*! version 1.1 10feb2025

Title

loevh2 -- Calculate Loevinger's H for two dichotomous variables

Syntax

loevh2 varlist [if] [in] [weight] [, options]

Main
table display cross-tabulation with expected frequencies

level(#) set confidence level; default is level(95)

abbreviate(#) abbreviate variable names to # characters; default is abbreviate(8)

by is allowed; see [D] by.

aweights and fweights are allowed; see weight.

Description

loevh2 calculates Loevinger's H coefficient of homogeneity for two dichotomous (0/1) variables.
Loevinger's H is a measure of association that indicates the degree to which two items form a Guttman scale.
The coefficient ranges from -1 to +1, where:

- H = 1 indicates perfect Guttman scalability

- H = 0 indicates no association beyond chance

- H < 0 indicates negative association

The program provides standard errors, z-statistics, p-values, and confidence intervals for the H coefficient
(van der Ark et al., 2008).

Loevinger's H is a key coefficient in Mokken scale analysis (Mokken, 1971), used to assess the scalability
of items. For a pair of items, H > 0.3 suggests sufficient scalability for Mokken scale analysis.

Warrens (2008) demonstrates that Loevinger's H is uniquely suited for this purpose, being "the only linear
transformation of the observed proportion of agreement that has zero value under independence and maximum
unity independent of the marginal distributions." This makes it particularly appropriate "in cases where
positive association needs to be distinguished from zero association, e.g., analyzing test items"
(Warrens, 2008, p. 787).

Options

table displays the cross-tabulation of the two variables with observed and expected frequencies.

level(#) specifies the confidence level, as a percentage, for confidence intervals.
The default is level(95) or as set by set level.

abbreviate(#) specifies the number of characters to which variable names are abbreviated in the output.
The default is abbreviate(8).

Examples

Basic usage

. loevh2 item1 item2

With frequency weights

. loevh2 item1 item2 [fw=freq]

Show cross-tabulation and use 99% confidence level

. loevh2 item1 item2, table level(99)

By-group analysis

. bysort group: loevh2 item1 item2

Stored results

loevh2 stores the following in r():

Scalars

r(loevh) Loevinger's H coefficient

r(se) standard error

r(lb) lower bound of confidence interval

r(ub) upper bound of confidence interval

r(level) confidence level

r(N) number of observations

Macros

r(var1) name of first variable

r(var2) name of second variable

r(weight_type) weight type used (if weights were used)

r(weight) weight variable name (if weights were used)

r(group) by-group variables (if by: used)

See also

loevh2_boot provides bootstrap confidence intervals for Loevinger's H, which may be more robust
when sample sizes are small or asymptotic assumptions are not met.

loevh (if installed) by Jean-Benoit Hardouin provides Loevinger's H coefficient for multiple items.
Install using net describe loevh, from(http://fmwww.bc.edu/RePEc/bocode/l).

Author

Dirk Enzmann

Version 1.0

09 Feb 2025

References

Mokken, R. J. (1971). A Theory and Procedure of Scale Analysis. The Hague: Mouton.

van der Ark, L. A., Croon, M. A., & Sijtsma, K. (2008). Mokken scale analysis for dichotomous items using marginal models.
Psychometrika, 73(2), 183-208. https://doi.org/10.1007/s11336-007-9034-z

Warrens, M. J. (2008). On association coefficients for 2×2 tables and properties that do not depend on the marginal distributions.
Psychometrika, 73(4), 777-789. https://doi.org/10.1007/s11336-008-9070-3