Man is a tool-using animal. Without tools he is nothing, with tools he is all.
simrel-m: A versatile tool for simulating multi-response linear model data
devtools::install_github( "therimalaya/simulatr", quiet = TRUE )
Run the shiny app:
shiny::runGitHub( "AppSimulatr", "therimalaya" )
Consider two sets of data, both having following common properties,
|Number of observation||100|
|Number of variables||16|
|Number of predictors relevant for each response components||5, 5, 5|
|Number of response variables||5|
|Relevant position of response component||1, 6; 2, 5; 3, 4|
|Position of Response components to rotate together||1, 4; 2, 5; 3|
The difference between the two datasets are
|Decay of eigenvalue \((\gamma)\)||0.2||0.8|
|Coef. of Determination \((\rho^2)\)||0.8, 0.8, 0.4||0.4, 0.4, 0.4|
For comparison, let’s consider the following estimation methods,
 S. Sæbø, T. Almøy, I.S. Helland, 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 (2015) 128–35.
 H. Wold, Partial least squares, Encyclopedia of Statistical Sciences (1985).
 U.G. Indahl, K.H. Liland, T. Næs, Canonical partial least squaresa unified pls approach to classification and regression problems, Journal of Chemometrics 23(9) (2009) 495–504.
 R.D. Cook, B. Li, F. Chiaromonte, Envelope models for parsimonious and efficient multivariate linear regression, Statistica Sinica (2010) 927–60.
 I.S. Helland, Partial least squares regression and statistical models, Scandinavian Journal of Statistics (1990) 97–114.