Title: Visualizing Collinearity Diagnostics
Version: 0.1.2
Date: 2023-09-05
Description: Provides methods to calculate diagnostics for multicollinearity among predictors in a linear or generalized linear model. It also provides methods to visualize those diagnostics following Friendly & Kwan (2009), "Where’s Waldo: Visualizing Collinearity Diagnostics", <doi:10.1198/tast.2009.0012>. These include better tabular presentation of collinearity diagnostics that highlight the important numbers, a semi-graphic tableplot of the diagnostics to make warning and danger levels more salient, and a "collinearity biplot" of the smallest dimensions of predictor space, where collinearity is most apparent.
Depends: R (≥ 3.5.0)
Suggests: car, corrgram, corrplot, dplyr, lmtest, knitr, tidyr
License: GPL (≥ 3)
Language: en-US
Encoding: UTF-8
RoxygenNote: 7.2.3
URL: https://github.com/friendly/VisCollin
BugReports: https://github.com/friendly/VisCollin/issues
NeedsCompilation: no
Packaged: 2023-09-05 15:50:59 UTC; friendly
Author: Michael Friendly ORCID iD [aut, cre]
Maintainer: Michael Friendly <friendly@yorku.ca>
Repository: CRAN
Date/Publication: 2023-09-05 16:10:02 UTC

Biomass Production in the Cape Fear Estuary

Description

Data collected by Rick Linthurst (1979) at North Carolina State University for the purpose of identifying the important soil characteristics influencing aerial biomass production of the marsh grass Spartina alterniflora in the Cape Fear Estuary of North Carolina. Three types of Spartina vegetation areas (devegetated “dead” areas, “short” Spartina areas, and “tall” Spartina areas) were sampled in each of three locations (Oak Island, Smith Island, and Snows Marsh)

Samples of the soil substrate from 5 random sites within each location–vegetation type (giving 45 total samples) were analyzed for 14 soil physico-chemical characteristics each month for several months.

Format

A data frame with 45 observations on the following 17 variables.

loc

location, a factor with levels OI SI SM

type

area type, a factor with levels DVEG SHRT TALL

biomass

aerial biomass in gm^{-2}, a numeric vector

H2S

hydrogen sulfide ppm, a numeric vector

sal

percent salinity, a numeric vector

Eh7

ester-hydrolase, a numeric vector

pH

acidity as measured in water, a numeric vector

buf

a numeric vector

P

phosphorus ppm, a numeric vector

K

potassium ppm, a numeric vector

Ca

calcium ppm, a numeric vector

Mg

magnesium ppm, a numeric vector

Na

sodium ppm, a numeric vector

Mn

manganese ppm, a numeric vector

Zn

zinc ppm, a numeric vector

Cu

copper ppm, a numeric vector

NH4

ammonium ion ppm, a numeric vector

Source

Rawlings, J. O., Pantula, S. G., & Dickey, D. A. (2001). Applied Regression Analysis: A Research Tool, 2nd Ed., Springer New York. Table 5.1.

References

R. A. Linthurst. Aeration, nitrogen, pH and salinity as factors affecting Spartina Alterniflora growth and dieback. PhD thesis, North Carolina State University, 1979.

Examples

data(biomass)
str(biomass)
biomass.mod <- lm (biomass ~ H2S + sal + Eh7 + pH + buf + P + K + Ca + Mg + Na +
                           Mn + Zn + Cu + NH4,
                 data=biomass)
car::vif(biomass.mod)

(cd <- colldiag(biomass.mod, add.intercept=FALSE, center=TRUE))
# simplified display
print(cd, fuzz=.3)

Cars Data

Description

Data from the 1983 ASA Data Exposition, held in conjunction with the Annual Meetings in Toronto, August 15-18, 1983, https://community.amstat.org/jointscsg-section/dataexpo/dataexpobefore1993 The data set was collected by Ernesto Ramos and David Donoho on characteristics of automobiles.

Format

A data frame with 406 observations on the following 10 variables:

make

make of car, a factor with levels amc audi bmw buick cadillac chev chrysler citroen datsun dodge fiat ford hi honda mazda mercedes mercury nissan oldsmobile opel peugeot plymouth pontiac renault saab subaru toyota triumph volvo vw

model

model of car, a character vector

mpg

miles per gallon, a numeric vector

cylinder

number of cylinders, a numeric vector

engine

engine displacement (cu. inches), a numeric vector

horse

horsepower, a numeric vector

weight

vehicle weight (lbs.), a numeric vector

accel

time to accelerate from O to 60 mph (sec.), a numeric vector

year

model year (modulo 100), a numeric vector ranging from 70 – 82

origin

region of origin, a factor with levels Amer Eur Japan

Source

The data was provided for the ASA Data Exposition in a "shar" file, http://lib.stat.cmu.edu/datasets/cars.data. It is a version of that used by Donoho and Ramos (1982) to illustrate PRIM-H.

References

Donoho, David and Ramos, Ernesto (1982), “PRIMDATA: Data Sets for Use With PRIM-H” (Draft).

Examples

data(cars)
cars.mod <- lm (mpg ~ cylinder + engine + horse + weight + accel + year,
                data=cars)
car::vif(cars.mod)

(cd <- colldiag(cars.mod, center=TRUE))

# simplified display
print(cd, fuzz=.3)

Draw one cell in a tableplot

Description

Draws a graphic representing one or more values for one cell in a tableplot, using shapes whose size is proportional to the cell values and other visual attributes (outline color, fill color, outline line type, ...). Several values can be shown in a cell, using different proportional shapes.

Usage

cellgram(
  cell,
  shape = 0,
  shape.col = "black",
  shape.lty = 1,
  cell.fill = "white",
  back.fill = "white",
  label = 0,
  label.size = 0.7,
  ref.col = "grey80",
  ref.grid = FALSE,
  scale.max = 1,
  shape.name = ""
)

Arguments

cell

Numeric value(s) to be depicted in the table cell

shape

Integer(s) or character string(s) specifying the shape(s) used to encode the numerical value of cell. Any of 0="circle", 1="diamond", 2="square". Recycled to match the number of values in the cell.

shape.col

Outline color(s) for the shape(s). Recycled to match the number of values in the cell.

shape.lty

Outline line type(s) for the shape(s). Recycled to match the number of values in the cell.

cell.fill

Inside color of |smallest| shape in a cell

back.fill

Background color of cell

label

Number of cell values to be printed in the corners of the cell; max is 4

label.size

Character size of cell label(s)

ref.col

color of reference lines

ref.grid

whether to draw ref lines in the cells or not

scale.max

scale values to this maximum

shape.name

character string to uniquely identify shapes to help fill in smallest one

Value

None. Used for its graphic side effect

Examples

# None

Collinearity Diagnostics

Description

Calculates condition indexes and variance decomposition proportions in order to test for collinearity among the independent variables of a regression model and identifies the sources of collinearity if present.

Usage

colldiag(mod, scale = TRUE, center = FALSE, add.intercept = FALSE)

## S3 method for class 'colldiag'
print(x, dec.places = 3, fuzz = NULL, fuzzchar = ".", ...)

Arguments

mod

A model object, such as computed by lm or glm, or a data-frame to be used as predictors in such a model.

scale

If FALSE, the data are left unscaled. If TRUE, the data are scaled, typically to mean 0 and variance 1 using scale. Default is TRUE.

center

If TRUE, data are centered. Default is FALSE.

add.intercept

if TRUE, an intercept is added. Default is FALSE.

x

A colldiag object

dec.places

Number of decimal places to use when printing

fuzz

Variance decomposition proportions less than fuzz are printed as fuzzchar

fuzzchar

Character for small variance decomposition proportion values

...

arguments to be passed on to or from other methods (unused)

Details

colldiag is an implementation of the regression collinearity diagnostic procedures found in Belsley, Kuh, and Welsch (1980). These procedures examine the “conditioning” of the matrix of independent variables.

It computes the condition indexes of the model matrix. If the largest condition index (the condition number) is large (Belsley et al suggest 30 or higher), then there may be collinearity problems. All large condition indexes may be worth investigating.

colldiag also provides further information that may help to identify the source of these problems, the variance decomposition proportions associated with each condition index. If a large condition index is associated two or more variables with large variance decomposition proportions, these variables may be causing collinearity problems. Belsley et al suggest that a large proportion is 50 percent or more.

Note that such collinearity diagnostics are often provided by other software for the model matrix including the constant term for the intercept (e.g., SAS PROC REG, with the option COLLIN). However, these are generally useless and misleading unless the intercept has some real interpretation and the origin of the regressors is contained within the prediction space, as explained by Fox (1997, p. 351). The default values for scale, center and add.intercept exclude the constant term, and correspond to the SAS option COLLINNOINT.

Value

A "colldiag" object, containing:

condindx

A one-column matrix of condition indexes

pi

A square matrix of variance decomposition proportions. The rows refer to the principal component dimensions, the columns to the predictor variables.

print.colldiag prints the condition indexes as the first column of a table with the variance decomposition proportions beside them. print.colldiag has a fuzz option to suppress printing of small numbers. If fuzz is used, small values are replaces by a period “.”. Fuzzchar can be used to specify an alternative character.

Note

Missing data is silently omitted in these calculations

Author(s)

John Hendrickx

Source

These functions were taken from the (now defunct) perturb package by John Hendrickx. He credits the Stata program coldiag by Joseph Harkness joe.harkness@jhu.edu, Johns Hopkins University.

References

Belsley, D.A., Kuh, E. and Welsch, R. (1980). Regression Diagnostics, New York: John Wiley & Sons.

Belsley, D.A. (1991). Conditioning diagnostics, collinearity and weak data in regression. New York: John Wiley & Sons.

Fox, J. (1997). Applied Regression Analysis, Linear Models, and Related Methods. thousand Oaks, CA: Sage Publications.

Friendly, M., & Kwan, E. (2009). Where’s Waldo: Visualizing Collinearity Diagnostics. The American Statistician, 63, 56–65.

See Also

lm, scale, svd, [car]vif, [rms]vif

Examples

data(cars)
cars.mod <- lm (mpg ~ cylinder + engine + horse + weight + accel + year,
                data=cars)
car::vif(cars.mod)

# SAS PROC REG / COLLIN option, including the intercept
colldiag(cars.mod, add.intercept = TRUE)

# Default settings: scaled, not centered, no intercept, like SAS PROC REG / COLLINNOINT
colldiag(cars.mod)

(cd <- colldiag(cars.mod, center=TRUE))

# fuzz small values
print(cd, fuzz = 0.5)

# Biomass data
data(biomass)

biomass.mod <- lm (biomass ~ H2S + sal + Eh7 + pH + buf + P + K +
                             Ca + Mg + Na + Mn + Zn + Cu + NH4,
                   data=biomass)
car::vif(biomass.mod)

cd <- colldiag(biomass.mod, center=TRUE)
# simplified display
print(colldiag(biomass.mod, center=TRUE), fuzz=.3)

# None yet

Consumption Function Dataset

Description

Example from pp 149-154 of Belsley (1991), Conditioning Diagnostics

Format

A data frame with 28 observations on the following 5 variables.

year

1947 to 1974

cons

total consumption, 1958 dollars

rate

the interest rate (Moody's Aaa)

dpi

disposable income, 1958 dollars

d_dpi

annual change in disposable income

References

Belsley, D.A. (1991). Conditioning diagnostics, collinearity and weak data in regression. New York: John Wiley & Sons.

Examples

data(consumption)

ct1 <- with(consumption, c(NA,cons[-length(cons)]))
# compare (5.3)
m1 <- lm(cons ~ ct1 + dpi + rate + d_dpi, data = consumption)
anova(m1)

# compare exhibit 5.11
with(consumption, cor(cbind(ct1, dpi, rate, d_dpi), use="complete.obs"))
# compare exhibit 5.12
cd<-colldiag(m1)
cd
print(cd,fuzz=.3)

Construct collection of pattern specifications for tableplot

Description

Construct collection of pattern specifications for tableplot

Usage

make.patterns(
  n = NULL,
  shape = 0,
  shape.col = "black",
  shape.lty = 1,
  cell.fill = "white",
  back.fill = "white",
  label = 0,
  label.size = 0.7,
  ref.col = "gray80",
  ref.grid = FALSE,
  scale.max = 1,
  as.data.frame = FALSE
)

Arguments

n

Number of patterns

shape

Shape(s) used to encode the numerical value of cell. Any of 0="circle", 1="diamond", 2="square". Recycled to match the number of values in the cell.

shape.col

Outline color(s) for the shape(s)

shape.lty

Outline line type(s) for the shape(s)

cell.fill

inside color of |smallest| shape in a cell

back.fill

background color of cell

label

how many cell values will be labeled in the cell; max is 4

label.size

size of cell label(s)

ref.col

color of reference lines

ref.grid

whether to draw ref lines in the cells or not

scale.max

scale values to this maximum

as.data.frame

whether to return a data.frame or a list.

Value

Returns either a data.frame of a list. If a data.frame, the pattern specifications appear as columns

Examples

# None

Tableplot: A Semi-graphic Display of a Table

Description

A tableplot (Kwan, 2008) is designed as a semi-graphic display in the form of a table with numeric values, but supplemented by symbols with size proportional to cell value(s), and with other visual attributes (shape, color fill, background fill, etc.) that can be used to encode other information essential to direct visual understanding. Three-way arrays, where the last dimension corresponds to levels of a factor for which the first two dimensions are to be compared are handled by superimposing symbols.

The specifications for each cell are given by the types argument, whose elements refer to the attributes specified in patterns.

Usage

tableplot(values, ...)

## Default S3 method:
tableplot(
  values,
  types,
  patterns = list(list(0, "black", 1, "white", "white", 0, 0.5, "grey80", FALSE, 1)),
  title = "Tableplot",
  side.label = "row",
  top.label = "col",
  table.label = TRUE,
  label.size = 1,
  side.rot = 0,
  gap = 2,
  v.parts = 0,
  h.parts = 0,
  cor.matrix = FALSE,
  var.names = "var",
  ...
)

Arguments

values

A matrix or 3-dimensional array of values to be displayed in a tableplot

...

Arguments passed down to tableplot.default

types

Matrix of specification assignments, of the same size as the first two dimensions of values. Entries refer to the sub-lists of patterns. Defaults to a matrix of all 1s, matrix(1, dim(values)[1], dim(values[2])), indicating that all cells use the same pattern specification.

patterns

List of lists; each list is one specification for the arguments to cellgram.

title

Main title

side.label

a character vector providing labels for the rows of the tableplot

top.label

a character vector providing labels for the columns of the tableplot

table.label

Whether to print row/column labels

label.size

Character size for labels

side.rot

Degree of rotation (positive for counter-clockwise)

gap

Width of the gap in each partition, if partitions are requested by v.parts and/or h.parts

v.parts

An integer vector giving the number of columns in two or more partitions of the table. If provided, sum must equal number of columns.

h.parts

An integer vector giving the number of rows in two or more partitions of the table. If provided, sum must equal number of rows.

cor.matrix

Logical. TRUE for a correlation matrix

var.names

a list of variable names

Value

None. Used for its graphic side effect

Note

The original version of tableplots was in the now-defunct tableplot package https://cran.r-project.org/package=tableplot. The current implementation is a modest re-design focused on its use for collinearity diagnostics, but usable in more general contexts.

Author(s)

Ernest Kwan and Michael Friendly

References

Kwan, E. (2008). Improving Factor Analysis in Psychology: Innovations Based on the Null Hypothesis Significance Testing Controversy. Ph. D. thesis, York University.

See Also

cellgram

Examples

data(cars)
cars.mod <- lm (mpg ~ cylinder + engine + horse + weight + accel + year,
                data=cars)
car::vif(cars.mod)

(cd <- colldiag(cars.mod, center=TRUE))
tableplot(cd, title = "Tableplot of cars data", cond.max = 30 )

data(baseball, package = "corrgram")

baseball$Years7 <- pmin(baseball$Years,7)

base.mod <- lm(logSal ~ Years7 + Atbatc + Hitsc + Homerc + Runsc + RBIc + Walksc,
               data=baseball)
car::vif(base.mod)

cd <- colldiag(base.mod, center=TRUE)
tableplot(cd)

Tableplot for Collinearity Diagnostics

Description

These methods produce a tableplot of collinearity diagnostics, showing the condition indices and variance proportions for predictors in a linear or generalized linear regression model. This encodes the condition indices using squares whose background color is red for condition indices > 10, green for values > 5 and green otherwise, reflecting danger, warning and OK respectively. The value of the condition index is encoded within this using a white square proportional to the value (up to some maximum value, cond.max),

Variance decomposition proportions are shown by filled circles whose radius is proportional to those values and are filled (by default) with shades ranging from white through pink to red. Rounded values of those diagnostics are printed in the cells.

Usage

## S3 method for class 'lm'
tableplot(values, ...)

## S3 method for class 'glm'
tableplot(values, ...)

## S3 method for class 'colldiag'
tableplot(
  values,
  prop.col = c("white", "pink", "red"),
  cond.col = c("#A8F48D", "#DDAB3E", "red"),
  cond.max = 100,
  prop.breaks = c(0, 20, 50, 100),
  cond.breaks = c(0, 5, 10, 1000),
  show.rows = nvar:1,
  title = "",
  patterns,
  ...
)

Arguments

values

A "colldiag", "lm" or "glm" object

...

other arguments, for consistency with generic

prop.col

A vector of colors used for the variance proportions. The default is c("white", "pink", "red").

cond.col

A vector of colors used for the condition indices

cond.max

Maximum value to scale the white squares for the condition indices

prop.breaks

Scale breaks for the variance proportions

cond.breaks

Scale breaks for the condition indices

show.rows

Rows of the eigenvalue decompositon of the model matrix to show in the display. The default nvar:1 puts the smallest dimensions at the top of the display.

title

title used for the resulting graphic

patterns

pattern matrix used for table plot.

Value

None. Used for its graphic side-effect

Author(s)

Michael Friendly

References

Friendly, M., & Kwan, E. (2009). "Where’s Waldo: Visualizing Collinearity Diagnostics." The American Statistician, 63, 56–65. Online: https://www.datavis.ca/papers/viscollin-tast.pdf.

Examples

# None yet