paretoPlot: Pareto plot (coefficient plot) for a factorial design model

In pid: Process Improvement using Data

Description

Creates a plot that shows the model coefficients from the least squares model as bars. The absolute value of the coefficients are taken. The coefficient's sign is represented by the bar colour: grey for negative and black for positive coefficients.

Usage

paretoPlot(lsmodel, xlab="Effect name", ylab="Magnitude of effect",
                       main="Pareto plot", legendtitle="Sign of coefficients",
                       negative=c("Negative", "grey"),
                       positive=c("Positive", "black"))

Arguments

lsmodel	a linear model object (least squares model) created by the lm(...) function.
xlab	label for horizontal axis in the bar plot.
ylab	label for vertical axis in the bar plot.
main	label for the plot.
legendtitle	an alternative to the default legend title.
negative	a two-element vector, both entries must be strings, the first of which provides the name for negative bars in the legend, and the second tells which colour to plot negative bars with. The default is: c("Negative", "grey").
positive	a two-element vector, both entries must be strings, the first of which provides the name for positive bars in the legend, and the second tells which colour to plot those bars with.

Details

Typical usage is to create a generic linear model with the lm(...) command, and supply that as the input to this function.

For example, a general design of experiments with 4 factors: A, B, C, and D can be built using lsmodel <- lm(y ~ A*B*C*D), and then the 2^4=16 coefficients visualized with this function using paretoPlot(lsmodel). Since the largest magnitude coefficients are mostly of interest, the coefficient bars are shown sorted from largest to smallest absolute magnitude. The sign information is retained though with the bar's colour: grey for negative and black for positive coefficients.

The coefficients are the exact coefficients from the linear model. When the linear model is in coded units (i.e. -1 for the low level, and +1 for the high level), then the coefficients represent the change in the experiment's response variable (y), for a 2-unit (not 1-unit) change in the input variable. This interpretation of course assumes the factors are independent, which is the case in a full factorial.

Please see the reference for more details.

Value

Returns a ggplot2 object, which, by default, is shown before being returned by this function. The ggplot2 object may be further manipulated, if desired.

Author(s)

Kevin Dunn, <[e-mail]>

References

A Pareto plot is similar in spirit to the Lenth plot, other than for the fact that absolute coefficients are shown. Please see Chapter 5 of the following book: Kevin Dunn, 2010 to 2019, Process Improvement using Data, https://learnche.org/pid

Examples

# 2-factor example
T <- c(-1, +1, -1, +1)  # centered and scaled temperature
S <- c(-1, -1, +1, +1)  # centered and scaled speed variable
y <- c(69, 60, 64, 53)  # conversion, is our response variable, y
doe.model <- lm(y ~ T + S + T * S)  # create a model with main effects, and interaction
paretoPlot(doe.model)

# 3-factor example
data(pollutant)
mod.full <- lm(y ~ C*T*S, data=pollutant)
paretoPlot(mod.full)

Example output

Loading required package: ggplot2
Loading required package: png
Loading required package: FrF2
Loading required package: DoE.base
Loading required package: grid
Loading required package: conf.design

Attaching package: 'DoE.base'

The following objects are masked from 'package:stats':

    aov, lm

The following object is masked from 'package:graphics':

    plot.design

The following object is masked from 'package:base':

    lengths

pid documentation built on May 2, 2019, 2:22 a.m.