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#' Guttman's 6 Lambda Coefficients
#'
#' @description Calculates all 6 of Guttman's lambda coefficients.
#'
#' @return
#' \item{Lambda1}{Guttman's Lambda1 estimate of reliability.}
#' \item{Lambda2}{Guttman's Lambda2 estimate of reliability.}
#' \item{Lambda3}{Guttman's Lambda3 estimate of reliability. Also known as Cronbach's alpha or coefficient alpha.}
#' \item{Lambda4}{Guttman's maximimal Lambda4 estimate of reliability.}
#' \item{Lambda5}{Guttman's Lambda5 estimate of reliability.}
#' \item{Lambda6}{Guttman's Lambda6 estimate of reliability.}
#'
#' @param x Can be either a data matrix or a covariance matrix
#' @param missing How to handle missing values.
#' @param standardize When TRUE Results are standardized by using the correlation matrix instead of the covariance matrix for computation.
#'
#' @note The estimate for Lambda4 is maximized.
#'
#' @references
#' Guttman L (1945). "A Basis for Analyzing Test-Retest Reliability." Psychometrika, 10, 255-282.
#' @author Tyler Hunt \email{tyler@@psychoanalytix.com}
#' @examples
#' guttman(Rosenberg)
#'
#' @export
guttman <- function(x, missing="complete", standardize=FALSE){
sigma <- impute.cov(x, missing)
if(standardize==TRUE){
sigma <- cov2cor(sigma)
}
Lambda1 <- as.numeric(lambda1(sigma))
Lambda2 <- as.numeric(lambda2(sigma))
Lambda3 <- as.numeric(lambda3(sigma)$lambda3[1])
Lambda4 <- as.numeric(cov.lambda4(sigma, show.splits=FALSE)$lambda4[2])
Lambda5 <- as.numeric(lambda5(sigma))
Lambda6 <- as.numeric(lambda6(sigma))
result <- list(Lambda1=Lambda1,
Lambda2=Lambda2,
Lambda3=Lambda3,
Lambda4=Lambda4,
Lambda5=Lambda5,
Lambda6=Lambda6)
class(result) <- c("guttman")
return(result)
}
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