comp_Model: Simulation for log-contrast model.
In jiji6454/compReg: Regression with Compositional Covariates

Description Usage Arguments Details Value Author(s) References Examples

Simulate data for log-contrast model with a single set of compositional data.

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comp_Model(n, p, rho = 0.2, sigma = 0.5, gamma = 0.5, add.on = 1:5,
           beta = c(c(1, -0.8, 0.6, 0, 0, -1.5, -0.5, 1.2), rep(0, times = p - 8)),
           beta0  = 1, intercept = TRUE)

`n`	sample size
`p`	number of components in the compositional data
`rho`	parameter used to generate the pp* autocorrelation matrix for correlations among the components. Default is 0.2.
`sigma`	standard deviation for the noise terms, which are iid normal with mean 0. Default is 0.5.
`gamma`	a scaler. For the high level mean component(s), `log(p * gamma)` is added to the "non-normalized" data `w_i` before the data are converted to compositional.
`add.on`	an index vector with value(s) in `[1,p]`, specifying which component(s) of compositions is of high level mean. Default is `1:5`.
`beta`	coefficients for the compositional variables.
`beta0`	coefficient for the intercept. Default is 1.
`intercept`	whether to include an intercept. Default is `FALSE`.

The setup of this simulation follows Lin, W., Shi, P., Peng, R. and Li, H. (2014) Variable selection in regression with compositional covariates, https://academic.oup.com/biomet/article/101/4/785/1775476.
Specifically, we first generate the correlation matrix among the components X.Sigma by rho with an autoregressive correlation structure. we then generate the "non-normalized" data w_i for each subject from multivariate normal distribution with covariance X.Sigma and mean determined by add.on and gamma. Each w_i is a vector of length p. Finally, the compositional covariates are obtained as

x_{ij}=exp(w_{ij})/∑_{k=1}^{p}exp(w_{ik}),

for each subject i=1,...,n and component j=1,...,p.

A list containing:

`y`	a n-vector of the simulated response
`X.comp`	a matrix of the simulated compositional predictors of dimension np*
`Z`	a matrix of the log-transformed compositional predictors
`Zc`	a matrix of the simulated covariates
`intercept`	whether an intercept is included
`beta`	the true coefficient vector

Zhe Sun and Kun Chen

Lin, W., Shi, P., Peng, R. and Li, H. (2014) Variable selection in regression with compositional covariates, https://academic.oup.com/biomet/article/101/4/785/1775476. Biometrika 101 785-979.

p = 30
beta = c(1, -0.8, 0.6, 0, 0, -1.5, -0.5, 1.2)
beta = c( beta, rep(0, times = p - length(beta)) )
Data = comp_Model(n = 50, p = p, intercept = FALSE,
                  rho = 0.2, sigma = 0.5, gamma  = 0.5, add.on = 1:5,
                  beta = beta)