Type: Package
Title: Analysis of Two-Way Tables
Version: 0.6.3
Maintainer: Michael Friendly <friendly@yorku.ca>
Description: Carries out analyses of two-way tables with one observation per cell, together with graphical displays for an additive fit and a diagnostic plot for removable 'non-additivity' via a power transformation of the response. It implements Tukey's Exploratory Data Analysis (1973) <ISBN: 978-0201076165> methods, including a 1-degree-of-freedom test for row*column 'non-additivity', linear in the row and column effects.
URL: https://github.com/friendly/twoway
BugReports: https://github.com/friendly/twoway/issues
License: GPL-3
Encoding: UTF-8
LazyData: true
RoxygenNote: 6.1.0
Language: en-US
Suggests: knitr, rmarkdown
NeedsCompilation: no
Packaged: 2020-06-25 21:46:13 UTC; friendly
Author: Michael Friendly ORCID iD [aut, cre], Richard M. Heiberger [aut], John Fox [ctb]
Repository: CRAN
Date/Publication: 2020-06-26 06:10:02 UTC

Mean monthly temperatures in Arizona

Description

This is the data set used by Tukey (1977) for the initial examples of twoway tables

Format

a matrix of 7 rows (Month) and 3 columns (City) where the value is mean monthly temperature in degrees F. The matrix has a responseName attribute, "Temperature"

References

Tukey, J. W. (1977). Exploratory Data Analysis, Reading MA: Addison-Wesley. Exhibit 1 of chapter 10, p. 333

Examples

data(Arizona)
(AR.2way <-twoway(Arizona, method="median"))

## plot(AR.2way)

ANOVA summary for a two-way table, including Tukey Additivity Test

Description

Test for a 1-df interaction in two-way ANOVA table by the Tukey test.

Usage

## S3 method for class 'twoway'
anova(object, ...)

Arguments

object

a class("twoway") object

...

other arguments passed down, but not used here

Details

At present, this function simply gives the results of the ANOVAs for the additive model, the model including the 1 df term for non-additivity, and an anova() comparison of the two. The analysis is based on row and column means.

Author(s)

Michael Friendly

Examples

data(sentRT)
sent.2way <- twoway(sentRT)
anova(sent.2way)

Convert a twoway object to a data frame This function converts a "twoway" object to a data.frame

Description

The rows and columns of the data table are strung out in standard R order in a vector, joined with row and column labels. Additional columns are added, representing the calculated values used in the two-way display.

Usage

## S3 method for class 'twoway'
as.data.frame(x, ...)

Arguments

x

a "twoway" object

...

other arguments, presently ignored

Value

a data.frame with r \times c rows corresponding to the input data table, and the following columns

row

row labels

col

column labels

data

the data value in the cell

fit

the fitted value,

roweff

the row effect

coleff

the column effect

nonadd

the 1 df for non-additivity value

Examples

data(sentRT)
sent.2way <- twoway(sentRT)
as.data.frame(sent.2way)

Create an initial twoway object representing the data before fitting

Description

Create an initial twoway object representing the data before fitting

Method for matrix input

Usage

as.twoway(x, ...)

## S3 method for class 'matrix'
as.twoway(x, ..., name = deparse(substitute(x)),
  responseName = name, varNames = names(dimnames(x)))

Arguments

x

a numeric matrix or numeric data frame with rownames

...

other arguments, unused here

name

Name of the data matrix

responseName

Name of the response variable

varNames

Names of the row and column variables

Value

An object of class c("twoway") with all effects(roweff, coleff, overall) set to zero, and method="Initial"

Author(s)

Richard M. Heiberger

Richard M. Heiberger

Examples

data(taskRT)
as.twoway(taskRT)

Scores for 5 subjects after being given each of 4 drugs

Description

The original source is Winer (1971), p. 268. This was used as an example in Friendly (1991).

References

Friendly, M. (1991). SAS System for Statistical Graphics Cary, NC: SAS Institute, Output 7.28

Examples

data(drugs)
twoway(drugs)

Number of U.S. housing starts by month for the years 1965 – 1973

Description

Number of U.S. housing starts by month for the years 1965 – 1973

Format

a 9 x 12 matrix, where the entries are the number of housing starts, in thousands

References

Becker, Chambers & Wilks (1988), The New S Language, Brooks Cole. Friendly, M. (1991). SAS System for Statistical Graphics Cary, NC: SAS Institute, p.380

Examples

hstart.2way <- twoway(hstart, method="mean")
plot(hstart.2way)

Counts of an insect for the combinations of 4 treatments and 6 areas of a field

Description

Counts of numbers of an insect, Leptinotarsa decemlineata (the Colorado potato beetle), each of which is the sum for two plots treated alike, for all combinations of 4 treatments and 6 areas of the field chosen to be relatively homogeneous.

Format

a 4 x 6 matrix, where the rows are treatments and the columns are areas of a field.

Details

These data are used in Tukey (1977) Exhibit 1 of Ch 11 and throughout the chapter as examples of median polish. Because the data are counts, either a sqrt or log transformation would be reasonable.

References

Tukey, J. W. (1977). Exploratory Data Analysis, Reading MA: Addison-Wesley. Exhibit 1 of chapter 111

Examples

insect.2way <- twoway(insectCounts, method="median")
print(insect.2way, digits=2)

plot(insect.2way)
plot(insect.2way, which="diagnose")

# try sqrt transformation
insect.sqrt <- twoway(sqrt(insectCounts), method="median")
print(insect.sqrt, digits=2)

plot(insect.sqrt)
plot(insect.sqrt, which="diagnose")

Find the nearest ladder-of-powers representation of a power transformation

Description

The input power value is rounded to the nearest integer or fractional powers, \pm 1/3, 1/2. The function is presently designed just for display purposes.

Usage

ladder_power(p)

Arguments

p

A numeric power, for use as a transformation of a response, y, of the form y^p, where p=0 is interpreted to mean log(y)

Details

In use, the transformation via the ladder of powers usually attaches a minus sign to the transformation when the power < 0, so that the order of the response values are preserved under the transformation. Thus, a result of power = -0.5 is interpreted to mean -1 / \sqrt{y}.

Value

a named list of two elements: power, the ladder-of-power value, and name, the name for the transformation

References

Tukey, J. W. (1977). Exploratory Data Analysis, Reading MA: Addison-Wesley.

Examples

ladder_power(0.6)
ladder_power(-0.6)

Fit a two-way table using row and column means

Description

Fit a two-way table using row and column means

Usage

meanfit(x, ..., na.rm=FALSE)

Arguments

x

a numeric matrix or data frame

...

other arguments passed down

na.rm

logical. Should missing values be removed?

Value

An object of class c("twoway") with the following named components:

overall

the fitted constant term.

roweff

the fitted row effects.

coleff

the fitted column effects.

residuals

the residuals.

name

the name of the dataset.

rownames

the names for the rows

colnames

the names for the columns

method

"median"

Fit a two-way table using median polish

Description

Fit a two-way table using median polish

Usage

medianfit(x, trace.iter = FALSE, ...)

Arguments

x

a numeric matrix or data frame

trace.iter

whether to give verbose output of iteration history in median polish.

...

other arguments passed down

Value

An object of class c("twoway", "medpolish") with the following named components:

overall

the fitted constant term.

roweff

the fitted row effects.

coleff

the fitted column effects.

residuals

the residuals.

name

the name of the dataset.

rownames

the names for the rows

colnames

the names for the columns

method

"median"

Plot methods for two-way tables

Description

Plots either the fitted values and residuals under additivity or a diagnostic plot for removable non-additivity by a power transformation

Usage

## S3 method for class 'twoway'
plot(x, which = c("fit", "diagnose"), ...,
  na.rm=any(is.na(x$residuals)))

## S3 method for class 'twoway.fit'
plot(x, main = paste0("Tukey two-way fit plot for ",
  x$name, " (method: ", x$method, ")"), xlab = expression(hat(mu) *
  " + Column Effect - Row Effect"), ylab = expression("Fit = " * hat(mu)
  * " + Column Effect + Row Effect"), rfactor = 1, rcolor = c("blue",
  "red"), lwd = 3, ylim = NULL, ...,
  na.rm=any(is.na(x$residuals)))

## S3 method for class 'twoway.diagnose'
plot(x, annotate = TRUE, jitter = FALSE,
  smooth = FALSE, pch = 16, ...)

Arguments

x

a class("twoway") object

which

one of "fit" or "diagnose"

...

other arguments, passed to plot

na.rm

logical. Should missing values be removed?

main

plot title

xlab

X axis label

ylab

Y axis label

rfactor

draw lines for abs(residuals) > rfactor*sqrt(MSPE)

rcolor

a vector of length 2 giving the color of lines for positive and negative residuals

lwd

line width for residual lines in the fit plot

ylim

Y axis limits

annotate

A logical value; if TRUE, the slope and power are displayed in the diagnostic plot

jitter

A logical value; if TRUE, the comparison values in the plot are jittered to avoid overplotting

smooth

A logical value; if TRUE, a smoothed loess curve is added to the plot

pch

Plot character for point symbols in the diagnostic plot

Details

For the which="fit" plot, the basic result comes from a plot of the row effects against the column fitted values, which appears as a rectangular grid in these coordinates. Rotating this 45 degrees counterclockwise give a plot in which the vertical coordinate is the fitted value for the two-way table, and the horizontal coordinate is the column fit minus the row effect. The spacing of the grid lines for the rows and columns of the table show the relative magnitudes of the row/column means or medians.

For the which="diagnose" plot, the interaction residuals from an additive model, y_{ij} = \mu + \alpha_i + \beta_j, are plotted against the estimated components \alpha_i \beta_j / \mu. If this plot shows a substantially non-zero slope, b, this analysis suggests that a power transformation, y \rightarrow y^(1-b) might reduce the apparent interaction effects.

For both plots, if you want to directly compare the result of method="mean" and method="median", it is essential to set the same xlim and ylim axes in the call.

Value

The diagnostic plot invisibly returns a list with elements c("slope", "power")

Examples

data(taskRT)
tw <- twoway(taskRT)
tw
twmed <- twoway(taskRT, method="median")
twmed
plot(tw,    xlim=c(2,7), ylim=c(2,7)) ## use the same xlim and ylim, for comparison
plot(twmed, xlim=c(2,7), ylim=c(2,7))

plot(tw,    which="diagnose", xlim=c(-.19, .19), ylim=c(-.5, .55))
plot(twmed, which="diagnose", xlim=c(-.19, .19), ylim=c(-.5, .55))

data(insectCounts)
twi <- twoway(insectCounts)
twimed <- twoway(insectCounts, method="median")

plot(twi,    xlim=c(-250, 700), ylim=c(-180, 900))
plot(twimed, xlim=c(-250, 700), ylim=c(-180, 900))

plot(twi,    which="diagnose", xlim=c(-160, 170), ylim=c(-200, 400))  ## power = .1
plot(twimed, which="diagnose", xlim=c(-160, 170), ylim=c(-200, 400))  ## power = .3

Print method for two-way tables

Description

Print method for two-way tables

Usage

## S3 method for class 'twoway'
print(x, digits = getOption("digits"), border = 2,
  zapsmall = TRUE, ...)

Arguments

x

a numeric matrix

digits

number of digits to print

border

if 0, the components "twoway" object ("overall", "roweff", "coleff", "residuals") are printed separately; if 1, the row, column and overall effects are joined to the residuals in a single table. if 2, row, column, overall and residuals are joined, and decorated with horizontal and vertical rules

zapsmall

a logical value; if TRUE small residuals are printed as 0.

...

other arguments passed down

Author(s)

Michael Friendly, Richard Heiberger

Examples

data(taskRT)
task.2way <- twoway(taskRT)
print(task.2way)
print(task.2way, border=0)

data(sentRT)
sent.2way <- twoway(sentRT)
print(sent.2way)
print(sent.2way, border=1)

Extract residuals from a twoway object

Description

Extract residuals from a twoway object

Extract fitted values from a twoway object

Usage

## S3 method for class 'twoway'
residuals(object, nonadd = FALSE, ...)

## S3 method for class 'twoway'
fitted(object, nonadd = FALSE, ...)

Arguments

object

A class="twoway" object

nonadd

If TRUE, the 1 degree of freedom term for non-additivity is subtracted from the additive residuals

...

other arguments (unused)

Value

A numeric matrix of residuals corresponding to the data supplied to twoway

A numeric matrix of fitted values corresponding to the data supplied to twoway

Examples

data(taskRT)
task.2way <- twoway(taskRT)
residuals(task.2way)
residuals(task.2way, nonadd=TRUE)

sum(residuals(task.2way)^2)               #  SSE for additive model
sum(residuals(task.2way, nonadd=TRUE)^2)  # SSPE, non-additive model
data(taskRT)
task.2way <- twoway(taskRT)
fitted(task.2way)
fitted(task.2way, nonadd=TRUE)

Reaction times for T/F judgments

Description

A demonstration 3 x 3 two-way table composed of reaction times for three subjects making T/F judgments on three types of sentences

References

Friendly, M. (1991). SAS System for Statistical Graphics Cary, NC: SAS Institute, Table 7.2

Examples

data(sentRT)
twoway(sentRT)

Data on reaction times for various tasks and topics

Description

A demonstration 3 x 4 two-way table composed of reaction times for tasks varying in difficulty, with content on different topics.

Format

A matrix of 3 rows and 4 columns, where the rows are the task difficulty levels and the columns are the the topics. The cell values are average reaction times (in sec.). The matrix has a responseName attribute, "RT"

Examples

data(taskRT)
twoway(taskRT)
twoway(taskRT, method="median")

Reshape a data.frame or matrix to a long data.frame

Description

Reshape a data.frame or matrix to a long data.frame

Reshape a data.frame or matrix to a wide data.frame

Usage

to_long(wide, rowname = NULL, colname = NULL,
  responseName = deparse(substitute(wide)), varNames = c("Row", "Col"))

to_wide(long, row = 1, col = 2, response = 3)

Arguments

wide

A data.frame or matrix in wide form

rowname

Name for the row variable

colname

Name for the column variable

responseName

Name for the response variable. If wide is a matrix with an attribute that begins with "response", that value is taken as the responseName. Otherwise, the name of the wide object is used.

varNames

Default names for the row and column variables if not passed as rowname or colname

long

A data.frame in long form

row

Column index or quoted name of the row variable

col

Column index or quoted name of the column variable

response

Column index or quoted name of the response variable

Value

A data.frame in long format

Author(s)

Michael Friendly and Richard M. Heiberger

Michael Friendly and Richard M. Heiberger

Examples

Arizona.long <- to_long(Arizona, varNames=c("Month", "City"))
Arizona.long

Arizona.long <- to_long(Arizona, varNames=c("Month", "City"))
# back the other way
to_wide(Arizona.long)

Analysis of a two-way table with one observation per cell

Description

Fits an additive model using either row and column means or Tukey's median polish procedure

Usage

twoway(x, ...)

## Default S3 method:
twoway(x, method = c("mean", "median"), ...,
  name = deparse(substitute(x)), responseName = attr(x, "response"),
  varNames = names(dimnames(x)))

Arguments

x

a numeric matrix or data frame.

...

other arguments passed down

method

one of "mean" or "median"

name

name for the input dataset

responseName

name for the response variable

varNames

names for the Row and Column variables

Details

The rownames(x) are used as the levels of the row factor and the colnames(x) are the levels of the column factor. For a numeric matrix, the function uses the names(dimnames(x)) as the names of these variables, and, if present, a responseName attribute as the name for the response variable.

Value

An object of class c("twoway") with the following named components:

overall

the fitted constant term.

roweff

the fitted row effects.

coleff

the fitted column effects.

residuals

the residuals.

name

the name of the dataset.

rownames

the names for the rows

colnames

the names for the columns

method

the fitting method

varNames

the names of the row and column variables

responseName

the name of the response variable

compValue

the comparison values, for the diagnostic plot

slope

the slope value, for the diagnostic plot

power

the suggested power transformation, 1-slope

An object of class "twoway", but supplemented by additional components used for labeling

Author(s)

Michael Friendly

References

Tukey, J. W. (1977). Exploratory Data Analysis, Reading MA: Addison-Wesley. Friendly, M. (1991). SAS System for Statistical Graphics Cary, NC: SAS Institute

See Also

codetwoway.formula, codemedpolish

medianfit, meanfit

Examples

data(taskRT)
twoway(taskRT)

Formula method for twoway analysis using a dataset in long format

Description

The formula method reshapes the data set from long to wide format and calls the default method.

Usage

## S3 method for class 'formula'
twoway(formula, data, subset, na.action, ...)

Arguments

formula

A formula of the form response ~ rowvar + colvar, where response is numeric

data

The name of the data set, containing a row vector, column factor and a numeric response

subset

An expression to subset the data (unused)

na.action

What to do with NAs? (unused)

...

other arguments, passed down

Author(s)

Michael Friendly and Richard Heiberger

References

the conversion of long to wide in a formula method was suggested on https://stackoverflow.com/questions/50469320/how-to-write-a-formula-method-that-converts-long-to-wide

Examples

longRT <- to_long(taskRT)
twoway(RT ~ Task + Topic, data=longRT)