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#' Post-Linkage Data Analysis Based on Mixture Modelling
#'
#'@description
#'\code{pldamixture} implements the "General Framework for Regression with
#' Mismatched Data" developed by Slawski et al., 2023. The framework uses a
#' mixture model for pairs of linked records whose two components reflect
#' distributions conditional on match status, i.e., correct match or mismatch.
#' Inference is based on composite likelihood and the EM algorithm.\cr\cr
#' The package contains 4 functions for usage:\cr \code{fit_mixture}\cr
#' \code{print.fitmixture}\cr \code{summary.fitmixture}\cr \code{predict.fitmixture}
#'
#' @name pldamixture-package
#' @docType package
#'
#' @note
#' The references below discuss the implemented framework in more detail.\cr\cr
#' *Corresponding Author (mslawsk3@gmu.edu)
#'
#' @references Slawski, M.*, West, B. T., Bukke, P., Diao, G., Wang, Z., & Ben-David, E. (2023).
#' A General Framework for Regression with Mismatched Data Based on Mixture Modeling.
#' Under Review. < \doi{10.48550/arXiv.2306.00909} >\cr
#'
#' Bukke, P., Ben-David, E., Diao, G., Slawski, M.*, & West, B. T. (2023).
#' Cox Proportional Hazards Regression Using Linked Data: An Approach Based on Mixture Modelling.
#' Under Review. \cr
#'
#' Slawski, M.*, Diao, G., Ben-David, E. (2021). A pseudo-likelihood approach to linear
#' regression with partially shuffled data. Journal of Computational and Graphical
#' Statistics. 30(4), 991-1003 < \doi{10.1080/10618600.2020.1870482} >
#'
#' @examples
#' # optional inputs for linear regression of age at death on year of birth,
#' # using a cubic polynomial specification.
#' ## use commonness of names as predictors of match status
#' ## first and last names were used for linkage
#' mformula <- ~commf + comml
#' ## hand-linked records are considered "safe" matches
#' safematches <- ifelse(lifem$hndlnk =="Hand-Linked At Some Level", TRUE, FALSE)
#' ## overall mismatch rate in the data set is assumed to be ~ 0.05
#' mrate <- 0.05
#'
#' fit <- fit_mixture(age_at_death ~ poly(unit_yob, 3, raw = TRUE), data = lifem,
#' family = "gaussian", mformula, safematches, mrate)
#' print(fit)
#' summary(fit)
#' predict(fit)
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