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Conjoint analysis is a popular experimental design used to measuremultidimensional preferences. Researchers examine how varying a factor ofinterest, while controlling for other relevant factors, influencesdecision-making. Currently, there exist two methodological approaches toanalyzing data from a conjoint experiment. The first focuses on estimating theaverage marginal effects of each factor while averaging over the other factors.Although this allows for straightforward design-based estimation, the resultscritically depend on the distribution of other factors and how interactioneffects are aggregated. An alternative model-based approach can compute variousquantities of interest, but requires researchers to correctly specify themodel, a challenging task for conjoint analysis with many factors and possibleinteractions. In addition, a commonly used logistic regression has poorstatistical properties even with a moderate number of factors whenincorporating interactions. We propose a new hypothesis testing approach basedon the conditional randomization test to answer the most fundamental questionof conjoint analysis: Does a factor of interest matter in any way given theother factors? Our methodology is solely based on the randomization of factors,and hence is free from assumptions. Yet, it allows researchers to use any teststatistic, including those based on complex machine learning algorithms. As aresult, we are able to combine the strengths of the existing design-based andmodel-based approaches. We illustrate the proposed methodology through conjointanalysis of immigration preferences and political candidate evaluation. We alsoextend the proposed approach to test for regularity assumptions commonly usedin conjoint analysis. An open-source software package is available forimplementing the proposed methodology.

Using Machine Learning to Test Causal Hypotheses in Conjoint Analysis