Marginal maximum likelihood (MML) estimation
of the logistic response model assumes a structure
for the distribution of ability (θ). If this assumption
is incorrect, the statistical properties of MML
estimates may not hold. Monte carlo methods were
used to evaluate MML estimation of item parameters
and maximum likelihood (ML) estimates of θ
in the two-parameter logistic model for varying
test lengths, sample sizes, and assumed θ distribution.
100 datasets were generated for each of
the combinations of factors, allowing for item-level
analyses based on means across replications.
MML estimates of item difficulty were generally
precise and stable in small samples, short tests,
and under varying distributional assumptions of θ.
When the true distribution of θ was normal, MML
estimates of item discrimination were also generally
precise and stable. ML estimates of θ were
generally precise and stable, although the distribution
of θ estimates was platykurtic and truncated
at the high and low ends of the score
range. Index terms: marginal maximum likelihood,
monte carlo, MULTILOG, two-parameter logistic
Stone, Clement A. (1992). Recovery of marginal maximum likelihood estimates in the two-parameter logistic response model: An evaluation of MULTILOG. Applied Psychological Measurement, 16, 1-16. doi:10.1177/014662169201600101
Stone, Clement A..
Recovery of marginal maximum likelihood estimates in the two-parameter logistic response model: An evaluation of MULTILOG.
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