Demo dataset

Description

It is a small data set to use as a demo for the SCOUTer package. It consists of normally distributed variables, with two Principal Components explaining an 80% of the total variance.

Usage

X

Format

A matrix data frame with 50 rows and 5 normally distributed variables.

barwithucl

Description

Single bar plot with Upper Control Limis. Customized title and labels. Y-Axis limits are fixed according to the range of the values in x.

Usage

barwithucl(
  x,
  iobs,
  ucl,
  plotname = "",
  ylabelname = "",
  xlabelname = "Obs. Index"
)

Arguments

Value

ggplot object with the individual value of a variable as a geom_col with an horizontal line reference.

Examples

barwithucl(c(1:10), 6, 5)
barwithucl(c(1:10), 6, 5, plotname = "Plot title", ylabelname = "Y label", 
xlabelname= "X label")

custombar

Description

Bar plot with customized title and labels. Y-Axis limits are fixed according to the range of the values in X.

Usage

custombar(X, iobs, plotname = "", ylabelname = "Contribution", xlabelname = "")

Arguments

Value

ggplot object with the values of a vector with a customized geom_col layer.

Examples

X <- as.matrix(X)
custombar(X, 2)
custombar(X, 2, plotname = "Observation 2", ylabelname = bquote(x.["j"]), 
xlabelname= "Variables")

distplot

Description

Returns the distance plot providing a dataset and a Principal Component Analysis model.

Usage

distplot(
  X,
  pcaref,
  obstag = matrix(0, nrow(X), 1),
  plottitle = "Distance plot\n"
)

Arguments

Details

Coordinates are expressed in terms of the Hotelling's T^2 (x-axis) and the Squared Prediction Error (y-axis) obtained projecting X on the provided model. Observations can be identified by the obstag input argument.

Value

ggplot object with the distance plot.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X, 2, 0.05, "cent")
distplot(X, pcamodel.ref)
tags <- dotag(X[1:40,], X[-c(1:40),])
distplot(X, pcamodel.ref, obstag = tags, plottitle = "D plot title")

displotsimple

Description

Returns the distance plot directly providing the coordinates and Upper Control Limits.

Usage

distplotsimple(
  T2,
  SPE,
  lim.t2,
  lim.spe,
  ncomp,
  obstag = matrix(0, length(T2), 1),
  alpha = 0.05,
  plottitle = "Distance plot\n"
)

Arguments

Details

Coordinates are expressed in terms of the Hotelling's T^2 (T^2, x-axis) and the Squared Prediction Error (SPE, y-axis). Observations can be identified by the obstag input argument.

Value

distplotobj ggplot object with the generated distance plot.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X[1:40,], 2, 0.05, "cent") # PCA-MB with first 40 
# observations
pcaproj <- pcame(X[-c(1:40),], pcamodel.ref) # Project last observations
distplotsimple(pcaproj$T2, pcaproj$SPE, pcamodel.ref$limt2, pcamodel.ref$limspe,
pcamodel.ref$ncomp)

pcaproj <- pcame(X, pcamodel.ref) # Project all observations
tags <- dotag(X[1:40,], X[-c(1:40),]) # 0's for observations used in PCA-MB
distplotsimple(pcaproj$T2, pcaproj$SPE, pcamodel.ref$limt2, pcamodel.ref$limspe, 
pcamodel.ref$ncomp, obstag = tags)

dotag

Description

Returns the tag vector to identify two different data sets

Usage

dotag(X.zeros = NA, X.ones = NA)

Arguments

Value

tag.all vector with 0 tags for observations in X.zeros and 1 tags for observations in X.ones.

Examples

X <- as.matrix(X)
dotag(X[1:40,], X[-c(1:40),])

dscplot

Description

Returns the distance plot and the score plot providing a data matrix and a Principal Component Analysis (PCA) model. Observations can be identified by the obstag input argument.

Usage

dscplot(
  X,
  pcamodel,
  obstag = matrix(0, nrow(X), 1),
  pcx = 1,
  pcy = 2,
  alpha = 0.05,
  nrow = 1,
  ncol = 2,
  legpos = "bottom"
)

Arguments

Value

ggplot object with the generated score plot.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X[1:40,], 3, 0.05, "cent")
dscplot(X, pcamodel.ref)
dscplot(X, pcamodel.ref, nrow = 2, ncol = 1)
tags <- dotag(X[1:40,], X[-c(1:40),])
dscplot(X, pcamodel.ref, obstag = tags, pcy = 3)

ht2info

Description

Returns information about the Hotelling's T^2 statistic for an observation. Two subplots show the information of an observation regarding its T^2 statistic, i.e.: a bar plot indicating the value of the statistic for the observation, and a bar plot with the contribution that each component had for the T^2 value. The term T^2_A makes reference to the T^2 for a model with A principal components (PCs).

Usage

ht2info(HT2, T2matrix, limht2, iobs = NA)

Arguments

Value

ggplot object with the generated bar plots.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X[1:40,], 2, 0.05, "cent") # PCA-MB with first 40 
# observations
pcaproj <- pcame(X[-c(1:40),], pcamodel.ref) # Project last observations
ht2info(pcaproj$T2, pcaproj$T2matrix, pcamodel.ref$limt2, 2) # Information about 
# the T^2 of the row #2

obscontribpanel

Description

Information about the Hotelling's T^2 and the Squared Predidiction Error (SPE) of an observation. The term T^2_A makes reference to the T^2 for a model with A principal components (PCs).

Usage

obscontribpanel(pcax, pcaref, obsid = NA)

Arguments

Value

ggplot object with the generated bar plots in a 1 x 4 subplots layout.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X[1:40,], 2, 0.05, "cent") # PCA-MB with first 
# 40 observations
pcaproj <- pcame(X[-c(1:40),], pcamodel.ref) # Project last observations
obscontribpanel(pcaproj, pcamodel.ref, 2) # Information about the SPE and T^2 
# of the row #2

pcamb_classic

Description

Principal Component Analysis (PCA) model fitting according to a matrix X using singular value decomposition (svd)

Usage

pcamb_classic(X, ncomp, alpha, prepro)

Arguments

Value

list with elements containing information about PCA model:

• m: mean vector.

• s: standard deviation vector.

• P: loading matrix with the loadings of each PC stored as columns.

• Pfull: full loading matrix obtained by the svd,

• lambda: vector with the variance of each PC.

• limspe: Upper Control Limit for the SPE with a confidence level (1-alpha)*100 %.

• limt2: Upper Control Limit for the T^2_A with a confidence level (1-alpha)*100 %.

• limits_t: Upper control Limits for the scores with a confidence level (1-alpha)*100 %.

• prepro: string indicating the type of preprocessing performed on X.

• ncomp: number of PCs of the PCA model, A.

• alpha: value of the type I risk assumed to calculate the Upper Control Limits of the SPE, T^2_A and scores.

• n: dimension of the number of rows in X.

• S: covariance matrix of X.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X, 3, 0.1, "autosc") # PCA-MB with all observations
pcamodel.ref <- pcamb_classic(X[1:40,], 2, 0.05, "cent") # PCA-MB with first 40 
# observations

pcame

Description

Projection of X onto a Principal Component Analysis (PCA) model.

Usage

pcame(X, pcaref)

Arguments

Details

pcame performs the projection of the data in X onto the PCA model stored as a list of parameters. It returns the projection of the observations in X, along with the Squared Prediction Errors (SPE), Hotelling's T^2_A, contribution elements and the reconstruction of X obtained by the PCA model.

Value

list with elements containing information about X in the PCA model:

• Xpreprocessed: matrix X preprocessed.

• Tscores: score matrix with the projection of X on each one of the A PCs.

• E: error matrix with the par of X not explained by the PCA model.

• SPE: vector with the SPE for each observation of X.

• T2: vector with the T^_A for each observation of X.

• T2matrix: matrix with the contributions of each PC to the T^2_A for each observation of X.

• Xrec: matrix with the reconstructed part of X, i.e. the part of X explained by the PCA model.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X, 3, 0.1, "autosc") # PCA-MB with all observations
pcame(X, pcamodel.ref) # Project all observations onto PCA model of pcamodel.ref

pcamodel.ref <- pcamb_classic(X[1:40,], 2, 0.05, "cent") # PCA-MB with first 40 observations
pcame(X[-c(1:40),], pcamodel.ref) # Project observations not used in PCA-MB onto PCA model 
# of pcamodel.ref

scoreplot

Description

Returns the score plot providing a dataset and a pca model. Observations can be identified by the obstag input argument.

Usage

scoreplot(
  X,
  pcamodel,
  obstag = matrix(0, nrow(X), 1),
  pcx = 1,
  pcy = 2,
  alpha = 0.05,
  plottitle = "Score plot\n"
)

Arguments

Value

ggplot object with the generated score plot.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X[1:40,], 3, 0.05, "cent")
scoreplot(X, pcamodel.ref)
tags <- dotag(X[1:40,], X[-c(1:40),])
scoreplot(X, pcamodel.ref, obstag = tags, pcx = 2, pcy = 3, alpha = 0.1, plottitle = "T-plot")

scoreplotsimple

Description

Returns the score plot providing the scores matrix, T. Observations can be identified by the obstag input argument.

Usage

scoreplotsimple(
  Tscores,
  pcx = 1,
  pcy = 2,
  obstag = matrix(0, nrow(Tscores), 1),
  alpha = 0.05,
  varT = stats::var(Tscores),
  plottitle = "Score plot\n"
)

Arguments

Value

ggplot object with the generated score plot.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X[1:40,], 3, 0.05, "cent")
pcaproj <- pcame(X, pcamodel.ref) # Project last observations
scoreplotsimple(pcaproj$Tscores)

pcaproj <- pcame(X[-c(1:40),], pcamodel.ref) # Project all observations
tags <- dotag(X[1:40,], X[-c(1:40),]) # 0's for observations used in PCA-MB
scoreplotsimple(pcaproj$Tscores, pcx = 2, pcy = 3, obstag = tags)

scout

Description

Shift of an observation following a selected pattern.

Usage

scout(
  X,
  pcaref,
  T2.y = NA,
  SPE.y = NA,
  nsteps = 1,
  nsteps.spe = 1,
  nsteps.t2 = 1,
  gspe = 1,
  gt2 = 1,
  mode = "simple"
)

Arguments

Value

list with elements:

• X: matrix with the new and shifted data.

• SPE: SPE of each one of the generated outliers in the list element X.

• T2: T^2 of each one of the generated outliers in the list element X.

• step.spe: step of each observation according to the shift of the SPE.

• step.t2: step of each observation according to the shift of the T^2.

• tag: is a vector of ones as long as the number of generated observations.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X, 3, 0.1, "autosc") # PCA-MB with all observations
# Shift the first observation:
outscout <- scout(X[1,], pcamodel.ref, T2.y = 40, SPE.y = 50, nsteps.spe = 3, nsteps.t2 = 2, 
gspe = 3, gt2 = 0.5, mode = "grid")

# Shift a set of observations increasing only the T^2 in one step:
outscout <- scout(X, pcamodel.ref, T2.y = matrix(40, nrow(X), 1), mode = "simple")

scoutgrid

Description

Shift of an array following a grid pattern.

Usage

scoutgrid(
  X,
  pcaref,
  T2.target = NA,
  SPE.target = NA,
  nsteps.t2 = 1,
  nsteps.spe = 1,
  gspe = 1,
  gt2 = 1
)

Arguments

Value

list with elements:

• X: matrix with the new and shifted data.

• SPE: SPE of each one of the generated outliers in the list element X.

• T2: T^2 of each one of the generated outliers in the list element X.

• step.spe: step of each observation according to the shift of the SPE.

• step.t2: step of each observation according to the shift of the T^2.

• tag: is a vector of ones as long as the number of generated observations.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X, 3, 0.1, "autosc") # PCA-MB with all observations
# Shift a set of observations increasing the T^2  and the SPE in 3 and 2 linear and 
# non-linear steps respectively:
outgrid <- scoutgrid(X, pcamodel.ref, T2.target = matrix(40, nrow(X), 1), 
SPE.target = matrix(50, nrow(X), 1), nsteps.t2 = 3, nsteps.spe = 2, gspe = 4)

scoutsimple

Description

Shift of an array with a single step.

Usage

scoutsimple(X, pcaref, T2.target = NA, SPE.target = NA)

Arguments

Value

list with elements:

• X: matrix with the new and shifted data.

• SPE: SPE of each one of the generated outliers in the list element X.

• T2: T^2 of each one of the generated outliers in the list element X.

• step.spe: step of each observation according to the shift of the SPE.

• step.t2: step of each observation according to the shift of the T^2.

• tag: is a vector of ones as long as the number of generated observations.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X, 3, 0.1, "autosc") # PCA-MB with all observations
# Shift a set of observations increasing only the T^2 in one step:
outsimple <- scoutsimple(X, pcamodel.ref, T2.target = matrix(40, nrow(X), 1))

scoutsteps

Description

Shift of an array following a step-wise pattern.

Usage

scoutsteps(
  X,
  pcaref,
  T2.target = NA,
  SPE.target = NA,
  nsteps = 1,
  gspe = 1,
  gt2 = 1
)

Arguments

Value

list with elements:

• X: matrix with the new and shifted data.

• SPE: SPE of each one of the generated outliers in the list element X.

• T2: T^2 of each one of the generated outliers in the list element X.

• step.spe: step of each observation according to the shift of the SPE.

• step.t2: step of each observation according to the shift of the T^2.

• tag: is a vector of ones as long as the number of generated observations.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X, 3, 0.1, "autosc") # PCA-MB with all observations
# Shift a set of observations increasing the T^2  and the SPE in 4 linear steps:
outsteps <- scoutsteps(X, pcamodel.ref, T2.target = matrix(40, nrow(X), 1), 
SPE.target = matrix(50, nrow(X), 1), nsteps = 4)
# Shift a set of observations increasing the SPE in 4 non-linear steps:
outsteps <- scoutsteps(X, pcamodel.ref, SPE.target = matrix(50, nrow(X), 1), nsteps = 4, 
gspe = 0.3)

speinfo

Description

Information about the Squared Prediction Error (SPE) of an observation. Two subplots show the information of an observation regarding its SPE statistic, i.e.: a bar plot indicating the value of the statistic for the observation, and a bar plot with the contribution that each variable had for the SPE value

Usage

speinfo(SPE, E, limspe, iobs = NA)

Arguments

Value

ggplot object with the generated bar plots.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X[1:40,], 2, 0.05, "cent") # PCA-MB with first 40 observations
pcaproj <- pcame(X[-c(1:40),], pcamodel.ref) # Project last observations
speinfo(pcaproj$SPE, pcaproj$E, pcamodel.ref$limspe, 2) # Information about the SPE of the 
# row #2

xshift

Description

Shift of an observation. The performed operation results as a combination of two main directions: the direction of maximum gradient for the SPE (weighted by the parameter b) and the direction of the projection of the observation on the model (weighted by the parameter a).

Usage

xshift(X, P, a, b)

Arguments

Value

Matrix with shifted observation as rows, keeping the order of the input matrix X.

Examples

X <- as.matrix(X)
pcamodel.ref <- pcamb_classic(X, 3, 0.1, "autosc") # PCA-MB with all observations
# Shift observation #10 increasing by a factor of 2 and 4 its T^2 and its SPE respectively
x.new <- xshift(X[10,], pcamodel.ref$P, sqrt(2) - 1, sqrt(4) - 1)