# multisimrel: Simulation of Multivariate Linear Model Data In simulatr/simrel: Simulation of Multivariate Linear Model Data

## Description

Simulation of Multivariate Linear Model Data

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```multisimrel( n = 100, p = 15, q = c(5, 4, 3), m = 5, relpos = list(c(1, 2), c(3, 4, 6), c(5, 7)), gamma = 0.6, R2 = c(0.8, 0.7, 0.8), eta = 0, ntest = NULL, muX = NULL, muY = NULL, ypos = list(c(1), c(3, 4), c(2, 5)) ) ```

## Arguments

 `n` Number of observations `p` Number of variables `q` Vector containing the number of relevant predictor variables for each relevant response components `m` Number of response variables `relpos` A list of position of relevant component for predictor variables. The list contains vectors of position index, one vector or each relevant response components `gamma` A declining (decaying) factor of eigen value of predictors (X). Higher the value of `gamma`, the decrease of eigenvalues will be steeper `R2` Vector of coefficient of determination (proportion of variation explained by predictor variable) for each relevant response components `eta` A declining (decaying) factor of eigenvalues of response (Y). Higher the value of `eta`, more will be the declining of eigenvalues of Y. `eta = 0` refers that all eigenvalues of responses (Y) are 1. `ntest` Number of test observation `muX` Vector of average (mean) for each predictor variable `muY` Vector of average (mean) for each response variable `ypos` List of position of relevant response components that are combined to generate response variable during orthogonal rotation

## Value

A simrel object with all the input arguments along with following additional items

 `X` Simulated predictors `Y` Simulated responses `W` Simulated predictor components `Z` Simulated response components `beta` True regression coefficients `beta0` True regression intercept `relpred` Position of relevant predictors `testX` Test Predictors `testY` Test Response `testW` Test predictor components `testZ` Test response components `minerror` Minimum model error `Xrotation` Rotation matrix of predictor (R) `Yrotation` Rotation matrix of response (Q) `type` Type of simrel object univariate or multivariate `lambda` Eigenvalues of predictors `SigmaWZ` Variance-Covariance matrix of components of response and predictors `SigmaWX` Covariance matrix of response components and predictors `SigmaYZ` Covariance matrix of response and predictor components `Sigma` Variance-Covariance matrix of response and predictors `RsqW` Coefficient of determination corresponding to response components `RsqY` Coefficient of determination corresponding to response variables

## References

Sæbø, S., Almøy, T., & Helland, I. S. (2015). simrel—A versatile tool for linear model data simulation based on the concept of a relevant subspace and relevant predictors. Chemometrics and Intelligent Laboratory Systems, 146, 128-135.

Almøy, T. (1996). A simulation study on comparison of prediction methods when only a few components are relevant. Computational statistics & data analysis, 21(1), 87-107.

simulatr/simrel documentation built on Sept. 15, 2021, 12:44 a.m.