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help for loevh                                             Jean-Benoit Hardouin
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Loevinger's H coefficients and non parametric Item Responses Models

        loevh varlist [, pairwise pair ppp pmm noadjust generror(newvar)
              replace graph monotonicity(string) nipmatrix(string)]

        varlist is a list of two or more existing dichotomous ou polytomous
              variables.

Description

    loevh allows verifying the fit of data to the Monotonely Homogeneous
        Mokken Model or to the Doubly Monotone Mokken Model.  It computes the
        Loevinger H scalability coefficients, and several indexes in the
        field of the Non parametric Item Response Theory.

Options

    pairwise. By default, all the individuals with one or more missing values
        are omitted. pairwise allows to use the complete information by pair
        of items.

    pair displays statistics and the value of the Loevinger H coefficient for
        each pair of items.

    ppp displays the P++ matrix.

    pmm displays the P-- matrix.

    noadjust approximates the tests statistics like the MSP software
        (Molenaar et al. (2000)).

    generror creates a new variable containing the number of Guttman errors
        produced by each individual.

    replace allows replacing the variable defined by the generror option.

    graph displays graphs (only with the ppp, pmm and generror options).

    monotonicity displays indexes in order to check the monotonicity of the
        data (Monotone Homogeneity Mokken Model). This option produces
        outputs similar to the MSP software.  The string contains several
        suboptions: minvi, minsize, siglevel and details. If you want use all
        the default values, type *.
          minvi defines the minimal size of a violation of
            monotonicity (0.03 by default)
          minsize defines the minimum size of groups of patients to
            check the monotonicity (by default, the number of
            individuals divided by 10 with more than 500 individuals,
            the same number divided by 5 with more than 250
            individuals, and the same number divided by 3 for a
            smaller number, with a minimum of 50)
          siglevel defines the significance level for the tests (0.05
            by default)
          details displays more details with polytomous items

    nipmatrix display indexes in order to check the non-intersection (Doubly
        Monotone Mokken Model). This option produces outputs similar to the
        MSP software.  The string contains several suboptions: minvi and
        siglevel. If you want use all the default values, type *.
          minvi defines the minimal size of a violation of
            non-intersection (0.03 by default)
          siglevel defines the significance level for the tests (0.05
            by default)


Remarks

    For detailed informations on the Loevinger's H coefficients, see
        Loevinger (1948) or Hemker and al. (1995). For details about the
        analysis of non parametric Mokken models, see for example the MSP 5.0
        manual.


Example

        
        . loevh itemA1-itemA7

        
        . loevh itemA*, pair monotonicity(*) ppp pmm nipmatrix(minvi(0.05)
        siglevel(0.01))

        
        . loevh item*, pairwise generror(error) graph

Results

    The Loevinger's H coefficients between all the pairs of items, for each
        item with respect of all the others items and for the set of items
        are respectively saved in the matrices r(loevHjk), r(loevHj) and in
        the scalar r(loevh).

    The empirical Guttman errors between all the pairs of items, associated
        to each item and relied to the scale are respectively saved in the
        matrices r(eGuttjk), r(eGuttj) and in the scalar e(Gutt).

    The theorical Guttman errors between all the pairs of items, associated
        to each item and relied to the scale are respectively saved in the
        matrices r(eGuttjk0), r(eGuttj0) and in the scalar e(Gutt0).

    The values of the Z statistics and the corresponding p-values associated
        to the Loevinger H coefficients are respectively saved in the
        matrices r(zHjk), r(pvalHjk), r(zHj), r(pvalHj) and in the scalars
        e(zH) and r(pvalH).

    The P++ and P-- matrices are saved in r(ppp) and r(pmm).

    The used number of individuals per items pair is saved in r(Obs).


References

    Hemker B. T., Sijtsma K. and Molenaar I. W., Selection of unidimensional
        scales from a multidimensional item bank in the polytomous Mokken IRT
        model, Applied Psychological Measurement, vol.19(4), 1995, pp.
        337-352.

    Loevinger J., The technique of homogeneous tests compared with some
        aspects of "scale analysis" and factor analysis. Psychological
        bulletin, vol. 45, 1948, pp. 507-530.

    Molenaar I. W., Sijtsma K. and Boer P. MSP5 for Windows - User's Manual,
        2000, 105 pages.

Author

    Jean-Benoit Hardouin, PhD, assistant professor
    EA 4275 "Team of Biostatistics, Clinical Research and Subjective Measures
        in Health Sciences"
    University of Nantes - Faculty of Pharmaceutical Sciences
    1, rue Gaston Veil - BP 53508
    44035 Nantes Cedex 1 - FRANCE
    Email:  jean-benoit.hardouin@univ-nantes.fr
    Websites AnaQol and FreeIRT

Also see

    Online: help for traces, msp, gengroup, mokken if installed.