dudi.hillsmith function

Ordination of Tables mixing quantitative variables and factors

performs a multivariate analysis with mixed quantitative variables and factors.

dudi.hillsmith(df, row.w = rep(1, nrow(df))/nrow(df), 
   scannf = TRUE, nf = 2)

Arguments

• df: a data frame with mixed type variables (quantitative and factor)
• row.w: a vector of row weights, by default uniform row weights are used
• scannf: a logical value indicating whether the eigenvalues bar plot should be displayed
• nf: if scannf FALSE, an integer indicating the number of kept axes

Details

If df contains only quantitative variables, this is equivalent to a normed PCA.

If df contains only factors, this is equivalent to a MCA.

This analysis is the Hill and Smith method and is very similar to dudi.mix function. The differences are that dudi.hillsmith allow to use various row weights, while dudi.mix deals with ordered variables.

The principal components of this analysis are centered and normed vectors maximizing the sum of :

squared correlation coefficients with quantitative variables

correlation ratios with factors

Returns

Returns a list of class mix and dudi (see dudi ) containing also - index: a factor giving the type of each variable : f = factor, q = quantitative

• assign: a factor indicating the initial variable for each column of the transformed table

• cr: a data frame giving for each variable and each score:

  the squared correlation coefficients if it is a quantitative variable

  the correlation ratios if it is a factor

References

Hill, M. O., and A. J. E. Smith. 1976. Principal component analysis of taxonomic data with multi-state discrete characters. Taxon, 25 , 249-255.

Author(s)

Stéphane Dray stephane.dray@univ-lyon1.fr

Anne-Béatrice Dufour anne-beatrice.dufour@univ-lyon1.fr

See Also

dudi.mix

Examples

data(dunedata)
attributes(dunedata$envir$use)$class <- "factor"   # use dudi.mix for ordered data
dd1 <- dudi.hillsmith(dunedata$envir, scann = FALSE)
if(adegraphicsLoaded()) {
  g <- scatter(dd1, row.plab.cex = 1, col.plab.cex = 1.5)
} else {
  scatter(dd1, clab.r = 1, clab.c = 1.5)
}