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Estimation of the parameters of a Multidimensional Marginally Sufficient Rasch> Model (MMSRM)

mmsrmvarlist[,partition(numlist)nodetailstraceiterate(#)adaptmethod(mml/gee)]

varlistis a list of two existing binary variables or more.

Description

mmsrmestimates by marginal maximum likelihood (MML) or generalized estimating equations (GEE) the parameters of the Multidimensional Marginally Sufficient Rasch Model (MMSRM) defined by Hardouin and Mesbah (2004). This model is an Item Response Model (IRM) with one or several latent traits. This is a particular multidimensionnal extension of the Rasch model. In this model, the items are separated in Q groups and each group of items is linked to one and only one latent trait. Each group fits a Rasch model relatively to the corresponding latent trait, so the score computed in each group of item is a sufficient statistics of this latent trait (to a specific value of this score is associated only one value for the latent trait). The program allows computing the parameter of a MMSRM with less than 4 latent traits. To improve the time of computing, the difficulty parameters are estimated in each unidimensional Rasch model and used as an offset variable to estimate the parameters of the distribution of the multidimensional latent trait. This model allows estimating the correlations between different latent traits measured by Rasch models.

Options

partitionallows defining the number of items relied to each latent trait. The sum of the numbers indicated in thenumlistmust be equal to the total number of items. The number of elements indicates the number of latent traits. The items are taken in the same order than this one ofvarlist. By default, only one latent trait is assumed (Rasch model). The number of elements ofpartitionmust be inferior or equal to 3.

methoddefines the estimation method between the marginal maximum likelihood (mml- by default) and the generalized estimating equations (gee). You cannot estimate the parameters of a MMSRM with 3 dimensions with the GEE method.

nodetailsdeletes the details about the procedure.

tracedisplays details about the estimation algorithm.

iteratedefines the maximal number of iterations of the estimation algorithm (30 by default).

adaptallows using the adaptive quadrature if you use the MML method of estimation. This option is useless if you use GEE.

Example. mmsrm item1-item9 , part(4 5) trace method(gee)

. mmsrm item1 item2 item3 item4 /*Rasch model*/

. mmsrm c1-c9 , part(3 3 3) nodetails adapt iterate(10)

ReferencesHardouin J.-B. and Mesbah M. Clustering binary variables in subscales using an extended Rasch model and Akaike Information Criterion.

Communications in Statistics - Theory and Methods,33(6), pp. 1277-1294, (2004).

AuthorJean-Benoit Hardouin, Regional Health Observatory (ORS) - 1, rue Porte Madeleine - BP 2439 - 45032 Orleans Cedex 1 - France. You can contact the author at jean-benoit.hardouin@neuf.fr and visit the