Type: Package
Title: Multivariate Estimates and Tests
Version: 0.1.0
Author: Yeonseok Choi [aut, cre], Yong-Seok Choi [ctb]
Maintainer: Yeonseok Choi <yeonseok3488@gmail.com>
Description: Multivariate estimation and testing, currently a package for testing parametric data. To deal with parametric data, various multivariate normality tests and outlier detection are performed and visualized using the 'ggplot2' package. Homogeneity tests for covariance matrices are also possible, as well as the Hotelling's T-square test and the multivariate analysis of variance test. We are exploring additional tests and visualization techniques, such as profile analysis and randomized complete block design, to be made available in the future and making them easily accessible to users.
License: MIT + file LICENSE
URL: https://github.com/YeonSeok-Choi/MVET
Encoding: UTF-8
RoxygenNote: 7.3.1
Depends: R (≥ 3.5.0)
Imports: stats, ggplot2 (≥ 3.4.0), gridExtra (≥ 2.3)
LazyData: true
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2024-06-05 09:24:02 UTC; GaeJu
Repository: CRAN
Date/Publication: 2024-06-06 16:40:02 UTC

Mean Value Parallel Coordinates Plot (Use to HT2test & VManova)

Description

Mean Value Parallel Coordinates Plot (Use to HT2test & VManova)

Usage

.mean_parallel_plot(data, grp.name, scale = FALSE)

Arguments

data

A numeric matrix or data frame. If data frame, group(class) column can be a factor or a string.

grp.name

The name of a column of string representing groups(classes) in the input data.

scale

If TRUE, the data will be scaled before calculating mean values and used in the plot. (default scale = FALSE)

Value

Mean Value Parallel Coordinates Plot

Hotelling T Square Test

Description

The mean vector test (Hotelling T square test) to compare one sample or two samples that satisfy the multivariate normality test and the homogeneity of covariance matrices test.

Usage

HT2test(data1,
        data2,
        mu0 = NULL,
        sample = "two",
        plot.scale = FALSE)

Arguments

data1

The data frame or matrix must consist of only numbers, and the data must consist of only a single group or class. It should not contain columns that separate groups or classes.

data2

The data frame or matrix must consist of only numbers, and the data must consist of only a single group or class. It should not contain columns that separate groups or classes. The data2 is for comparison with data1 and is not used to compare one sample to another.

mu0

The mu0 is used to test the mean vector hypothesis of data1. It is only used to compare one-sample.

sample

The options for specifying the number of groups for group comparisons are one and two, where one is used to compare one-sample and two is used to compare two-samples. (default sample = two)

plot.scale

If TRUE, the data will be scaled before calculating mean values and used in the plot. It has no direct effect on the data. It only applies to two samples. (default plot.scale = FALSE)

Value

One.HT2

The Hotelling T square test in one-sample, showing the degrees of freedom required for the F test, the Hotelling t square statistic, the F test statistic, and the probability of significance.

Mean.val.plot

Plot the mean value parallel coordinates, representing the two samples using the mean values for each variable.

Two.HT2

The Hotelling T square test in two-sample, showing the degrees of freedom required for the F test, the Hotelling t square statistic, the F test statistic, and the probability of significance.

References

Johnson, R. A., & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis (6th ed.). Pearson Prentice Hall.

See Also

mardiatest for multivariate normality (Includes outlier remove)

PPCCtest for multivariate normality

SPCCtest for multivariate normality

boxMtest for homogeneity of covariance matrices

Examples

data(wine)
class1.wine <- subset(wine, class == 1)[, -1]
class2.wine <- subset(wine, class == 2)[, -1]
modified.class2.wine <- outlier(class2.wine, lim = 0, level = 0.05, option = "all")$modified.data

## one sample
value <- 0
p <- ncol(class1.wine)
mu0 <- matrix(rep(value, p), nrow = p, ncol = 1)
HT2test(data1 = class1.wine, mu0 = mu0, sample = "one")

## two sample
HT2test(data1 = class1.wine, data2 = modified.class2.wine, sample = "two", plot.scale = TRUE)

Probability Plot Correlation Coefficient(PPCC) Test for Multivariate Normality Test

Description

The correlation coefficient of the quantiles and mahalanobis square are tested by using the critical value table by Filliben (1975) for the multivariate normality test.

Usage

PPCCtest(data,
         level = 0.05)

Arguments

data

A numeric matrix or data frame.

level

At the 0.01 or 0.05 significance level, the critical value. (default = 0.05)

Value

data.cnt

Observation n data count.

PPCC.value

Correlation coefficient value.

critical.value

Critical value proposed by Filliben (1975), corresponding to data.cnt and PPCC.value.

test.res

Final result of multivariate normality.

QQPlot

Shows Chi-Square Q-Q plot.

References

Filliben, J. J. (1975), The Probability Plot Correlation Coefficient Test for Normality, Technometrics 17, 111-117.

Examples

data(wine)
class1.wine <- subset(wine, class == 1)[, -1]
PPCCtest(class1.wine, level = 0.05)

Srivastava Plot Correlation Coefficient(SPCC) Test for Multivariate Normality Test

Description

Using principal component analysis, the number of eigenvalues is selected such that the ratio of eigenvalues exceeds 70%. The principal component score vectors corresponding to these selected eigenvalues are used, and testing is conducted using the threshold defined by Filliben (1975). Users have the option to select the number of eigenvalues for the analysis based on their requirements.

Usage

SPCCtest(data,
         k = 0,
         level = 0.05)

Arguments

data

A numeric matrix or data frame.

k

The number of principal components can be manually selected. If 0 is entered, it automatically finds k components such that the explained variance ratio is at least 70%. (default = 0)

level

At the 0.01 or 0.05 significance level, the critical value. (default = 0.05)

Value

Srivastava.QQplot

Shows a chi-Square Q-Q plot for each PCs using ggplot2.

data.cnt

Observation n data count.

explain.ratio

Displays all explained variance ratios.

critical.value

Critical value proposed by Filliben (1975), corresponding to data.cnt and PPCC.value.

result

Final result of multivariate normality.

References

Srivastava, M. S. (1984), A measure of skewness and kurtosis and a graphical method for assessing multivariate normality. Statistics & Probability Letters, 2(5), 263-267.

Filliben, J. J. (1975), The Probability Plot Correlation Coefficient Test for Normality, Technometrics 17, 111-117.

Examples

data(wine)
class1.wine <- subset(wine, class == 1)[, -1]
SPCCtest(class1.wine, k = 5, level = 0.05)

Various Multivariate Anova(VManova)

Description

Perform various types of multivariate analysis of variance (MANOVA) that satisfy tests of multivariate normality and homogeneity of covariance matrices.

Usage

VManova(data,
        grp1.name,
        grp2.name,
        way = "one",
        method = "all",
        plot.scale = FALSE)

Arguments

data

A numeric matrix or data frame. If data frames, group(class) column can be a factor or a string.

grp1.name

The name of the first group (or class) column in the input data, specified as a string.

grp2.name

The name of the second group (or class) column in the input data, specified as a string. Used to represent the second group(class) in a two-way MANOVA.

way

The type of MANOVA to perform ("one" for one-way or "two" for two-way). (default = "one")

method

The method for MANOVA analysis. "Wilks" represents Wilks' lambda, "LH" represents Lawley-Hotelling trace, "Pillai" represents Pillai-Bartlett trace, "Roy" represents Roy's largest root, and "all" represents all methods. (default is "all")

plot.scale

If TRUE, the data will be scaled before calculating mean values and used in the plot. It has no direct effect on the MANOVA analysis itself. (default plot.scale = FALSE)

Value

Mean.val.plot

Plot the mean value parallel coordinates, representing the two samples using the mean values for each variable.

One.all

Outputs the results of a one-way MANOVA test. It displays the degrees of freedom (Df1, Df2) of the F-distribution, statistics for Wilks, Lawley-Hotelling, Pillai, and Roy, the F-distribution test statistic, and the significance level in that order.

Two.all

Outputs the results of a two-way MANOVA test. It displays the degrees of freedom (Df1, Df2) of the F-distribution, statistics for Wilks, Lawley-Hotelling, Pillai, and Roy, the F-distribution test statistic, and the significance level in that order.

References

Rencher, A. C., & Christensen, W. F. (2002). Methods of Multivariate Analysis. John Wiley & Sons, Inc., New York.

See Also

mardiatest for multivariate normality (Includes outlier remove)

PPCCtest for multivariate normality

SPCCtest for multivariate normality

boxMtest for homogeneity of covariance matrices

Examples

data(wine)

## one way
VManova(wine, grp1.name = "class", way = "one", method = "all", plot.scale = TRUE)

## two way
newwine <- wine
# (1: low, 2: medium, 3: high)
newwine$v4 <- ifelse(wine$v4 <= 17, 1,
                     ifelse(wine$v4 <= 22, 2, 3))
VManova(newwine, grp1.name = "class", grp2.name = "v4",
        way = "two", method = "all", plot.scale = TRUE)

Box's M-test

Description

Performs Box's M-test for homogeneity of covariance matrices derived from multivariate normality data according to a single classification factor. This test is based on the chi-square approximation.

Usage

boxMtest(data,
         group)

Arguments

data

A numeric matrix or data frame.

group

In either vector or factor form, the length of the group must correspond to the number of observations n in the data.

Value

M.stat

Box's M-test statistic approximates the chi-square distribution.

df

The degree of freedom is related to the test statistic.

p.value

The p-value of the test statistic.

See Also

mardiatest

Examples

data(wine)
class <- wine$class
winedata <- subset(wine, select = -class)
boxMtest(winedata, class)

Mardia Test for Multivariate Normality Test

Description

Performs a multivariate normality test by conducting a mardia test using skewness and kurtosis. If both skewness and kurtosis are satisfied, multivariate normality is satisfied.

Usage

mardiatest(data,
           level = 0.05,
           showplot = FALSE,
           showoutlier = FALSE,
           outlieropt = "all",
           shownewdata = FALSE)

Arguments

data

A numeric matrix or data frame.

level

The significance level of the skewness and kurtosis statistics. (default = 0.05)

showplot

If TRUE, show a chi-square Q-Q plot using ggplot2. If 'showoutlier' is TRUE, outliers are also displayed. (default = FALSE)

showoutlier

If TRUE, show the outliers number and count. (default = FALSE)

outlieropt

An "option" in the outlier function. (default = "all")

shownewdata

If TRUE Shows the new data with outliers removed. (default = FALSE)

Value

mult.nomality

Calculate statistics and p-values for skewness and kurtosis to ultimately determine whether multivariate normality is satisfied.

QQPlot

Shows Chi-Square Q-Q plot.

...

Same as the result of outlier

References

Mardia, K. V. (1970), Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530.

Mardia, K. V. (1974), Applications of Some Measures of Multivariate Skewness and Kurtosis in Testing Normality and Robustness Studies. Sankhya, 36, 115-128.

See Also

outlier

Examples

## Simple Mardia Test
data(wine)
class2.wine <- subset(wine, class == 2)[, -1]
mardiatest(class2.wine, level = 0.05, showplot = TRUE)

## Mardia Test and Outlier Detection
data(wine)
class2.wine <- subset(wine, class == 2)[, -1]
mardiatest(class2.wine, level = 0.05, showplot = TRUE,
           showoutlier = TRUE, outlieropt = "all", shownewdata = TRUE)

Outliers Detection

Description

Using the mardia test, outliers are detected based on skewness and kurtosis. However, outliers don't detect more than half of the total observation data.(Can be modified with the lim option.)

Usage

outlier(data,
        lim = 0,
        level = 0.05,
        option = "all")

Arguments

data

A numeric matrix or data frame.

lim

The number of outliers detected can be limited. If 0 is entered, detection is possible up to half of the data. (default = 0)

level

The significance level of the skewness and kurtosis statistics of the "madiatest" function. (default = 0.05)

option

"skew" refers to skewness, "kurt" refers to kurtosis, "all" refers to skewness and kurtosis. Outliers are detected until the corresponding option in the mardiatest is “Accept”. (default = "all")

Value

modified.data

The modified data without outliers.

modified.mvn

The modified Mardia test result without outliers.

outlier.num

The position of outliers.

outlier.cnt

Total number of outliers.

References

Jobson, J. D.(1992). Applied Multivariate Data Analysis, Springer-Verlag, New York.

See Also

mardiatest

Examples

data(wine)
class2.wine <- subset(wine, class == 2)[, -1]
outlier(class2.wine, lim = 0, level = 0.05, option = "all")

Wine Dataset

Description

These data are the results of a chemical analysis of wines grown in the same region in Italy but derived from three different cultivars. The analysis determined the quantities of 13 constituents found in each of the three types of wines.

Usage

wine

Format

A data frame with 178 observations on the following 14 variables:

class

The class vector, the three different cultivars of wine are reprensented by the three integers(1 to 3).

v1

Alcohol

v2

Malic acid

v3

Ash

v4

Alcalinity of ash

v5

Magnesium

v6

Total phenols

v7

Flavanoids

v8

Nonflavanoid phenols

v9

Proanthocyanins

v10

Color intensity

v11

Hue

v12

OD280/OD315 of diluted wines

v13

Proline

Source

http://archive.ics.uci.edu/ml/datasets/Wine.