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Using the data points x ^ i (t j ) to generate a suitable initial guess, parameter estimation may proceed via a nonlinear programming approach (see Methods, Additional file 1).
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Moreover, as a variation-based method, we find that the convergence and the synthesized results of the LMO method are strongly dependent on the initial guess parameters.
Therefore, the "first guess" parameters must be relatively close to those of the best fit.
The more the pseudo-guess parameter approaches zero, the better the quality of the measurement.
We assimilate these synthetic slip velocity data through the adjoint data assimilation method to check whether the "first-guess" parameter values are updated to their true values.
Other parameters include item discrimination and guessing parameter.
The 2PL model in the three tests assumes that questions have no guessing parameter.
The parameter c j is a "guessing parameter" measuring the likelihood that a very low-ability examinee would respond correctly simply by guessing.
For each discrimination parameter a j we used a Γ(1,1) prior, and for each guessing parameter c j a Unif 0,1) prior.
Since the measure is used observationally by teachers, the guessing parameter (in 3 PL IRT model) is not considered in the analysis.
Where G i is the guessing parameter which accounts for the possibility that all students even the ones with very low ability have a non-zero probability of answering a question correctly by guessing.
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