Reflect Columns in an Object, reversing the sign of all elements

candisc and cancor objects have coefficients for the X and Y and weighted scores for these, whose signs are arbitrary, in the sense that a given column can be reflected (multiplied by -1) without changing the fit. But, often you will want to reverse the direction of one or more dimensions for ease of interpretation.

This function allows you to reflect any columns of the variable coefficients (and corresponding observation scores). This is often useful for interpreting a biplot, for example when a component (often the first) has all negative signs.

Usage

reflect(object, columns = 1:2, ...)

# S3 method for class 'data.frame'
reflect(object, columns = 1:2, ...)

# S3 method for class 'cancor'
reflect(object, columns = 1:2, ...)

# S3 method for class 'candisc'
reflect(object, columns = 1:2, ...)

Arguments

object: An object whose columns are to be reflected
columns: a vector of indices of the columns to reflect
...: Unused

Value

The object with specified columns of the appropriate components (variable coefficients, observation scores, ...) multiplied by -1.

Details

reflect methods are available for:

data.frames, for numeric columns
"cancor" objects, for the coefficients and scores of the X and Y variables
"candisc" objects, for the coefficients, structure correlations and scores

Note that plot.candisc() and plot.candisc() can handle this internally using the argument rev.axes.

Methods (by class)

reflect(data.frame): "data.frame" method.
reflect(cancor): "cancor" method.
reflect(candisc): "candisc" method.

Author

Michael Friendly

Examples

# reflect cols in a data.frame
X <- data.frame(x1 = 1:4, x2 = 5:8)
reflect(X)
#>   x1 x2
#> 1 -1 -5
#> 2 -2 -6
#> 3 -3 -7
#> 4 -4 -8
reflect(X, 1)
#>   x1 x2
#> 1 -1  5
#> 2 -2  6
#> 3 -3  7
#> 4 -4  8
reflect(X, 2)
#>   x1 x2
#> 1  1 -5
#> 2  2 -6
#> 3  3 -7
#> 4  4 -8
cbind (X, letters[1:4]) |> reflect(1)
#>   x1 x2 letters[1:4]
#> 1 -1  5            a
#> 2 -2  6            b
#> 3 -3  7            c
#> 4 -4  8            d

# reflect a candisc 
iris.mod <- lm(cbind(Petal.Length, Sepal.Length, Petal.Width, Sepal.Width) ~ Species, data=iris)
iris.can <- candisc(iris.mod, data=iris)
coef(iris.can)
#>                    Can1        Can2
#> Petal.Length  0.9472572  0.40103782
#> Sepal.Length -0.4269548 -0.01240753
#> Petal.Width   0.5751608 -0.58103986
#> Sepal.Width  -0.5212417 -0.73526131
# reflect Can1
iris.can |> reflect(1) |> coef()
#>                    Can1        Can2
#> Petal.Length -0.9472572  0.40103782
#> Sepal.Length  0.4269548 -0.01240753
#> Petal.Width  -0.5751608 -0.58103986
#> Sepal.Width   0.5212417 -0.73526131

# reflect a cancor
data(Rohwer, package="heplots")
X <- as.matrix(Rohwer[,6:10])  # the PA tests
Y <- as.matrix(Rohwer[,3:5])   # the aptitude/ability variables
Rohwer.can <- cancor(X, Y, set.names=c("PA", "Ability"))
coef(Rohwer)
#> NULL
Rohwer.can |> reflect() |> coef()
#>          Xcan1        Xcan2       Xcan3
#> n   0.07746734  0.046929646  0.13442728
#> s  -0.05421146 -0.111867775  0.23331362
#> ns -0.11348543 -0.221792097 -0.09291490
#> na  0.13877865  0.094120811 -0.05069181
#> ss  0.08919774  0.008243993 -0.03600015