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Use scaled sum coding

Source: R/contrasts_scaled_sum.R
scaled_sum_code.Rd

Contrast coding scheme with a centered intercept and comparisons from a baseline reference level.

Usage

scaled_sum_code(n)

Arguments

n

Integer umber of factor levels to compute contrasts for.

Value

A contrast matrix with dimensions n rows and (n-1) columns.

Details

The name for this contrast scheme varies widely in different fields and across experimental psychology papers. It has been called simple, sum, contrast, sum-to-zero, and deviation coding (among other names). This package uses scaled sum coding to explicitly differentiate it from sum coding, which has an implementation in base R with contr.sum.

For n levels of factors, generate a matrix with n-1 comparisons where:

  • Reference level = -1/n

  • Comparison level = (n-1)/n

  • All others = -1/n

Example interpretation for a 4 level factor:

  • Intercept = Grand mean (mean of the means of each level)

  • grp2 = mean(grp2) - mean(grp1)

  • grp3 = mean(grp3) - mean(grp1)

  • grp4 = mean(grp4) - mean(grp1)

Note: grp coefficient estimates are the same as with contr.treatment, but the intercept is changed to the grand mean instead of the mean of grp1.

It's also important to note that this coding scheme is NOT the same as contr.sum/2 when the number of levels is greater than 2. When n=2, estimates with contr.sum can be interpreted as "half the distance between levels" but when k>2, contr.sum is to be interpreted as "the distance between this level and the GRAND MEAN". You may be tempted to use contr.sum(n)/2, but this tests the hypothesis that 3/2 times the mean of a level is equal to half the sum of the means of the other levels, i.e., \(1.5\mu_1 - .5\mu_2 - .5\mu_3 - .5\mu_4 = 0\), which is not likely to be what you're looking for.

Examples

# Compare these two, note that contr.sum(4)/2 is not the same
scaled_sum_code(4)
#>       2     3     4
#> 1 -0.25 -0.25 -0.25
#> 2  0.75 -0.25 -0.25
#> 3 -0.25  0.75 -0.25
#> 4 -0.25 -0.25  0.75
contr.sum(4)
#>   [,1] [,2] [,3]
#> 1    1    0    0
#> 2    0    1    0
#> 3    0    0    1
#> 4   -1   -1   -1

# Here they happen to be equivalent (modulo reference level)
scaled_sum_code(2)
#>      2
#> 1 -0.5
#> 2  0.5
contr.sum(2) / 2
#>   [,1]
#> 1  0.5
#> 2 -0.5

mydf <- data.frame(
  grp = gl(4,5),
  resp = c(seq(1, 5), seq(5, 9), seq(10, 14), seq(15, 19))
)

mydf <- set_contrasts(mydf, grp ~ scaled_sum_code)

lm(resp ~ grp, data = mydf)
#> 
#> Call:
#> lm(formula = resp ~ grp, data = mydf)
#> 
#> Coefficients:
#> (Intercept)         grp2         grp3         grp4  
#>        9.75         4.00         9.00        14.00  
#>