Box's test for equivalence of covariance matrices

Description

The function performs Box's test for testing the null hypothesis that two or more covariance matrices are equal.

Usage

BoxMTest(X, cl, alpha = 0.05, test = "any")

Arguments

Details

If the size of any group is at least 20 units (sufficiently large), the test takes a Chi-square approximation, otherwise it takes an F approximation.

Value

A list with the following elements:

• MBox - The value of the Box's M statistic.

• ChiSq or F - The approximation statistic test.

• p - An observed significance level.

Author(s)

Andy Liaw and Aleš Žiberna (minor modifications)

References

Stevens, J. (1996). Applied multivariate statistics for the social sciences . 1992. Hillsdale, NJ: Laurence Erlbaum.

Examples

BoxMTest(X = mtcars[, c(1, 3, 4, 5)], cl = as.factor(mtcars[, 2]), alpha = 0.05)

KNN-imputation method

Description

Function that fills in all NA values using the k-nearest-neighbours of each case with NA values. By default it uses the values of the neighbours and obtains an weighted (by the distance to the case) average of their values to fill in the unknows. If meth='median' it uses the median/most frequent value, instead.

Usage

KNNimp(data, k = 10, scale = TRUE, meth = "weighAvg", distData = NULL)

Arguments

Details

This function uses the k-nearest neighbours to fill in the unknown (NA) values in a data set. For each case with any NA value it will search for its k most similar cases and use the values of these cases to fill in the unknowns. If meth='median' the function will use either the median (in case of numeric variables) or the most frequent value (in case of factors), of the neighbours to fill in the NAs. If meth='weighAvg' the function will use a weighted average of the values of the neighbours. The weights are given by exp(-dist(k,x) where dist(k,x) is the euclidean distance between the case with NAs (x) and the neighbour k.

Value

A dataframe with imputed values.

Note

This is a slightly modified function from package DMwR by Luis Torgo. The modification allows the units with missing values at almost all variables.

Author(s)

Luis Torgo

References

Torgo, L. (2010) Data Mining using R: learning with case studies, CRC Press (ISBN: 9781439810187).

See Also

seqKNNimp

Examples

mtcars$mpg[sample(1:nrow(mtcars), size = 5, replace = FALSE)] <- NA
KNNimp(data = mtcars)

Simple version of omega coefficient - measure of measurement internal consistency based on factor analysis

Description

The function omega coefficient, which is a measure of measurement internal consistency based on factor analysis, based on the covariance or correlation matrix. psych::fa is used to preform factor analysis.

Usage

Omega(
  C,
  fm = "ml",
  nfactors = 1,
  covar = TRUE,
  usePsych = TRUE,
  returnFaRes = FALSE,
  rotation = "none",
  ...
)

Arguments

Value

By default just the value of the omega coefficient. If returnFaRes is TRUE, then a list with two elements:

• omega - The value of the omega coefficient.

• faRes - The result of factor analysis.

Author(s)

Ales Ziberna

Examples

Omega(C=cor(mtcars[,1:6]),nfactors=1)
Omega(C=cor(mtcars[,1:6]),nfactors=1,returnFaRes=TRUE)

Theta coefficient - measure of measurement internal consistency based on principal component analysis

Description

The function theta coefficient, which is a measure of measurement internal consistency based on principal component analysis, or more precisely first eigenvalue.

Usage

Theta(C)

Arguments

Value

The value of the theta coefficient.

Author(s)

Ales Ziberna

Examples

Theta(C=cor(mtcars[,1:6]))

Anti-image matrix

Description

The function computes anti-image matrix (i.e., with partial correlations on the off-diagonal and with KMO-MSAs on the diagonal) and the overall KMO.

Usage

antiImage(X)

Arguments

Value

A list with two elements:

• AIR - Anti-image matrix.

• KMO - Overall KMO.

Author(s)

Marjan Cugmas

References

Kaiser, H. F., & Rice, J. (1974). Little Jiffy, Mark Iv. Educational & Psychological Measurement, 34(1), 111.

Examples

antiImage(X = mtcars[, c(1, 3, 4, 5)])

Break a string

Description

The function breaks a string after around the specified number of characters.

Usage

breakString(x, nChar = 20)

Arguments

Value

A string with inserted \n.

Author(s)

Marjan Cugmas

Examples

someText <- "This is the function that breaks a string."
breakString(x = someText, nChar = 20)

Canonical correlations

Description

The function computes canonical correlations (by using cc or cancor functions) and provides with the test of canonical correlations and with the eigenvalues of the canonical roots (including with the proportion of explained variances by correlation and other related statistics).

Usage

cancorPlus(x, y, xcenter = TRUE, ycenter = TRUE, useCCApackage = FALSE)

Arguments

Value

The function returns the same output as functions cancor or cc with the following additional elements:

• $sigTest

  • WilksL - Value of the Wilk's lambda statistic (it is a generalization of the multivariate R2; values near 0 indicate high correlation while values near 1 indicate low correlation).

  • F - Corresponding (to Wilk's lambda) F-ratio.

  • df1 - Degrees of freedom for the corresponding F-ratio.

  • df2 - Degrees of freedom for the corresponding F-ratio.

  • p - Probability value (p-value) for the corresponding F-ratio (Ho: The current and all the later canonical correlations equal to zero).

• $eigModel

  • Eigenvalues - Eigenvalues of the canonical roots.

  • % - Proportion of explained variance of correlation.

  • Cum % - Cumulative proportion of explained variance of correlation.

  • Cor - Canonical correlation coefficient.

  • Sq. Cor - Squared canonical correlation coefficient.

Author(s)

Adapted by Aleš Žiberna based on the source in References.

References

R Data Analysis Examples: Canonical Correlation Analysis, UCLA: Statistical Consulting Group. From http://www.ats.ucla.edu/stat/r/dae/canonical.htm (accessed Decembar 27, 2013).

See Also

testCC

Examples

cancorPlus(x = mtcars[, c(1,2,3)], y = mtcars[, c(4,5, 6)])

Compare factor loadings

Description

The function compares two sets of factor loadings by considering different possible orders of factors and different possible signs of factor loadings.

Usage

compLoad(L1, L2)

Arguments

Value

A list with the following elements:

• err - Sum of squared differences between the values of L1 and L2 (for the corresponding permuation and signs).

• perm - Permutation of columns of L1 that results in the lowest err value.

• sign - Signs of factor loadings of L1. The first value corresponds to the first column of L1 and the second value corresponds to the second column of L1.

Author(s)

Aleš Žiberna and Friedrich Leisch (permutations)

Examples

L1 <- cbind(c(0.72, 0.81, 0.92, 0.31, 0.22, 0.15), c(0.11, 0.09, 0.17, 0.77, 0.66, 0.89))
L2 <- cbind(c(-0.13, -0.08, -0.20, -0.78, -0.69, -0.88), c(0.72, 0.82, 0.90, 0.29, 0.20, 0.17))
compLoad(L1, L2)

Compute correlations and test their statistical significance

Description

The function computes the whole correlation matrix and corresponding sample sizes and p-values. Print method is also available.

Usage

corTestDf(X, method = "p", use = "everything", ...)

## S3 method for class 'corTestDf'
print(x, digits = c(3, 3), format = NULL, ...)

printCorTestDf(l, digits = c(3, 3), format = NULL, ...)

Arguments

Author(s)

Ales Ziberna

See Also

cor.test

Examples

corTestDf(mtcars[, 3:5])

Transform continuous variable to a discrete variable

Description

The function transforms a continuous variable to a k-point discrete variable (similar to a Likert-item type variable). Different styles of answering to a survey are possible.

Usage

discretize(x, type = "eq", q = 1.5, k = 5, r = range(x), num = TRUE)

Arguments

Value

Transformed values are organized into a vector.

Author(s)

Aleš Žiberna

Examples

x <- rnorm(1000)
hist(x = discretize(x, type = "eq"), breaks = 0:5+0.5, xlab = "answer", main = "type = 'eq'")
hist(x = discretize(x, type = "yes"), breaks = 0:5+0.5, xlab = "answer", main = "type = 'yes'")
hist(x = discretize(x, type = "no"), breaks = 0:5+0.5, xlab = "answer", main = "type = 'no'")
hist(x = discretize(x, type = "avg"), breaks = 0:5+0.5, xlab = "answer", main = "type = 'avg'")

Create a frequency table

Description

The function creates a frequency table with percentages for the selected categorical variable.

Usage

freqTab(x, dec = 2, cum = TRUE, ...)

Arguments

Value

A frequency table (as a dataframe).

Author(s)

Aleš Žiberna

Examples

freqTab(mtcars[,2], dec = 1)

Histogram with normal curve

Description

The function draws a histogram with a normal density curve. The parameters (mean and standard deviation) are estimated on the empirical data.

Usage

histNorm(y, breaks = "Sturges", freq = TRUE, ...)

Arguments

Value

A list with two elements:

• x - breaks, see graphics::hist.

• y - frequencies or relative frequencies, see graphics::hist.

Author(s)

Marjan Cugmas

Examples

histNorm(rnorm(1000), freq = TRUE)
histNorm(rnorm(1000), freq = FALSE)

Linear discriminant analysis

Description

The function performs a linear discriminant analysis (by using the MASS::lda function). Compared to the MASS::lda function, the ldaPlus function enable to consider the prior probabilities to predict the values of a categorical variable, it provides with predicted values and with (Jack-knife) classification table and also with statistical test of canonical correlations between the variable that represents groups and numeric variables.

Usage

ldaPlus(x, grouping, pred = TRUE, CV = TRUE, usePriorBetweenGroups = TRUE, ...)

Arguments

Details

The specified prior is not taken into account when computing eigenvalues and all statistics based on them (everything in components eigModel and sigTest of the returned value).

Value

The following objects are also a part of what is returned by the MASS::lda function.

• prior - Prior probabilities of class membership taken to estimate the model (it can be estimated based on the sample data or it can be provided by a reseacher).

• counts - Number of units in each category of categorical variable taken to estimate the model.

• means - Group means.

• scaling - Matrix that transforms observations to discriminant functions, normalized so that within groups covariance matrix is spherical.

• lev - Levels (groups) of the categorical variable.

• svd - Singular values, that give the ratio of the between-group and within-group standard deviations on linear discriminant variables. Their squares are the canonical F-statistics.

• N - Number of observations used.

• call - the (matched) function call.

The additional following objects are generated by the multiUS::ldaPlus function.

• standCoefWithin - Standardized coefficients (within groups) of discriminant function.

• standCoefTotal - Standardized coefficients of discriminant function.

• betweenGroupsWeights - Proportions/priors used when estimating the model.

• sigTest - Test of canonical correlations between the variable that represent groups (binary variable) and numeric variables (see function testCC for more details) (Ho: The current and all the later canonical correlations equal to zero.).

• eigModel - Table with eigenvalues and canonical correlations (see function testCC for more details).

• centroids - Means of discriminant variables by levels of categorical variable (not predicted, but actual).

• corr - Pooled correlations within groups (correlations between values of numerical variables and values of linear discriminat function(s)).

• pred

  • class - Predicted values of categorical variable

  • posterior - Posterior probabilities (the values of the Fisher's calcification linear discrimination function)

  • x - Estimated values of discriminat function(s) for each unit

• class - Classification table:

  • orgTab - Frequency table.

  • perTab - Percentages.

  • corPer - Percentage of correctly predicted values (alternatively, percentage of correctly classified units).

• classCV - Similar to class but based on cross validation (Jack-knife).

Author(s)

Aleš Žiberna

References

R Data Analysis Examples: Canonical Correlation Analysis, UCLA: Statistical Consulting Group. From http://www.ats.ucla.edu/stat/r/dae/canonical.htm (accessed Decembar 27, 2013).

Examples

ldaPlus(x = mtcars[,c(1, 3, 4, 5, 6)], grouping = mtcars[,10])

Make factor labels

Description

The function transforms a numeric varibale into categorical one, based on the attribute data from a given SPSS file.

Usage

makeFactorLabels(x, reduce = TRUE, ...)

Arguments

Details

Data have to be imported by using the foreign::read.spss function. The use of the function make sence when the parameter use.value.lables in the function read.spss is set to FALSE.

Value

Categorical variable (vector).

Author(s)

Aleš Žiberna

LDA mapping

Description

The function draws two dimensional map of discriminant functions.

Usage

mapLda(
  object,
  xlim = c(-2, 2),
  ylim = c(-2, 2),
  npoints = 101,
  prior = object$prior,
  dimen = 2,
  col = NULL
)

Arguments

Value

No return value, called for side effects (plotting a map).

Author(s)

Aleš Žiberna

Examples

# Estimate the LDA model:
ldaCars <- ldaPlus(x = mtcars[,c(1, 3, 4, 5, 6)], grouping = mtcars[,10])
# Plot LDA map:
mapLda(ldaCars)

Plot a solution of canonical correlations

Description

It plots the canonical solution that is obtained by the function multiUS::cancorPlus.

Usage

plotCCA(
  ccRes,
  xTitle = "X",
  yTitle = "Y",
  inColors = TRUE,
  scaleLabelsFactor = 1/2,
  what = "reg",
  nDigits = 2,
  mar = c(1, 2, 1, 1)
)

Arguments

Value

It plots the plot.

Author(s)

Marjan Cugmas

Examples

tmp<-cancorPlus(x = mtcars[, c(1,2,3)], y = mtcars[, c(4,5, 6)], useCCApackage = TRUE)
plotCCA(tmp, scaleLabelsFactor = 1/2, what = "cor")

Plot the means

Description

The function plots the means of several numerical variables by the levels of one categorical variable.

Usage

plotMeans(
  x,
  by,
  plotCI = TRUE,
  alpha = 0.05,
  ylab = "averages",
  xlab = "",
  plotLegend = TRUE,
  inset = 0.01,
  xleg = "topleft",
  legPar = list(),
  gap = 0,
  labels = NULL,
  ...
)

Arguments

Value

A list with the following elements:

• means - mean values by groups.

• CI - widths of confidence intervals by groups.

Author(s)

Aleš Žiberna

Examples

plotMeans(x = mtcars[, c(1, 3, 5)], by = mtcars[,8])

Predict the values of a categorical variable based on a linear discriminant function

Description

The function predicts the values of a categorical variable based on a linear discriminat function.

Usage

## S3 method for class 'ldaPlus'
predict(
  object,
  newdata,
  prior = object$prior,
  dimen,
  method = c("plug-in", "predictive", "debiased"),
  betweenGroupsWeights = object$betweenGroupsWeights,
  ...
)

Arguments

Value

A list with the following elements:

• class - Predicted values of categorical variable.

• posterior - Posterior probabilities (the values of the Fisher's calsification linear discrimination function).

• x - Estimated values of discriminat function(s) for each unit.

Author(s)

Aleš Žiberna

See Also

MASS::predict

Examples

# Use the first 20 cars to estimate the model and the rest of cars to predict
# (for each car) wheter it has a V-shape engine or a straight engine.
ldaCars <- ldaPlus(x = mtcars[1:20,c(1, 2, 4, 5, 6)], grouping = mtcars[1:20,8])
predict.ldaPlus(object = ldaCars, newdata = mtcars[20:32,c(1, 2, 4, 5, 6)])

Print p-value

Description

The function round and prints p-value.

Usage

printP(p)

Arguments

Value

A string (formatted p-value).

Author(s)

Marjan Cugmas

Examples

printP(p = 0.523)
printP(p = 0.022)
printP(p = 0.099)

Rename variables

Description

The function for renaming one or several variables in a dataframe.

Usage

renameVar(data, renames)

Arguments

Value

A dataframe with renamed columns.

Author(s)

Marjan Cugmas

Examples

renameVar(mtcars, list("cyl" = "Cylinders", "wt" = "Weight", "am" = "Transmission"))

Sequential KNN imputation method

Description

This function estimates missing values sequentially from the units that has least missing rate, using weighted mean of k nearest neighbors.

Usage

seqKNNimp(data, k = 10)

Arguments

Details

The function separates the dataset into an incomplete set with missing values and into a complete set without missing values. The values in an incomplete set are imputed in the order of the number of missing values. A missing value is filled by the weighted mean value of a corresponding column of the nearest neighbour units in the complete set. Once all missing values for a given unit are imputed, the unit is moved into the complete set and used for the imputation of the rest of units in the incomplete set. In this process, all missing values for one unit can be imputed simultaneously from the selected neighbour units in the complete set. This reduces execution time from previously developed KNN method that selects nearest neighbours for each imputation.

Value

A dataframe with imputed values.

Note

This is the function from package SeqKNN by Ki-Yeol Kim and Gwan-Su Yi.

Author(s)

Ki-Yeol Kim and Gwan-Su Yi

References

Ki-Yeol Kim, Byoung-Jin Kim, Gwan-Su Yi (2004.Oct.26) "Reuse of imputed data in microarray analysis increases imputation efficiency", BMC Bioinformatics 5:160.

See Also

KNNimp

Examples

mtcars$mpg[sample(1:nrow(mtcars), size = 5, replace = FALSE)] <- NA
seqKNNimp(data = mtcars)

Recoding the smallest categories to "other" value in case of too many or too small categories.

Description

The smallest categories are recoded to "other" or user specified string. The variables is converted to factor if not already.

Usage

small2other(
  x,
  maxLevels = 12,
  minFreq = 0,
  otherValue = "other",
  convertNA = TRUE,
  orderLevels = FALSE,
  otherLast = FALSE
)

Arguments

Test of canonical correlations

Description

The function perform the Wilk's test for the statistical significance of canonical correlations.

Usage

testCC(cor, n, p, q)

Arguments

Value

The results are organized in a list format with two data tables:

sigTest

• WilksL - Value of the Wilk's lambda statistic (it is a generalization of the multivariate R2; values near 0 indicate high correlation while values near 1 indicate low correlation).

• F - Corresponding (to Wilk's lambda) F-ratio.

• df1 - Degrees of freedom for the corresponding F-ratio.

• df2 - Degrees of freedom for the corresponding F-ratio.

• p - Probability value (p-value) for the corresponding F-ratio (Ho: The current and all the later canonical correlations equal to zero).

eigModel

• Eigenvalues - Eigenvalues of the canonical roots.

• % - Proportion of explained variance of correlation.

• Cum % - Cumulative proportion of explained variance of correlation.

• Cor - Canonical correlation coeficient.

• Sq. Cor - Squared canonical correlation coeficient.

Author(s)

Aleš Žiberna

References

R Data Analysis Examples: Canonical Correlation Analysis, UCLA: Statistical Consulting Group. From http://www.ats.ucla.edu/stat/r/dae/canonical.htm (accessed Decembar 27, 2013).

Examples

testCC(cor = c(0.76, 0.51, 0.35, 0.28, 0.10), n = 51, p = 5, q = 5)

Calculate the value of the Ward criterion function

Description

The function calculate the value of the Ward criterion function, based on a set of numerical variables and one categorical variable (partition).

Usage

wardKF(X, clu)

wardCF(X, clu)

Arguments

Value

The value of the Ward criterion function.

Author(s)

Aleš Žiberna