Computational protocol: Cognitive reflection vs. calculation in decision making

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Protocol publication

[…] We estimated a model identical to Böckenholt's () Cognitive Miser model of the CRT. Their approach (unlike that of Campitelli and Gerrans, ) allows the estimation of individual differences and differences between items, accounts for measurement error, and allows the two abilities to be correlated. It is theoretically grounded in the Item Response Theory tradition. We used the nlme package Version 3.1 for linear and non-linear mixed-effects models (Pinheiro et al., ) to fit Böckenholt's model because it handles missing observations and allows for dichotomous response variables. De Boeck and Partchev () described in detail how a package for generalized linear mixed-effects models can be used to fit an IRTree model, of which the Cognitive Miser model is one example (see also Böckenholt, ). We describe this method briefly below.Responses to the five CRT items were treated as up to 10 repeated measures because it is assumed that participants complete a two-step process when answering a CRT problem. To respond correctly, they must successfully complete both steps. In Step A, they attempt to avoid the intuitive response; if they fail to avoid it, processing is terminated and the incorrect intuitive response is given. If they avoid the intuitive response, then participants proceed to Step B and determine a non-intuitive response. If a participant reported the incorrect intuitive response, the process was assumed to have terminated in Step A. Thus, Step B was never performed, and the Step B response was treated as missing data. See Table for a depiction of how data were coded. We used model comparisons to test an hypothesis concerning whether two separate abilities (vs. a single ability) were responsible for completing steps A and B. […]

Pipeline specifications

Software tools nlme, lme4
Application Mathematical modeling