MAINT.Data (version 2.4.1)

snda-methods: Skew-Normal Discriminant Analysis of Interval Data

Description

snda performs discriminant analysis of Interval Data based on estimates of mixtures of Skew-Normal models

Usage

# S4 method for IData
snda(x, grouping, prior="proportions", CVtol=1.0e-5, subset=1:nrow(x),
  CovCase=1:4, SelCrit=c("BIC","AIC"), Mxt=c("Loc","Gen"), k2max=1e6, … )
# S4 method for IdtLocSNMANOVA
snda( x, prior="proportions", selmodel=BestModel(H1res(x)),
  egvtol=1.0e-10, silent=FALSE, k2max=1e6, … )
# S4 method for IdtLocNSNMANOVA
snda( x, prior="proportions",
  selmodel=BestModel(H1res(x)@SNMod), egvtol=1.0e-10, silent=FALSE, k2max=1e6, … )
# S4 method for IdtGenSNMANOVA
snda( x, prior="proportions", selmodel=BestModel(H1res(x)),
  silent=FALSE, k2max=1e6, … )
# S4 method for IdtGenNSNMANOVA
snda( x, prior="proportions",
  selmodel=BestModel(H1res(x)@SNMod), silent=FALSE, k2max=1e6, … )

Arguments

x

An object of class '>IData, '>IdtLocSNMANOVA, '>IdtLocNSNMANOVA,'>IdtGenSNMANOVA or '>IdtGenNSNMANOVA with either the original Interval Data, or the results of a Interval Data Skew-Normal MANOVA, from which the discriminant analysis will be based.

grouping

Factor specifying the class for each observation.

prior

The prior probabilities of class membership. If unspecified, the class proportions for the training set are used. If present, the probabilities should be specified in the order of the factor levels.

CVtol

Tolerance level for absolute value of the coefficient of variation of non-constant variables. When a MidPoint or LogRange has an absolute value within-groups coefficient of variation below CVtol, it is considered to be a constant.

subset

An index vector specifying the cases to be used in the analysis.

CovCase

Configuration of the variance-covariance matrix: a set of integers between 1 and 4.

SelCrit

The model selection criterion.

Mxt

Indicates the type of mixing distributions to be considered. Current alternatives are “Loc” (location model -- groups differ only on the location parameters of a Skew-Normal model) and “Gen” (general model -- groups differ on all parameters of a Skew-Normal models).

silent

A boolean flag indicating wether a warning message should be printed if the method fails.

selmodel

Selected model from a list of candidate models saved in object x.

egvtol

Tolerance level for the eigenvalues of the product of the inverse within by the between covariance matrices. When a eigenvalue has an absolute value below egvtol, it is considered to be zero.

k2max

Maximal allowed l2-norm condition number for correlation matrices. Correlation matrices with condition number above k2max are considered to be numerically singular, leading to degenerate results.

…

Other named arguments.

References

Azzalini, A. and Dalla Valle, A. (1996), The multivariate skew-normal distribution. Biometrika 83(4), 715--726.

Brito, P., Duarte Silva, A. P. (2012), Modelling Interval Data with Normal and Skew-Normal Distributions. Journal of Applied Statistics 39(1), 3--20.

Duarte Silva, A.P. and Brito, P. (2015), Discriminant analysis of interval data: An assessment of parametric and distance-based approaches. Journal of Classification 39(3), 516--541.

See Also

lda, qda, Roblda, Robqda, '>IData, '>IdtLocSNMANOVA, '>IdtLocNSNMANOVA, '>IdtGenSNMANOVA,'>IdtGenSNMANOVA

Examples

# NOT RUN {
# }
# NOT RUN {
# Create an Interval-Data object containing the intervals for 899 observations 
# on the temperatures by quarter in 60 Chinese meteorological stations.

ChinaT <- IData(ChinaTemp[1:8],VarNames=c("T1","T2","T3","T4"))

# Skew-Normal based discriminant analysis, asssuming that the different regions differ
# only in location parameters

ChinaT.locsnda <- snda(ChinaT,ChinaTemp$GeoReg,Mxt="Loc")

cat("Temperatures of China -- SkewNormal location model discriminant analysis results:\n")
print(ChinaT.locsnda)

#Estimate error rates by three-fold cross-validation without replication  

CVlocsnda <- DACrossVal(ChinaT,ChinaTemp$GeoReg,TrainAlg=snda,Mxt="Loc",
  CovCase=CovCase(ChinaT.locsnda),kfold=3,CVrep=1)

summary(CVlocsnda[,,"Clerr"])

glberrors <- 
  apply(CVlocsnda[,,"Nk"]*CVlocsnda[,,"Clerr"],1,sum)/apply(CVlocsnda[,,"Nk"],1,sum)

cat("Average global classification error =",mean(glberrors),"\n")

# Skew-Normal based discriminant analysis, asssuming that the different regions may differ
# in all SkewNormal parameters

ChinaT.gensnda <- snda(ChinaT,ChinaTemp$GeoReg,Mxt="Gen")

cat("Temperatures of China -- SkewNormal general model discriminant analysis results:\n")
print(ChinaT.gensnda)

#Estimate error rates by three-fold cross-validation without replication  

CVgensnda <- DACrossVal(ChinaT,ChinaTemp$GeoReg,TrainAlg=snda,Mxt="Gen",
  CovCase=CovCase(ChinaT.gensnda),kfold=3,CVrep=1)

summary(CVgensnda[,,"Clerr"])

glberrors <- 
  apply(CVgensnda[,,"Nk"]*CVgensnda[,,"Clerr"],1,sum)/apply(CVgensnda[,,"Nk"],1,sum)

cat("Average global classification error =",mean(glberrors),"\n")

# }
# NOT RUN {
# }