Ahhh, sample likelihood! It hasn’t yielded up all its secrets, not even in the two decades since I carried out some research on this exact topic whilst on sabbatical at the University of Southampton. The seminar I gave on my return to Canberra was called “Round the World with Maximum Likelihood”. The likelihood of another round-the-world trip is pretty low at the moment, but opportunities to engage with the concept are clearly still plentiful.
Associate Professor Robert Clark of the Research School of Finance, Actuarial Studies as and Statistics gave this seminar to the School via Zoom on Thursday 3 September. He’s been working on this topic with Dr Francis Hui, also of RSFAS.
Robert put his talk in the context of regression analysis of complex survey data. Why is this a thing? Why can’t you just request a regresssion in your avourite stats package, declare a vector of weights, and be done with it? Well you can do that, it’s called maximum pseudo-likelihood (Skinner et al 1989), and it’s a pretty common solution. However it ignores the extra layers of relationship in the sample design and so more nuanced solutions are definitely desirable.
Robert particularly introduced the complete sample likelihood approach, inspired by the maximum sample likelihood models of Pfeffermann et al (1998). He (or rather Francis) fitted these model using the TMB package in R. Model checking includes the use of the randomised quantile residuals published by Dunn & Smyth (1996). The complete sample likelihood estimates should eventually be as easy to implement as the pseudo-likelihood ones, with the benefit of smaller standard errors.
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