# bisimrel: Simulation of Multivariate Linear Model data with response In simulatr/simrel: Simulation of Multivariate Linear Model Data

## Description

Simulation of Multivariate Linear Model data with response

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```bisimrel( n = 50, p = 100, q = c(10, 10, 5), rho = c(0.8, 0.4), relpos = list(c(1, 2), c(2, 3)), gamma = 0.5, R2 = c(0.8, 0.8), ntest = NULL, muY = NULL, muX = NULL, sim = NULL ) ```

## Arguments

 `n` Number of training samples `p` Number of x-variables `q` Vector of number of relevant predictor variables for first, second and common to both responses `rho` A 2-element vector, unconditional and conditional correlation between y_1 and y_2 `relpos` A list of position of relevant component for predictor variables. The list contains vectors of position index, one vector or each response `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 for each response `ntest` Number of test observation `muY` Vector of average (mean) for each response variable `muX` Vector of average (mean) for each predictor variable `sim` A simrel object for reusing parameters setting

## Value

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

 `X` Simulated predictors `Y` Simulated responses `beta` True regression coefficients `beta0` True regression intercept `relpred` Position of relevant predictors `testX` Test Predictors `testY` Test Response `minerror` Minimum model error `Rotation` Rotation matrix of predictor (R) `type` Type of simrel object, in this case bivariate `lambda` Eigenvalues of predictors `Sigma` Variance-Covariance matrix of response and predictors

## 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.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```sobj <- bisimrel( n = 100, p = 10, q = c(5, 5, 3), rho = c(0.8, 0.4), relpos = list(c(1, 2, 3), c(2, 3, 4)), gamma = 0.7, R2 = c(0.8, 0.8) ) # Regression Coefficients from this simulation sobj\$beta ```

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