A latent class model for individual differences in the interpretation of conditionals

The authors opted for two different types of latent class analyses on the two problems sets instead of one joint analysis on all 30 problems together (the six problems of the first set and the 24 problems of the second set) for the following two reasons. First, for the set of six DA+ and AC+ problems, different interpretations of the conditional should lead to qualitatively different answers: conditional reasoners should answer 'undecidable', whereas biconditional reasoners should answer ''necessarily true'. For the set of 24 MP+ and MT+ problems, the correct answer is independent of the interpretation of the conditional. Interpretation is only supposed to affect the difficulty of those problems. The consequence is that the answers on the MP+ and MT+ problems can be dichotomized (correct/incorrect) without much loss of information, unlike the answers on the DA+ and AC+ problems, calling for a different modeling approach for the two sets of problems. Second, The two different types of analyses reflect two stages in modeling. We will first check whether there are latent classes corresponding with the interpretation of a conditional by conducting an unrestricted latent class analysis on the DA+ and AC+ problems. If the existence of different interpretations is revealed, we can be confident that it is appropriate to construct a confirmatory model for the set of MP+ and MT+ problems, based on the three-level hypothesis for conditional reasoning.

We would like to thank an anonymous reviewer for suggesting effect coding for the independent variables of the logistic regression, so that the intercept corresponds to the mean on a logistic scale of the solution probabilities.