El mundo del vino en Castilla y León y sus Denominaciones de Origen

The existence of regressive saccades (both intra-word and inter-word) within a trial was another outcome I examined. Regressive saccades occur when the first pass at reading does not give sufficient information to the reader (Vitu & McConkie, 2000). The location of the beginning and end point of the regressive saccade are also interesting to analyze. Probabilistic information about then- grams might be able to help predict the location of the regressive saccade, but due to the complexity of the analysis, it was not attempted. Would my measures of probability and information content be predictive of the existence of regressive saccades? As with my analysis of reading duration, I proceeded with a similar forward stepwise model selection analysis, attempting to add all of my predictors to increasingly complex models. The dependent measure was a binary variable that I set to 1 if there were one or more regressive saccades in a trial. Most of the trials (74.9%) contained no regressive saccades, 21.6% contained one, 3.1% contained two, 0.4% contained three and 0.1% contained four, meaning that 25.1% of the trials had one or more saccades.

Since the outcome is binary in nature (no regressive saccades vs. one or more regressive saccades), I proceeded to use logistic GAMs with a logit link function instead of the Gaussian type. I also included a random intercept for each subject in all of the models, but did not include random intercepts for each item as this did not improve the fitness of any of the models.

To begin the stepwise forward model selection, I built a base GAM model, Model 1, using only the parametric model elements (PC1-PC5, cc1-cc3, sTrial

Table 3.5: Model Comparisons for models predicting probability of one or more regressive saccades in a trial. ∆AIC denotes the change in AIC between two models.

AIC ∆AIC

Relative Model Likelihood Model 1: Random intercepts for participant, PC1-PC5, cc3, sTrial

and Previous Trial Regressive Saccade

17363

Model 2: Model 1 +n-gram frequency⊗sTIC 17342 -21 4e+04 Model 3: Model 2 + sPMI⊗sTIC 17268 -74 1e+16

and Previous Trial Regressive Saccade) and the random intercepts for each subject. I then added interactions of interest one by one, and only retained models that were superior to a simpler model when a Log Likelihood Ratio Test (LLRT) was performed. A listing of all these nested models and their AIC measure of model fitness is shown in Table 3.5. After each new term is added, I report the relative model likelihood of each model when compared to the previous model. Each of the non-linear interactions added caused the new model to be over 100 times more likely than the previous model, confirming the relevance of all of the interactions to improving the final model. Model 2 added the non-linear interaction of trigram frequency and total information content to Model 1. Finally, Model 3 added the non-linear interaction of pointwise mutual information and total information content to Model 2. First I will explain the parametric effects of the predictors shown in Table 3.6, and then move on to the non-linear interactions listed in Table 3.7.

Each of the principal components made a contribution, accounting for the effects of unigram frequencies, bigram frequencies, length and completeness. The effect of having a closed class word in the first or second positions increased the probability of making a regressive saccade, whereas having a closed class word in the third position was inhibitory for regressive saccades. There was also a decrease in the probability of making a regressive saccade as participants progressed in the experiment, likely a practice effect. There was an increase in the probability of making a regressive saccade when a participant made one or more regressive saccades on the immediately preceding trial, an inter-

−8 −6 −4 −2 0 2 −3 −2 −1 0 1 2 3

A

Log Ngram Frequency sTIC 0.16 0.16 0.18 0.18 0.2 0.22 0.22 0.24 _0.26 −2 −1 0 1 2 3 4 −3 −2 −1 0 1 2 3

B

sPMI sTIC 0.1 0.15 0.15 0.2 0.2 0.25 0.3 0.35 0.4

Figure 3.3: Partial effects on the probability of a regressive saccade during a trial for A) Interaction between n-gram frequency and sTIC. B) Interaction between sPMI and sTIC. The dependent measure was transformed from logits to probabilities before plotting.

¯ β SE(β) z p|z| Intercept -1.453 0.194 -7.48 7.7e-14 PC1 0.138 0.025 5.62 1.9e-08 PC2 0.134 0.026 5.17 2.4e-07 PC3 -0.091 0.020 -4.54 5.7e-06 PC4 -0.195 0.025 -7.78 7.2e-15 PC5 0.263 0.029 8.93 4.1e-19 cc1 0.239 0.061 3.92 8.8e-05 cc2 0.388 0.062 6.22 5e-10 cc3 -0.485 0.062 -7.80 6.2e-15 sTrial -0.369 0.020 -18.93 7e-80

Regr Sacc on Prev Trial 0.238 0.043 5.58 2.4e-08

Table 3.6: Model Coefficients for linear predictors in Regressive Saccade probability GAM

trial spillover effect. The predictors related to the probabilistic measures for the wholen-gram frequency and information content were only predictive when entered into non-linear interactions. The first interaction that was added to the base model was an interaction between n-gram frequency and TIC. Visualized in Figure 3.3A, this surface has a peak in regressive saccade probability when the sTIC is high (between 0 and 3), with a peak for trigrams that have a log frequency of around -2. The probability of a regressive saccade was lower for very low frequency words (log frequency ≤-6) across the range of TIC values.

Estimated Df Estimated Residual Df

F pbayseian

N-gram Frequency⊗sTIC 6.01 7.37 64.34 3.2e-11 sTIC⊗sPMI 7.78 10.25 78.72 1.2e-12 Random Intercept for Subject 17.79 18.00 1331.96 5.7e-272

Table 3.7: Regressive Saccade Model Parameters for smooth predictors in the GAM

The next non-linear interaction detected was between PMI and TIC. This surface, shown in Figure 3.3B, has a peak probability when sTIC is less than -2 and the sPMI is below -1. When sPMI is between -0.5 and -2, the probability falls for all values of sTIC. Less cohesive trigrams that are less predictable induced regressive saccades more often than other trigrams.

3.5.4

Discussion

Again, as I saw with the total duration analysis, TIC had an interactive re- lationship with PMI. Unlike in the total duration analysis though, TIC did interact with frequency in the best model of predicting regressive saccades. In- teractive relationships trumped simple relationships during my stepwise mod- elling and frequency, PMI and TIC were both involved. N-grams with a higher TIC and a medium or high frequency were more likely to cause regressive sac- cades. The familiar n-grams with higher average surprisal may have forced a reassessment of the stimulus. Low PMI generally increased the likelihood of a regressive saccade, with a small modulation based on the TIC.

How good is my model at discriminating the observed existence of saccades using the model’s predictions? The Somers’ Dxy Rank Correlation for my model is 0.5, 95% CI: 0.49 - 0.52 and the ROC-AUC (Receiver Operating Characteristic - Area Under Curve) is 0.75, 95% CI: 0.74 - 0.76, a fair level of discrimination.

The next dependent measure I will analyze is the total number of fixations in each trial.

In document La mujer rural en el mundo del vino Itinerarios formativo laborales a partir de un análisis en las bodegas adscritas a las D O Ribera del Duero y Rueda (página 48-55)