YA_full_optiontaskanalysis
Young adults - options task
Participants
The young adult analysis recruited 88 participants.
1 experimental dataset excluded as did experiment twice.
1 participant had incomplete questionnaire data for Dimensional Apathy Scale - not included in these analyses.
3 rows with RT <0.3s removed
1 participant had low accuracy but retained as seemingly normal RT
Analysis notes
New analysis uses a combined variable called ‘Difficulty’ which is the mean of the inverse value difference between 2 best options and the effort level of the best option. This is because…
- Value difference and bestoption cannot be considered independent of eachother and therefore violates assumptions for linear models and introduces problems of collinearity: The value of ‘bestoption’ is dependent on the value difference (i.e. one cannot have bestoption of 5 and value difference of 4) and the two values are negatively correlated. This introduces problems with interpretation of parameters - especially in the context of two- and three-way interactions between (inverse) value difference and bestoption, e.g.:
Here, the estimated marginal means from an accuracy model finding a significant two-way interaction between value difference and bestoption suggest a steeper decline in accuracy in ‘hard’ (high inverse value difference) choices with high bestoption values - however this is a non-existent condition in the data.
However both value difference and bestoption are important attributes of choice difficulty. Both correlate with RT, accuracy and subjective choice difficulty. Although in the design choice difficulty was manipulated primarily by value difference, bestoption is an even stronger predictor (particularly of RT) and is necessary to fully capture the essence of choice difficulty.
I have previously explored various ways to incorporate both bestoption and value difference, including inclusion of bestoption as a control variable to hold at its mean value, or as an interacting variable. However bestoption captures much of the variance and, in drift diffusion models, leads to difficulty in intepreting models with multiple terms and three-way interactions, produces divergences and inconsistent model findings (and weird effects, such as bimodal peaks for non-decision time).
Therefore I have found the most suitable way to address this is to combine both bestoption and (inverse) value difference into a new variable called difficulty - which is the mean of both (i.e. a linear combination, which appears a valid way to approach this and gets round all problems of model violations and interpretability). This new variable also correlates extremely well with RT, accuracy and subjective difficulty ratings:
Analyses
For linear models of RT, I could either use a GLMM with gamma log link to account for skewed data, or log transform RTs in LMM. The advantage of the latter is you can use buildmer to refine random effects, as I haven’t for the life of me been able to find a way it can apply the gamma log link function.
The format of mixed models is therefore:
Mixed models
Effort task only (n=86)
LMM: logRT ~ Difficulty * Options + (1 +Difficulty * Options | ID)
GLMM (binomial): accuracy ~ Difficulty * Options + (1 +Difficulty * Options | ID)
GLMM (gamma link): Rating ~ Difficulty * Options + (1 +Difficulty * Options | ID)
GLMM (negative binomial): Timeouts ~ Difficulty * Options + (1 + Difficulty * Options | ID)
LMM : Force (AUC) ~ Option worked * Apathy
Models of above also including main, two- and three way interactions with DAS total, DAS executive, DAS auto-activation, DAS emotional-affective.
Effort and reward task (n=62)
LMM: logRT ~ Difficulty * Options * Task + (1 +Difficulty * Options * Task | ID)
GLMM (binomial): accuracy ~ Difficulty * Options * Task + (1 +Difficulty * Options * Task | ID)
GLMM (gamma link): Rating ~ Difficulty * Options + (1 +Difficulty * Options * Task | ID)
GLMM (negative binomial): Timeouts ~ Difficulty * Options + (1 + Difficulty * Options * Task | ID)
Drift diffusion modelling
(a=threshold, v=drift, z=bias, t=non-decision-time)
Start with most complex model:
a ~ Difficulty + Options + Difficulty:Options + (1 +Difficulty + Options + Difficulty:Options | ID)
v ~ Difficulty + Options + Difficulty:Options + (1 +Difficulty + Options + Difficulty:Options | ID)
z (group-level)
t (group-level)
Refine sequentially on basis of variance contribution and test with loo-cv.
Also try models with collapsing bounds.
Results
Reaction times
Base models
The base model of reaction times in 87 participants doing effort task:
| RT | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 1.00 | 0.95 – 1.04 | 0.871 |
| Difficulty sc | 1.16 | 1.14 – 1.18 | <0.001 |
| noopts s2z1 | 0.92 | 0.91 – 0.93 | <0.001 |
| Difficulty sc × noopts s2z1 |
0.99 | 0.98 – 0.99 | <0.001 |
| Random Effects | |||
| σ2 | 0.08 | ||
| τ00 shortid | 0.01 | ||
| τ11 shortid.Difficulty_sc | 0.00 | ||
| τ11 shortid.noopts_s2z1 | 0.00 | ||
| τ11 shortid.Difficulty_sc:noopts_s2z1 | 0.00 | ||
| ρ01 | -0.38 | ||
| 0.17 | |||
| 0.30 | |||
| ICC | 0.10 | ||
| N shortid | 87 | ||
| Observations | 13852 | ||
| Marginal R2 / Conditional R2 | 0.244 / 0.320 | ||
The base model of reaction times incorporating task as dummy main and interacting variable, in 61 participants who did both effort and reward task: -Faster in reward task -Faster particularly in easy choices in reward vs effort task -Fsster particularly in two option choices in reward vs effort task
| RT | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 1.02 | 0.97 – 1.08 | 0.447 |
| Difficulty sc | 1.15 | 1.13 – 1.17 | <0.001 |
| noopts s2z1 | 0.92 | 0.92 – 0.93 | <0.001 |
| Task [Reward_task] | 0.86 | 0.82 – 0.90 | <0.001 |
| Difficulty sc × noopts s2z1 |
0.99 | 0.98 – 1.00 | 0.001 |
| Difficulty sc × Task [Reward_task] |
1.03 | 1.01 – 1.05 | 0.009 |
| noopts s2z1 × Task [Reward_task] |
0.98 | 0.97 – 0.99 | <0.001 |
| (Difficulty sc × noopts s2z1) × Task [Reward_task] |
1.00 | 0.99 – 1.00 | 0.330 |
| Random Effects | |||
| σ2 | 0.08 | ||
| τ00 shortid | 0.01 | ||
| τ11 shortid.Difficulty_sc | 0.00 | ||
| τ11 shortid.noopts_s2z1 | 0.00 | ||
| τ11 shortid.TaskReward_task | 0.01 | ||
| τ11 shortid.Difficulty_sc:noopts_s2z1 | 0.00 | ||
| τ11 shortid.Difficulty_sc:TaskReward_task | 0.00 | ||
| τ11 shortid.noopts_s2z1:TaskReward_task | 0.00 | ||
| ρ01 | -0.36 | ||
| 0.16 | |||
| -0.66 | |||
| 0.24 | |||
| 0.30 | |||
| -0.13 | |||
| ICC | 0.09 | ||
| N shortid | 61 | ||
| Observations | 19482 | ||
| Marginal R2 / Conditional R2 | 0.302 / 0.362 | ||
Models incorporating apathy
Below shows the model incorporating DAS (Dimensional Apathy Score) total score:
| RT | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 1.00 | 0.96 – 1.05 | 0.956 |
| Difficulty sc | 1.16 | 1.14 – 1.18 | <0.001 |
| noopts s2z1 | 0.92 | 0.91 – 0.93 | <0.001 |
| DAS total sc | 1.04 | 1.00 – 1.09 | 0.060 |
| Difficulty sc × noopts s2z1 |
0.99 | 0.98 – 0.99 | <0.001 |
| Difficulty sc × DAS total sc |
0.99 | 0.97 – 1.00 | 0.148 |
| noopts s2z1 × DAS total sc |
1.01 | 1.00 – 1.01 | 0.146 |
| (Difficulty sc × noopts s2z1) × DAS total sc |
1.00 | 0.99 – 1.00 | 0.644 |
| Random Effects | |||
| σ2 | 0.08 | ||
| τ00 shortid | 0.01 | ||
| τ11 shortid.Difficulty_sc | 0.00 | ||
| τ11 shortid.noopts_s2z1 | 0.00 | ||
| τ11 shortid.Difficulty_sc:noopts_s2z1 | 0.00 | ||
| ρ01 | -0.38 | ||
| 0.15 | |||
| 0.31 | |||
| ICC | 0.09 | ||
| N shortid | 86 | ||
| Observations | 13692 | ||
| Marginal R2 / Conditional R2 | 0.257 / 0.327 | ||
And below, incorporating DAS executive score: -Slower responses with higher executive apathy -Slower responses especially in easier tasks in those with higher apathy
| RT | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 1.00 | 0.96 – 1.05 | 0.947 |
| Difficulty sc | 1.16 | 1.14 – 1.18 | <0.001 |
| noopts s2z1 | 0.92 | 0.91 – 0.93 | <0.001 |
| DAS Exec sc | 1.05 | 1.01 – 1.10 | 0.027 |
| Difficulty sc × noopts s2z1 |
0.99 | 0.98 – 0.99 | <0.001 |
| Difficulty sc × DAS Exec sc |
0.98 | 0.96 – 0.99 | 0.002 |
| noopts s2z1 × DAS Exec sc | 1.01 | 1.00 – 1.02 | 0.061 |
| (Difficulty sc × noopts s2z1) × DAS Exec sc |
1.00 | 1.00 – 1.01 | 0.757 |
| Random Effects | |||
| σ2 | 0.08 | ||
| τ00 shortid | 0.01 | ||
| τ11 shortid.Difficulty_sc | 0.00 | ||
| τ11 shortid.noopts_s2z1 | 0.00 | ||
| τ11 shortid.Difficulty_sc:noopts_s2z1 | 0.00 | ||
| ρ01 | -0.36 | ||
| 0.14 | |||
| 0.28 | |||
| ICC | 0.09 | ||
| N shortid | 86 | ||
| Observations | 13692 | ||
| Marginal R2 / Conditional R2 | 0.264 / 0.332 | ||
There are no signfiicant main or interacting effects of DAS auto-activation or DAS emotional-affective dimensions on RT (not shown).
When effort and reward subtasks are analysed separately (for 61 participants that did both), significant difficulty:DAS executive interaction is only seen in effort task (Effort task: p=0.014; Reward task p=0.77).
Accuracy
Base models
Below shows the base model for accuracy:
| accuracy | |||
|---|---|---|---|
| Predictors | Odds Ratios | CI | p |
| (Intercept) | 36.26 | 27.17 – 48.39 | <0.001 |
| Difficulty sc | 0.28 | 0.25 – 0.32 | <0.001 |
| noopts s2z1 | 1.22 | 1.12 – 1.34 | <0.001 |
| Difficulty sc × noopts s2z1 |
0.99 | 0.93 – 1.07 | 0.868 |
| Random Effects | |||
| σ2 | 3.29 | ||
| τ00 shortid | 1.42 | ||
| τ11 shortid.Difficulty_sc | 0.15 | ||
| ρ01 shortid | -0.55 | ||
| ICC | 0.32 | ||
| N shortid | 87 | ||
| Observations | 13852 | ||
| Marginal R2 / Conditional R2 | 0.251 / 0.493 | ||
Below shows the base accuracy model incorporating Task: -Higher accuracy in more difficult choices in reward versus effort task
| accuracy | |||
|---|---|---|---|
| Predictors | Odds Ratios | CI | p |
| (Intercept) | 34.11 | 24.43 – 47.62 | <0.001 |
| Difficulty sc | 0.28 | 0.24 – 0.33 | <0.001 |
| noopts s2z1 | 1.17 | 1.05 – 1.30 | 0.003 |
| Task [Reward_task] | 1.10 | 0.78 – 1.56 | 0.579 |
| Difficulty sc × noopts s2z1 |
1.00 | 0.92 – 1.09 | 0.933 |
| Difficulty sc × Task [Reward_task] |
1.40 | 1.14 – 1.73 | 0.002 |
| noopts s2z1 × Task [Reward_task] |
0.93 | 0.80 – 1.08 | 0.343 |
| (Difficulty sc × noopts s2z1) × Task [Reward_task] |
1.00 | 0.88 – 1.13 | 0.942 |
| Random Effects | |||
| σ2 | 3.29 | ||
| τ00 shortid | 1.32 | ||
| τ11 shortid.Difficulty_sc | 0.15 | ||
| τ11 shortid.TaskReward_task | 1.07 | ||
| τ11 shortid.Difficulty_sc:TaskReward_task | 0.26 | ||
| ρ01 | -0.55 | ||
| -0.72 | |||
| 0.38 | |||
| ICC | 0.26 | ||
| N shortid | 61 | ||
| Observations | 19482 | ||
| Marginal R2 / Conditional R2 | 0.220 / 0.420 | ||
Models incorporating apathy
No models show significant effects of DAS total or any of the three subscales on accuracy.
Timeouts
Timeouts have been analysed in two ways:
- A simple negative binomial regression model specified as count of timeouts ~ apathy score. In 86 people doing effort task, hese find significant effects of DAS total (p=0.049), DAS executive (p=0.007), but neither DAS auto-activation or DAS emotional. A similar linear model with predictors of Task*Task order in 61 ppts that did both effort and reward task finds significant effects of Task (less timeouts in reward task, p=0.011) and no effect of task order or interaction. Incorporating apathy scores into this model shows main effects of DAS total and DAS executive but no interactions with task.
- A mixed effects binomial regression with timeout (yes or no) as the dependent variable and Difficulty + Options + Difficuly:Options as predictors. The base model shows significant main effects of difficulty (p<0.001), options (p<0.001) but no interaction. Incorporating apathy into models shows main effects of DAS executive (p=0.015). No interactions with DAS executive, and no main or interacting effects of DAS total or any other subscales.
Ratings
Below shows the mixed effect linear model for subjective ratings (z-scored to individual participants) in 87 participants who did effort task. Here a gamma log link is applied for skewed data.
| Dependent variable | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 1.39 | 1.14 – 1.70 | 0.001 |
| Difficulty | 1.59 | 1.51 – 1.68 | <0.001 |
| noopts s2z1 | 0.96 | 0.91 – 1.00 | 0.068 |
| Difficulty × noopts s2z1 | 0.98 | 0.94 – 1.03 | 0.469 |
| Random Effects | |||
| σ2 | 0.70 | ||
| τ00 shortid | 0.84 | ||
| ICC | 0.55 | ||
| N shortid | 87 | ||
| Observations | 2953 | ||
| Marginal R2 / Conditional R2 | 0.124 / 0.603 | ||
Interestingly, incorporating apathy scores into these subjective rating models produces some interesting results. There is a positive effect of DAS executive score on ratings, and also a highly significant Difficulty:Executive apathy score interaction, in accordance with the data - more apathetic people find particularly easier decisions more subjectively difficulty
| Dependent variable | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 1.40 | 1.15 – 1.69 | 0.001 |
| Difficulty | 1.60 | 1.52 – 1.68 | <0.001 |
| noopts s2z1 | 0.96 | 0.91 – 1.00 | 0.078 |
| DAS Exec sc | 1.26 | 1.04 – 1.53 | 0.018 |
| Difficulty × noopts s2z1 | 0.99 | 0.94 – 1.04 | 0.675 |
| Difficulty × DAS Exec sc | 0.88 | 0.84 – 0.92 | <0.001 |
| noopts s2z1 × DAS Exec sc | 1.01 | 0.97 – 1.06 | 0.545 |
| (Difficulty × noopts s2z1) × DAS Exec sc |
1.00 | 0.95 – 1.05 | 0.999 |
| Random Effects | |||
| σ2 | 0.70 | ||
| τ00 shortid | 0.80 | ||
| ICC | 0.53 | ||
| N shortid | 86 | ||
| Observations | 2919 | ||
| Marginal R2 / Conditional R2 | 0.163 / 0.609 | ||
There is also a significant interaction between difficulty and the auto-activation dimension. The emmeans plots suggest this is in the opposite direction - that those with greater behavioural apathy find less difficulty decisions easier and more difficult decisions harder. However the mean plots below don’t support this interaction with the auto-activation dimension. Of note there are no main effects or interactions with DAS total or DAS emotional scores.
| Dependent variable | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 1.39 | 1.14 – 1.70 | 0.001 |
| Difficulty | 1.59 | 1.51 – 1.67 | <0.001 |
| noopts s2z1 | 0.96 | 0.91 – 1.00 | 0.074 |
| DAS Behav sc | 0.87 | 0.71 – 1.07 | 0.188 |
| Difficulty × noopts s2z1 | 0.98 | 0.94 – 1.03 | 0.462 |
| Difficulty × DAS Behav sc | 1.11 | 1.05 – 1.17 | <0.001 |
| noopts s2z1 × DAS Behav sc |
1.00 | 0.95 – 1.05 | 0.930 |
| (Difficulty × noopts s2z1) × DAS Behav sc |
0.99 | 0.94 – 1.03 | 0.561 |
| Random Effects | |||
| σ2 | 0.71 | ||
| τ00 shortid | 0.89 | ||
| ICC | 0.56 | ||
| N shortid | 86 | ||
| Observations | 2919 | ||
| Marginal R2 / Conditional R2 | 0.134 / 0.616 | ||
Control analyses
One question is whether observed effects of apathy are due to worse learning of stimulus-associations causing slower responses. This seems unlikely as no correlations with accuracy and effects are greater in easier tasks which are well-learned. It is also possible that unsatisfacory learning for certain stimuli may skew results (i.e. consistently get one stimulus wrong).
Therefore can perform subanalysis on participants of good learners by excluding those who consistently scored below 50% on accuracy on at least one of the different stimuli. This excludes 24 participants however the executive apathy results remain significant:
| RT | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.98 | 0.93 – 1.03 | 0.357 |
| Difficulty sc | 1.17 | 1.15 – 1.19 | <0.001 |
| noopts s2z1 | 0.92 | 0.91 – 0.93 | <0.001 |
| DAS Exec sc | 1.05 | 1.00 – 1.10 | 0.055 |
| Difficulty sc × noopts s2z1 |
0.99 | 0.98 – 0.99 | <0.001 |
| Difficulty sc × DAS Exec sc |
0.98 | 0.96 – 1.00 | 0.029 |
| noopts s2z1 × DAS Exec sc | 1.00 | 1.00 – 1.01 | 0.337 |
| (Difficulty sc × noopts s2z1) × DAS Exec sc |
1.00 | 0.99 – 1.01 | 0.787 |
| Random Effects | |||
| σ2 | 0.08 | ||
| τ00 shortid | 0.01 | ||
| τ11 shortid.Difficulty_sc | 0.00 | ||
| τ11 shortid.noopts_s2z1 | 0.00 | ||
| τ11 shortid.Difficulty_sc:noopts_s2z1 | 0.00 | ||
| ρ01 | -0.32 | ||
| 0.13 | |||
| 0.26 | |||
| ICC | 0.09 | ||
| N shortid | 62 | ||
| Observations | 9885 | ||
| Marginal R2 / Conditional R2 | 0.294 / 0.358 | ||
Another question is whether the effects of apathy relate to adaptive speeding of responses over time, particularly after stimuli have been presented multiple times (the Gratton effect) - as opposed to static slowed responses, relating either to executive impairments or effort aversion.
To look into this you can separate choices into stimulus of the option chosen and plot RT against trial number of choosing that stimulus. Here trials are shown up to the point at which 50% of participants have selected that option.
Specifying a linear model of RT ~ Trial * DAS executive * Option chosen + (1 | ID) (more complex models don’t converge) suggests that both effects are present:
-Main effect of DAS executive - apathy associated with slower responses
-Interaction between DAS executive and trial - less adaptive speeding with time.
-Same DAS executive and Option chosen interaction as demonstrated previously - lower apathy individuals have quicker responses in low effort (easy) tasks
| RT | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.97 | 0.93 – 1.01 | 0.176 |
| Option chosen | 1.14 | 1.12 – 1.16 | <0.001 |
| DAS Exec sc | 1.06 | 1.01 – 1.11 | 0.012 |
| it | 0.98 | 0.97 – 0.98 | <0.001 |
| Option chosen × DAS Exec sc |
0.98 | 0.96 – 1.00 | 0.013 |
| Option chosen × it | 0.99 | 0.99 – 1.00 | 0.069 |
| DAS Exec sc × it | 1.01 | 1.01 – 1.02 | <0.001 |
| (Option chosen × DAS Exec sc) × it |
1.00 | 0.99 – 1.00 | 0.445 |
| Random Effects | |||
| σ2 | 0.08 | ||
| τ00 shortid | 0.01 | ||
| τ11 shortid.scale(Option_chosen) | 0.00 | ||
| ρ01 shortid | -0.25 | ||
| ICC | 0.10 | ||
| N shortid | 86 | ||
| Observations | 12020 | ||
| Marginal R2 / Conditional R2 | 0.211 / 0.288 | ||
Force
I have analysed force (AUC as a proportion of max AUC over all trials in effort task). I have specified a model of Force ~ Option worked * Apathy score + (1 + Option worked | ID).
These show that the executive apathy domain is the main driver of less force, although there are weaker correlations with DAS total and DAS behavioural.
# A tibble: 7 × 2
Option_worked `mean(AUC_norm)`
<int> <dbl>
1 1 0.196
2 2 0.277
3 3 0.365
4 4 0.467
5 5 0.523
6 6 0.569
7 7 0.581| AUC_norm | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.31 | 0.29 – 0.34 | <0.001 |
| Option worked | 0.11 | 0.10 – 0.12 | <0.001 |
| DAS total | 0.00 | -0.02 – 0.03 | 0.796 |
| Option worked × DAS total | -0.01 | -0.02 – 0.00 | 0.052 |
| Random Effects | |||
| σ2 | 0.03 | ||
| τ00 shortid | 0.01 | ||
| τ11 shortid.scale(Option_worked) | 0.00 | ||
| ρ01 shortid | 0.57 | ||
| ICC | 0.33 | ||
| N shortid | 87 | ||
| Observations | 13900 | ||
| Marginal R2 / Conditional R2 | 0.227 / 0.486 | ||
| AUC_norm | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.31 | 0.29 – 0.34 | <0.001 |
| Option worked | 0.11 | 0.10 – 0.12 | <0.001 |
| DAS Behav | 0.00 | -0.02 – 0.03 | 0.779 |
| Option worked × DAS Behav | -0.01 | -0.02 – 0.00 | 0.088 |
| Random Effects | |||
| σ2 | 0.03 | ||
| τ00 shortid | 0.01 | ||
| τ11 shortid.scale(Option_worked) | 0.00 | ||
| ρ01 shortid | 0.57 | ||
| ICC | 0.33 | ||
| N shortid | 87 | ||
| Observations | 13900 | ||
| Marginal R2 / Conditional R2 | 0.227 / 0.486 | ||
| AUC_norm | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 0.31 | 0.29 – 0.34 | <0.001 |
| Option worked | 0.11 | 0.10 – 0.12 | <0.001 |
| DAS Exec | -0.01 | -0.03 – 0.02 | 0.522 |
| Option worked × DAS Exec | -0.01 | -0.02 – -0.00 | 0.007 |
| Random Effects | |||
| σ2 | 0.03 | ||
| τ00 shortid | 0.01 | ||
| τ11 shortid.scale(Option_worked) | 0.00 | ||
| ρ01 shortid | 0.55 | ||
| ICC | 0.33 | ||
| N shortid | 87 | ||
| Observations | 13900 | ||
| Marginal R2 / Conditional R2 | 0.231 / 0.486 | ||
This does not seem to be related to the number of failures in a simple linear model of per participant failures count of failures being predicted by apathy scores (ps all >0.3) or cumulative force production (sum of AUC for all trials).
Distractor effects
Finally I have looked at effects of distracting options. Here I have only analysed 3 option tasks. I have split task on the basis of the best option and second best option, and divided choices into low distractor value (DV) and high distractor value. This equates to:
| Bestoption | Second best | Low DV | High DV | Excluded |
|---|---|---|---|---|
| 1 | 2 | 3 4 | 6 7 | 5 |
| 2 | 3 | 4 5 | 6 7 | |
| 3 | 4 | 5 | 7 | 6 |
| 4 | 5 | 6 | 7 | |
| 5 | 6 | - | - | 7 |
In these plots the best option goes across the x axis at the top and second best option along the y axis. Most difficult choices (lowest value difference) therefore lie across the diagnoal. First I have plotted participants’ mean RTs:
Although the effect sizes look small, there is a significant effect of distractor value:
| RT | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | 1.02 | 0.97 – 1.08 | 0.377 |
| bestoption | 1.18 | 1.15 – 1.22 | <0.001 |
| value difference | 0.98 | 0.96 – 1.01 | 0.169 |
| dval [low] | 0.97 | 0.95 – 0.99 | 0.008 |
| bestoption × value difference |
1.01 | 0.99 – 1.03 | 0.271 |
| bestoption × dval [low] | 0.98 | 0.95 – 1.00 | 0.085 |
| value difference × dval [low] |
0.99 | 0.97 – 1.02 | 0.504 |
| (bestoption × value difference) × dval [low] |
0.99 | 0.97 – 1.01 | 0.360 |
| Random Effects | |||
| σ2 | 0.08 | ||
| τ00 shortid | 0.01 | ||
| τ11 shortid.scale(bestoption) | 0.00 | ||
| τ11 shortid.scale(value_difference) | 0.00 | ||
| ρ01 | -0.22 | ||
| 0.16 | |||
| ICC | 0.17 | ||
| N shortid | 87 | ||
| Observations | 4161 | ||
| Marginal R2 / Conditional R2 | 0.231 / 0.362 | ||
I have also looked at accuracy but this doesn’t show anything significant.
| accuracy | |||
|---|---|---|---|
| Predictors | Odds Ratios | CI | p |
| (Intercept) | 67.17 | 33.86 – 133.23 | <0.001 |
| bestoption | 0.54 | 0.34 – 0.86 | 0.009 |
| value difference | 7.28 | 4.15 – 12.76 | <0.001 |
| dval [low] | 1.00 | 0.66 – 1.50 | 0.988 |
| bestoption × value difference |
0.66 | 0.45 – 0.97 | 0.032 |
| bestoption × dval [low] | 0.97 | 0.57 – 1.65 | 0.896 |
| value difference × dval [low] |
0.97 | 0.65 – 1.45 | 0.869 |
| (bestoption × value difference) × dval [low] |
1.08 | 0.68 – 1.71 | 0.757 |
| Random Effects | |||
| σ2 | 3.29 | ||
| τ00 shortid | 2.74 | ||
| τ11 shortid.scale(bestoption) | 0.17 | ||
| τ11 shortid.scale(value_difference) | 0.78 | ||
| ρ01 | 0.34 | ||
| 0.97 | |||
| ICC | 0.52 | ||
| N shortid | 87 | ||
| Observations | 4161 | ||
| Marginal R2 / Conditional R2 | 0.460 / 0.739 | ||