% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/proj_LogBip.R
\name{proj_LogBip}
\alias{proj_LogBip}
\title{Fit a Binary Logistic Biplot with Missing Data via Block Coordinate Descent}
\usage{
proj_LogBip(x, k = 5, max_iters = 1000, random_start = FALSE, epsilon = 1e-05)
}
\arguments{
\item{x}{A binary matrix, possibly containing \code{NA} values.}

\item{k}{Number of dimensions. Default is \code{k = 5}.}

\item{max_iters}{Maximum number of iterations. Default is \code{1000}.}

\item{random_start}{Logical; if \code{TRUE}, parameters are initialised
randomly. Default is \code{FALSE} (SVD initialisation).}

\item{epsilon}{Convergence tolerance for the relative decrease in the loss
function. Default is \code{1e-5}.}
}
\value{
A named list with components:
  \describe{
    \item{\code{mu}}{Estimated intercept vector of length \eqn{p}.}
    \item{\code{A}}{Estimated row-marker matrix (\eqn{n \times k}).}
    \item{\code{B}}{Estimated column-marker matrix (\eqn{p \times k}).}
    \item{\code{x_est}}{Imputed binary matrix (missing entries replaced by
      fitted values).}
    \item{\code{iter}}{Number of iterations performed.}
    \item{\code{loss_funct}}{Vector of normalised loss-function values at each
      iteration.}
  }
}
\description{
Estimates the intercept vector \eqn{\mu}, the row-marker matrix \strong{A},
and the column-marker matrix \strong{B} using a data-projection model with a
block coordinate descent algorithm. Missing values in the binary matrix are
imputed iteratively during model fitting. This function also allows new
individuals to be projected as supplementary rows without refitting the model,
since the row markers are derived directly from the estimated column markers.
This is the low-level function called by \code{\link{LogBip}} when
\code{method = "PDLB"}.
}
\examples{
\donttest{
data("Methylation")
set.seed(12345)
n <- nrow(Methylation); p <- ncol(Methylation)
miss <- matrix(rbinom(n * p, 1, 0.2), n, p)
miss <- ifelse(miss == 1, NA, miss)
x_miss <- Methylation + miss
out <- proj_LogBip(x = x_miss, k = 2, max_iters = 1000)
}
}
\references{
Babativa-Marquez, J. G., & Vicente-Villardon, J. L. (2026). Logistic biplot
with missing data. \emph{In process}.

Babativa-Marquez, J. G., & Vicente-Villardon, J. L. (2021). Logistic biplot
by conjugate gradient algorithms and iterated SVD. \emph{Mathematics},
\emph{9}(16), 2015. \doi{10.3390/math9162015}

Vicente-Villardon, J. L., & Galindo, M. P. (2006). Logistic biplots. In
M. Greenacre & J. Blasius (Eds.), \emph{Multiple Correspondence Analysis and
Related Methods} (pp. 503--521). Chapman & Hall.
}
\seealso{
\code{\link{LogBip}}, \code{\link{cv_LogBip}}
}
\author{
Giovany Babativa <jgbabativam@unal.edu.co>
}
