Rasch Model Estimation - Conditional Maximum Likelihood

Conditional Maximum Likelihood

The conditional likelihood function is defined as

\Lambda = \prod_{n} \Pr\{(x_{ni})\mid r_n\} =\frac{\exp(\sum_i -s_i\delta_i)}{\prod_{n} \gamma_r}

in which

\gamma_r = \sum_{(x) \mid r}\exp(-\sum_i x_{ni}\delta_i)

is the elementary symmetric function of order r, which represents the sum over all combinations of r items. For example, in the case of three items,

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