Percent Maximum Difference (PMD)
The Percent Maximum Difference (PMD).[1], is an association measure similar in intent to Cramér's V[2][3], that quantifies how similar or different columns are based on the composition of the rows of a contingency table. It takes as input a count matrix (of any m x n dimensionality), and yields a correlation-like metric between 0 and 1 indicating how similar (0) or dissimilar (1) the columns are, based on the composition of the rows. It was introduced due to several properties that distinguish it from other approaches including bias-corrected[3] Cramér's V[2], Chi-squared, or Chi-squared's -log10(p-value), including: linearity[1], robustness to differences in the Poisson sampling depth of the columns (after bias correction)[1], and robustness to differences in the number of rows given that relative composition is unchanged[1]
Usage and interpretation
PMD was originally introduced[1] for quantification of batch-to-batch (column) similarity/difference based on cluster (row) composition in unsupervised clustering analyses in single-cell RNAseq data. A value of 0 indicates that batches (columns) of the contingency table have nearly identical cluster (row) composition, and a PMD value of 1 indicates that batches (columns) are completely different, and share no similarity in the composition of the clusters (rows).
References
- ↑ 1.0 1.1 1.2 1.3 1.4 Tyler, Scott R; Bunyavanich, Supinda; Schadt, Eric E (2021-11-19). "PMD Uncovers Widespread Cell-State Erasure by scRNAseq Batch Correction Methods". bioRxiv. doi:10.1101/2021.11.15.468733. Unknown parameter
|s2cid=ignored (help) - ↑ 2.0 2.1 Cramér, Harald (1946). "21. The two-dimensional case". Mathematical Methods of Statistics. Princeton University Press. p. 282. ISBN 0-691-08004-6. Search this book on
- ↑ 3.0 3.1 Bergsma, Wicher (September 2013). "A bias-correction for Cramér's and Tschuprow's". Journal of the Korean Statistical Society. 42 (3): 323–328. doi:10.1016/j.jkss.2012.10.002.
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