Las Bodegas de la D.O de Ribera del Duero y la participación de las

The analysis of the sub-gaze measures differs slightly from the previous analy- ses in that new predictors for word length. All of my previous analyses included the number of letters in the whole trigram, but I wanted to account for the effect of the length of the first word in my analysis of SG1, the sum of fixations on the first word. I added this predictor to my standard set predictors and called it SG1Len, with the centered and scaled version called sSG1Len. All the other predictors in these models are the same predictors described in Table 3.1. To confirm that I did not increase the amount of multi-collinearity by adding this predictor, I re-calculated κ for all of my predictors, and it was 50, which is high and could lead to an increased risk of suppression or enhancement.

Friedman and Wall (2005) have looked at regression when predictors are highly correlated, and they note that it is often beneficial to include predictors that are inter-correlated in a regression model. They note that “it is reasonable to consider highly correlated independent variables.” (Friedman & Wall, 2005, p.135). To test for any impact of suppression and enhancement due to the collinearity of sSG1Len and PC3 (r = 0.62) on my regression coefficients, I compared all models with a sub-model that did not contain PC3. In all cases neither the direction nor the reliability of the effects of the remaining predictors in the models changed, indicating that the collinearity was acceptable.

I found a correlation between the first sub-gaze time and and the total reading time on the trial before it (r =0.13, 95% CI: 0.11 - 0.14). I did not find a relationship between SG1 and the position in the stimulus list ( r=-0.0022, 95% CI: -0.017 - 0.014). I added random slopes for each subject for both of these predictors in all of the models, and despite the lack of a correlation in the aggregate, the random effect of sTrial for subjects was a beneficial predictor in all models. The fixed effect of sTrial, though, did not contribute, and was

Table 3.11: Model Comparisons for models predicting SG1 for a trigram. ∆AIC denotes the change in AIC between two models. All random slopes were for for the random effect of subject.

AIC ∆AIC

Relative Model Likelihood Model 1: Random intercepts for Participants and Items, sSG1Len and

random slopes for same

10036

Model 2: Model 1 + random slopes for sTrial 9831 -205 3e+44 Model 3: Model 2 + sPMI and random slopes for same 9818 -14 9e+02 Model 4: Model 3 + PrevTrialDur and random slopes for same 9691 -127 3e+27 Model 5: Model 4 + PC1, PC2, PC3, and PC5 9298 -393 2e+85 Model 6: Model 5 + cc1 9287 -11 3e+02 Model 7: Model 6 + Ngram Freq 9274 -13 7e+02 Model 8: Model 7 + sPMI×cc1 9255 -18 8e+03

dropped during model selection.

Table 3.12: MCMC-based estimates for the coefficients for the fixed effects in the linear mixed effects model fitted to the observed SG1.

Estimatedβ β¯M CM C HPD lower HPD upper pM CM C

Intercept 5.0802 5.0800 4.9636 5.2034 0.001 sPMI 0.0653 0.0649 0.0479 0.0825 0.001 cc1 -0.0395 -0.0390 -0.0587 -0.0187 0.001 n-gram frequency -0.0089 -0.0087 -0.0131 -0.0045 0.001 PC1 -0.0407 -0.0405 -0.0474 -0.0333 0.001 PC2 -0.0167 -0.0166 -0.0255 -0.0085 0.001 PC3 0.0353 0.0353 0.0285 0.0415 0.001 PC5 0.0321 0.0321 0.0228 0.0414 0.001 sSG1Len 0.0978 0.0980 0.0828 0.1164 0.001 PrevTrialDur 0.0780 0.0781 0.0670 0.0899 0.001 sPMI×cc1 -0.0323 -0.0321 -0.0463 -0.0201 0.001

Before adding any fixed effects, I added random subject effects for certain predictors. In this process, I retained four new random slopes for each subject: the effect of the length of the first word (cSG1Len), the effect of the position in the experiment (sTrial), the effect of the trigram’s pointwise mutual infor- mation (sPMI) and the duration of the previous trial (PrevTrialDur). As can be seen from Table 3.11 the addition of these random slopes greatly improved the nested models. I continued to add predictors one by one, but for brevity’s sake, I report a smaller number of models here, grouping similar predictors. In Model 5, I added the first set of fixed effects: the effects of first word length, previous trial duration and closed/open class category of the first word (cc2 and cc3 did not contribute anything). These three predictors improved the

Table 3.13: MCMC-based estimates for the random effects in the linear mixed effects model fitted to the observed SG1.

Standard Dev HPD lower HPD upper Random Intercept: Item 0.069 0.057 0.069 Random Intercept: Subject 0.081 0.021 0.138 Random Slope: sPMI for Subjects 0.021 0.015 0.033 Random Slope: sSG1Len for Subjects 0.037 0.027 0.057 Random Slope: sTrial for Subjects 0.015 0.008 0.025 Random Slope: PrevTrialDur for Subjects 0.011 0.001 0.016

Residual 0.307 0.305 0.312

model, despite the fact there were already random slopes for PrevTrialDur and sSG1Len in the model. Also, the position in the experiment, sTrial, did not improve the model, and so it was left out. The second of the standard predictors to be dropped during the stepwise forward modeling was PC4. In Model 6, PC4 did not contribute to improving the fitness of the model. To help understand this fact, I point to the loading for this principle component, shown in appendix 3.8. PC4 is most strongly correlated with the mean completeness rating. In the context of the first sub-gaze, the lack of a contribution from the completeness of the trigram is sensible, as the participants have not yet seen much of the second or third word. In Model 7 I added only n-gram frequency, PMI and first bigram information content, as all the other information-related predictors did not improve the model fitness. The final model, Model 8, added an interaction between the PMI for the trigram and the class of the first word. This was the best fitting model found, and I will now report the parameter estimates for this model.

In Table 3.12, the estimated coefficients for all of the fixed effects are shown along with the MCMC simulation results. All of the 95% highest posterior density credible intervals did not contain zero, showing that none of the fixed effects were null effects. The partial effects of all of these predictors (except for PC1, PC2, PC3 and PC5) are shown in Figure 3.5. Due to the combination of effects in each of the principle components, I can only report that my model accounted for variability due to the inputs to the PCA: word and bigram frequency, trigram length and completeness. The effect of increasing PMI was an increase in sub-gaze time. When the first word was a closed class word, all

−2 −1 0 1 2 3 4 280 300 320 340 360 380 400 sPMI Sub−g aze 1 (ms) no W

ord 1 is closed class.

yes

Figure 3.5: Partial effect of the interaction between Pointwise Mutual Infor- mation and class of first word in predicting SG1.

other things, including word length, being equal, subgaze time was shorter. Another early effect of a whole n-gram property was found: the first subgaze was shorter for trigrams that were more frequent. The largest of the fixed effects was the length of the first word, with shorter words having a shorter sub-gaze than longer words.

There was also an inter-trial temporal dependency, with a slowdown in the first sub-gaze in trials that were preceded by a slow trial.

The final fixed effect was the interaction between the class of the first word and the PMI of the trigram. For trigrams with high PMI, the trigrams that started with a closed class word had a shorter first word sub-gaze than those that started with an open class word. The sub-gaze times were not influenced by the class of the first word for low-PMI trigrams (Figure 3.5).

The estimated standard deviations for all of the random effects in my model are reported in Table 3.13 along with the 95% highest posterior density credible intervals from the MCMC simulations. All of the standard deviations are will within the 95% HPD intervals.

3.5.8

Discussion

The early impact of probabilistic measures for the whole sequence (n-gram frequency and PMI) show how sensitive the visual system is to the context around words. The amount of information about the second word that is available during the reading time for SG1 is not large, and yet I found whole- trigram effects. The PMI of the trigram influenced the reading time of the first word in the trigram, even after taking into account the frequency and lexical class of the first word. In the same way, a trigram with a greater frequency had a faster reading time of the first word than one with a lower frequency. These results imply that coherence, entrenchment and predictability of the trigram have a very early influence on the reading of the trigram.

The interaction between cc1 and PMI implies a very early interaction be- tween lexical class and coherence. N-grams with open class words in the first position had a larger slowdown due to PMI than n-grams with closed class words in the first position. As with the fixation data, the coherency of tri-

grams made the readers proceed with caution.

I now move on to the final dependent measure, the second sub-gaze, SG2.