Looking back in L2 text production

1 Brief summary

This analysis is addressing on to what extent writing L2 is associated with more re-reading to previously written text (without revisions) than in text production in L1. In other words, the analysis of lookbacks will focus on transitions that do not involve text editing. This is because it is less clear why people look back in the text without editing (i.e. if it is not to correct an error); this could be happening to refreshing the memory of previously written text, used words, checking for coherence, etc. However, all statistical models included data from both editing and non-editing events; the results for lookbacks with text revision can be found in the appendix.

Findings:

For L2 …

  • Text data:
    • L2 writers produce less text but edit as much as L1 writers.
    • Shorter writing sequences without editing interruption.
    • Fewer transitions that are not terminated by an editing operation (i.e. shorter texts) but about as many transitions as in L1 that are terminated by an editing operation.
    • Higher probability that a transition is terminated by an editing operation.
  • Eye data: (transitions without editing)
    • Possible interpretation: lookbacks in L2 do not show evidence of more / sustained rereading of the produced text but show evidence of uncertainty what to say next; i.e. more frequent lookbacks with more fixations but fewer long fixations in spite of longer transition durations.
    • More looks back into already-produced text for before and within-word transitions but not for before sentence transitions; more fixations for before-sentence transitions.
    • For before-sentence transitions, larger lookback probability for short transitions but lower probability (than in L1) for long transitions.
    • Lower probability of long lookback fixations during before-sentence transitions but no fixation-duration difference otherwise.
    • Yet, transition duration of lookbacks is longer.

2 Data analysis

All data were analysed in Bayesian mixed-effects models using the R package brms (Bürkner, 2017b, 2017a) and the probabilistic programming language Stan (Carpenter et al., 2016; Hoffman & Gelman, 2014). All models were fitted with random intercepts for participants and by-participant slope adjustments for Language (text written in L1 or L2). As predictors we used combinations of Language (levels: L1, L2), Transitions location (levels: before sentence, before word, within word), Lookback (levels: lookback, no lookback), Edit (levels: editing, no editing) and their interactions. Edit and Lookback will be used as predictor variables in some analysis; yet both are observed and will be analysed separately.

We report the most probable posterior (i.e. inferred) parameter value \(\beta\) as well as the interval around \(\beta\) that contains 95% of the posterior probability mass; 95% probability intervals (henceforth, PI).

We calculated the statistical support for the effects of interest and the support for the alternative hypothesis over the null hypothesis. This evidence was obtained using Bayes Factors (henceforth, BF\(_{10}\)) calculated using the Savage-Dickey method (see, e.g., Dickey et al., 1970; Wagenmakers et al., 2010). A BF\(_{10}\) larger than 5 indicate moderate and larger than 10 strong evidence for a statistically meaningful effect compared to the null hypothesis (see, e.g., Baguley, 2012; Jeffreys, 1961; Lee & Wagenmakers, 2014). For example BF\(_{10}\)=2 reflect that the alternative hypothesis is two times more likely than the null hypothesis given the evidence. Priors for all effects were normal distributed centered around 0 with a standard deviation of 1. We used these weakly informative priors favoring the null hypothesis over the alternative hypothesis for the slope parameters because BFs are sensitive to the distribution of the prior. Thus, our priors are not favoring the alternative hypothesis.

Transition duration and total-fixation duration were analysed in mixture models as described in Roeser et al. (2021). This is important for both variables to distinguish between relatively normal durations and those that results from processing difficulty are higher levels of activation. For the fixation duration this is related to different types of activities such as re-reading of a single word to refresh the writer’s memory and more demanding events such as reading entire sentences to ensure text coherence. For transition durations we must distinguish between normal transition durations associated with a smooth flow of activation from higher levels of activation into finger movements and transitions that were inhibited by, for example, difficulty to retrieve correct spelling or the right word. Rather than imposing threshold values to distinguish between simple and more demanding events, mixture models model the data as a combination of two processes using a mixing weight to capture the probability of processing difficulty occurring. The random-effects structure of the mixture models is identical to the mixed-effects models. In addition, mixture models included by-participant mixing proportions allowing to capture individual differences in typing style (Roeser et al., 2021).

Distributions used for all other outcome variables are indicated below.

3 Text data

3.1 Sample

Data come from 39 participants of which each produced a text in their L1 (English) or their L2 (Spanish).

Table 3.1: Total number of events for analysis by language.
Participant id L1 L2
1 2938 2103
2 3541 2027
3 2041 984
4 2360 1973
5 4007 2009
6 721 858
7 1988 1164
8 2477 1394
9 2523 1037
10 3572 1956
11 3141 1310
12 5561 1783
13 3412 2255
14 3265 1692
15 3549 1111
16 3594 1496
17 3722 2553
18 1581 1266
19 5245 2591
20 3042 2266
21 2771 1627
22 2959 2467
23 6165 3661
24 2116 1107
25 5901 2095
26 3520 1228
27 6022 4520
28 4366 2315
29 3202 2021
30 5227 3359
31 4807 3316
32 2257 1606
33 2853 807
34 3701 1088
35 4291 2782
36 7241 2790
37 4467 1177
38 2386 1957
39 1527 946

3.2 Length of production sequence

#source("../scripts/brms_production_sequence.R)
# Load posterior
fit <- readRDS(file = "../stanout/production_sequence.rda")
fit$formula
pseq_len ~ 0 + Lang + (Lang | SubNo)

Lang is Language (levels: L1, L2) and pseq_len is the length of a sequence of keystrokes without (before) editing. The difference between L1 and L2 was calculated from the posterior.

fit$family

Family: negbinomial 
Link function: log

There was strong evidence for longer production sequences (log \(\hat\beta_{\text{diff}}=\) 0.43 [0.36 – 0.51], \(BF_{10}\) > 100) when writing in L1 (\(\hat\beta=\) 21.5, PI = [19.2 – 23.9]) than in L2 (\(\hat\beta=\) 13.9, PI = [12.7 – 15.3]).

3.3 Editing frequency

# Run model
#source("../scripts/brms_editing_frequency_simple.R")

# Load model posterior
fit <- readRDS(file = "../stanout/editing_frequency.rda")
fit$formula
edits | trials(total) ~ 1 + condition + (Lang | SubNo)

condition was coded with main effects of Language (levels: L1, L2), Transition location 1 (levels: before sentence, before word), Transition location 2 (levels: before word / sentence, within word) and all two and three-way interactions by-Transition location (i.e. no interactions that involve both Transition location 1 and Transition location 2). An analysis of editing frequency separated by Lookbacks can be found in the appendix.

fit$family

Family: binomial 
Link function: logit
Table 3.2: Editing frequency effects on logit scale.
Predictor Estimate with 95% PI \(BF_{10}\)
Main effects
Language (L1, L2) -1.63 [-1.94 – -1.31] > 100
Location 1 (before sentence, before word) 1.53 [1.31 – 1.75] > 100
Location 2 (before word / sentence, within word) 3.65 [3.42 – 3.89] > 100
Two-way interactions
Language : Location 1 0.03 [-0.19 – 0.25] 0.12
Language : Location 2 -0.41 [-0.64 – -0.18] 40.39
Note:
Colon indicates interactions. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis
\label{fig:editingfig1}Estimated cell means for editing frequency with 95\% PIs (probability intervals).

Figure 3.1: Estimated cell means for editing frequency with 95% PIs (probability intervals).

Table 3.3: Editing frequency. Cell means for L1 and L2 in proportion and language difference on logit scale both shown with 95% PIs in brackets.
Transition location L1 L2 Language effect \(BF_{10}\)
within word 0.05 [0.04 – 0.06] 0.07 [0.07 – 0.08] -0.41 [-0.5, -0.32] >100
before word 0.07 [0.06 – 0.08] 0.13 [0.12 – 0.14] -0.64 [-0.74, -0.54] >100
before sentence 0.15 [0.12 – 0.17] 0.24 [0.21 – 0.27] -0.62 [-0.85, -0.4] >100
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

3.4 Number of transitions

# Run model
#source("../scripts/brms_transition_counts.R")
# Load model posterior
fit <- readRDS(file = "../stanout/transition_counts.rda")
fit$formula
n_transitions ~ 1 + condition + (Lang | SubNo)

condition was coded with main effects of Language (levels: L1, L2), Edit (levels: editing, no editing), Transition location 1 (levels: before sentence, before word), Transition location 2 (levels: before word / sentence, within word) and all two and three-way interactions by-Transition location (i.e. no interactions that involve both Transition location 1 and Transition location 2). An analysis of transition counts separated by Lookback can be found in the appendix.

fit$family

Family: negbinomial 
Link function: log

In addition we fitted a binomial model to account for the overall number of transitions by participant and language.

# Run model
#source("../scripts/brms_transition_binomial.R")
# Load model posterior
fit_binom <- readRDS(file = "../stanout/transition_binomial.rda")
fit_binom$formula
n_transitions | trials(total) ~ condition + (Lang | SubNo) 
fit_binom$family

Family: binomial 
Link function: logit
Table 3.4: Transition-count coefficients.
log number of transitions
logit prop. of transitions
Predictor Estimate with 95% PI \(BF_{10}\) Estimate with 95% PI \(BF_{10}\)
Main effects
Language (L1, L2) 1.84 [1.18 – 2.48] > 100 -1.53 [-1.73 – -1.32] > 100
Location 1 (before sentence, before word) -9.76 [-10.09 – -9.44] > 100 -10.38 [-10.59 – -10.18] > 100
Location 2 (before word / sentence, within word) -18.36 [-18.83 – -17.87] > 100 -24.28 [-24.5 – -24.06] > 100
Edit (edit, no edit) -12.18 [-12.54 – -11.81] > 100 -15.27 [-15.48 – -15.06] > 100
Two-way interactions
Language : Location 1 -0.56 [-0.88 – -0.24] 52.03 -0.54 [-0.75 – -0.34] > 100
Language : Location 2 -0.5 [-0.94 – -0.05] 2.39 -0.47 [-0.7 – -0.26] > 100
Language : Edit -1.54 [-1.9 – -1.18] > 100 -1.59 [-1.79 – -1.38] > 100
Location 1 : Edit 1.86 [1.54 – 2.18] > 100 2.18 [1.98 – 2.39] > 100
Location 2 : Edit 3.88 [3.42 – 4.33] > 100 8.81 [8.59 – 9.03] > 100
Three-way interactions
Location 1 : Edit : Language 0.09 [-0.23 – 0.41] 0.19 0.13 [-0.07 – 0.33] 0.23
Location 2 : Edit : Language -0.36 [-0.82 – 0.09] 0.78 -0.31 [-0.53 – -0.09] 4.81
Note:
Colon indicates interactions. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis
\label{fig:transfig}Estimated cell means for transition counts with 95\% PIs (probability intervals).

Figure 3.2: Estimated cell means for transition counts with 95% PIs (probability intervals).

Table 3.5: Transition counts and percentages. Cell means for L1 and L2 as counts and percentages, and their respective language differences on log scale. 95% PIs in brackets.
Number of transitions
% transitions
Transition location L1 L2 Language effect \(BF_{10}\) L1 L2 Language effect \(BF_{10}\)
Editing
within word 128 [108 – 152] 102 [87 – 120] 0.23 [0.07 – 0.38] 4.38 4.1 [3.9 – 4.2] 5.9 [5.7 – 6] -0.39 [-0.43 – -0.35] > 100
before word 49 [42 – 59] 44 [37 – 52] 0.12 [-0.05 – 0.28] 0.23 1.6 [1.5 – 1.6] 2.5 [2.4 – 2.6] -0.48 [-0.54 – -0.42] > 100
before sentence 5 [4 – 6] 6 [5 – 7] -0.15 [-0.39 – 0.1] 0.25 0.2 [0.1 – 0.2] 0.3 [0.3 – 0.4] -0.73 [-0.92 – -0.55] > 100
Writing
within word 2,428 [2,054 – 2,865] 1,302 [1,115 – 1,522] 0.62 [0.47 – 0.77] > 100 74 [74 – 75] 74 [73 – 74] 0.04 [0.01 – 0.06] 2.72
before word 624 [528 – 738] 294 [251 – 343] 0.75 [0.61 – 0.9] > 100 19 [19 – 19] 17 [16 – 17] 0.16 [0.14 – 0.19] > 100
before sentence 27 [23 – 33] 18 [15 – 21] 0.44 [0.26 – 0.62] > 100 0.8 [0.8 – 0.9] 1 [0.9 – 1.1] -0.16 [-0.25 – -0.07] 10.58
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

3.5 Productivity

Text length was analysed using a binomial model as a function for the number of text elements in the final production over the number of transitions during the process.

# Run model
#source("../scripts/brms_textlength_binomial.R")
# Load model posterior
fit <- readRDS(file = "../stanout/textlength_binomial.rda")
fit$formula
N_product | trials(N_transitions) ~ condition + (lang | subno)

condition was coded with main effects of Language (levels: L1, L2), Transition location 1 (levels: before sentence, before word), Transition location 2 (levels: before word / sentence, within word) and both two-way interactions.

fit$family

Family: binomial 
Link function: logit
Table 3.6: Text-length coefficients as a function of transitions in logit probability indicating productivity.
Predictor Estimate with 95% PI \(BF_{10}\)
Main effects
Language (L1, L2) 0.3 [-0.19 – 0.79] 0.19
Location 1 (before sentence, before word) -2.03 [-2.2 – -1.85] > 100
Location 2 (before word / sentence, within word) -0.98 [-1.16 – -0.8] > 100
Two-way interactions
Language : Location 1 0.01 [-0.16 – 0.18] 0.03
Language : Location 2 0.09 [-0.09 – 0.27] 0.05
Note:
Colon indicates interactions. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis
\label{fig:transfig}Estimated cell means for writing productivity measured as textlength over number of transitions with 95\% PIs (probability intervals).

Figure 3.3: Estimated cell means for writing productivity measured as textlength over number of transitions with 95% PIs (probability intervals).

Table 3.7: Text productivity estimates and language effect. Cell means for L1 and L2 as proportion, and their respective language differences on log scale. 95% PIs in brackets.
Text element L1 L2 Language effect \(BF_{10}\)
before sentence 0.71 [0.66 – 0.76] 0.69 [0.63 – 0.74] 0.12 [-0.1 – 0.34] 0.2
before word 0.87 [0.85 – 0.9] 0.86 [0.83 – 0.88] 0.11 [-0.05 – 0.27] 0.21
within word 0.84 [0.81 – 0.87] 0.83 [0.8 – 0.86] 0.07 [-0.08 – 0.23] 0.12
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

4 Lookback during writing

4.1 Lookback probability

4.1.1 Lookback probability

# Run model
#source("../scripts/brms_lookback.R")

# Load posterior
fit <- readRDS("../stanout/lookback.rda")
fit$formula
lookbacks | trials(total) ~ 1 + condition + (Lang | SubNo)

condition was coded with main effects of Language (levels: L1, L2), Edit (levels: editing, no editing), Transition location 1 (levels: before sentence, before word), Transition location 2 (levels: before word / sentence, within word) and all two and three-way interactions by-Transition location (i.e. no interactions that involve both Transition location 1 and Transition location 2).

fit$family

Family: binomial 
Link function: logit
Table 4.1: Lookback probability on logit scale.
Predictor Estimate with 95% PI \(BF_{10}\)
Main effects
Language (L1, L2) -1.96 [-2.87 – -0.98] > 100
Location 1 (before sentence, before word) 6.32 [5.87 – 6.77] > 100
Location 2 (before word / sentence, within word) 20.95 [20.35 – 21.56] > 100
Edit (edit, no edit) 8.95 [8.45 – 9.45] > 100
Two-way interactions
Language : Location 1 0.87 [0.42 – 1.32] > 100
Language : Location 2 0.84 [0.24 – 1.45] 12.66
Language : Edit 1.37 [0.87 – 1.86] > 100
Location 1 : Edit -1.6 [-2.05 – -1.15] > 100
Location 2 : Edit -7.31 [-7.92 – -6.71] > 100
Three-way interactions
Location 1 : Edit : Language -0.63 [-1.08 – -0.18] 8.5
Location 2 : Edit : Language -0.79 [-1.4 – -0.19] 8.08
Note:
Colon indicates interactions. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis
\label{fig:lookbackfig}Estimated cell means for lookback probability with 95\% PIs (probability intervals).

Figure 4.1: Estimated cell means for lookback probability with 95% PIs (probability intervals).

Table 4.2: Lookback probability. Cell means for L1 and L2 are proportions, and language difference on logit scale. 95% PIs in brackets.
Transition location L1 L2 Language effect \(BF_{10}\)
Editing
within word 0.056 [0.047 – 0.067] 0.066 [0.054 – 0.082] -0.18 [-0.41, 0.04] 0.41
before word 0.166 [0.142 – 0.194] 0.202 [0.169 – 0.24] -0.24 [-0.46, -0.01] 1.01
before sentence 0.531 [0.451 – 0.609] 0.546 [0.465 – 0.625] -0.06 [-0.48, 0.36] 0.22
Writing
within word 0.002 [0.002 – 0.003] 0.006 [0.005 – 0.008] -1 [-1.22, -0.78] > 100
before word 0.037 [0.031 – 0.043] 0.084 [0.07 – 0.1] -0.88 [-1.05, -0.7] > 100
before sentence 0.31 [0.27 – 0.353] 0.35 [0.297 – 0.407] -0.18 [-0.44, 0.07] 0.35
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

4.1.2 Lookback as function of transition duration

# Run model
#source("../scripts/brms_lookback_with_transdur.R")

# Load posterior
fit <- readRDS("../stanout/lookback_with_transdur.rda")
fit$formula
lookbacks | trials(total) ~ 1 + condition * log_transition_dur_ctr + (Lang | SubNo)

condition was coded with main effects of Language (levels: L1, L2), Edit (levels: editing, no editing), Transition location 1 (levels: before sentence, before word), Transition location 2 (levels: before word/ sentence, within word) and all two and three-way interactions by-Transition location (i.e. no interactions that involve both Transition location 1 and Transition location 2). All categorical predictors were sum-coded. Transition duration was log transformed and centred.

fit$family

Family: binomial 
Link function: logit
Table 4.3: Lookback probability with transition duration adjustment on logit scale.
Predictor Estimate with 95% PI \(BF_{10}\)
Main effects
Language (L1, L2) -2.49 [-3.63 – -1.29] > 100
Location 1 (before sentence, before word) 9.03 [8.46 – 9.6] > 100
Location 2 (before word / sentence, within word) 21.91 [21.12 – 22.69] > 100
Edit (edit, no edit) 12.43 [11.8 – 13.06] > 100
Two-way interactions
Language : Location 1 1.54 [0.97 – 2.11] > 100
Language : Location 2 -0.1 [-0.89 – 0.68] 0.42
Language : Edit 1.9 [1.28 – 2.54] > 100
Location 1 : Edit -2.98 [-3.54 – -2.41] > 100
Location 2 : Edit -8.38 [-9.17 – -7.59] > 100
Three-way interactions
Location 1 : Edit : Language -0.94 [-1.51 – -0.38] 50.41
Location 2 : Edit : Language 0.07 [-0.71 – 0.84] 0.4
Transition duration (log’ed, centred)
Transition duration 1.55 [1.5 – 1.6] > 100
Language (L1, L2) : Transition duration 2.42 [1.82 – 3.03] > 100
Location 1 : Transition duration -2.27 [-2.82 – -1.7] > 100
Location 2 : Transition duration -1.7 [-2.4 – -1] > 100
Edit : Transition duration -2.21 [-2.8 – -1.61] > 100
Language : Location 1 : Transition duration -0.52 [-1.08 – 0.03] 1.6
Language : Location 2 : Transition duration 0.36 [-0.35 – 1.08] 0.59
Language : Edit : Transition duration -0.6 [-1.2 – -0.01] 2.09
Location 1 : Edit : Transition duration 0.42 [-0.13 – 0.97] 0.85
Location 2 : Edit : Transition duration 3.19 [2.5 – 3.9] > 100
Location 1 : Edit : Language : Transition duration -0.41 [-0.98 – 0.14] 0.8
Location 2 : Edit : Language : Transition duration -0.29 [-1 – 0.41] 0.51
Note:
Colon indicates interactions. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis
\label{fig:fixbackfigwriting}Writing data. Estimated lookback probabilities over transition duration with 95\% PIs (probability intervals).

Figure 4.2: Writing data. Estimated lookback probabilities over transition duration with 95% PIs (probability intervals).

\label{fig:fixbackfigediting}Editing data. Estimated lookback probabilities over transition duration with 95\% PIs (probability intervals).

Figure 4.3: Editing data. Estimated lookback probabilities over transition duration with 95% PIs (probability intervals).

Table 4.4: Lookback probability (after accounting for transition duration). Cell means for L1 and L2 are shown as proportions, and language difference are on logit scale. 95% PIs in brackets.
Transition location L1 L2 Language effect \(BF_{10}\)
Editing
within word 0.055 [0.039 – 0.085] 0.078 [0.052 – 0.13] -0.36 [-0.69, -0.05] 2.4
before word 0.145 [0.105 – 0.214] 0.218 [0.153 – 0.33] -0.5 [-0.84, -0.17] 15.04
before sentence 0.644 [0.539 – 0.76] 0.671 [0.557 – 0.796] -0.12 [-0.63, 0.38] 0.29
Writing
within word 0.001 [0 – 0.001] 0.002 [0.001 – 0.004] -1.21 [-1.61, -0.82] > 100
before word 0.01 [0.007 – 0.016] 0.052 [0.034 – 0.087] -1.68 [-2, -1.38] > 100
before sentence 0.32 [0.247 – 0.432] 0.424 [0.325 – 0.571] -0.45 [-0.81, -0.11] 4.95
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

4.2 Number of fixation during lookback

# Run model
#source("../scripts/brms_number_fixations_lookback.R")

# Load posterior
fit <- readRDS("../stanout/number_fixations_lookback.rda")
fit$formula
n_fixes ~ 1 + condition + (Lang | SubNo)

condition was coded with main effects of Language (levels: L1, L2), Edit (levels: editing, no editing), Transition location 1 (levels: before sentence, before word), Transition location 2 (levels: before word / sentence, within word) and all two and three-way interactions by-Transition location (i.e. no interactions that involve both Transition location 1 and Transition location 2).

fit$family

Family: negbinomial 
Link function: log
Table 4.5: Number of fixations during lookback on log scale.
Predictor Estimate with 95% PI \(BF_{10}\)
Main effects
Language (L1, L2) -0.7 [-1.2 – -0.19] 8.76
Location 1 (before sentence, before word) 3.39 [3.12 – 3.66] > 100
Location 2 (before word / sentence, within word) 7.71 [7.21 – 8.2] > 100
Edit (edit, no edit) 1.3 [0.97 – 1.64] > 100
Two-way interactions
Language : Location 1 -0.19 [-0.46 – 0.07] 0.35
Language : Location 2 -0.28 [-0.76 – 0.21] 0.46
Language : Edit 0.04 [-0.3 – 0.38] 0.17
Location 1 : Edit 0.41 [0.15 – 0.68] 14.44
Location 2 : Edit -0.43 [-0.91 – 0.05] 1.08
Three-way interactions
Location 1 : Edit : Language 0 [-0.26 – 0.27] 0.13
Location 2 : Edit : Language -0.11 [-0.6 – 0.38] 0.27
Note:
Colon indicates interactions. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis
\label{fig:fixbackfig}Estimated cell means for number of fixations during lookback with 95\% PIs (probability intervals).

Figure 4.4: Estimated cell means for number of fixations during lookback with 95% PIs (probability intervals).

Table 4.6: Number of fixations during lookback. Cell means for L1 and L2 as counts, and language difference on log scale. 95% PIs in brackets.
Transition location L1 L2 Language effect \(BF_{10}\)
Editing
within word 3.65 [3.25 – 4.11] 3.82 [3.34 – 4.38] -0.05 [-0.2 – 0.11] 0.09
before word 5.5 [4.94 – 6.12] 6.05 [5.34 – 6.84] -0.1 [-0.24 – 0.03] 0.21
before sentence 13.58 [11.65 – 15.86] 16.42 [14 – 19.3] -0.2 [-0.41 – 0.01] 0.56
Writing
within word 2.67 [2.33 – 3.06] 2.94 [2.57 – 3.35] -0.12 [-0.29 – 0.05] 0.24
before word 5.11 [4.69 – 5.56] 5.58 [5.02 – 6.2] -0.09 [-0.19 – 0.01] 0.29
before sentence 10.24 [9.23 – 11.36] 12.34 [10.79 – 14.1] -0.2 [-0.35 – -0.06] 3.72
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

4.3 Total-fixation duration of lookback

Table 4.7: Mixture model results of the total-fixation duration with the predictor estimates for the distribution of short and long fixations (on log scale) and the probability of long fixations (on logit scale). Estimates are shown with 95% PI.
Short fixations
Slowdow for long fixations
Probability of long fixations
Predictor Estimate \(BF_{10}\) Estimate \(BF_{10}\) Estimate \(BF_{10}\)
Main effects
Language (L1, L2) -0.06 [-0.17 – 0.02] 0.09 -0.08 [-0.27 – 0.12] 0.14 -0.5 [-1.48 – 0.2] 0.76
Location 1 (before sentence, before word) -0.01 [-0.12 – 0.12] 0.05 0.49 [0.3 – 0.68] > 100 1.83 [1 – 3.03] > 100
Location 2 (before word / sentence, within word) 0.03 [-0.04 – 0.12] 0.04 0.59 [0.31 – 0.82] 73.42 2.27 [1.39 – 3.57] > 100
Edit (edit, no edit) 0.08 [0 – 0.19] 0.16 0.11 [-0.09 – 0.29] 0.19 0.86 [0.16 – 1.86] 6.2
Two-way interactions
Language : Location 1 0.09 [-0.11 – 0.33] 0.13 0.05 [-0.32 – 0.42] 0.19 -1.67 [-3.75 – -0.06] 6.67
Language : Location 2 -0.02 [-0.17 – 0.11] 0.07 -0.17 [-0.65 – 0.3] 0.32 0.97 [-0.75 – 2.51] 2.03
Language : Edit 0 [-0.16 – 0.16] 0.07 0.01 [-0.37 – 0.4] 0.18 -0.04 [-1.5 – 1.3] 0.67
Location 1 : Edit 0.15 [-0.05 – 0.43] 0.21 0.09 [-0.29 – 0.45] 0.21 1.72 [0.11 – 3.82] 6.79
Location 2 : Edit 0.17 [0.01 – 0.36] 0.42 0.28 [-0.23 – 0.72] 0.52 1.72 [0.18 – 3.9] 8.48
Three-way interactions
Location 1 : Edit : Language 0.19 [-0.23 – 0.66] 0.26 0.1 [-0.64 – 0.84] 0.38 -3.35 [-7.5 – -0.13] 13.34
Location 2 : Edit : Language 0.05 [-0.23 – 0.34] 0.14 0.35 [-0.61 – 1.3] 0.63 -1.94 [-5.01 – 1.5] 4.04
Note:
Colon indicates interactions. PI is the probability interval. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.
Estimated cell means of total-fixation durations during lookbacks with 95\% PIs (probability intervals). Shown are the estimates for each mixture components (short and long fixations) and the probability of long fixations

Figure 4.5: Estimated cell means of total-fixation durations during lookbacks with 95% PIs (probability intervals). Shown are the estimates for each mixture components (short and long fixations) and the probability of long fixations

Table 4.8: Total-fixation duration of lookbacks. Cell means for L1 and L2 with values in msecs for durations and proportion for probability of long fixations. Language difference are shown on log scale (for fixation durations) and logit scale for probability of long fixations. 95% PIs in brackets.
Editing Transition location L1 L2 Language effect \(BF_{10}\)
Short fixations
Editing before sentence 880 [711 – 1,111] 900 [691 – 1,233] -0.02 [-0.36 – 0.28] 0.11
before word 877 [752 – 1,025] 967 [824 – 1,128] -0.1 [-0.29 – 0.06] 0.13
within word 856 [738 – 989] 915 [800 – 1,043] -0.07 [-0.23 – 0.08] 0.1
Writing before sentence 850 [717 – 1,022] 850 [704 – 1,024] 0 [-0.22 – 0.22] 0.09
before word 784 [691 – 891] 872 [760 – 1,005] -0.11 [-0.26 – 0.03] 0.16
within word 772 [664 – 884] 843 [754 – 938] -0.09 [-0.24 – 0.04] 0.12
Slowdown for long fixations
Editing before sentence 3,157 [2,040 – 4,543] 3,435 [2,539 – 4,519] -0.06 [-0.5 – 0.39] 0.23
before word 1,216 [748 – 1,854] 1,426 [900 – 2,261] -0.03 [-0.41 – 0.32] 0.18
within word 797 [334 – 1,668] 1,159 [509 – 2,406] -0.15 [-0.7 – 0.37] 0.3
Writing before sentence 2,492 [1,682 – 3,505] 2,269 [1,628 – 3,179] 0.07 [-0.29 – 0.42] 0.2
before word 1,327 [895 – 2,068] 1,606 [1,108 – 2,312] -0.06 [-0.34 – 0.24] 0.16
within word 380 [16 – 1,350] 749 [196 – 1,997] -0.24 [-0.95 – 0.51] 0.46
Probability of long fixations
Editing before sentence 0.81 [0.61 – 0.97] 0.95 [0.86 – 1] -1.91 [-4.91 – 0.37] 4.8
before word 0.64 [0.41 – 0.84] 0.58 [0.37 – 0.76] 0.26 [-0.95 – 1.59] 0.67
within word 0.36 [0.1 – 0.62] 0.31 [0.12 – 0.53] 0.21 [-1.39 – 1.74] 0.79
Writing before sentence 0.67 [0.48 – 0.84] 0.88 [0.73 – 0.98] -1.41 [-3.09 – 0.04] 4.27
before word 0.44 [0.27 – 0.59] 0.49 [0.32 – 0.66] -0.23 [-1.19 – 0.73] 0.55
within word 0.22 [0.01 – 0.49] 0.17 [0.05 – 0.33] 0.09 [-2.76 – 2.02] 1.04
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

Model comparisons between the mixture model and a unimodal unequal variance linear mixed effects model.

Table 4.9: Predictive performance was estimated as the expected log predictive density (\(\widehat{elpd}\)) Vehtari et al. (2017). A negative difference \(\Delta\widehat{elpd}\) denotes lower predictive performance compared to the model with the highest predictive performance (top row). Standard error is shown in parentheses.
Model \(\Delta\widehat{elpd}\) \(\widehat{elpd}\)
Mixture model 0 (0) -41,652 (99)
LMM (unequal variance) -157 (18) -41,809 (100)
Note. LMM = linear mixed-effects model.

4.4 Transition duration of lookback

# Stan code for mixture model
# readLines("../stan/mogrslopes.stan")

# Run model
# source("../scripts/mogrslopes_totalfixdur_lookback.R")

# Load posterior
ps <- read_csv("../stanout/transdur_lookback_posterior.csv")
Table 4.10: Mixture model results of the transition duration of lookback transitions with predictor estimates for the distribution of short and long transitions (on log scale) and the probability of long transitions (on logit scale). Estimates are shown with 95% PI.
Short transitions
Slowdown for long transitions
Probability of long transitions
Predictor Estimate \(BF_{10}\) Estimate \(BF_{10}\) Estimate \(BF_{10}\)
Main effects
Language (L1, L2) -0.24 [-0.36 – -0.11] 14.89 -0.08 [-0.31 – 0.13] 0.13 0.09 [-0.42 – 0.71] 0.05
Location 1 (before sentence, before word) 0.58 [0.31 – 0.74] > 100 0.23 [-0.05 – 0.49] 0.62 0.24 [-0.37 – 1.52] 0.08
Location 2 (before word / sentence, within word) 0.84 [0.67 – 0.97] > 100 0.53 [0.23 – 0.76] 24.27 0.4 [-0.09 – 1.57] 0.07
Edit (edit, no edit) 0 [-0.17 – 0.11] 0.06 0.26 [0.06 – 0.48] 2.54 0.14 [-0.3 – 0.92] 0.06
Two-way interactions
Language : Location 1 -0.01 [-0.31 – 0.34] 0.15 0.08 [-0.41 – 0.62] 0.26 -0.21 [-1.98 – 1.02] 0.13
Language : Location 2 0.08 [-0.13 – 0.27] 0.15 -0.23 [-0.73 – 0.21] 0.35 0.32 [-0.55 – 1.84] 0.11
Language : Edit -0.03 [-0.25 – 0.21] 0.11 0.07 [-0.34 – 0.56] 0.21 -0.16 [-1.52 – 0.85] 0.09
Location 1 : Edit -0.2 [-0.68 – 0.12] 0.24 0.32 [-0.19 – 0.84] 0.63 0.45 [-0.7 – 2.67] 0.15
Location 2 : Edit 0.09 [-0.17 – 0.29] 0.18 0.63 [0.19 – 1.09] 9.98 0.2 [-0.69 – 1.56] 0.12
Three-way interactions
Location 1 : Edit : Language -0.02 [-0.63 – 0.68] 0.3 0.16 [-0.82 – 1.24] 0.51 -0.43 [-3.95 – 2.03] 0.26
Location 2 : Edit : Language -0.17 [-0.54 – 0.26] 0.31 0.45 [-0.42 – 1.46] 0.71 -0.63 [-3.68 – 1.1] 0.21
Note:
Colon indicates interactions. PI is the probability interval. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.
Estimated cell means of transition duration of lookbacks with 95\% PIs (probability intervals). Shown are the estimates for each mixture components (short and long transitions) and the probability of long transitions.

Figure 4.6: Estimated cell means of transition duration of lookbacks with 95% PIs (probability intervals). Shown are the estimates for each mixture components (short and long transitions) and the probability of long transitions.

Table 4.11: Transition duration of lookbacks. Cell means for L1 and L2 with values in msecs for durations and proportion for probability of long transitions. Language difference are shown on log scale (for transition durations) and logit scale for probability of long fixations. 95% PIs in brackets.
Editing Transition location L1 L2 Language effect \(BF_{10}\)
Short transitions
Editing before sentence 2,295 [1,409 – 3,169] 3,235 [1,634 – 4,613] -0.33 [-0.81 – 0.26] 0.78
Editing before word 1,371 [1,106 – 1,650] 1,710 [1,472 – 1,987] -0.22 [-0.48 – -0.01] 0.87
Editing within word 944 [808 – 1,096] 1,069 [937 – 1,214] -0.12 [-0.31 – 0.05] 0.23
Writing before sentence 2,702 [2,135 – 3,235] 3,363 [2,625 – 4,107] -0.22 [-0.49 – 0.06] 0.57
Writing before word 1,418 [1,235 – 1,628] 1,919 [1,605 – 2,235] -0.3 [-0.47 – -0.07] 3.1
Writing within word 738 [645 – 833] 944 [832 – 1,068] -0.25 [-0.41 – -0.08] 6.16
Slowdown for long transitions
Editing before sentence 6,784 [3,500 – 10,768] 9,005 [4,521 – 14,914] 0.04 [-0.53 – 0.61] 0.27
Editing before word 2,473 [1,325 – 3,887] 4,083 [1,872 – 8,328] -0.17 [-0.78 – 0.32] 0.28
Editing within word 1,059 [443 – 2,077] 1,798 [817 – 3,974] -0.22 [-0.84 – 0.31] 0.34
Writing before sentence 6,220 [4,050 – 8,933] 7,593 [3,080 – 13,868] 0.03 [-0.43 – 0.56] 0.23
Writing before word 2,594 [1,066 – 5,388] 2,914 [1,857 – 4,147] 0.08 [-0.38 – 0.61] 0.27
Writing within word 225 [16 – 594] 636 [154 – 1,497] -0.24 [-0.77 – 0.26] 0.42
Probability of long transitions
Editing before sentence 0.47 [0.26 – 0.85] 0.5 [0.25 – 0.91] -0.14 [-1.97 – 1.25] 0.12
Editing before word 0.44 [0.25 – 0.73] 0.34 [0.15 – 0.56] 0.43 [-0.59 – 2.3] 0.16
Editing within word 0.35 [0.14 – 0.54] 0.3 [0.11 – 0.47] 0.21 [-0.88 – 1.61] 0.12
Writing before sentence 0.38 [0.21 – 0.62] 0.4 [0.19 – 0.77] -0.11 [-1.83 – 1.26] 0.12
Writing before word 0.36 [0.13 – 0.65] 0.41 [0.24 – 0.67] -0.25 [-2.19 – 1.12] 0.12
Writing within word 0.37 [0.21 – 0.55] 0.29 [0.1 – 0.46] 0.38 [-0.42 – 1.83] 0.14
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

4.5 Number of words fixated

# Run model
#source("../scripts/brms_nwordsfixated.R")

# Load posterior
fit <- readRDS("../stanout/nwordsfixated.rda")
fit$formula
fix_nwords ~ 1 + condition + (Lang | SubNo)

condition was coded with main effects of Language (levels: L1, L2), Edit (levels: editing, no editing), Transition location 1 (levels: before sentence, before word), Transition location 2 (levels: before word / sentence, within word) and all two and three-way interactions by-Transition location (i.e. no interactions that involve both Transition location 1 and Transition location 2).

fit$family

Family: negbinomial 
Link function: log
Table 4.12: Number of words fixated during lookback on log scale.
Predictor Estimate with 95% PI \(BF_{10}\)
Main effects
Language (L1, L2) -0.49 [-0.97 – -0.01] 1.77
Location 1 (before sentence, before word) 3.45 [3.18 – 3.72] > 100
Location 2 (before word / sentence, within word) 7.7 [7.2 – 8.19] > 100
Edit (edit, no edit) 1.33 [0.99 – 1.68] > 100
Two-way interactions
Language : Location 1 -0.16 [-0.43 – 0.11] 0.27
Language : Location 2 -0.31 [-0.82 – 0.18] 0.52
Language : Edit 0.05 [-0.29 – 0.39] 0.18
Location 1 : Edit 0.39 [0.13 – 0.67] 7.58
Location 2 : Edit -0.41 [-0.9 – 0.08] 0.9
Three-way interactions
Location 1 : Edit : Language 0.03 [-0.24 – 0.3] 0.14
Location 2 : Edit : Language -0.06 [-0.54 – 0.43] 0.25
Note:
Colon indicates interactions. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis
\label{fig:nwordfixfig}Estimated cell means for number of words fixated during lookback with 95\% PIs (probability intervals).

Figure 4.7: Estimated cell means for number of words fixated during lookback with 95% PIs (probability intervals).

Table 4.13: Number of words fixated during lookback. Cell means for L1 and L2 as counts, and language difference on log scale. 95% PIs in brackets.
Transition location L1 L2 Language effect \(BF_{10}\)
Editing
within word 3.41 [3.02 – 3.84] 3.44 [3.01 – 3.93] 0 [-0.16 – 0.15] 0.16
before word 5.08 [4.56 – 5.66] 5.45 [4.84 – 6.14] -0.07 [-0.2 – 0.07] 0.22
before sentence 12.85 [10.99 – 15.05] 14.73 [12.6 – 17.28] -0.13 [-0.34 – 0.07] 0.46
Writing
within word 2.5 [2.18 – 2.87] 2.62 [2.3 – 2.99] -0.06 [-0.23 – 0.11] 0.23
before word 4.67 [4.28 – 5.08] 4.97 [4.49 – 5.49] -0.06 [-0.15 – 0.04] 0.2
before sentence 9.54 [8.58 – 10.63] 11.18 [9.83 – 12.74] -0.16 [-0.31 – -0.02] 1.98
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

5 Transition duration of non-lookbacks

This analysis focuses on transition duration that did not involve lookbacks. Transition duration shorter than (or equal to) 50 msecs (M=2.17%, SE=0.29%) or longer than (or equal to) 30 secs (M=0.02%, SE=0.01%) were removed from the analysis.

Selected a random subset of 200 observations per participant, Language, Location, and Editing to reduce the time and computational power necessary to run the statistical models. This mean, all before-sentence transitions were included in the analysis, and a sub-sample of before-word transitions (M=51.31%, SE=8%) and within-word transitions (M=16.79%, SE=5.99%).

Table 5.1: Mixture model results of the transition duration of non-lookback transitions with predictor estimates for the distribution of short and long transition durations (on log scale) and the probability of long transition durations (on logit scale). Estimates are shown with 95% PI.
Short transitions
Slowdown for long transitions
Probability of long transitions
Predictor Estimate \(BF_{10}\) Estimate \(BF_{10}\) Estimate \(BF_{10}\)
Main effects
Language (L1, L2) -0.21 [-0.26 – -0.16] > 100 -0.24 [-0.34 – -0.14] > 100 -0.59 [-0.87 – -0.32] > 100
Location 1 (before sentence, before word) 0.41 [0.34 – 0.49] > 100 0.71 [0.57 – 0.85] > 100 0.65 [0.26 – 1.06] 49.77
Location 2 (before word / sentence, within word) 0.4 [0.37 – 0.44] > 100 0.59 [0.5 – 0.68] > 100 1.46 [1.2 – 1.72] > 100
Edit (edit, no edit) 0.56 [0.51 – 0.61] > 100 0.06 [-0.04 – 0.16] 0.11 0.17 [-0.12 – 0.45] 0.28
Two-way interactions
Language : Location 1 -0.16 [-0.3 – -0.01] 0.69 0.03 [-0.26 – 0.3] 0.15 0.87 [0.11 – 1.64] 4.88
Language : Location 2 0.12 [0.04 – 0.19] 2.92 0.32 [0.15 – 0.49] 76.73 -0.37 [-0.86 – 0.12] 0.76
Language : Edit -0.22 [-0.32 – -0.12] > 100 -0.21 [-0.41 – -0.01] 0.86 0.04 [-0.52 – 0.59] 0.28
Location 1 : Edit 0.59 [0.45 – 0.74] > 100 -0.04 [-0.33 – 0.24] 0.15 -0.02 [-0.8 – 0.77] 0.41
Location 2 : Edit 1.39 [1.32 – 1.46] > 100 0.21 [0.04 – 0.38] 1.6 0.51 [0 – 1.02] 1.8
Three-way interactions
Location 1 : Edit : Language -0.32 [-0.6 – -0.02] 1.38 0.05 [-0.52 – 0.61] 0.29 1.75 [0.22 – 3.27] 9.8
Location 2 : Edit : Language -0.24 [-0.38 – -0.08] 5.95 -0.64 [-0.99 – -0.3] > 100 0.74 [-0.23 – 1.72] 1.5
Note:
Colon indicates interactions. PI is the probability interval. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.
Estimated cell means of transition duration of non-lookbacks with 95\% PIs (probability intervals). Shown are the estimates for each mixture components (short and long transitions durations in msecs on log scale) and the probability of long transition durations.

Figure 5.1: Estimated cell means of transition duration of non-lookbacks with 95% PIs (probability intervals). Shown are the estimates for each mixture components (short and long transitions durations in msecs on log scale) and the probability of long transition durations.

Table 5.2: Transition duration of non-lookbacks. Cell means for L1 and L2 with values in msecs for durations and proportion for probability of long fixations. Language difference are shown on log scale (for fixation durations) and logit scale for probability of long fixations. 95% PIs in brackets.
Editing Transition location L1 L2 Language effect \(BF_{10}\)
Short transitions
Editing before sentence 409 [336 – 518] 425 [367 – 491] -0.04 [-0.27 – 0.23] 0.14
before word 424 [399 – 449] 485 [454 – 516] -0.13 [-0.18 – -0.09] > 100
within word 403 [381 – 426] 465 [439 – 492] -0.14 [-0.17 – -0.11] > 100
Writing before sentence 373 [342 – 408] 700 [603 – 791] -0.63 [-0.76 – -0.48] > 100
before word 184 [173 – 194] 228 [214 – 242] -0.21 [-0.25 – -0.18] > 100
within word 136 [129 – 144] 155 [146 – 164] -0.13 [-0.15 – -0.11] > 100
Slowdown for long transitions
Editing before sentence 1,841 [1,029 – 3,009] 2,041 [1,381 – 2,860] -0.07 [-0.55 – 0.4] 0.25
before word 668 [504 – 863] 1,332 [1,049 – 1,667] -0.37 [-0.6 – -0.15] 22.29
within word 669 [560 – 794] 724 [619 – 842] 0.04 [-0.09 – 0.17] 0.08
Writing before sentence 1,411 [1,079 – 1,821] 5,428 [4,218 – 6,566] -0.61 [-0.83 – -0.38] > 100
before word 245 [220 – 273] 526 [482 – 573] -0.35 [-0.42 – -0.28] > 100
within word 133 [106 – 164] 181 [153 – 211] -0.09 [-0.22 – 0.04] 0.17
Probability of long transitions
Editing before sentence 0.6 [0.36 – 0.81] 0.71 [0.56 – 0.84] -0.5 [-1.71 – 0.71] 0.84
before word 0.23 [0.17 – 0.31] 0.34 [0.26 – 0.43] -0.53 [-1.06 – 0.01] 1.75
within word 0.15 [0.12 – 0.19] 0.29 [0.23 – 0.35] -0.8 [-1.24 – -0.37] > 100
Writing before sentence 0.49 [0.38 – 0.6] 0.38 [0.29 – 0.49] 0.44 [-0.19 – 1.07] 0.84
before word 0.35 [0.29 – 0.42] 0.66 [0.59 – 0.73] -1.28 [-1.7 – -0.85] > 100
within word 0.09 [0.07 – 0.12] 0.2 [0.15 – 0.25] -0.87 [-1.31 – -0.43] > 100
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

6 Transition duration (across lookbacks and non-lookbacks)

This analysis focuses on transition duration collapsing both lookback and non-looksback transitions. Transition duration shorter than (or equal to) 50 msecs (M=2.12%, SE=0.29%) or longer than (or equal to) 30 secs (M=0.05%, SE=0.01%) were removed from the analysis.

Selected a random subset of 200 observations per participant, Language, Location, and Editing to reduce the time and computational power necessary to run the statistical models. This mean, all before-sentence transitions were included in the analysis, and a sub-sample of before-word transitions (M=50.48%, SE=8.01%) and within-word transitions (M=17.02%, SE=6.02%).

Table 6.1: Mixture model results of the transition duration with predictor estimates for the distribution of short and long transitions (on log scale) and the probability of long transitions (on logit scale). Estimates are shown with 95% PI.
Short transitions
Slowdown for long transitions
Probability of long transitions
Predictor Estimate \(BF_{10}\) Estimate \(BF_{10}\) Estimate \(BF_{10}\)
Main effects
Language (L1, L2) -0.16 [-0.24 – -0.09] > 100 -0.1 [-0.17 – -0.04] 3.29 -0.77 [-1.03 – -0.5] > 100
Location 1 (before sentence, before word) 0.36 [0.27 – 0.48] > 100 0.88 [0.79 – 0.97] > 100 1.29 [0.91 – 1.68] > 100
Location 2 (before word / sentence, within word) 0.37 [0.32 – 0.43] > 100 0.84 [0.78 – 0.9] > 100 2.08 [1.83 – 2.33] > 100
Edit (edit, no edit) 0.61 [0.54 – 0.68] > 100 0.19 [0.12 – 0.26] > 100 0.53 [0.26 – 0.8] > 100
Two-way interactions
Language : Location 1 0 [-0.21 – 0.21] 0.1 0.13 [-0.05 – 0.31] 0.25 0.5 [-0.23 – 1.24] 0.91
Language : Location 2 0.04 [-0.06 – 0.15] 0.07 0.12 [0 – 0.25] 0.41 -0.09 [-0.57 – 0.38] 0.26
Language : Edit -0.13 [-0.29 – 0] 0.49 -0.1 [-0.24 – 0.04] 0.2 -0.3 [-0.83 – 0.24] 0.49
Location 1 : Edit 0.72 [0.51 – 0.93] > 100 0.3 [0.11 – 0.48] 11.75 0.72 [-0.02 – 1.47] 2.3
Location 2 : Edit 1.46 [1.35 – 1.56] > 100 0.43 [0.3 – 0.56] > 100 1.22 [0.74 – 1.71] > 100
Three-way interactions
Location 1 : Edit : Language 0 [-0.43 – 0.41] 0.21 0.26 [-0.1 – 0.63] 0.5 1.01 [-0.46 – 2.47] 1.82
Location 2 : Edit : Language -0.08 [-0.29 – 0.13] 0.14 -0.25 [-0.5 – 0.01] 0.81 0.18 [-0.76 – 1.14] 0.52
Note:
Colon indicates interactions. PI is the probability interval. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.
Estimated cell means of transition duration with 95\% PIs (probability intervals). Shown are the estimates for each mixture components (short and long transition durations in msecs on log scale) and the probability of long transition durations.

Figure 6.1: Estimated cell means of transition duration with 95% PIs (probability intervals). Shown are the estimates for each mixture components (short and long transition durations in msecs on log scale) and the probability of long transition durations.

Table 6.2: Transition duration. Cell means for L1 and L2 with values in msecs for durations and proportion for probability of long transition durations. Language difference are shown on log scale (for transition durations) and logit scale for probability of long transition durations. 95% PIs in brackets.
Editing Transition location L1 L2 Language effect \(BF_{10}\)
Short transitions
Editing before sentence 433 [337 – 588] 437 [376 – 523] -0.02 [-0.31 – 0.33] 0.19
before word 423 [399 – 449] 480 [449 – 513] -0.13 [-0.17 – -0.08] > 100
within word 407 [385 – 430] 474 [447 – 503] -0.15 [-0.18 – -0.12] > 100
Writing before sentence 382 [351 – 416] 540 [434 – 737] -0.34 [-0.66 – -0.12] 16.23
before word 187 [176 – 197] 235 [221 – 250] -0.23 [-0.27 – -0.19] > 100
within word 138 [130 – 145] 156 [148 – 166] -0.13 [-0.15 – -0.1] > 100
Slowdown for long transitions
Editing before sentence 3,454 [2,527 – 4,677] 4,016 [3,217 – 4,935] -0.13 [-0.41 – 0.16] 0.21
before word 1,087 [912 – 1,286] 1,380 [1,170 – 1,619] -0.08 [-0.24 – 0.07] 0.14
within word 739 [635 – 856] 794 [688 – 912] 0.05 [-0.07 – 0.17] 0.09
Writing before sentence 2,523 [2,154 – 2,932] 3,694 [2,961 – 4,901] -0.03 [-0.18 – 0.12] 0.08
before word 349 [310 – 392] 711 [650 – 779] -0.34 [-0.42 – -0.26] > 100
within word 136 [108 – 168] 183 [156 – 214] -0.09 [-0.23 – 0.04] 0.17
Probability of long transitions
Editing before sentence 0.79 [0.61 – 0.91] 0.86 [0.78 – 0.92] -0.47 [-1.59 – 0.62] 0.78
before word 0.37 [0.3 – 0.45] 0.54 [0.46 – 0.63] -0.71 [-1.19 – -0.24] 18.72
within word 0.19 [0.15 – 0.24] 0.31 [0.25 – 0.38] -0.66 [-1.08 – -0.26] 34.97
Writing before sentence 0.62 [0.53 – 0.7] 0.73 [0.57 – 0.83] -0.5 [-1.21 – 0.3] 1.01
before word 0.34 [0.28 – 0.41] 0.64 [0.57 – 0.71] -1.26 [-1.68 – -0.85] > 100
within word 0.08 [0.06 – 0.1] 0.19 [0.15 – 0.23] -0.99 [-1.43 – -0.56] > 100
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.
Mixture model plot for before-word transition durations that did not terminate in an editing operation. Shown are the distributions for both mixture components (short and long transition durations) and their respective weighting for every language group.

Figure 6.2: Mixture model plot for before-word transition durations that did not terminate in an editing operation. Shown are the distributions for both mixture components (short and long transition durations) and their respective weighting for every language group.

Model comparisons between the mixture model and a unimodal unequal variance linear mixed effects model.

Table 6.3: Predictive performance was estimated as the expected log predictive density (\(\widehat{elpd}\)) Vehtari et al. (2017). A negative difference \(\Delta\widehat{elpd}\) denotes lower predictive performance compared to the model with the highest predictive performance (top row). Standard error is shown in parentheses.
Model \(\Delta\widehat{elpd}\) \(\widehat{elpd}\)
Mixture model 0 (0) -317,661 (382)
LMM (unequal variance) -6632 (135) -324,294 (405)
Note. LMM = linear mixed-effects model.

7 Appendix

7.1 Text data separated by lookback

7.1.1 Editing frequency

edits | trials(total) ~ 1 + condition + (Lang | SubNo) 

Family: binomial 
Link function: logit
Table 7.1: Editing frequency effects on logit scale.
Predictor Estimate with 95% PI \(BF_{10}\)
Main effects
Language (L1, L2) -1.63 [-2.26 – -0.98] > 100
Location 1 (before sentence, before word) 1.33 [0.88 – 1.77] > 100
Location 2 (before word / sentence, within word) -0.76 [-1.37 – -0.15] 6.05
Lookback (lookback, no lookback) -9.68 [-10.18 – -9.19] > 100
Two-way interactions
Language : Location 1 -0.37 [-0.81 – 0.07] 0.83
Language : Location 2 -1.61 [-2.21 – -1.01] > 100
Language : Lookback -1.54 [-2.04 – -1.05] > 100
Location 1 : Lookback 1.07 [0.63 – 1.51] > 100
Location 2 : Lookback 6.73 [6.11 – 7.34] > 100
Three-way interactions
Location 1 : Lookback : Language 0.46 [0.02 – 0.91] 1.74
Location 2 : Lookback : Language 0.78 [0.18 – 1.39] 7.61
Note:
Colon indicates interactions. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis
\label{fig:editingfig}Estimated cell means for editing frequency with 95\% PIs (probability intervals).

Figure 7.1: Estimated cell means for editing frequency with 95% PIs (probability intervals).

Table 7.2: Editing frequency. Cell means for L1 and L2 in proportion and language difference on logit scale both shown with 95% PIs in brackets.
Transition location L1 L2 Language effect \(BF_{10}\)
Lookback
within word 0.53 [0.48 – 0.58] 0.43 [0.39 – 0.48] 0.46 [0.22, 0.7] 97.98
before word 0.26 [0.23 – 0.29] 0.26 [0.23 – 0.29] -0.03 [-0.21, 0.15] 0.1
before sentence 0.23 [0.19 – 0.28] 0.32 [0.27 – 0.37] -0.51 [-0.83, -0.2] 27.57
No lookback
within word 0.05 [0.04 – 0.05] 0.07 [0.06 – 0.08] -0.4 [-0.49, -0.31] >100
before word 0.06 [0.06 – 0.07] 0.11 [0.1 – 0.13] -0.64 [-0.74, -0.53] >100
before sentence 0.11 [0.09 – 0.14] 0.18 [0.15 – 0.22] -0.67 [-0.98, -0.37] >100
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

7.1.2 Number of transitions

n_transitions ~ 1 + condition + (Lang | SubNo) 

Family: negbinomial 
Link function: log
Table 7.3: Transition-count effects on log scale.
Predictor Estimate with 95% PI \(BF_{10}\)
Main effects
Language (L1, L2) 1.63 [0.52 – 2.71] 27.99
Location 1 (before sentence, before word) -11.98 [-13.01 – -10.89] > 100
Location 2 (before word / sentence, within word) -14.04 [-15.44 – -12.59] > 100
Edit (edit, no edit) -12.86 [-13.97 – -11.7] > 100
Lookback (lookback, no lookback) 21.15 [19.84 – 22.39] > 100
Two-way interactions
Language : Location 1 -0.26 [-1.18 – 0.65] 0.53
Language : Location 2 -0.05 [-1.26 – 1.15] 0.61
Language : Edit -1.07 [-2.09 – -0.05] 3.95
Location 1 : Edit 2.85 [1.94 – 3.78] > 100
Location 2 : Edit 1.84 [0.62 – 3.09] 43.16
Language : Lookback 2.02 [1 – 3.03] > 100
Location 1 : Lookback -6.02 [-6.93 – -5.09] > 100
Location 2 : Lookback -15.71 [-17.17 – -14.2] > 100
Edit : Lookback -8.36 [-9.39 – -7.33] > 100
Three-way interactions
Location 1 : Edit : Language -0.01 [-0.91 – 0.89] 0.45
Location 2 : Edit : Language -0.76 [-1.97 – 0.46] 1.32
Location 1 : Language : Lookback -0.8 [-1.7 – 0.12] 1.9
Location 2 : Language : Lookback -0.66 [-1.87 – 0.56] 1.05
Language : Edit : Lookback -1.47 [-2.49 – -0.45] 27.37
Location 1 : Edit : Lookback 1.45 [0.55 – 2.36] 57.13
Location 2 : Edit : Lookback 5.53 [4.3 – 6.75] > 100
Four-way interactions
Location 1 : Edit : Language : Lookback 0.28 [-0.64 – 1.19] 0.54
Location 2 : Edit : Language : Lookback 0.41 [-0.8 – 1.62] 0.74
Note:
Colon indicates interactions. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis
\label{fig:transfig2}Estimated cell means for transition counts with 95\% PIs (probability intervals).

Figure 7.2: Estimated cell means for transition counts with 95% PIs (probability intervals).

Table 7.4: Transition counts. Cell means for L1 and L2 as counts and percentage (within Language and Lookback), and language difference on log scale. 95% PIs in brackets.
Transition location L1 L2 Language effect \(BF_{10}\)
Lookback / Edit
within word 11 [9 – 14], 14.5 % 11 [8 – 14], 13.2 % 0.09 [-0.16 – 0.34] 0.16
before word 12 [10 – 16], 16.2 % 13 [10 – 17], 16.3 % -0.08 [-0.33 – 0.17] 0.15
before sentence 7 [5 – 10], 9.4 % 7 [5 – 10], 8.9 % -0.1 [-0.42 – 0.23] 0.2
Lookback / No edit
within word NA NA -0.41 [-0.67 – -0.15] 16.41
before word NA NA -0.07 [-0.28 – 0.14] 0.14
before sentence NA NA 0.24 [-0.02 – 0.5] 0.7
No lookback / Edit
within word 81 [66 – 98], 4.9 % 67 [56 – 82], 7 % 0.24 [0.04 – 0.44] 1.66
before word 46 [37 – 58], 2.8 % 40 [32 – 50], 4.1 % 0.17 [-0.03 – 0.38] 0.41
before sentence 8 [6 – 10], 0.5 % 8 [6 – 11], 0.8 % -0.14 [-0.48 – 0.2] 0.24
No lookback / No edit
within word NA NA 0.63 [0.43 – 0.82] > 100
before word NA NA 0.8 [0.61 – 1] > 100
before sentence NA NA 0.5 [0.27 – 0.72] > 100
Note:
PIs are probability intervals. \(BF_{10}\) is the evidence in favour of the alternative hypothesis over the null hypothesis.

7.2 Random effects

7.2.1 Lookback probability

# Run model
#source("../scripts/brms_lookback.R")

# Load posterior
fit <- readRDS("../stanout/lookback.rda")
fit$formula
lookbacks | trials(total) ~ 1 + condition + (Lang | SubNo)

condition was coded with main effects of Language (levels: L1, L2), Edit (levels: editing, no editing), Transition location 1 (levels: before sentence, before word), Transition location 2 (levels: before word / sentence, within word) and all two and three-way interactions by-Transition location (i.e. no interactions that involve both Transition location 1 and Transition location 2).

fit$family

Family: binomial 
Link function: logit
\label{fig:lookbackpptfig}Estimated participant means for lookback probability with 95\% PIs (probability intervals). Shown is deviation from the intercept (shown as dotted line).

Figure 7.3: Estimated participant means for lookback probability with 95% PIs (probability intervals). Shown is deviation from the intercept (shown as dotted line).

7.2.2 Lookback probability with transition duration adjustment

\label{fig:lookbackpptfig}Estimated participant means for lookback probability with 95\% PIs (probability intervals) after adjusting for transition duration. Shown is deviation from the intercept (shown as dotted line).

Figure 7.4: Estimated participant means for lookback probability with 95% PIs (probability intervals) after adjusting for transition duration. Shown is deviation from the intercept (shown as dotted line).

7.2.3 Number of fixation during lookback

\label{fig:nfixlookbackppt}Estimated participant means for number of lookback fixations with 95\% PIs (probability intervals). Shown is deviation from the intercept (shown as dotted line).

Figure 7.5: Estimated participant means for number of lookback fixations with 95% PIs (probability intervals). Shown is deviation from the intercept (shown as dotted line).

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