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Sensitivity to initial values in full non-parametric maximum-likelihood estimation of the two-parameter logistic model


  • Anton K. Forman unfortunately passed away before this paper was published.

Correspondence should be addressed to Ingo W. Nader, Department of Basic Psychological Research, Faculty of Psychology, University of Vienna, Liebiggasse 5, 1010 Vienna, Austria (e-mail:


Parameters of the two-parameter logistic model are generally estimated via the expectation–maximization (EM) algorithm by the maximum-likelihood (ML) method. In so doing, it is beneficial to estimate the common prior distribution of the latent ability from data. Full non-parametric ML (FNPML) estimation allows estimation of the latent distribution with maximum flexibility, as the distribution is modelled non-parametrically on a number of (freely moving) support points. It is generally assumed that EM estimation of the two-parameter logistic model is not influenced by initial values, but studies on this topic are unavailable. Therefore, the present study investigates the sensitivity to initial values in FNPML estimation. In contrast to the common assumption, initial values are found to have notable influence: for a standard convergence criterion, item discrimination and difficulty parameter estimates as well as item characteristic curve (ICC) recovery were influenced by initial values. For more stringent criteria, item parameter estimates were mainly influenced by the initial latent distribution, whilst ICC recovery was unaffected. The reason for this might be a flat surface of the log-likelihood function, which would necessitate setting a sufficiently tight convergence criterion for accurate recovery of item parameters.