Multivariate Data Analysis Laboratory (mvdalab)

Description

Implementation of latent variables methods. The focus is on explorative anlaysis using dimensionality reduction methods, such as Principal Component Analysis (PCA), and on multivariate regression based on Partial Least Squares regression (PLS). PLS analyses are supported by embedded bootstrapping and variable selection procedures.

Details

Author(s)

Nelson Lee Afanador (nelson.afanador@gmail.com), Thanh Tran (thanh.tran@mvdalab.com), Lionel Blanchet (lionel.blanchet@mvdalab.com), Richard Baumgartner (richard_baumgartner@merck.com)

Maintainer: Nelson Lee Afanador (nelson.afanador@gmail.com)

Generates a biplot from the output of an 'mvdareg' and 'mvdapca' object

Description

Generates a 2D Graph of both the scores and loadings for both "mvdareg" and "mvdapca" objects.

Usage

BiPlot(object, diag.adj = c(0, 0), axis.scaling = 2,
                          cov.scale = FALSE, comps = c(1, 2), 
                          col = "red", verbose = FALSE)

Arguments

Details

"BiPlot" is used to extract a 2D graphical summary of the scores and loadings of PLS and PCA models.

The singular values are scaled so that the approximation becomes X = GH':

X = ULV' = (UL^alpha1)(L^alpha2V') = GH', and where alpha2 is = to (1 = alpha)

The rows of the G matrix are plotted as points, corresponding to observations. The rows of the H matrix are plotted as vectors, corresponding to variables. The choice of alpha determines the following:

c(0, 0): variables are scaled to unit length and treats observations and variables symmetrically.

c(0, 1): This biplot attempts to preserve relationships between variables wherein the distance betweein any two rows of G is proportional to the Mahalanobis distance between the same observations in the data set.

c(1, 0): This biplot attempts to preserve the distance between observations where in the positions of the points in the biplot are identical to the score plot of first two principal components, but the distance between any two rows of G is equal to the Euclidean distance between the corresponding observations in the data set.

cov.scale = FALSE sets diag.adj to c(0, 0) and multiples G by sqrt(n - 1) and divides H by sqrt(n - 1). In this biplot the rows of H approximate the variance of the corresponding variable, and the distance between any two points of G approximates the Mahalanobis distance between any two rows.

Additional scalings may be implemented.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

SAS Stat Studio 3.11 (2009), User's Guide.

Additional information pertaining to biplots can be obtained from the following:

Friendly, M. (1991), SAS System for Statistical Graphics , SAS Series in Statistical Applications, Cary, NC: SAS Institute

Gabriel, K. R. (1971), "The Biplot Graphical Display of Matrices with Applications to Principal Component Analysis," Biometrika , 58(3), 453–467.

Golub, G. H. and Van Loan, C. F. (1989), Matrix Computations , Second Edition, Baltimore: Johns Hopkins University Press.

Gower, J. C. and Hand, D. J. (1996), Biplots , London: Chapman & Hall.

Jackson, J. E. (1991), A User's Guide to Principal Components , New York: John Wiley & Sons.

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
BiPlot(mod1, diag.adj = c(0, 0), axis.scaling = 2, cov.scale = FALSE)

## Not run: 
data(Penta)
mod2 <- pcaFit(Penta[, -1], ncomp = 4)
BiPlot(mod2, diag.adj = c(0, 0), axis.scaling = 2.25, cov.scale = FALSE)

## End(Not run)

Data for College Level Examination Program and the College Qualification Test

Description

Scores obtained from 87 college students on the College Level Examination Program and the College Qualification Test.

Usage

College

Format

A data frame with 87 observations and the following 3 variables.

Science

Science (CQT) - numerical vector

Social

Social science and history (CLEP) - numerical vector

Verbal

Verbal (CQT) - numerical vector

Source

Johnson, R.A., Wichern, D.W. (2002) Applied Multivariate Statistical Analysis. Prentice Hall.

Traditional Multivariate Mean Vector Comparison

Description

Performs a traditional multivariate comparison of mean vectors drawn from two populations.

Usage

MVComp(data1, data2, level = .95)

Arguments

Details

This function provides a T2-statistic for testing the equality of two mean vectors. This test is appropriate for testing two populations, assuming independence.

Assumptions:

The sample for both populations is a random sample from a multivariate population.

-Both populations are independent

-Both populations are multivariate normal

-Covariance matrices are approximately equal

Value

This function returns the simultaneous confidence intervals for the p-variates and its corresponding confidence ellipse at the stated confidence level.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Johnson, R.A., Wichern, D.W. (2002) Applied Multivariate Statistical Analysis. Prentice Hall.

Examples

data(College)
dat1 <- College
#Generate a 'fake' difference of 15 units
dat2 <- College + matrix(rnorm(nrow(dat1) * ncol(dat1), mean = 15), 
        nrow = nrow(dat1), ncol = ncol(dat1))

Comparison <- MVComp(dat1, dat2, level = .95)
Comparison
plot(Comparison, Diff2Plot = c(1, 2), include.zero = FALSE)
plot(Comparison, Diff2Plot = c(1, 2), include.zero = TRUE)

plot(Comparison, Diff2Plot = c(2, 3), include.zero = FALSE)
plot(Comparison, Diff2Plot = c(2, 3), include.zero = TRUE)


data(iris)
dat1b <- iris[, -5]
#Generate a 'fake' difference of .5 units
dat2b <- dat1b + matrix(rnorm(nrow(dat1b) * ncol(dat1b), mean = .5), 
          nrow = nrow(dat1b), ncol = ncol(dat1b))

Comparison2 <- MVComp(dat1b, dat2b, level = .90)
plot(Comparison2, Diff2Plot = c(1, 2), include.zero = FALSE)
plot(Comparison2, Diff2Plot = c(1, 2), include.zero = TRUE)

plot(Comparison2, Diff2Plot = c(3, 4), include.zero = FALSE)
plot(Comparison2, Diff2Plot = c(3, 4), include.zero = TRUE)

Calculate Hotelling's T2 Confidence Intervals

Description

Calculate joint confidence intervals (Hotelling's T2 Intervals).

Usage

MVcis(data, segments = 51, level = .95, Vars2Plot = c(1, 2), include.zero = F)

Arguments

Details

This function calculates the Hotelling's T2 Intervals for a mean vector.

Assumption:

Population is a random sample from a multivariate population.

If the confidence ellipse does not cover c(0, 0), we reject the NULL that the joint confidence region is equal to zero (at the stated alpha level).

Value

This function returns the Hotelling's T2 confidence intervals for the p-variates and its corresponding confidence ellipse at the stated confidence level.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Johnson, R.A., Wichern, D.W. (2002) Applied Multivariate Statistical Analysis. Prentice Hall.

See Also

MVComp

Examples

data(College)
MVcis(College, Vars2Plot = c(1, 2), include.zero = TRUE)

Principal Component Based Multivariate Process Capability Indices

Description

Provides three multivariate capability indices for correlated multivariate processes based on Principal Component Analysis.

Usage

MultCapability(data, lsls, usls, targets, ncomps = NULL, Target = FALSE)

Arguments

Details

ncomps has to be set prior to running the analysis. The user is strongly encouraged to use pcaFit in order to determine the optimal number of principal components using cross-validation.

When the parameter targets is not specified, then is estimated of centered way as targets = lsls + (usls - lsls)/2.

Ppk values are provided to allow the user to compare the multivariate results to the univariate results.

Value

A list with the following elements:

For mpca_wang, the following is returned:

For mcp_xe, the following is returned:

For mpca_wang_2, the following is returned:

For Ppk, the following is returned:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Wang F, Chen J (1998). Capability index using principal components analysis. Quality Engineering, 11, 21-27.

Xekalaki E, Perakis M (2002). The Use of principal component analysis in the assessment of process capability indices. Proceedings of the Joint Statistical Meetings of the American Statistical Association, The Institute of Mathematical Statistics, The Canadian Statistical Society. New York.

Wang, C (2005). Constructing multivariate process capability indices for short-run production. The International Journal of Advanced Manufacturing Technology, 26, 1306-1311.

Scagliarini, M (2011). Multivariate process capability using principal component analysis in the presence of measurement errors. AStA Adv Stat Anal, 95, 113-128.

Santos-Fernandez E, Scagliarini M (2012). "MPCI: An R Package for Computing Multivariate Process Capability Indices". Journal of Statistical Software, 47(7), 1-15, URL http://www.jstatsoft.org/v47/i07/.

Examples

data(Wang_Chen_Sim)
lsls1 <- c(2.1, 304.5, 304.5)
usLs1 <- c(2.3, 305.1, 305.1)
targets1 <- c(2.2, 304.8, 304.8)

MultCapability(Wang_Chen_Sim, lsls = lsls1, usls = usLs1, targets = targets1, ncomps = 2)

data(Wang_Chen)
targets2 <- c(177, 53)
lsls2 <- c(112.7, 32.7)
usLs2 <- c(241.3, 73.3)

MultCapability(Wang_Chen, lsls = lsls2, usls = usLs2, targets = targets2, ncomps = 1)

Percent Explained Variation of X

Description

This function provides both the cumulative and individual percent explained for the X-block for an mvdareg and mvdapca objects.

Usage

PE(object, verbose = FALSE)

Arguments

Details

This function provides both the cumulative and individual percent explained for the X-block for an mvdareg or mvdapca objects.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "none")
PE(mod1)

## Not run: 
data(Penta)
mod2 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
PE(mod2)

## End(Not run)

Penta data set

Description

This data is obtained from drug discovery and includes measurements pertaining to size, lipophilicity, and polarity at various sites on a molecule.

Usage

Penta

Format

A data frame with 30 observations and the following 17 variables.

Obs.Name

Categorical ID Variable

S1

numeric predictor vector

L1

numeric predictor vector

P1

numeric predictor vector

S2

numeric predictor vector

L2

numeric predictor vector

P2

numeric predictor vector

S3

numeric predictor vector

L3

numeric predictor vector

P3

numeric predictor vector

S4

numeric predictor vector

L4

numeric predictor vector

P4

numeric predictor vector

S5

numeric predictor vector

L5

numeric predictor vector

P5

numeric predictor vector

log.RAI

numeric response vector

Source

Umetrics, Inc. (1995), Multivariate Analysis (3-day course), Winchester, MA.

SAS/STAT(R) 9.22 User's Guide, "The PLS Procedure".

Cross-validated R2, R2 for X, and R2 for Y for PLS models

Description

Functions to report the cross-validated R2 (CVR2), explained variance in the predictor variables (R2X), and the reponse (R2Y) for PLS models.

Usage

R2s(object)

Arguments

Details

R2s is used to extract a summary of the cross-validated R2 (CVR2), explained variance in the predictor variables (R2X), and the reponse (R2Y) for PLS models.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
R2s(mod1)
## Not run: 
plot(R2s(mod1))

## End(Not run)

Generates a score contribution plot

Description

Generates a the Score Contribution Graph both mvdareg and mvdapca objects.

Usage

ScoreContrib(object, ncomp = 1:object$ncomp, obs1 = 1, obs2 = NULL)

Arguments

Details

ScoreContrib is used to generates the score contributions for both PLS and PCA models. Up to two groups of score(s) can be selected. If only one group is selected, the contribution is measured to the model average. For PLS models the PCA loadings are replaced with the PLS weights.

Value

The output of ScoreContrib is a matrix of score contributions for the specified observation(s).

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

MacGregor, Process Monitoring and Diagnosis by Multiblock PLS Methods, May 1994 Vol. 40, No. 5 AIChE Journal.

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "none")
Score.Contributions1 <- ScoreContrib(mod1, ncomp = 1:2, obs1 = 1, obs2 = 3)
plot(Score.Contributions1, ncomp = 2)

## Not run: 
data(Penta)
mod2 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "none")
Score.Contributions2 <- ScoreContrib(mod2, obs1 = 1, obs2 = 3)
plot(Score.Contributions2)
Score.Contributions3 <- ScoreContrib(mod1, obs1 = c(1, 3), obs2 = c(5:10))
plot(Score.Contributions3)

## End(Not run)

###  PLS MODEL FIT WITH method = 'wrtpls' and validation = 'none', i.e. WRT-PLS is performed ###
## Not run: 
mod3 <- plsFit(Sepal.Length ~., scale = TRUE, data = iris,
               method = "wrtpls", validation = "none") #ncomp is ignored
Score.Contributions4 <- ScoreContrib(mod3, ncomp = 1:5, obs1 = 1, obs2 = 3)
plot(Score.Contributions4, ncomp = 5)

## End(Not run)

#PCA Model
pc1 <- pcaFit(Penta[, -1], ncomp = 2)
Score.Contributions1 <- ScoreContrib(pc1, obs1 = 1, obs2 = 3)
plot(Score.Contributions1)

Sequential Expectation Maximization (EM) for imputation of missing values.

Description

Missing values are sequentially updated via an EM algorithm.

Usage

SeqimputeEM(data, max.ncomps = 5, max.ssq = 0.99, Init = "mean", 
            adjmean = FALSE, max.iters = 200, 
            tol = .Machine$double.eps^0.25)

Arguments

Details

A completed data frame is returned that mirrors the model matrix. NAs are replaced with convergence values as obtained via Seqential EM algorithm. If object contains no NAs, it is returned unaltered.

Value

Author(s)

Thanh Tran (thanh.tran@mvdalab.com), Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

NOTE: Publication Pending

Examples

dat <- introNAs(iris, percent = 25)
SeqimputeEM(dat)

Generates a Hotelling's T2 Graph

Description

Generates a Hotelling's T2 Graph both mvdareg and mvdapca objects.

Usage

T2(object, ncomp = object$ncomp, phase = 1, conf = c(.95, .99), verbose = FALSE)

Arguments

Details

T2 is used to generates a Hotelling's T2 graph both PLS and PCA models.

Value

The output of T2 is a graph of Hotelling's T2 and a data frame listing the T2 values.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Hotelling, H. (1931). "The generalization of Student's ratio". Annals of Mathematical Statistics 2 (3): 360:378.

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
T2(mod1, ncomp = 2)

Bivariate process data.

Description

Twenty-five observations where 'H' represents brinell hardness and 'S' represents tensile strength.

Usage

Wang_Chen

Format

A data frame with 25 observations and the following 2 variables.

H

brinell hardness

S

tensile strength

Source

Wang F, Chen J (1998). "Capability index using principal components analysis." Quality Engineering, 11, 21-27.

Simulated process data from a plastics manufacturer.

Description

Fifty observations where 'D' represents depth, 'L' represents length, and 'W' represents width.

Usage

Wang_Chen_Sim

Format

A simulated data frame with 50 observations and the following 3 variables.

D

depth

L

length

W

width

Source

Data simulated by Nelson Lee Afanador from average and covariance estimates provided in Wang F, Chen J (1998). "Capability index using principal components analysis." Quality Engineering, 11, 21-27.

Generates a Graph of the X-residuals

Description

Generates a graph of the X-residuals for both mvdareg and mvdapca objects.

Usage

Xresids(object, ncomp = object$ncomp, conf = c(.95, .99),
        normalized = TRUE, verbose = FALSE)

Arguments

Details

Xresids is used to generates a graph of the X-residuals for both PLS and PCA models.

Value

The output of Xresids is a graph of X-residuals and a data frame listing the X-residuals values.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

MacGregor, Process Monitoring and Diagnosis by Multiblock PLS Methods, May 1994 Vol. 40, No. 5 AIChE Journal.

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
Xresids(mod1, ncomp = 2)

Generates the squared prediction error contributions and contribution plot

Description

Generates the squared prediction error (SPE) contributions and graph both mvdareg and mvdapca objects.

Usage

XresidualContrib(object, ncomp = object$ncomp, obs1 = 1)

Arguments

Details

XresidualContrib is used to generates the squared prediction error (SPE) contributions and graph for both PLS and PCA models. Only one observation at a time is supported.

Value

The output of XresidualContrib is a matrix of score contributions for a specified observation and the corresponding graph.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

MacGregor, Process Monitoring and Diagnosis by Multiblock PLS Methods, May 1994 Vol. 40, No. 5 AIChE Journal

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
XresidualContrib(mod1, ncomp = 2, obs1 = 3)

## Not run: 
#PCA Model
pc1 <- pcaFit(Penta[, -1], ncomp = 4)
XresidualContrib(pc1, ncomp = 3, obs1 = 3)

## End(Not run)

Plot of Auto-correlation Funcion

Description

This function computes the autocorrelation function estimates for a selected parameter.

Usage

acfplot(object, parm = NULL)

Arguments

Details

This function computes the autocorrelation function estimates for a selected parameter, via acf, and generates a graph that allows the analyst to assess the need for an autocorrelation adjustment in the smc.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

This function is built using the acf function in the stats R package.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer-Verlag.

See Also

smc, smc.acfTest

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
acfplot(mod1, parm = NULL)

Actual versus Predicted Plot and Residuals versus Predicted

Description

This function provides the actual versus predicted and actual versus residuals plot as part of a model assessment

Usage

ap.plot(object, ncomp = object$ncomp, verbose = FALSE)

Arguments

Details

This function provides the actual versus predicted and residuals versus predicted plot as part of model a assessment across the desired number of latent variables. A smooth fit (dashed line) is added in order to detect curvature in the fit.

Value

The output of ap.plot is a two facet graph for actual versus predicted and residuals versus predicted plots.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

See Also

plsFit

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
ap.plot(mod1, ncomp = 2)

Bias-corrected and Accelerated Confidence Intervals

Description

Computes bootstrap BCa confidence intervals for chosen parameters for PLS models fitted with validation = "oob".

Usage

bca.cis(object, conf = .95, type = c("coefficients",
        "loadings", "weights"))

Arguments

Details

The function computes the bootstrap BCa confidence intervals for any fitted mvdareg model. Should be used in instances in which there is reason to suspectd the percentile intervals. Results provided across all latent variables (LVs). As such, it may be slow for models with a large number of LVs.

Value

A bca.cis object contains component results for the following:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

There are many references explaining the bootstrap and its implementation for confidence interval estimation. Among them are:

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman & Hall.

Hinkley, D.V. (1988) Bootstrap methods (with Discussion). Journal of the Royal Statistical Society, B, 50, 312:337, 355:370.

See Also

plsFit, mvdaboot, boot.plots

Examples

data(Penta)
## Number of bootstraps set to 250 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "oob", boots = 250)
bca.cis(mod1, conf = .95, type = "coefficients")
## Not run: 
bca.cis(mod1, conf = .95, type = "loadings")
bca.cis(mod1, conf = .95, type = "weights")

## End(Not run)

Bidiag2 PLS

Description

Bidiagonalization algorithm for PLS1

Usage

bidiagpls.fit(X, Y, ncomp, ...)

Arguments

Details

This function should not be called directly, but through plsFit with the argument method="bidiagpls". It implements the Bidiag2 scores algorithm.

Value

An object of class mvdareg is returned. The object contains all components returned by the underlying fit function. In addition, it contains the following:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com), Thanh Tran (thanh.tran@mvdalab.com)

References

Indahl, Ulf G., (2014) The geometry of PLS1 explained properly: 10 key notes on mathematical properties of and some alternative algorithmic approaches to PLS1 modeling. Journal of Chemometrics, 28, 168:180.

Manne R., Analysis of two partial-least-squares algorithms for multi-variate calibration. Chemom. Intell. Lab. Syst. 1987; 2: 187:197.

See Also

plsFit

Plots of the Output of a Bootstrap Simulation for an mvdareg Object

Description

This takes an mvdareg object fitted with validation = "oob" and produces a graph of the bootstrap distribution and its corresponding normal quantile plot for a variable of interest.

Usage

boot.plots(object, comp = object$ncomp, parm = NULL,
           type = c("coefs", "weights", "loadings"))

Arguments

Details

The function generates the bootstrap distribution and normal quantile plot for a bootstrapped mvdareg model given validation = "oob" for type = c("coefs", "weights", "loadings"). If parm = NULL a paramater is chosen at random.

Value

The output of boot.plots is a histogram of the bootstrap distribution and the corresponding normal quantile plot.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

See Also

bca.cis

Examples

data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "oob", boots = 300)
boot.plots(mod1, type = "coefs", parm = NULL)

Extract Information From a plsFit Model

Description

Functions to extract information from mvdalab objects.

Usage

## S3 method for class 'mvdareg'
coef(object, ncomp = object$ncomp, type = c("coefficients",
    "loadings", "weights", "y.loadings"), conf = .95, ...)

Arguments

Details

These are usually called through their generic functions coef and residuals, respectively. coef.mvdareg is used to extract the regression coefficients, loadings, or weights of a PLS model.

If comps is missing (or is NULL), all parameter estimates are returned.

Value

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

See Also

coef, coefficients.boots, coefficients, loadings, loadings.boots, weights, weight.boots

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
coef(mod1, type = "coefficients")

BCa Summaries for the coefficient of an mvdareg object

Description

Computes bootstrap BCa confidence intervals for regression coefficients, along with expanded bootstrap summaries.

Usage

coefficients.boots(object, ncomp = object$ncomp, conf = 0.95)

Arguments

Details

The function computes the bootstrap BCa confidence intervals for fitted mvdareg models where valiation = "oob". Should be used in instances in which there is reason to suspectd the percentile intervals. Results provided across all latent variables or for specific latent variables via ncomp.

Value

A coefficients.boots object contains component results for the following:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

There are many references explaining the bootstrap. Among them are:

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman & Hall.

Hinkley, D.V. (1988) Bootstrap methods (with Discussion). Journal of the Royal Statistical Society, B, 50, 312:337, 355:370.

See Also

coef, coefficients, coefsplot, coefficients

Examples

data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "oob", boots = 300)
coefficients.boots(mod1, ncomp = 2, conf = .95)

Extract Summary Information Pertaining to the Coefficients resulting from a PLS model

Description

Functions to extract regression coefficient bootstrap information from mvdalab objects.

Usage

## S3 method for class 'mvdareg'
coefficients(object, ncomp = object$ncomp, conf = .95, ...)

Arguments

Details

coefficients is used to extract a bootstrap summary of the regression of a PLS model.

If comps is missing (or is NULL), summaries for all regression estimates are returned. Otherwise, if comps is given parameters for a model with only the requested component comps is returned.

Boostrap summaries provided are for actual regression coefficients, bootstrap percentiles, bootstrap mean, skewness, and bias. These summaries can also be extracted using coefficients.boots

Value

A coefficients object contains a data frame with columns:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

See Also

coef, coefficients.boots, coefficients

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
coefficients(mod1)

2-Dimensionsl Graphical Summary Information Pertaining to the Coefficients of a PLS

Description

Functions to extract 2D graphical coefficients information from mvdalab objects.

Usage

coefficientsplot2D(object, comps = c(1, 2), verbose = FALSE)

Arguments

Details

coefficientsplot2D is used to extract a graphical summary of the coefficients of a PLS model. If comp is missing (or is NULL), a graphical summary for the 1st and 2nd components is returned.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

See Also

loadingsplot2D, weightsplot2D

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
coefficientsplot2D(mod1, comp = c(1, 2))

Graphical Summary Information Pertaining to the Regression Coefficients

Description

Functions to extract regression coefficient bootstrap information from mvdalab objects.

Usage

coefsplot(object, ncomp = object$ncomp, conf = 0.95, verbose = FALSE)

Arguments

Details

coefficients is used to extract a graphical summary of the regression coefficients of a PLS model.

If comps is missing (or is NULL), a graphical summary for the nth component regression estimates are returned. Otherwise, if comps is given parameters for a model with only the requested component comps is returned.

Bootstrap graphcal summaries provided are when method = oob.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
coefsplot(mod1, ncomp = 1:2)

Cell Means Contrast Matrix

Description

This function generates a cell means contrast matrix to support PLS models.

Usage

contr.niets(n, contrasts)

Arguments

Details

This function uses contr.treatment to generate a cell means contrast matrix in support of PLS models.

Value

For datasets with categorical variables it produces the needed design matrix.

Author(s)

Nelson Lee Afanador

Examples

# Three levels
levels <- LETTERS[1:3]
contr.niets(levels)

# Two levels
levels <- LETTERS[1:2]
contr.niets(levels)

Ellipses, Data Ellipses, and Confidence Ellipses

Description

This function draws econfidence ellipses for covariance and correlation matrices derived from from either a matrix or dataframe.

Usage

ellipse.mvdalab(data, center = c(0, 0), radius = "chi", scale = TRUE,
  segments = 51, level = c(0.95, 0.99), plot.points = FALSE, pch = 1, size = 1,
  alpha = 0.5, verbose = FALSE, ...)

Arguments

Details

ellipse uses the singular value decomposition in order to generate the desired confidence regions. The default confidence ellipse is based on the chisquare statistic.

Value

Returns a graph with the ellipses at the stated as levels, as well as the ellipse coordinates.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Fox, J. (2008) Applied Regression Analysis and Generalized Linear Models, Second Edition. Sage.

Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition, Sage.

Examples

data(iris)
ellipse.mvdalab(iris[, 1:2], plot.points = FALSE)
ellipse.mvdalab(iris[, 1:2], center = colMeans(iris[, 1:2]), plot.points = TRUE)

Naive imputation of missing values.

Description

Imputes the mean or median for continous variables; highest frequency for categorical variables.

Usage

imputeBasic(data, Init = "mean")

Arguments

Details

A completed data frame is returned. For numeric variables, NAs are replaced with column means or medians. For categorical variables, NAs are replaced with the most frequent levels. If object contains no NAs, it is returned unaltered.

Value

imputeBasic returns a list containing the following components:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

dat <- introNAs(iris, percent = 25)
imputeBasic(dat)

Expectation Maximization (EM) for imputation of missing values.

Description

Missing values are iterarively updated via an EM algorithm.

Usage

imputeEM(data, impute.ncomps = 2, pca.ncomps = 2, CV = TRUE, Init = "mean",
         scale = TRUE, iters = 25, tol = .Machine$double.eps^0.25)

Arguments

Details

A completed data frame is returned that mirrors a model.matrix. NAs are replaced with convergence values as obtained via EM. If object contains no NAs, it is returned unaltered.

Value

imputeEM returns a list containing the following components:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com), Thanh Tran (thanh.tran@mvdalab.com)

References

B. Walczak, D.L. Massart. Dealing with missing data, Part I. Chemom. Intell. Lab. Syst. 58 (2001); 15:27

Examples

dat <- introNAs(iris, percent = 25)
imputeEM(dat)

Quartile Naive Imputation of Missing Values

Description

Missing value imputed as 'Missing'.

Usage

imputeQs(data)

Arguments

Details

A completed data frame is returned. For continous variables with missing values, missing values are replaced with 'Missing', while the non-missing values are replaced with their corresponding quartile assignment. For categorical variable with missing values, missing values are replaced with 'Missing'. This procedure can greatly increases the dimensionality of the data.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

dat <- introNAs(iris, percent = 25)
imputeQs(dat)

Naive Imputation of Missing Values for Dummy Variable Model Matrix

Description

After generating a cell means model matrix, impute expected values (mean or median for continous; hightest frequency for categorical).

Usage

imputeRough(data, Init = "mean")

Arguments

Details

A completed data frame is returned that mirrors a model.matrix. NAs are replaced with column means or medians. If object contains no NAs, it is returned unaltered. This is the starting point for imputeEM.

Value

imputeRough returns a list containing the following components:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

dat <- introNAs(iris, percent = 25)
imputeRough(dat)

Introduce NA's into a Dataframe

Description

Function for testing missing value imputation algorithms

Usage

introNAs(data, percent = 25)

Arguments

Details

A completed data frame is returned with the desired percentage of missing data. NAs are assigned at random.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

dat <- introNAs(iris)
dat

Jackknife After Bootstrap

Description

This function calculates the jackknife influence values from a bootstrap output mvdareg object and plots the corresponding jackknife-after-bootstrap plot.

Usage

jk.after.boot(object, ncomp = object$ncomp,
              type = c("coefficients", "loadings", "weights"),
              parm = NULL)

Arguments

Details

The centred jackknife quantiles for each observation are estimated from those bootstrap samples in which a particular observation did not appear. These are then plotted against the influence values.

The resulting plots are useful diagnostic tools for looking at the way individual observations affect the bootstrap output.

The plot will consist of a number of horizontal dotted lines which correspond to the quantiles of the centred bootstrap distribution. For each data point the quantiles of the bootstrap distribution calculated by omitting that point are plotted against the jackknife values. The observation number is printed below the plots. To make it easier to see the effect of omitting points on quantiles, the plotted quantiles are joined by line segments. These plots provide a useful diagnostic tool in establishing the effect of individual observations on the bootstrap distribution. See the references below for some guidelines on the interpretation of the plots.

Value

There is no returned value but a graph is generated on the current graphics display.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Efron, B. (1992) Jackknife-after-bootstrap standard errors and influence functions (with Discussion). Journal of the Royal Statistical Society, B, 54, 83:127.

Examples

data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "oob", boots = 300)
jk.after.boot(mod1, type = "coefficients")
## Not run: 
jk.after.boot(mod1, type = "loadings")
jk.after.boot(mod1, type = "weights")

## End(Not run)

Summary Information Pertaining to the Bootstrapped Loadings

Description

Functions to extract loadings bootstrap information from mvdalab objects.

Usage

## S3 method for class 'mvdareg'
loadings(object, ncomp = object$ncomp, conf = .95, ...)

Arguments

Details

loadings is used to extract a summary of the loadings of a PLS or PCA model. If ncomps is missing (or is NULL), summaries for all loadings estimates are returned. Otherwise, if comps is given parameters for a model with only the requested component comps is returned.

Boostrap summaries are provided for mvdareg objects where validation = "oob". These summaries can also be extracted using loadings.boots

Value

A loadings object contains a data frame with columns:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

There are many references explaining the bootstrap. Among them are:

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Efron, B. (1992) Jackknife-after-bootstrap standard errors and influence functions (with Discussion). Journal of the Royal Statistical Society, B, 54, 83:127.

See Also

loadingsplot, loadings.boots, loadingsplot2D

Examples

data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "oob", boots = 300)
loadings(mod1, ncomp = 2, conf = .95)

data(iris)
pc1 <- pcaFit(iris)
loadings(pc1)

BCa Summaries for the loadings of an mvdareg object

Description

Computes bootstrap BCa confidence intervals for the loadings, along with expanded bootstrap summaries.

Usage

loadings.boots(object, ncomp = object$ncomp, conf = .95)

Arguments

Details

The function computes the bootstrap BCa confidence intervals for fitted mvdareg models where valiation = "oob". Should be used in instances in which there is reason to suspectd the percentile intervals. Results provided across all latent variables or for specific latent variables via ncomp.

Value

A loadings.boots object contains component results for the following:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

There are many references explaining the bootstrap. Among them are:

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Efron, B. (1992) Jackknife-after-bootstrap standard errors and influence functions (with Discussion). Journal of the Royal Statistical Society, B, 54, 83:127.

Examples

data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "oob", boots = 300)
loadings.boots(mod1, ncomp = 2, conf = .95)

Graphical Summary Information Pertaining to the Loadings

Description

Functions to extract graphical loadings information from mvdareg and mvdapca object.

Usage

loadingsplot(object, ncomp = object$ncomp, conf = 0.95, verbose = FALSE)

Arguments

Details

"loadingsplot" is used to extract a graphical summary of the loadings of a PLS model. If "comps" is missing (or is NULL), a graphical summary for the nth component estimates are returned. Otherwise, if comps is given parameters for a model with only the requested component comps is returned.

Bootstrap graphcal summaries provided are when "method = oob"

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

See Also

loadings, loadings.boots, loadingsplot2D

Examples

data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "oob", boots = 300)
loadingsplot(mod1, ncomp = 1:2)

2-Dimensionsl Graphical Summary Information Pertaining to the Loadings of a PLS or PCA Analysis

Description

Functions to extract 2D graphical loadings information from mvdalab objects.

Usage

loadingsplot2D(object, comps = c(1, 2), verbose = FALSE)

Arguments

Details

loadingsplot2D is used to extract a graphical summary of the loadings of a PLS model. If comp is missing (or is NULL), a graphical summary for the 1st and 2nd componentsare returned.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

See Also

coefficientsplot2D, weightsplot2D

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
loadingsplot2D(mod1, comp = c(1, 2))

## Not run: 
data(Penta)
mod2 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
loadingsplot2D(mod2, comp = c(1, 2))

## End(Not run)

data(iris)
pc1 <- pcaFit(iris)
loadingsplot2D(pc1, comp = c(1, 2))

Generates a Hotelling's T2 Graph of the Multivariate Exponentially Weighted Average

Description

Generates a Hotelling's T2 Graph for mewma objects.

Usage

mewma(X, phase = 1, lambda = 0.2, conf = c(0.95, 0.99), 
                      asymptotic.form = FALSE) 

Arguments

Details

mewma is used to generates a Hotelling's T2 graph for the multivariate EWMA.

Value

The output of mewma is a graph of Hotelling's T2 for the Multivariate EWMS, and a list containing a data frame of univariate EWMAs and the multivariate EWMA T2 values.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Lowry, Cynthia A., et al. "A multivariate exponentially weighted moving average control chart." Technometrics 34.1 (1992): 46:53.

Examples

mewma(iris[, -5], phase = 1, lambda = 0.2, conf = c(0.95, 0.99), 
                      asymptotic.form = FALSE)

model.matrix creates a design (or model) matrix.

Description

This function returns the model.matrix of an mvdareg object.

Usage

## S3 method for class 'mvdareg'
model.matrix(object, ...)

Arguments

Details

"model.matrix.mvdareg" is used to returns the model.matrix of an mvdareg object.

Value

The design matrix for a PLS model with the specified formula and data.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], 
               ncomp = 2, validation = "loo")
model.matrix(mod1)

Bootstrapping routine for mvdareg objects

Description

When validation = 'oob' this routine effects the bootstrap procedure for mvdareg objects.

Usage

mvdaboot(X, Y, ncomp, method = "bidiagpls", scale = FALSE, n_cores, parallel,
          boots, ...)

Arguments

Details

This function should not be called directly, but through the generic function plsFit with the argument validation = 'oob'.

Value

Provides the following bootstrapped results as a list for mvdareg objects:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com), Thanh Tran (thanh.tran@mvdalab.com)

References

There are many references explaining the bootstrap and its implementation for confidence interval estimation. Among them are:

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman & Hall.

Hinkley, D.V. (1988) Bootstrap methods (with Discussion). Journal of the Royal Statistical Society, B, 50, 312:337, 355:370.

NOTE: This function is adapted from mvr in package pls with extensive modifications by Nelson Lee Afanador and Thanh Tran.

See Also

plsFit, mvdaloo

Examples

data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], 
               ncomp = 2, validation = "oob", boots = 300)

## Run line below to see bootstrap results
## mod1$validation

Leave-one-out routine for mvdareg objects

Description

When validation = 'loo' this routine effects the leave-one-out cross-validation procedure for mvdareg objects.

Usage

mvdaloo(X, Y, ncomp, weights = NULL, method = "bidiagpls", 
        scale = FALSE, boots = NULL, ...)

Arguments

Details

This function should not be called directly, but through the generic function plsFit with the argument validation = 'loo'.

Value

Provides the following bootstrapped results as a list for mvdareg objects:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com), Thanh Tran (thanh.tran@mvdalab.com)

References

NOTE: This function is adapted from mvr in package pls with extensive modifications by Nelson Lee Afanador and Thanh Tran.

See Also

plsFit, mvdaboot

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], 
        ncomp = 2, method = "bidiagpls", validation = "loo")

mod1$validation$cvR2
mod1$validation$PRESS
mod1$validation$MSPRESS
mod1$validation$RMSPRESS
mod1$validation$in.bag  

Simulate from a Multivariate Normal, Poisson, Exponential, or Skewed Distribution

Description

Produces one or more samples from the specified multivariate distribution.

Usage

mvrnorm.svd(n = 1, mu = NULL, Sigma = NULL, tol = 1e-06, empirical = FALSE, 
            Dist = "normal", skew = 5, skew.mean = 0, skew.sd = 1, 
            poisson.mean = 5)

Arguments

Details

"mvrnorm.svd" The matrix decomposition is done via svd

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

Sigma <- matrix(c(1, .5, .5, .5, 1, .5, .5, .5, 1), 3, 3)
Means <- rep(0, 3)

Sim.dat.norm <- mvrnorm.svd(n = 1000, Means, Sigma, Dist = "normal")
plot(as.data.frame(Sim.dat.norm))

Sim.dat.pois <- mvrnorm.svd(n = 1000, Means, Sigma, Dist = "poisson")
plot(as.data.frame(Sim.dat.pois))

Sim.dat.exp <- mvrnorm.svd(n = 1000, Means, Sigma, Dist = "exp")
plot(as.data.frame(Sim.dat.exp))

Sim.dat.skew <- mvrnorm.svd(n = 1000, Means, Sigma, Dist = "skewnorm")
plot(as.data.frame(Sim.dat.skew))

Create a Design Matrix with the Desired Constrasts

Description

This function generates a dummy variable data frame in support various functions.

Usage

my.dummy.df(data, contr = "contr.niets")

Arguments

Details

my.dummy.df takes a data.frame with categorical variables, and returns a data.frame in which all the categorical variables columns are expanded as dummy variables.

The argument contr is passed to the default contr.niets; contr.helmert, contr.poly, contr.sum, contr.treatment are also supported.

Value

For datasets with categorical variables it produces the specified design matrix.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(iris)
my.dummy.df(iris)

Delete Intercept from Model Matrix

Description

Deletes the intercept from a model matrix.

Usage

no.intercept(mm)

Arguments

Value

A model matrix without intercept column.

Author(s)

Nelson Lee Afanador

PCA with the NIPALS algorithm

Description

Implements the Nonlinear Iterative Partial Least Squares (NIPALS) algorithm for computing PCA scores and loadings and intermediate steps to convergence.

Usage

pca.nipals(data, ncomps = 1, Iters = 500, start.vec = NULL, tol = 1e-08)

Arguments

Details

The NIPALS algorithm is a popular algorithm in multivariate data analysi for computing PCA scores and loadings. This function is specifically designed to help explore the subspace prior to convergence. Currently only mean-centering is employed.

Value

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

There are many good references for the NIPALS algorithm:

Risvik, Henning. "Principal component analysis (PCA) & NIPALS algorithm." (2007).

Wold, Svante, Kim Esbensen, and Paul Geladi. "Principal component analysis." Chemometrics and intelligent laboratory systems 2.1-3 (1987): 37:52.

Examples

my.nipals <- pca.nipals(iris[, 1:4], ncomps = 4, tol = 1e-08)
names(my.nipals)

#Check results
my.nipals$Loadings
svd(scale(iris[, 1:4], scale = FALSE))$v

nipals.scores <- data.frame(my.nipals$Scores)
names(nipals.scores) <- paste("np", 1:4)
svd.scores <- data.frame(svd(scale(iris[, 1:4], scale = FALSE))$u)
names(svd.scores) <- paste("svd", 1:4)
Scores. <- cbind(nipals.scores, svd.scores)
plot(Scores.)

my.nipals$Loading.Space
my.nipals$Score.Space

Principal Component Analysis

Description

Function to perform principal component analysis.

Usage

pcaFit(data, scale = TRUE, ncomp = NULL)

Arguments

Details

The calculation is done via singular value decomposition of the data matrix. Dummy variables are automatically created for categorical variables.

Value

pcaFit returns a list containing the following components:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Everitt, Brian S. (2005). An R and S-Plus Companion to Multivariate Analysis. Springer-Verlag.

Edoardo Saccentia, Jos? Camacho, (2015) On the use of the observation-wise k-fold operation in PCA cross-validation, J. Chemometrics 2015; 29: 467-478.

See Also

loadingsplot2D, T2, Xresids, ScoreContrib

Examples

data(iris)
pc1 <- pcaFit(iris, scale = TRUE, ncomp = NULL)
pc1

print(pc1) #Model summary
plot(pc1) #MSEP
PE(pc1) #X-explained variance

T2(pc1, ncomp = 2) #T2 plot

Xresids(pc1, ncomp = 2) #X-residuals plot

scoresplot(pc1) #scoresplot variable importance

(SC <- ScoreContrib(pc1, obs1 = 1:9, obs2 = 10:11))  #score contribution
plot(SC)  #score contribution plot

loadingsplot(pc1, ncomp = 1) #loadings plot
loadingsplot(pc1, ncomp = 1:2) #loadings plot
loadingsplot(pc1, ncomp = 1:3) #loadings plot
loadingsplot(pc1, ncomp = 1:7) #loadings plot
loadingsplot2D(pc1, comps = c(1, 2)) #2-D loadings plot
loadingsplot2D(pc1, comps = c(2, 3)) #2-D loadings plot

Percentile Bootstrap Confidence Intervals

Description

Computes percentile bootstrap confidence intervals for chosen parameters for plsFit models fitted with validation = "oob"

Usage

perc.cis(object, ncomp = object$ncomp, conf = 0.95, 
        type = c("coefficients", "loadings", "weights"))

Arguments

Details

The function fits computes the bootstrap percentile confidence intervals for any fitted mvdareg model.

Value

A perc.cis object contains component results for the following:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

There are many references explaining the bootstrap and its implementation for confidence interval estimation. Among them are:

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman & Hall.

Hinkley, D.V. (1988) Bootstrap methods (with Discussion). Journal of the Royal Statistical Society, B, 50, 312:337, 355:370.

Examples

data(Penta)
## Number of bootstraps set to 250 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], 
               ncomp = 2, validation = "oob", boots = 250)
perc.cis(mod1, ncomp = 1:2, conf = .95, type = "coefficients")

Plot of R2

Description

Plots for the cross-validated R2 (CVR2), explained variance in the predictor variables (R2X), and the reponse (R2Y).

Usage

## S3 method for class 'R2s'
plot(x, ...)

Arguments

Details

plot.R2s is used to generates the graph of the cross-validated R2 (CVR2), explained variance in the predictor variables (R2X), and the reponse (R2Y) for PLS models.

Value

The output of plot.R2s is a graph of the stated explained variance summary.

Author(s)

Thanh Tran (thanh.tran@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
plot(R2s(mod1))

Plotting Function for Score Contributions.

Description

This function generates a plot an object of class score.contribution

Usage

## S3 method for class 'cp'
plot(x, ncomp = "Overall", ...)

Arguments

Details

A graph of the score contributions for ScoreContrib objects.

Value

The output of plot is a graph of score contributions for the specified observation(s).

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, method = "bidiagpls", validation = "loo")
Score.Contributions1 <- ScoreContrib(mod1, obs1 = 1, obs2 = 3)
plot(Score.Contributions1, ncomp = 1)

## Not run: 
data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod2 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "oob", boots = 300)
Score.Contributions2 <- ScoreContrib(mod2, obs1 = 1, obs2 = 3)
plot(Score.Contributions2, ncomp = 1)

## End(Not run)

#PCA Model
pc1 <- pcaFit(Penta[, -1], ncomp = 3)
Score.Contributions1 <- ScoreContrib(mod1, obs1 = 1, obs2 = 3)
plot(Score.Contributions1, ncomp = 1)

Plot of Multivariate Mean Vector Comparison

Description

Plot a comparison of mean vectors drawn from two populations.

Usage

## S3 method for class 'mvcomp'
plot(x, Diff2Plot = c(3, 4), segments = 51, include.zero = FALSE, ...)

Arguments

Details

This function provides a plot of the T2-statistic for testing the equality of two mean vectors. This test is appropriate for testing two populations, assuming independence.

Assumptions:

The sample for both populations is a random sample from a multivariate population.

-Both populations are independent

-Both populations are multivariate normal

-Covariance matrices are approximately equal

If the confidence ellipse does not cover c(0, 0), we reject the NULL that the differnece between mean vectors is equal to zero (at the stated alpha level).

Value

This function returns a plot of the simultaneous confidence intervals for the p-variates and its corresponding confidence ellipse at the stated confidence level.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Johnson, R.A., Wichern, D.W. (2002) Applied Multivariate Statistical Analysis. Prentice Hall.

Examples

data(College)
dat1 <- College
#Generate a 'fake' difference of 15 units
dat2 <- College + matrix(rnorm(nrow(dat1) * ncol(dat1), mean = 15), 
        nrow = nrow(dat1), ncol = ncol(dat1))

Comparison <- MVComp(dat1, dat2, level = .95)
Comparison
plot(Comparison, Diff2Plot = c(1, 2), include.zero = FALSE)
plot(Comparison, Diff2Plot = c(1, 2), include.zero = TRUE)

plot(Comparison, Diff2Plot = c(2, 3), include.zero = FALSE)
plot(Comparison, Diff2Plot = c(2, 3), include.zero = TRUE)


data(iris)
dat1b <- iris[, -5]
#Generate a 'fake' difference of .5 units
dat2b <- dat1b + matrix(rnorm(nrow(dat1b) * ncol(dat1b), mean = .5), 
          nrow = nrow(dat1b), ncol = ncol(dat1b))

Comparison2 <- MVComp(dat1b, dat2b, level = .90)
plot(Comparison2, Diff2Plot = c(1, 2), include.zero = FALSE)
plot(Comparison2, Diff2Plot = c(1, 2), include.zero = TRUE)

plot(Comparison2, Diff2Plot = c(3, 4), include.zero = FALSE)
plot(Comparison2, Diff2Plot = c(3, 4), include.zero = TRUE)

General plotting function for mvdareg and mvdapaca objects.

Description

A general plotting function for a mvdareg and mvdapca objects.

Usage

## S3 method for class 'mvdareg'
plot(x, plottype = c("PE", "scoresplot", "loadingsplot",
                    "loadingsplot2D", "T2", "Xresids", "coefsplot", "ap.plot",
                    "weightsplot", "weightsplot2D", "acfplot"), ...)

Arguments

Details

The following plotting functions are supported:

PE, scoreplot, loadingsplot, loadingsplot2D, T2, Xresids, coefsplot, ap.plot, weightsplot, weightsplot2D, acfplot

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
plot(mod1, plottype = "scoresplot")
## Not run: 
plot(mod1, plottype = "loadingsplot2D")
plot(mod1, plottype = "T2", ncomp = 2, phase = 1, conf = c(.95, .99))

## End(Not run)

2D Graph of the PCA scores associated with a plusminusFit

Description

Generates a 2-dimensional graph of the scores for both plusminus objects.

Usage

## S3 method for class 'plusminus'
plot(x, ncomp = 2, comps = c(1, 2), ...)

Arguments

Details

plot.plusminus is used to extract a 2D graphical summary of the PCA scores associated with a plusminus object.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

###  PLUS-Minus CLASSIFIER WITH validation = 'none', i.e. no CV ###
data(plusMinusDat)
mod1 <- plusminusFit(Y ~., data = plusMinusDat, validation = "none", n_cores = 2)
plot(mod1, ncomp = 2, comps = c(1, 2))

###  Plus-Minus CLASSIFIER WITH validation = 'loo', i.e. leave-one-out CV ###
## Not run: 
data(plusMinusDat)
mod2 <- plusminusFit(Y ~., data = plusMinusDat, validation = "loo", n_cores = 2)
plot(mod2, ncomp = 2, comps = c(1, 2))

## End(Not run)

Plotting function for Significant Multivariate Correlation

Description

This function generates a plot an object of class smc.

Usage

## S3 method for class 'smc'
plot(x, variables = "all", ...)

Arguments

Details

plot.smc is used to generates the graph of the significant multivariate correlation from smc objects.

Value

The output of plot.smc is a graph of the significant multivariate correlation for the specified observation(s).

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], 
               ncomp = 2, validation = "loo")
smc(mod1)
plot(smc(mod1))

Plotting function for Selectivity Ratio.

Description

This function provides the ability to plot an object of class sr

Usage

## S3 method for class 'sr'
plot(x, variables = "all", ...)

Arguments

Details

plot.sr is used to generates the graph of the selectivity ratio from sr objects.

Value

The output of plot.sr is a graph of the selectivity ratio for the specified observation(s).

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], 
               ncomp = 2, validation = "loo")
sr(mod1)
plot(sr(mod1))

Plots of the Output of a Permutation Distribution for an mvdareg Object with method = "bidiagpls"

Description

This takes an mvdareg object fitted with method = "bidiagpls" and produces a graph of the bootstrap distribution and its corresponding normal quantile plot for a variable of interest.

Usage

## S3 method for class 'wrtpls'
plot(x, comp = 1:object$ncomp, distribution = "log", ...)

Arguments

Details

The function generates the permutation distribution and normal quantile plot for a mvdareg model when method = "bidiagpls" is specified.

Value

The output of plot.wrtpls is a histogram of the permutation distribution with the following vertical line indicators.

Solid line = Actual Value; Dashed Line = Critical Value from t-distribution at the model specifed alpha; Dotted line = Quantile at the model specifed alpha

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

See Also

bca.cis

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               method = "wrtpls", validation = "none")
## Not run
## plot.wrtpls(mod1, distribution = "log")

Partial Least Squares Regression

Description

Functions to perform partial least squares regression with a formula interface. Bootstraping can be used. Prediction, residuals, model extraction, plot, print and summary methods are also implemented.

Usage

plsFit(formula, data, subset, ncomp = NULL, na.action, 
method = c("bidiagpls", "wrtpls"), scale = TRUE, n_cores = 2, 
alpha = 0.05, perms = 2000, validation = c("none", "oob", "loo"), 
boots = 1000, model = TRUE, parallel = FALSE,
x = FALSE, y = FALSE, ...) 
## S3 method for class 'mvdareg'
summary(object, ncomp = object$ncomp, digits = 3, ...)

Arguments

Details

The function fits a partial least squares (PLS) model with 1, ..., ncomp number of latent variables. Multi-response models are not supported.

The type of model to fit is specified with the method argument. Currently two PLS algorithms are available: the bigiag2 algorithm ("bigiagpls" and "wrtpls").

The formula argument should be a symbolic formula of the form response ~ terms, where response is the name of the response vector and terms is the name of one or more predictor matrices, usually separated by +, e.g., y ~ X + Z. See lm for a detailed description. The named variables should exist in the supplied data data frame or in the global environment. The chapter Statistical models in R of the manual An Introduction to R distributed with R is a good reference on formulas in R.

The number of components to fit is specified with the argument ncomp. It this is not supplied, the maximal number of components is used.

Note that if the number of samples is <= 15, oob validation may fail. It is recommended that you PLS with validation = "loo".

If method = "bidiagpls" and validation = "oob", bootstrap cross-validation is performed. Bootstrap confidence intervals are provided for coefficients, weights, loadings, and y.loadings. The number of bootstrap samples is specified with the argument boots. See mvdaboot for details.

If method = "bidiagpls" and validation = "loo", leave-one-out cross-validation is performed.

If method = "bidiagpls" and validation = "none", no cross-validation is performed. Note that the number of components, ncomp, is set to min(nobj - 1, npred)

If method = "wrtpls" and validation = "none", The Weight Randomization Test for the selection of the number of components is performed. Note that the number of components, ncomp, is set to min(nobj - 1, npred)

Value

An object of class mvdareg is returned. The object contains all components returned by the underlying fit function. In addition, it contains the following:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com), Thanh Tran (thanh.tran@mvdalab.com)

References

NOTE: This function is adapted from mvr in package pls with extensive modifications by Nelson Lee Afanador and Thanh Tran.

See Also

bidiagpls.fit, mvdaboot, boot.plots, R2s, PE, ap.plot, T2, Xresids, smc, scoresplot, ScoreContrib, sr, loadingsplot, weightsplot, coefsplot, coefficientsplot2D, loadingsplot2D, weightsplot2D, bca.cis, coefficients.boots, loadings.boots, weight.boots, coefficients, loadings, weights, BiPlot, jk.after.boot

Examples

###  PLS MODEL FIT WITH method = 'bidiagpls' and validation = 'oob', i.e. bootstrapping ###
data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], method = "bidiagpls",
               ncomp = 2, validation = "oob", boots = 300)
summary(mod1) #Model summary

###  PLS MODEL FIT WITH method = 'bidiagpls' and validation = 'loo', i.e. leave-one-out CV ###
## Not run: 
mod2 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], method = "bidiagpls",
               ncomp = 2, validation = "loo")
summary(mod2) #Model summary

## End(Not run)

###  PLS MODEL FIT WITH method = 'bidiagpls' and validation = 'none', i.e. no CV is performed ###
## Not run: 
mod3 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], method = "bidiagpls",
               ncomp = 2, validation = "none")
summary(mod3) #Model summary

## End(Not run)
###  PLS MODEL FIT WITH method = 'wrtpls' and validation = 'none', i.e. WRT-PLS is performed ###
## Not run: 
mod4 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               method = "wrtpls", validation = "none")
summary(mod4) #Model summary
plot.wrtpls(mod4)

## End(Not run)

plusMinusDat data set

Description

A simulated dataset for demonstrating the performance of a plusminusFit analysis.

Usage

plusMinusDat

Format

A data frame with 201 observations, 200 input variables (X) and one response variable (Y).

Source

Richard Baumgartner (richard_baumgartner@merck.com)

PlusMinus (Mas-o-Menos)

Description

Plus-Minus classifier

Usage

plusminus.fit(XX, YY, ...)

Arguments

Details

This function should not be called directly, but through plusminusFit with the argument method="plusminus". It implements the Plus-Minus algorithm.

Value

An object of class plusminus is returned. The object contains all components returned by the underlying fit function. In addition, it contains the following:

Author(s)

Richard Baumgartner (richard_baumgartner@merck.com), Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Zhao et al. (2014) Mas-o-menos: a simple sign averaging method for discriminationin genomic data analysis. Bioinformatics, 30(21):3062-3069.

See Also

plusminusFit

Leave-one-out routine for plusminus objects

Description

When validation = 'loo' this routine effects the leave-one-out cross-validation procedure for plusminus objects.

Usage

plusminus.loo(X, Y, method = "plusminus", n_cores, ...)

Arguments

Details

This function should not be called directly, but through the generic function plusminusFit with the argument validation = 'loo'.

Value

Provides the following crossvalideted results as a list for plusminus objects:

Author(s)

Richard Baumgartner (richard_baumgartner@merck.com), Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

NOTE: This function is adapted from mvr in package pls with extensive modifications by Nelson Lee Afanador and Thanh Tran.

See Also

plusminusFit

Examples

data(plusMinusDat)
mod1 <- plusminusFit(Y ~., data = plusMinusDat, validation = "loo", n_cores = 2)
## Not run: 
summary(mod1)
mod1$validation$cvError
mod1$validation$in.bag

## End(Not run)

Plus-Minus (Mas-o-Menos) Classifier

Description

Functions to perform plus-minus classifier with a formula interface. Leave one out crossvalidation also implemented. Model extraction, plot, print and summary methods are also implemented.

Usage

plusminusFit(formula, data, subset, na.action, method = "plusminus", n_cores = 2,
                         validation = c("loo", "none"), model = TRUE,
                         x = FALSE, y = FALSE, ...)

## S3 method for class 'plusminus'
summary(object,...)

Arguments

Details

The function fits a Plus-Minus classifier.

The formula argument should be a symbolic formula of the form response ~ terms, where response is the name of the response vector and terms is the name of one or more predictor matrices, usually separated by +, e.g., y ~ X + Z. See lm for a detailed description. The named variables should exist in the supplied data data frame or in the global environment. The chapter Statistical models in R of the manual An Introduction to R distributed with R is a good reference on formulas in R.

If validation = "loo", leave-one-out cross-validation is performed. If validation = "none", no cross-validation is performed.

Value

An object of class plusminus is returned. The object contains all components returned by the underlying fit function. In addition, it contains the following:

Author(s)

Richard Baumgartner (richard_baumgartner@merck.com), Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Zhao et al.: Mas-o-menos: a simple sign averaging method for discriminationin genomic data analysis. Bioinformatics, 30(21):3062-3069,2014.

See Also

plusminus.fit, plusminus.loo

Examples

###  PLUS-Minus CLASSIFIER WITH validation = 'none', i.e. no CV ###
data(plusMinusDat)
mod1 <- plusminusFit(Y ~., data = plusMinusDat, validation = "none", n_cores = 2)
summary(mod1)

###  Plus-Minus CLASSIFIER WITH validation = 'loo', i.e. leave-one-out CV ###
## Not run: 
data(plusMinusDat)
mod2 <- plusminusFit(Y ~., data = plusMinusDat, validation = "loo", n_cores = 2)
summary(mod2)

## End(Not run)

Model Predictions From a plsFit Model

Description

predict provides predictions from the results of a pls model.

Usage

## S3 method for class 'mvdareg'
predict(object, newdata, ncomp = object$ncomp,
            na.action = na.pass, ...)

Arguments

Details

predict.mvdareg produces predicted values, obtained by evaluating the regression function in the frame newdata (which defaults to model.frame(object). If newdata is omitted the predictions are based on the data used for the fit.

If comps is missing (or is NULL), predictions of the number of latent variables is provided. Otherwise, if comps is given parameters for a model with only the requested components is returned. The generic function residuals return the model residuals for all the components specified for the model. If the model was fitted with na.action = na.exclude (or after setting the default na.action to na.exclude with options), the residuals corresponding to excluded observations are returned as NA; otherwise, they are omitted.

Value

predict.mvdareg produces a vector of predictions or a matrix of predictions

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

NOTE: This function is adapted from mvr in package pls with extensive modifications by Nelson Lee Afanador.

See Also

coef, coefficients.boots, coefficients, loadings, loadings.boots, weights, weight.boots

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
predict.mvdareg(mod1)
## Not run: 
residuals(mod1)

## End(Not run)

Print Methods for mvdalab Objects

Description

Summary and print methods for mvdalab objects.

Usage

## S3 method for class 'mvdareg'
print(x, ...)

Arguments

Details

print.mvdalab Is a generic function used to print mvdalab objects, such as print.empca for imputeEM, print.mvdapca for mvdapca objects, and summary.mvdareg for mvdareg objects.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], 
               ncomp = 2, validation = "loo")
print(mod1, ncomp = 2)
summary(mod1, ncomp = 2)

Print Methods for plusminus Objects

Description

Summary and print methods for plusminus objects.

Usage

## S3 method for class 'plusminus'
print(x, ...)

Arguments

Details

print.plusminus Is a generic function used to print plusminus objects, such as print.plusminus for plusminus objects.

Author(s)

Richard Baumgartner (richard_baumgartner@merck.com), Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

## Not run: 
data(plusMinusDat)
mod1 <- plusminusFit(Y ~., data = plusMinusDat, validation = "loo", n_cores = 2)
print(mod1)

## End(Not run)

Comparison of n-point Configurations vis Procrustes Analysis

Description

Implementation of Procrustes Analysis in the spirit of multidimensional scaling.

Usage

proCrustes(X, Y, scaling = TRUE, standardize = FALSE, scale.unit = F, ...)

Arguments

Details

This function implements Procrustes Analysis as described in the reference below. That is to say:

Translation: Fixed displacement of points through a constant distance in a common direction

Rotation: Fixed displacement of all points through a constant angle

Dilation: Stretching or shrinking by a contant amount

Value

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Krzanowski, Wojtek. Principles of multivariate analysis. OUP Oxford, 2000.

Examples

X <- iris[, 1:2]
Y <- iris[, 3:4]

proc <- proCrustes(X, Y)
proc
names(proc)

2D Graph of the scores

Description

Generates a 2-dimensional graph of the scores for both mvdareg and mvdapca objects.

Usage

scoresplot(object, comps = c(1, 2), alphas = c(.95, .99),
           segments = 51, verbose = FALSE)

Arguments

Details

scoresplot is used to extract a 2D graphical summary of the scores of PLS and PCA models.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
scoresplot(mod1, comp = c(1, 2))

Significant Multivariate Correlation

Description

This function calculates the significant multivariate correlation (smc) metric for an mvdareg object

Usage

smc(object, ncomps = object$ncomp, corrected = F)

Arguments

Note that hidden objects include the smc modeled matrix and error matrices

Details

smc is used to extract a summary of the significant multivariae correlation of a PLS model.

If comps is missing (or is NULL), summaries for all smc estimates are returned. Otherwise, if comps are given parameters for a model with only the requested component comps is returned.

Value

The output of smc is an smc summary detailing the following:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Thanh N. Tran, Nelson Lee Afanador, Lutgarde M.C. Buydens, Lionel Blanchet, Interpretation of variable importance in Partial Least Squares with Significance Multivariate Correlation (sMC). Chemom. Intell. Lab. Syst. 2014; 138: 153:160.

Nelson Lee Afanador, Thanh N. Tran, Lionel Blanchet, Lutgarde M.C. Buydens, Variable importance in PLS in the presence of autocorrelated data - Case studies in manufacturing processes. Chemom. Intell. Lab. Syst. 2014; 139: 139:145.

See Also

smc.acfTest, sr

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
smc(mod1)
plot(smc(mod1))

###  PLS MODEL FIT WITH method = 'wrtpls' and validation = 'none', i.e. WRT-PLS is performed ###
## Not run: 
mod2 <- plsFit(Sepal.Length ~., scale = TRUE, data = iris,
               method = "wrtpls", validation = "none") #ncomp is ignored
plot(smc(mod2, ncomps = 2))

## End(Not run)

Test of the Residual Significant Multivariate Correlation Matrix for the presence of Autocorrelation

Description

This function peforms a 1st order test of the Residual Significant Multivariate Correlation Matrix in order to help determine if the smc should be performed correcting for 1st order autocorrelation.

Usage

smc.acfTest(object, ncomp = object$ncomp)

Arguments

Details

This function computes a test for 1st order auto correlation in the smc residual matrix.

Value

The output of smc.acfTest is a list detailing the following:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Thanh N. Tran, Nelson Lee Afanador, Lutgarde M.C. Buydens, Lionel Blanchet, Interpretation of variable importance in Partial Least Squares with Significance Multivariate Correlation (sMC). Chemom. Intell. Lab. Syst. 2014; 138: 153:160.

Nelson Lee Afanador, Thanh N. Tran, Lionel Blanchet, Lutgarde M.C. Buydens, Variable importance in PLS in the presence of autocorrelated data - Case studies in manufacturing processes. Chemom. Intell. Lab. Syst. 2014; 139: 139:145.

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], 
               ncomp = 2, validation = "loo")
smc.acfTest(mod1, ncomp = 2)

Selectivity Ratio

Description

This function calculates the Selectivity Ratio (sr) metric for an mvdareg object

Usage

sr(object, ncomps = object$ncomp)

Arguments

Details

sr is used to extract a summary of the significant multivariae correlation of a PLS model.

If comps is missing (or is NULL), summaries for all sr estimates are returned. Otherwise, if comps are given parameters for a model with only the requested component comps is returned.

Value

The output of sr is an sr summary detailing the following:

Note that hidden objects include the SR modeled matrix and error matrices.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

O.M. Kvalheim, T.V. Karstang, Interpretation of latent-variable regression models. Chemom. Intell. Lab. Syst., 7 (1989), pp. 39:51

O.M. Kvalheim, Interpretation of partial least squares regression models by means of target projection and selectivity ratio plots. J. Chemom., 24 (2010), pp. 496:504

See Also

smc

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
sr(mod1)
plot(sr(mod1))

## Not run: 
mod2 <- plsFit(Sepal.Length ~., scale = TRUE, data = iris,
               method = "wrtpls", validation = "none") #ncomp is ignored
plot(sr(mod2, ncomps = 2))

## End(Not run)

BCa Summaries for the weights of an mvdareg object

Description

Computes weights bootstrap BCa confidence intervals, along with expanded bootstrap summaries.

Usage

weight.boots(object, ncomp = object$ncomp, conf = .95)

Arguments

Details

The function fits computes the bootstrap BCa confidence intervals for fitted mvdareg models where valiation = "oob". Should be used in instances in which there is reason to suspectd the percentile intervals. Results provided across all latent variables or for specific latent variables via ncomp.

Value

A weight.boots object contains component results for the following:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Efron, B. (1992) Jackknife-after-bootstrap standard errors and influence functions (with Discussion). Journal of the Royal Statistical Society, B, 54, 83:127.

Examples

data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "oob", boots = 300)
weight.boots(mod1, ncomp = 2, conf = .95)

Extract Summary Information Pertaining to the Bootstrapped weights

Description

Functions to extract weights bootstrap information from mvdalab objects.

Usage

## S3 method for class 'mvdareg'
weights(object, ncomp = object$ncomp, conf = .95, ...)

Arguments

Details

weights is used to extract a summary of the weights of a PLS. If ncomps is missing (or is NULL), summaries for all regression estimates are returned. Otherwise, if comps is given parameters for a model with only the requested component comps is returned.

For mvdareg objects only, boostrap summaries provided are for actual regression weights, bootstrap percentiles, bootstrap mean, skewness, and bias. These summaries can also be extracted using weight.boots

Value

A weights object contains a data frame with columns:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

References

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Efron, B. (1992) Jackknife-after-bootstrap standard errors and influence functions (with Discussion). Journal of the Royal Statistical Society, B, 54, 83:127.

See Also

weightsplot, weight.boots, weightsplot2D

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
weights(mod1, ncomp = 2, conf = .95)

Extract Graphical Summary Information Pertaining to the Weights

Description

Functions to extract regression coefficient bootstrap information from mvdalab objects.

Usage

weightsplot(object, ncomp = object$ncomp, conf = .95, verbose = FALSE)

Arguments

Details

weightsplot is used to extract a graphical summary of the weights of a PLS model.

If comps is missing (or is NULL), a graphical summary for the nth component regression estimates are returned. Otherwise, if comps is given parameters for a model with only the requested component comps is returned.

Boostrap graphcal summaries provided are when method = oob.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "oob", boots = 300)
weightsplot(mod1, ncomp = 1:2)

Extract a 2-Dimensional Graphical Summary Information Pertaining to the weights of a PLS Analysis

Description

Functions to extract 2D graphical weights information from mvdalab objects.

Usage

weightsplot2D(object, comps = c(1, 2), verbose = FALSE)

Arguments

Details

weightsplot2D is used to extract a graphical summary of the weights of a PLS model.

If comp is missing (or is NULL), a graphical summary for the 1st and 2nd componentsare returned.

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1],
               ncomp = 2, validation = "loo")
weightsplot2D(mod1, comp = c(1, 2))

Weight Randomization Test PLS

Description

Weight Randomization Test algorithm for PLS1

Usage

wrtpls.fit(X, Y, ncomp, perms, alpha, ...)

Arguments

Details

This function should not be called directly, but through plsFit with the argument method="wrtpls". It implements the Bidiag2 scores algorithm with a permutation test for selecting the statistically significant components.

Value

An object of class mvdareg is returned. The object contains all components returned by the underlying fit function. In addition, it contains the following:

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com), Thanh Tran (thanh.tran@mvdalab.com)

References

Indahl, Ulf G., (2014) The geometry of PLS1 explained properly: 10 key notes on mathematical properties of and some alternative algorithmic approaches to PLS1 modeling. Journal of Chemometrics, 28, 168:180.

Manne R., Analysis of two partial-least-squares algorithms for multi-variate calibration. Chemom. Intell. Lab. Syst. 1987; 2: 187:197.

Thanh Tran, Ewa Szymanska, Jan Gerretzen, Lutgarde Buydens, Nelson Lee Afanador, Lionel Blanchet, Weight Randomization Test for the Selection of the Number of Components in PLS Models. Chemom. Intell. Lab. Syst., accepted for publication - Jan 2017.

See Also

plsFit

Extract Summary Information Pertaining to the y-loadings

Description

Functions to extract the y-loadings from mvdareg and mvdapca objects.

Usage

y.loadings(object, conf = .95)

Arguments

Details

y.loadings is used to extract a summary of the y-loadings from a PLS or PCA model.

If comps is missing (or is NULL), summaries for all regression estimates are returned. Otherwise, if comps is provided the requested component comps are returned.

For mvdareg objects only, boostrap summaries provided are for actual regression y.loadings, bootstrap percentiles, bootstrap mean, skewness, and bias. These summaries can also be extracted using y.loadings.boots

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], 
               ncomp = 2, validation = "loo")
y.loadings(mod1)

Extract Summary Information Pertaining to the y-loadings

Description

Functions to extract the y-loadings from mvdareg and mvdapca objects.

Usage

y.loadings.boots(object, ncomp = object$ncomp, conf = 0.95)

Arguments

Details

y.loadings.boots is used to extract a summary of the y-loadings from a PLS or PCA model.

If comps is missing (or is NULL), summaries for all regression estimates are returned. Otherwise, if comps is provided the requested component comps are returned.

For mvdareg objects only, boostrap summaries provided are for actual regression y.loadings, bootstrap percentiles, bootstrap mean, skewness, and bias. These summaries can also be extracted using y.loadings.boots

Author(s)

Nelson Lee Afanador (nelson.afanador@mvdalab.com)

Examples

data(Penta)
## Number of bootstraps set to 300 to demonstrate flexibility
## Use a minimum of 1000 (default) for results that support bootstraping
mod1 <- plsFit(log.RAI ~., scale = TRUE, data = Penta[, -1], 
               ncomp = 2, validation = "oob", boots = 300)
y.loadings(mod1)
y.loadings.boots(mod1)