simrel-m
A simulation tool and its application
11 June, 2017
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
Why simrel-m
-
By changing few parameters, we can simulate wide range of linear model data. For example,
- Controlling degree of multicollinearity in the simulated data
- Specifying the relevant principle components for prediction
- It is easy to use and has wide application
The idea behind
simrel[1] package
How it works
- Gets parameter setting from users
- Creates Covariance matrix
- Creates Rotation Matrix
- Rotates the sampled Latent variables
How it works
- Gets parameter setting from users
- Creates Covariance matrix
- Creates Rotation Matrix
- Rotates the sampled Latent variables
A web interface
How to get it
Install simrel-m:
devtools::install_github(
"therimalaya/simulatr",
quiet = TRUE
)Run the shiny app:
shiny::runGitHub(
"AppSimulatr",
"therimalaya"
)Documentation:
An example of comparison of estimation methods
Design Properties
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 (γ) | 0.2 | 0.8 |
| Coef. of Determination (ρ2) | 0.8, 0.8, 0.4 | 0.4, 0.4, 0.4 |
Estimation Methods
For comparison, let’s consider the following estimation methods,
- Ordinary Least Squares (
ols) - Principle Component Regression (
pcr) - Partial Least Squares (
pls) [2] - Canonical Partial Least Squares (
cpls) [3] - Envelope Estimation of predictor space (
env) [4]
A Comparison
Some Cases
Case I
- Testing new estimation Methods
- Studying its properties
- Studying its performance in data with various properties
Case II
- Educational use
- Students can learn how a method such as variable selection removes irrelevant variables
- Students can observe and study the loading weights on relevant and irrelevant principle components
Case III
- Comparing various methods (estimation methods, variable selection techniques)
References
References
[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.
