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 datasimrel-m
simrel
[1] package
Install simrel-m:
devtools::install_github(
"therimalaya/simulatr",
quiet = TRUE
)
Run the shiny app:
shiny::runGitHub(
"AppSimulatr",
"therimalaya"
)
Documentation:
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
Design1 | Design2 | |
---|---|---|
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,
ols
)pcr
)pls
) [2]cpls
) [3]env
) [4]Case I
Case II
Case III
[1] 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.
[2] H. Wold, Partial least squares, Encyclopedia of Statistical Sciences (1985).
[3] 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.
[4] R.D. Cook, B. Li, F. Chiaromonte, Envelope models for parsimonious and efficient multivariate linear regression, Statistica Sinica (2010) 927–60.
[5] I.S. Helland, Partial least squares regression and statistical models, Scandinavian Journal of Statistics (1990) 97–114.