R/uscrime.R

In nipals: Principal Components Analysis using NIPALS or Weighted EMPCA, with Gram-Schmidt Orthogonalization

# uscrime.R

#' U.S. Crime rates per 100,00 people
#' 
#' U.S. Crime rates per 100,00 people for 7 categories in each of the 50 U.S.
#' states in 1977.
#' 
#' There are two missing values.
#' 
#' @format
#' A data frame with 50 observations on the following 8 variables.
#' \describe{
#'   \item{state}{U.S. state}
#'   \item{murder}{murders}
#'   \item{rape}{rapes}
#'   \item{robbery}{robbery}
#'   \item{assault}{assault}
#'   \item{burglary}{burglary}
#'   \item{larceny}{larceny}
#'   \item{autotheft}{automobile thefts}
#' }
#' 
#' @source
#' Documentation Example 3 for PROC HPPRINCOMP.
#' http://documentation.sas.com/api/docsets/stathpug/14.2/content/stathpug_code_hppriex3.htm?locale=en
#' 
#' @references
#' SAS/STAT User's Guide: High-Performance Procedures.  The HPPRINCOMP Procedure.
#' http://support.sas.com/documentation/cdl/en/stathpug/67524/HTML/default/viewer.htm#stathpug_hpprincomp_toc.htm
#' 
#' @examples
#' 
#' library(nipals)
#' head(uscrime)
#' 
#' # SAS deletes rows with missing values
#' dat <- uscrime[complete.cases(uscrime), ]
#' dat <- as.matrix(dat[ , -1])
#' m1 <- nipals(dat) # complete-data method
#' 
#' # Traditional NIPALS with missing data  
#' dat <- uscrime
#' dat <- as.matrix(dat[ , -1])
#' m2 <- nipals(dat, gramschmidt=FALSE) # missing 
#' round(crossprod(m2$loadings),3) # Prin Comps not quite orthogonal
#'   
#' # Gram-Schmidt corrected NIPALS
#' m3 <- nipals(dat, gramschmidt=TRUE) # TRUE is default
#' round(crossprod(m3$loadings),3) # Prin Comps are orthogonal
#'
"uscrime"