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

Ingo W Nader¹, Ulrich S Tran, Anton K Formann

¹Faculty of Psychology, University of Vienna, Austria. ingo.nader@univie.ac.at

The British Journal of Mathematical and Statistical Psychology

|April 16, 2011

Summary

Initial values significantly impact parameter estimation in the two-parameter logistic model using full non-parametric maximum likelihood (FNPML) and the expectation-maximization (EM) algorithm. Stricter convergence criteria are needed for accurate item parameter recovery.

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Area of Science:

Psychometrics
Statistical modeling
Educational measurement

Background:

The two-parameter logistic model is commonly estimated using the expectation-maximization (EM) algorithm and maximum-likelihood (ML) method.
Estimating the latent ability distribution non-parametrically offers greater flexibility.
Full non-parametric ML (FNPML) estimation models the latent distribution on freely moving support points.

Purpose of the Study:

To investigate the sensitivity of FNPML estimation to initial values in the two-parameter logistic model.
To challenge the assumption that EM estimation is unaffected by initial values.

Main Methods:

Utilized full non-parametric maximum likelihood (FNPML) estimation.
Employed the expectation-maximization (EM) algorithm for parameter estimation.
Varied convergence criteria to assess the influence of initial values on item parameter and item characteristic curve (ICC) recovery.

Main Results:

Initial values were found to significantly influence item discrimination and difficulty parameter estimates under standard convergence criteria.
Item characteristic curve (ICC) recovery was also affected by initial values with standard convergence criteria.
Under more stringent convergence criteria, item parameter estimates were primarily influenced by the initial latent distribution, while ICC recovery remained unaffected.

Conclusions:

The common assumption that EM estimation is not influenced by initial values is challenged.
A flat log-likelihood function surface may explain the sensitivity to initial values.
Implementing sufficiently tight convergence criteria is crucial for accurate item parameter recovery in FNPML estimation.