Morpho (version 2.1)

typprob: calculate typicality probabilities

Description

calculate typicality probabilities

Usage

typprob(x, data, small = FALSE, method = c("chisquare", "wilson"),
  center = NULL, cova = NULL)
typprobClass(x, data, groups, small = FALSE, method = c("chisquare",
  "wilson"), outlier = 0.01, sep = FALSE)

Arguments

x

vector or matrix of data the probability is to be calculated.

data

Reference data set.

small

adjustion of Mahalanobis D^2 for small sample sizes as suggested by Wilson (1981), only takes effect when method="wilson".

method

select method for probability estimation. Available options are "chisquare" (or any abbreviation) or "wilson". "chisquare" exploits simply the chisquare distribution of the mahalanobisdistance, while "wilson" uses the methods suggested by Wilson(1981). Re

center

vector: specify custom vector to calculate distance to. If not defined, group mean will be used.

cova

covariance matrix to calculate mahalanobis-distance: specify custom covariance matrix to calculate distance.

groups

vector containing grouping information.

outlier

probability threshold below which a specimen will not be assigned to any group-

sep

logical: if TRUE, probability will be calculated from the pooled within group covariance matrix.

Value

• typprob: returns a vector of probabilities.

  typprobClass:

• probs
  matrix of probabilities for each group
• groupaffin
  vector of groups each specimen has been assigned to. Outliers are classified "none"

Details

get the probability for an observation belonging to a given multivariate nromal distribution

References

Albrecht G. 1992. Assessing the affinities of fossils using canonical variates and generalized distances Human Evolution 7:49-69.

Wilson S. 1981. On comparing fossil specimens with population samples Journal of Human Evolution 10:207 - 214.

Examples

library(shapes)
data <- procSym(gorf.dat)$PCscores[,1:3]
probas <- typprob(data,data,small=TRUE)### get probability for each specimen

### now we check how this behaves compared to the mahalanobis distance
maha <- mahalanobis(data,apply(data,2,mean),cov(data))
plot(probas,maha,xlab="Probability",ylab="Mahalanobis D^2")

data2 <- procSym(abind(gorf.dat,gorm.dat))$PCscores[,1:3]
fac <- as.factor(c(rep("female",dim(gorf.dat)[3]),rep("male",dim(gorm.dat)[3])))
typClass <- typprobClass(data2,data2,fac,method="w",small=TRUE)
## only 59 specimen is rather small.
typClass2 <- typprobClass(data2,data2,fac,method="c")## use default settings

### check results for first method:
ct <- table(fac,typClass$groupaffin)
ct #view classification table
### get percentage of correct classification
prop.table(ct, 1)

### check results for second method:
ct1 <- table(fac,typClass2$groupaffin)
ct1 #view classification table ### one specimen has been tagged an outlier.
### get percentage of correct callification
prop.table(ct1, 1)