Compute several balance measures to check whether the covariate distributions are balanced across treatment arms.
balance_measures(X, D)Covariate matrix (no intercept).
Treatment assignment vector.
Prints LATEX code in the console.
For each covariate in X, balance_measures computes sample averages and standard deviations
for both treatment arms. Additionally, two balance measures are computed:
Norm. Diff.Normalized differences, computed as the differences in the means of each covariate across treatment arms, normalized by the sum of the within-arm variances. They provide a measure of the discrepancy between locations of the covariate distributions across treatment arms.
Log S.D.Log ratio of standard deviations are computed as the logarithm of the ratio of the within-arm standard deviations. They provide a measure of the discrepancy in the dispersion of the covariate distributions across treatment arms.
Compilation of the LATEX code requires the following packages: booktabs, float, adjustbox.
## Generate data.
set.seed(1986)
n <- 1000
k <- 3
X <- matrix(rnorm(n * k), ncol = k)
colnames(X) <- paste0("x", seq_len(k))
D <- rbinom(n, size = 1, prob = 0.5)
mu0 <- 0.5 * X[, 1]
mu1 <- 0.5 * X[, 1] + X[, 2]
y <- mu0 + D * (mu1 - mu0) + rnorm(n)
## Print table.
balance_measures(X, D)
#> \begingroup
#> \setlength{\tabcolsep}{8pt}
#> \renewcommand{\arraystretch}{1.1}
#> \begin{table}[H]
#> \centering
#> \begin{adjustbox}{width = 0.75\textwidth}
#> \begin{tabular}{@{\extracolsep{5pt}}l c c c c c c}
#> \\[-1.8ex]\hline
#> \hline \\[-1.8ex]
#> & \multicolumn{2}{c}{Treated} & \multicolumn{2}{c}{Controls} & \multicolumn{2}{c}{Overlap measures} \\ \cmidrule{6-7}
#> & \multicolumn{2}{c}{($n_t = 502 $)} & \multicolumn{2}{c}{($n_c = 498 $)} & \\ \cmidrule{2-5}
#> & Mean & (S.D.) & Mean & (S.D.) & $\hat{\Delta}_j$ & $\hat{\Gamma}_j$ \\
#> \addlinespace[2pt]
#> \hline \\[-1.8ex]
#>
#> \texttt{x1} & 0.080 & (1.011) & 0.028 & (1.004) & 0.052 & 0.007 \\
#> \texttt{x2} & -0.005 & (1.026) & -0.009 & (0.999) & 0.003 & 0.027 \\
#> \texttt{x3} & -0.026 & (1.015) & 0.013 & (0.979) & -0.039 & 0.036 \\
#>
#> \addlinespace[3pt]
#> \\[-1.8ex]\hline
#> \hline \\[-1.8ex]
#> \end{tabular}
#> \end{adjustbox}
#> \caption{Balance between treatment and control groups. The last two columns report the estimated normalized differences ($\hat{\Delta}_j$) and logarithms of the ratio of standard deviations ($\hat{\Gamma}_j$).}
#> \label{table:descriptive.stats}
#> \end{table}
#> \endgroup