distancefactor: Factor for dissimilarity of mixed type data

Description

Computes a factor that can be used to standardise ordinal categorical variables and binary dummy variables coding categories of nominal scaled variables for Euclidean dissimilarity computation in mixed type data. See Hennig and Liao (2010).

Usage

distancefactor(cat,n=NULL, catsizes=NULL,type="categorical",
               normfactor=2,qfactor=ifelse(type=="categorical",1/2,
                             1/(1+1/(cat-1))))

Arguments

cat

integer. Number of categories of the variable to be standardised. Note that for type="categorical" the number of categories of the original variable is required, although the distancefactor is used to standardise dumm

integer. Number of data points.

catsizes

vector of integers giving numbers of observations per category. One of n and catsizes must be supplied. If catsizes=NULL, rep(round(n/cat),cat) is used (this may be appropriate as well if num

type

"categorical" if the factor is used for dummy variables belonging to a nominal variable, "ordinal" if the factor is used for an ordinal variable ind standard Likert coding.

normfactor

numeric. Factor on which standardisation is based. As a default, this is E(X_1-X_2)^2=2 for independent unit variance variables.

qfactor

numeric. Factor q in Hennig and Liao (submitted) to adjust for clumping effects due to discreteness.

Value

A factor by which to multiply the variable in order to make it comparable to a unit variance continuous variable when aggregated in Euclidean fashion for dissimilarity computation, so that expected effective difference between two realisations of the variable equals qfactor*normfactor.

References

Hennig, C. and Liao, T. (2010) Comparing latent class and dissimilarity based clustering for mixed type variables with application to social stratification. Research report no. 308, Department of Statistical Science, UCL. http://www.ucl.ac.uk/Stats/research/reports/psfiles/rr308.pdf Revised version accepted for publication by Journal of the Royal Statistical Society Series C.

Examples

Run this code

set.seed(776655)
  d1 <- sample(1:5,20,replace=TRUE)
  d2 <- sample(1:4,20,replace=TRUE)
  ldata <- cbind(d1,d2)
  lc <- cat2bin(ldata,categorical=1)$data
  lc[,1:5] <- lc[,1:5]*distancefactor(5,20,type="categorical")
  lc[,6] <- lc[,6]*distancefactor(4,20,type="ordinal")