MAINT.Data (version 0.5.1)

MAINT.Data-package: Modelling and Analizing Interval Data

Description

MAINT.DATA implements methodologies for modelling Interval Data, considering five different possible configurations structures for the variance-covariance matrix. It introduces a data class for representing interval data and includes functions and methods for parametric modelling and analysing of interval data. It performs maximum likelihood estimation and statistical tests as well as (M)ANOVA and Linear and Quadratic Discriminant Analysis for all considered configurations.

Details

In the classical model of multivariate data analysis, data is represented in a data-array where n ``individuals" (usually in rows) take exactly one value for each variable (usually in columns). Symbolic Data Analysis (see, e.g., Noirhomme-Fraiture and Brito (2011)) provides a framework where new variable types allow to take directly into account variability and/or uncertainty associated to each single ``individual", by allowing multiple, possibly weighted, values for each variable. New variable types - interval, categorical multi-valued and modal variables - have been introduced. We focus on the analysis of interval data, i.e., where elements are described by variables whose values are intervals. Parametric inference methodologies based on probabilistic models for interval variables are developed in Brito and Duarte Silva (2012) where each interval is represented by its midpoint and log-range,for which Normal and Skew-Normal distributions are assumed. The intrinsic nature of the interval variables leads to special structures of the variance-covariance matrix, which are represented by five different possible configurations. MAINT.DATA implements the proposed methodologies in R, introducing a data class for representing interval data; it includes functions for modelling and analysing interval data, in particular maximum likelihood estimation and statistical tests for the different considered configurations. Methods for (M)ANOVA and Linear and Quadratic Discriminant Analysis of this data class are also provided.

Package:

MAINT.Data

Type:

Package

Version:

0.5.1

Date:

2015-10-20

License:

GPL-2

LazyLoad:

yes

LazyData:

yes

References

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

Noirhomme-Fraiture, M., Brito, P. (2011): "Far Beyond the Classical Data Models: Symbolic Data Analysis". Statistical Analysis and Data Mining, Volume 4, Issue 2, 157-170.

Examples

# 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"))

#Display the first and last observations
head(ChinaT)
tail(ChinaT)

#Print summary statistics
summary(ChinaT)

#Create a new data set considering only the Winter (1st and 4th) quarter intervals

ChinaWT <- ChinaT[,c(1,4)]

# Estimate parameters by maximum likelihood, assuming 
# the classical (unrestricted) covariance configuration C1
ChinaWTE.C1 <- mle(ChinaWT,Config=1)
cat("Winter temperatures of China -- maximum likelhiood estimation results:\n")
print(ChinaWTE.C1)
cat("Standard Errors of Estimators:\n") ; print(stdEr(ChinaWTE.C1))

# Estimate parameters by maximum likelihood, 
# assuming that one of the C3, C4 or C5 restricted covariance configurations holds
ChinaWTE.C345 <- mle(ChinaWT,Config=3:5)
cat("Winter temperatures of China -- maximum likelhiood estimation results:\n")
print(ChinaWTE.C345)
cat("Standard Errors of Estimators:\n") ; print(stdEr(ChinaWTE.C345))

#MANOVA tests assuming that configuariton 1 (unrestricted covariance) 
# or 4 (MidPoints independent of Log-Ranges) holds.  
ManvChinaWT.C14 <- MANOVA(ChinaWT,ChinaTemp$GeoReg,Config=c(1,4))
cat("Winter temperatures of China -- MANOVA by geografical regions results:\n")
print(ManvChinaWT.C14)

#Linear Discriminant Analysis
ChinaWT.lda <- lda(ManvChinaWT.C14)
cat("Winter temperatures of China -- linear discriminant analysis results:\n")
print(ChinaWT.lda)
cat("lda Prediction results:\n")
print(predict(ChinaWT.lda,ChinaWT)$class)

#Estimate error rates by ten-fold cross-validation 
CVlda <- DACrossVal(ChinaWT,ChinaTemp$GeoReg,TrainAlg=lda,
Config=BestModel(ManvChinaWT.C14@H1res),CVrep=1)
summary(CVlda[,,"Clerr"])
glberrors <- 
  apply(CVlda[,,"Nk"]*CVlda[,,"Clerr"],1,sum)/apply(CVlda[,,"Nk"],1,sum)
cat("Average global classification error =",mean(glberrors),"\n")