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Three studies presented a two stage choice to participants, one as a forced binary choice between two presented profiles and one ternary choice containing an opt-out [ 68– 70].
The use of a two stage choice, with both a forced choice and a choice with an opt-out option, seems pragmatic until sufficient information is gleaned on the likely distribution of responses.
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For example, Huang et al. used the Hill function with high co-operativity coefficients to qualitatively compare computer predictions with experimental evidence [ 14], giving support to the idea that lineage choice occurs as a two stage process, first priming and then differentiating.
We therefore supplemented the OLS models with fixed effects with a two stage least square model (2SLS) where instruments for choice and mobility were included.
The study had a two stage design.
In this model, we assume that the choices between two stages (stage 1: choice between screening test; stage 2: choice between participation and opt-out) are not independent.
Kocher (2004) categorized the cichlid speciation events into three stages: 1) choice of habitat, 2) morphological diversification due to trophic status, and 3) diversification of male color pattern followed by that of mate recognition.
We also fitted a bivariate probit model in which the choices from two stages were treated as two binary outcomes [ 38].
We also fitted a bivariate probit model with cluster-robust SE treating the choices from two stages as two correlated binary outcomes.
And with every choice comes a million more choices.
When the choice on the immediately preceding trial was correct, the fluid reward volume for the current trial was increased in two stages up to a maximal quantity.
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