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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
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.
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.
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