Opción “Sustancias”

Among all 191 participants, five did not choose the dominant option in at least seven out of the nine screening items (see the histogram in Figure 3.3 for a full distribution of the number of dominant choices among the nine screening items) and thus were excluded from the formal analysis, leaving us with data from 186 participants in the analysis. Note that the results were the same when all data were included in the following analysis.

Figure 3.3. Histogram of the number of dominant choices of the nine screening items.

Attention effect. A preliminary check of the attention effect is by comparing

the proportion of LL choices in the two experimental conditions. Participants in the outcome-focus condition made 40.1% LL choices while those in the delay-focus condition only chose 29.5% LL, showing a sizable attention effect on intertemporal choice. The Bayesian estimation of the attention effect in Model (1) confirmed that participants from the outcome-focus condition were much more likely to choose LL

CHAPTER 3 ATTENTION AND INTERTEMPORAL CHOICE

68 than those from the delay-focus condition (Mdβ1 = 0.581,95% HDIβ1 = [0.506, 0.657]; see Table 3.1).

Background contrast effect. As explained earlier, this manipulation of

attention would also change the background contrast at the item level as a by-product. Specifically, we distinguished between two types of background contrast: the global background contrast and the local background contrast. The global background contrast referred to all the tradeoffs in the experiment that have been exposed before the current tradeoff. Because of the randomization of both blocks and items within blocks, any two items would appear prior to or after each other with even odds in both conditions, so global contrast was counterbalanced between conditions at the aggregate level.

The local background contrast referred to all the tradeoff in the same block

that have been exposed before the current tradeoff. Because the SS option was constant across items, we quantified the local background contrast with the relative rank of the LL option of all LL options in the same block, ranging from -1 (dominated by all other LL options), through 0, to 1 (dominating all other LL options).21 _{Practically, it was} calculated with the difference between the proportion of LL options that an LL option dominated and the proportion of LL options that dominated the LL proportion among all other items in the same block. For example, in the outcome-focus condition, $150 in 8 months dominated three LL options and were dominated by five LL options in the same block. Its local background contrast is quantified as 3/8 – 5/8 = -0.25. In the delay-focus condition, $150 in 8 months dominated six LL options and were dominated by two LL options in the same block. Its local background contrast is quantified as 6/8 – 2/8 = 0.5.

Model (2) involved the quantified local background contrast and thus statistically controlled the background contrast effect. The result from this model was consistent with Model (1) in terms the attention effect on intertemporal choice (Mdβ1 = 0.563,95% HDIβ1 = [0.483, 0.641]; see Table 3.1). In addition, it revealed a strong background contrast effect in the predicted direction: The more dominated LL options (or the less dominating LL options) there were in the same block, the more likely the

21 _{Theoretically, only the items that appeared before the current one is the “background”. Because the}

order of items in a block is randomized, each item has even odd to appear before or after another item. So when data are aggregated across participants, the overall pattern should be a good approximation of

current LL is to be chosen (Mdβ2 = 0.484,95% HDIβ2 = [0.404, 0.564]). Local contrast did not influence the attention effect (Mdβ2 = 0.044,95% HDIβ2 = [-0.146, 0.235]).

Table 3.1 Model evaluation and parameter estimation (Experiment 1)

Fixed-effect Parameter Estimation

(1) (2) Attention β1 0.581 [0.506, 0.657] 0.563 [0.483, 0.641] Background Contrast β2 0.484 [0.404, 0.564] Attention× Background Contrast β3 0.044 [-0.146, 0.235] DIC 1036.535 930.558

Note.Attention is an effect-coded variable: -0.5 = delay-focus; 0.5 = outcome-focus.

Background contrast ranges from -1 to 1, by an increment of 0.25. The estimates outside of the brackets are the median (Md) and the estimates in the brackets are the 95% High Density Intervals (95% HDIs) of the 150,000 samples from the posterior distribution. The 95% HDIs of the cells in boldface do not cross 0.

Involving the local background contrast in the model increased the performance of the model. According to DIC, Model (2), which involved background contrast as a fixed-effect predictor along with attention, performed better than Model (1), which involved attention as the only fixed-effect predictor (DICM1 = 1036.535; DICM2 = 930.558). To further check the goodness of fit of Model (2) to data, we ran a posterior predictive check by comparing the predicted probability of choosing LL based on posterior distributions of parameters with the original proportion of LL choice (Figure 3.4). We found that Model (2) described the data in Experiment 1 very well. Ninety-eight percent (159 out of 162) of the original LL proportions from data are accommodated within the predicted 95% HDIs based on the posterior distribution of parameters.

To summarise, Experiment 1 showed a strong attention effect on intertemporal choice, with an attention-driven shift of preference of 10.6% LL choices (40.1% vs. 29.5%). The robustness of this effect was confirmed by two mixed-effect Bayesian models (Models 1-2 in Table 3.1). The finding was consistent with both attribute-wise and component-wise attention effects on intertemporal choice, which predicted that

CHAPTER 3 ATTENTION AND INTERTEMPORAL CHOICE

70 attending to the LL outcome, relative to attending to the LL delay, reduced impatience, (see Figure 3.1b-c).

Figure 3.4. Posterior predictive check of Model (2) for Experiment 1. The dots represent original proportions of LL choices and the vertical lines represent the 95% high density intervals (HDIs) of the predicted probability of choosing LL based on the 150,000 samples drawn from posterior distributions.