5.4 Joint maximum likelihood estimation

When assuming all students are independent, the joint likelihood $L (Y | α, g, s) = \prod_{i = 1}^{N} L (Y_{i} | α_{i})$ The joint maximum likelihood estimation (JMLE) finds $α, g, s$ that can maximize $L (Y | α, g, s)$ or its logarithm.

Neyman & Scott (1948) has showed that JMLE produced problematic estimates of parameters related with individuals.

References

Neyman, J., & Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica, 16, 1–32.