1), 2)
cal <- calibrate_vm(sigma.target, skewness = c(1, 2), excesskurtosis = c(2, 7))
samples <- stats::simulate(cal, nsim = 5, N = 1000)

covsim documentation built on Oct. 29, 2026, 5:06 p.m.