Quality of Life Research Vol. 16, Aug., 2007 Evaluating Measurement Equivalence Using the Item Response Theory Log-Likelihood Ratio (IRTLR) Method to Assess Differential Item Functioning (DIF): ...

A likelihood function for the frequency of the A1 allele when 2 A1 alleles are observed in a sample of 10 alleles. The vertical dashed line is drawn through the maximum value of the likelihood ...

This note gives examples where these properties of likelihood ratios do not hold; in some examples $\hat {L}_ {n}$ does not even tend to zero. The examples show that some of the regularity assumptions ...