What follows is an abstract for a paper that I do not have time to write, but which I think would be a useful contribution to the literature, assuming what follows is actually true. Please feel free to do the actual research to find out. Let me know!
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Conjoint experiments have experienced explosive growth in political science. The standard methodology for analysing them in political science involves using linear regression methods to estimate Average Marginal Component Effects (AMCEs, Hainmueller, Hopkins & Yamamoto 2014). While this approach is attractive for deriving results related to clearly defined causal estimands, given the binary (sometimes ordered ternary) responses generated by forced choice conjoint experiments, limited dependent variable (LDV, eg logistic) regression methods have some potential advantages. These advantages derive from the fact that such models are likely to better describe the data generating process, as many conjoint experiments have strong effects and the bounds on the predicted probabilities are therefore important to fitting the data well. By virtue of fitting the data generating process better, LDV models may reduce the sensitivity of estimates to the choice of conjoint randomization. Where this is the case, LDV models can then be used to more reliably generate estimates of various quantities of interest, including AMCEs with respect to populations that are not the one implicitly defined by the conjoint randomization. This approach involves moving from narrowly estimating a particular causal estimand dictated by the conjoint randomization to estimating a more general behavioural model which is then projected (post-stratified) onto populations of interest in order to generate a wider range of causal estimands. The resulting tradeoff is one of additional model dependency for greater flexibility in the quantities of interest that can be modelled from a single experiment.