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

Fit a linearly constrained linear model with lasso regularization.

classo(y, Z, Zc = NULL, intercept = TRUE, pf = rep(1, times = p),
       lam = NULL, nlam = 100,lambda.factor = ifelse(n < p, 0.05, 0.001),
       dfmax = p, pfmax = min(dfmax * 1.5, p),
       u = 1, mu_ratio = 1.01, tol = 1e-10,
       outer_maxiter = 3e+08, outer_eps = 1e-8,
       inner_maxiter = 1e+6, inner_eps = 1e-8,
       A = rep(1, times = p), b = 0, beta.ini)

`y`	a response vector with length n.
`Z`	a design matrix, with dimension np*.
`Zc`	design matrix for unpenalized variables. Default value is NULL.
`intercept`	Boolean, specifying whether to include an intercept. Default is TRUE.
`pf`	penalty factor, a vector of length p. Zero implies no shrinkage. Default value for each entry is 1.
`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 the `lam` sequence, where `min(lam)` = `lambda.factor` * `max(lam)`. `max(lam)` is the smallest value of `lam` for which all penalized coefficients become zero. If n >= p, the default is `0.001`. If n < p, 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)`.
`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, with value at least 1, for `u`. Default value is 1.01. Inital values for scaled Lagrange multipliers are set as 0. If `mu_ratio` < 1, the program automatically set `u` as 0 and `outer_maxiter` as 1, indicating that there is no linear constraint.
`tol`	tolerance for the estimated coefficients to be considered as non-zero, i.e., if abs(β_j) < `tol`, set β_j as 0. Default value is 1e-10.
`outer_maxiter, outer_eps`	`outer_maxiter` is the maximum number of loops allowed for the augmented Lanrange method; and `outer_eps` is the corresponding convergence tolerance.
`inner_maxiter, inner_eps`	`inner_maxiter` is the maximum number of loops allowed for the coordinate descent; and `inner_eps` is the corresponding convergence tolerance.
`A, b`	linear equalities of the form Aβ_p = b, where b is a scaler, and A is a row-vector of length `p`. Default values: b is 0 and `A = matrix(1, ncol = p)`.
`beta.ini`	inital value of the coefficients. Can be unspecified.

A list of

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