Morpho (version 2.12)

typprob: calculate typicality probabilities

Description

calculate typicality probabilities

Usage

typprob(
  x,
  data,
  small = FALSE,
  method = c("chisquare", "wilson"),
  center = NULL,
  cova = NULL,
  robust = c("classical", "mve", "mcd"),
  ...
)
typprobClass(
  x,
  data,
  groups,
  small = FALSE,
  method = c("chisquare", "wilson"),
  outlier = 0.01,
  sep = FALSE,
  cv = TRUE,
  robust = c("classical", "mve", "mcd"),
  ...
)

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"

probsCV

cross-validated matrix of probabilities for each group

groupaffinCV

cross-validated vector of groups each specimen has been assigned to. Outliers are classified "none"

self

logical: if TRUE, the data has been classified by self-inference.

Arguments

x

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

data

Reference data set. If missing x will be used.

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). Results will be similar in general.

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.

robust

character: determines covariance estimation methods, allowing for robust estimations using MASS::cov.rob. Default is the standard product-moment covariance matrix.

...

additional parameters passed to MASS::cov.rob for robust covariance and mean estimations.

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.

cv

logical: if data is missing and cv=TRUE, the resulting classification will be validated by leaving-one-out crossvalidation.

Author

Stefan Schlager

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

if (require(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,colMeans(data),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,groups=fac,method="w",small=TRUE,cv=TRUE)
## only 59 specimen is rather small.
typClass2 <- typprobClass(data2,groups=fac,method="c",cv=TRUE)## use default settings

### check results for first method:
typClass


### check results for second method:
typClass2
}