cglasso: Fit a linearly constrained linear regression model with group...
In jiji6454/compReg: Regression with Compositional Covariates

Fit a linearly constrained regression model with group lasso regularization.

cglasso(y, Z, Zc = NULL, k, W = rep(1, times = p), intercept = TRUE,
        A =  kronecker(matrix(1, ncol = p), diag(k)), b = rep(0, times = k),
        u = 1, mu_ratio = 1.01,
        lam = NULL, nlam = 100,lambda.factor = ifelse(n < p1, 0.05, 0.001),
        dfmax = p, pfmax = min(dfmax * 1.5, p), tol = 1e-8,
        outer_maxiter = 1e+6, outer_eps = 1e-8,
        inner_maxiter = 1e+4, inner_eps = 1e-8)

`y`	respones vector with length n.
`Z`	design matrix of dimension np1*.
`Zc`	design matrix for unpenalized variables. Default value is NULL.
`k`	the group size in Z. The number of groups is p = p1 / k .
`W`	a vector in length p (the total number of groups), or a matrix with dimension `p1*p1`. Default value is rep(1, times = p). a vector of penalization weights for the groups of coefficients. A zero weight implies no shrinkage. a diagonal matrix with positive diagonal elements.
`intercept`	Boolean, specifying whether to include an intercept. Default is TRUE.
`A, b`	linear equalities of the form Aβ_{p1} = b, where b is a vector with length k, and A is a kp1* matrix. Default values: b is a vector of 0's and `A = kronecker(matrix(1, ncol = p), diag(k))`.
`u`	the inital value of the penalty parameter of the augmented Lagrange method adopted in the outer loop. Default value is 1.
`mu_ratio`	the increasing ratio of the penalty parameter `u`. Default value is 1.01. Inital values for scaled Lagrange multipliers are set as 0's. If `mu_ratio` < 1, the program automatically set the initial penalty parameter `u` as 0 and `outer_maxiter` as 1, indicating that there is no linear constraint.
`lam`	a user supplied lambda sequence. If `lam` is provided as a scaler and `nlam`>1, `lam` sequence is created starting from `lam`. To run a single value of `lam`, set `nlam`=1. The program will sort user-defined `lambda` sequence in decreasing order.
`nlam`	the length of the `lam` sequence. Default is 100. No effect if `lam` is provided.
`lambda.factor`	the factor for getting the minimal lambda in `lam` sequence, where `min(lam)` = `lambda.factor` * `max(lam)`. `max(lam)` is the smallest value of `lam` for which all penalized group are 0's. If n >= p1, the default is `0.001`. If n < p1, the default is `0.05`.
`dfmax`	limit the maximum number of groups in the model. Useful for handling very large p, if a partial path is desired. Default is p.
`pfmax`	limit the maximum number of groups ever to be nonzero. For example once a group enters the model along the path, no matter how many times it re-enters the model through the path, it will be counted only once. Default is `min(dfmax*1.5, p)`.
`tol`	tolerance for coefficient to be considered as non-zero. Once the convergence criterion is satisfied, for each element β_j in coefficient vector β, β_j = 0 if β_j < tol.
`outer_maxiter, outer_eps`	`outer_maxiter` is the maximun number of loops allowed for the augmented Lagrange method; and `outer_eps` is the corresponding convergence tolerance.
`inner_maxiter, inner_eps`	`inner_maxiter` is the maximum number of loops allowed for blockwise-GMD; and `inner_eps` is the corresponding convergence tolerance.

A list of

`beta`	a matrix of coefficients.
`lam`	the sequence of lambda values.
`df`	a vector, the number of nonzero groups in estimated coefficients for `Z` at each value of lambda.
`npass`	total number of iteration.
`error`	a vector of error flag.