Thanks to Kit Baum an update of loevh2 (now version 3.3) is available on SSC.
loevh2 calculates the H-coefficient of homogeneity according to Loevinger (Loevinger, 1947, pp. 29–31) for two dichotomous (0/1) variables; this coefficient is not influenced by the base rates (marginal proportions). The program returns standard errors, z-statistics, p-values, and various types of confidence intervals for the H-coefficient. H can be used as a base-rate-independent measure of the overlap in the 1/1 cell in a 2×2 table of two positively correlated dichotomous variables, corrected for chance and ceiling effect; that is, it is independent of how rare or common either of the two variables is. H is particularly useful when comparing H values between groups (see also Yule, 1912).
Loevinger's H is identical to RIOC (relative improvement over chance, see Copas & Loeber, 1990), see also rioc (SSC) by daniel klein.
daniel klein's critical comments and his suggestion to use nlcom to calculate Loevinger's H with population weighting was the key idea behind writing the package's loevh2_svy (see also Update of loevh2 (on SSC)).
Additionally, the program descriptions in the help files have been improved and substantially expanded, now including results of Monte Carlo simulations examining the coverage of loevh2's default large-sample confidence interval, its small-sample interval, loevh2_boot's bootstrap interval, and the confidence intervals of loevh2_svy with population weights across a wide grid of N, true H, and base-rate combinations.
The update includes:
References:
loevh2 calculates the H-coefficient of homogeneity according to Loevinger (Loevinger, 1947, pp. 29–31) for two dichotomous (0/1) variables; this coefficient is not influenced by the base rates (marginal proportions). The program returns standard errors, z-statistics, p-values, and various types of confidence intervals for the H-coefficient. H can be used as a base-rate-independent measure of the overlap in the 1/1 cell in a 2×2 table of two positively correlated dichotomous variables, corrected for chance and ceiling effect; that is, it is independent of how rare or common either of the two variables is. H is particularly useful when comparing H values between groups (see also Yule, 1912).
Loevinger's H is identical to RIOC (relative improvement over chance, see Copas & Loeber, 1990), see also rioc (SSC) by daniel klein.
daniel klein's critical comments and his suggestion to use nlcom to calculate Loevinger's H with population weighting was the key idea behind writing the package's loevh2_svy (see also Update of loevh2 (on SSC)).
Additionally, the program descriptions in the help files have been improved and substantially expanded, now including results of Monte Carlo simulations examining the coverage of loevh2's default large-sample confidence interval, its small-sample interval, loevh2_boot's bootstrap interval, and the confidence intervals of loevh2_svy with population weights across a wide grid of N, true H, and base-rate combinations.
The update includes:
- loevh2 (version 3.3): Calculate Loevinger's H (= RIOC) with SE/CI
Differences to Version 3.2 (13-Jul-2026):
- Removed aweight support entirely -- users with pweighted (and/or clustered/stratified) data should use loevh2_svy instead. loevh2 now accepts only fweight
- Added an "overlap" summary line
- Returnes as new scalars r(Hbar_se) and r(Hbar_N).
- Added a brief "When to trust the results" section to loevh2.sthlp.
- Removed the abbreviate(#) option, now always displays full (untruncated) variable names.
- The immediate command loevhi allows compare.
- Added the meta(filename, replace|append) option.
- loevh2i (version 3.3): Immediate command (analogous to rioci version 1.0.0 by Daniel Klein)
Differences to first Version 3.2 [sic!] (13-Jul-2026):
- Added a compare option, allowing loevh2i to test the equality of H's across two ore more 2×2 tables directly from the command line.
- Added the meta(filename, replace|append) option
- loveh2_boot (version 3.3): Bootstraping for Loevinger's H
Differences to Version 3.2 (13-Jul-2026):
- Added an "overlap" summary line.
- Added a new option, bccorrect
- Added a brief "When to trust the results" section to loevh2_boot.sthlp
- Removed the abbreviate(#) option, now always displays full (untruncated) variable names.
- The immediate command loevh2_booti allows compare
- Added the meta(filename, replace|append) option
- loevh2_booti (version 3.3): Immediate command (amalogous to rioci version 1.0.0 by Daniel Klein)
Differences to first [sic!] Version 3.2 (13-Jul-2026):
- Added a compare option, allowing loevh2_booti to test the equality of H's across two or more 2×2 tables directly from the command line.
- Added the meta(filename, replace|append) option
- loevh2_svy (new, version 1.0): Design-based (survey) H/SE/CI for Loevinger's H (e.g. to use with pweight)
References:
- Copas, J. B., & Loeber, R. (1990). Relative improvement over chance (RIOC) for 2×2 tables. British Journal of Mathematical and Statistical Psychology, 43(2), 293–307.
- Loevinger, J. A. (1947). A systematic approach to the construction and evaluation of tests of ability. Psychological Monographs, 61(4), i–49.
- Yule, G. U. (1912). On the methods of measuring association between two attributes. Journal of the Royal Statistical Society, 75(6), 579–642.
