The smd package provides the smd method to
compute standardized mean differences between two groups for continuous
values (numeric and integer data types) and
categorical values (factor, character, and
logical). The method also works on matrix,
list, and data.frame data types by applying
smd() over the columns of the matrix or
data.frame and each item of the list. The
package is based on Yang and Dalton
(2012).
The smd function computes the standardized mean
difference for each level \(k\) of a
grouping variable compared to a reference \(r\) level:
\[ d_k = \sqrt{(\bar{x}_r - \bar{x}_{k})^{\intercal}S_{rk}^{-1}(\bar{x}_r - \bar{x}_{k})} \]
where \(\bar{x}_{\cdot}\) and \(S_{rk}\) are the sample mean and covariances for reference group \(r\) and group \(k\), respectively. In the case that \(x\) is categorical, \(\bar{x}\) is the vector of proportions of each category level within a group, and \(S_{rk}\) is the multinomial covariance matrix.
Standard errors are computed using the formula described in Hedges and Olkin (1985):
\[ \sqrt{ \frac{n_r + n_k}{n_rn_k} + \frac{d_k^2}{2(n_r + n_k)} } \]
set.seed(123)
xn <- rnorm(90)
gg2 <- rep(LETTERS[1:2], each = 45)
gg3 <- rep(LETTERS[1:3], each = 30)
smd(x = xn, g = gg2)
#> term estimate
#> 1 B 0.03413269
smd(x = xn, g = gg3)
#> term estimate
#> 1 B -0.25169577
#> 2 C -0.07846864
smd(x = xn, g = gg2, std.error = TRUE)
#> term estimate std.error
#> 1 B 0.03413269 0.2108339
smd(x = xn, g = gg3, std.error = TRUE)
#> term estimate std.error
#> 1 B -0.25169577 0.2592192
#> 2 C -0.07846864 0.2582982smd with dplyrlibrary(dplyr, verbose = FALSE)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
df$g <- gg2
df %>%
summarize_at(
.vars = vars(dplyr::matches("^x")),
.funs = list(smd = ~ smd(., g = g)$estimate))
#> xn_smd xi_smd xc_smd xf_smd xl_smd
#> 1 0.03413269 0.1687339 0.1946887 0.1946887 0