In the Rasch model, logit[P(Y_it= 1)] = α_i+ β_t, α_iis a fixed effect.

a. Assuming independence of responses for different subjects and for different observations on the same subject, show that the log likelihood is

b. Show that the likelihood equations are y_+t = ˆ‘_i P(Y_it = 1) and y_i+ = ˆ‘_t P(Y_it = 1) for all i and t. Explain why conditioning on {y_i+} yields a distribution that does not depend on {α_i}.

Transcribed Image Text:

ΣΣαν. + ΣΣΒΥ ΣΣog[1 + exp(α + exp(a + β )]