This article investigated the form of item log-likelihood
surface under two- and three-parameter logistic
models. Graphs of the log-likelihood surfaces for
items under two-parameter and three-parameter (with a
fixed value of c) models were very similar, but were
characterized by the presence of a ridge. These graphs
suggest that the task of finding the maximum of the
surface should be roughly equivalent under these two
models when c is fixed in the three-parameter model.
For two items, the item log-likelihood surface was
plotted for several values of c to obtain the contour
line of the maxima. For an item whose value of
Lord's b − 2/a index was less than the criterion value,
the contour line was relatively flat. The item having
an index value above the criterion value had a contour
line with a very sharp peak. Thus, under a three-parameter
model, finding the maximum of the item log-likelihood
is more difficult when the criterion for
Lord’s index is not met. These results confirm that the
LOGIST program procedures used to locate the maximum
of the likelihood function are consistent with the
form of the item log-likelihood surface. Index
terms: estimation, item parameter; likelihood surfaces;
LOGIST procedures; log-likelihood; maximum likelihood
Baker, Frank B. (1988). The item log-likelihood surface for two- and three-parameter item characteristic curve models. Applied Psychological Measurement, 12, 387-395. doi:10.1177/014662168801200407
Baker, Frank B..
The item log-likelihood surface for two- and three-parameter item characteristic curve models.
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