What is the dependent variable

In my research I have been looking at target advantage as my dependent variable. Which is the advantage of fixation proportions towards the target, over the competitor.

Here is how it is calculated.

"# Calculate empirical logit for the competitor (IA_2_C)
dat5$elogComp <- log((dat5$IA_2_C + 0.5) / (dat5$NSamples - dat5$IA_2_C + 0.5))

# Calculate empirical logit for the target (IA_1_C)
dat5$elogTarg <- log((dat5$IA_1_C + 0.5) / (dat5$NSamples - dat5$IA_1_C + 0.5))

# Calculate empirical logit target advantage
dat5$elogTarAdv <- dat5$elogTarg - dat5$elogComp"
## [1] "# Calculate empirical logit for the competitor (IA_2_C)\ndat5$elogComp <- log((dat5$IA_2_C + 0.5) / (dat5$NSamples - dat5$IA_2_C + 0.5))\n\n# Calculate empirical logit for the target (IA_1_C)\ndat5$elogTarg <- log((dat5$IA_1_C + 0.5) / (dat5$NSamples - dat5$IA_1_C + 0.5))\n\n# Calculate empirical logit target advantage\ndat5$elogTarAdv <- dat5$elogTarg - dat5$elogComp"

Pior to this, here is what a view of the fixation proportions look like (not yet empirical logit target advantage)

Here we see two lines for the fixation proportions to the target and competitor, further defined by either it being a congruent or incongruent trial.

In this case, if a GV speaker said ‘blade’, this would be a congruent target (in line with biases towards GV accent as having increased aggression) If the GV speaker said ‘book’, this would be an incongruent target. If the SSBE speaker said ‘book’, this would be a congruent target, and ‘blade’ for them would be an incongruent target.

Elogit Target Advantage

Research can simplify this further by viewing the advantage of fixations to the target over the competitor. This is my current dependent variable.

We now have the two lines just to show the congruent and incongruent trials, where the target had the advantage over the competitor. A positive elog value shows that the target did indeed receive greater fixation proportions to the competitor.

As we discussed, I am starting to wonder on the benefits of looking at it in this way. And whether it doesn’t matter whether the word is heard (target) or not (competitor). But rather, we are interested in whether the fixations went to the congruent option to that accent when anticipating whatever the upcoming word would be.

I was thinking of maybe applying the same principle of elogTarget advantage to create congruent advantage.

Congruent advantage

Agg.win2 <- Agg.win2 %>%
  mutate(
    # Creating an elog Congruent for congruency with biased accent, regardless of targ/comp
    elogCongruent = case_when(
      condition == 'congruent' ~ elogTarg,   
      condition == 'incongruent' ~ elogComp,  
      TRUE ~ NA_real_                          
    ),
    # Same for incongruent
    # if an incongruent competitor - 
    elogIncongruent = case_when(
      condition == 'congruent' ~ elogComp,   
      condition == 'incongruent' ~ elogTarg,  
      TRUE ~ NA_real_
    )
  )

Agg.win2$elogCongAdv <- Agg.win2$elogCongruent - Agg.win2$elogIncongruent

The code above is mapping the pre-calculated empirical logit values (target and competitor) into two new columns, based on wehther the trail is congruent or incongruent. elogCongruent is the elogit preference for the accent-congruent item, regardless of their target/competitor role in the trial (if they were heard or not)

I feel like I have written this and got my head around it, but once I’m away and look back I nearly self combust. So please tell me if this logic is wrong!

Visualising Congruency Advantage and what it means

If we filtered the GV accent, and look at variation in pre and post data. In this scenario (not accounting for media type), we can see an initial spike of the elogit congruency advantage in the pre. Meaning that they were more inclined to initially look at the biased option in the pre-phase, but this declined over time, and then also they did not rely on the bias as much in the post phase.

So, we could go a step further and look at congruency advantage (the advantage of the biased anticipations) in pre and post, and across media for GV.

I do wonder whether this may be a good option for a dependent variable. The utterance frame is identical and it is not as if we have some form of phonological/morphological manipulation like we see in Clara’s ‘predict this rock’ example. So, does it really matter to us whether the word spoken by the GV speaker is indeed blade or book? Because our question is whether the anticipation of the upcoming word is being informed by listener’s biases of that accent. So, even if the GV speaker ended up saying book, the listener may be looking at blade.

This could be a potential way to streamline the data some more. I often question myself on the benefits of whether we need to include congruency condition and target advantage, when perhaps for us the congruency advantage (inclination to look at the biased option in the anticipatory part of the time-course) is what we are focused upon.

Right, off to stare at a wall for a few hours to rest my brain - ha!