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This is the accepted author manuscript version of an article published as:

Liu, Y., Yu, L., & Reichle, E. D. (2019). The dynamic adjustment of saccades during Chinese reading: Evidence from eye movements and simulations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 45(3), 535–543.

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The Dynamic Adjustment of Saccades During Chinese Reading:

Evidence from Eye Movements and Simulations

Yanping Liu, Sun Yat-sen University, China

Lei Yu, Sun Yat-sen University, China

Erik D. Reichle, Macquarie University, Australia

Author Note

Address correspondence to Yanping Liu, Department of Psychology, Guangdong

Provincial Key Laboratory of Social Cognitive Neuroscience and Mental Health, Sun

Yat-sen University, 135 Xingang Xi Rd, Guangzhou, China, 510275; e-mail:

[email protected]. This research was supported by the National Natural

Science Foundation of China (31500890), the Fundamental Research Funds for the

Central Universities (17wkpy64), and the U.S. National Institute of Health

(RO1HD075800).

Word count = 5,000

2

Abstract

This article reports an eye-movement experiment in which participants scanned

continuous sequences of Landolt-Cs for target circles to examine the visual and

oculomotor constraints that might jointly determine where the eyes move in a task that

engages many of the perceptual and motor processes involved in Chinese reading but

without lexical or linguistic processing. The lengths of the saccades entering the

Landolt-C clusters were modulated by the processing difficulty (i.e., gap sizes) of

those clusters. Simulations using implemented versions of default-targeting (Yan,

Kliegl, Richter, Nuthmann, & Shu, 2010) versus dynamic-adjustment (Liu, Reichle, &

Li, 2016) models of saccadic targeting indicated that the latter provided a better

account of our participants’ eye movements, further supporting the hypothesis that

Chinese readers “decide” where to move their eyes by adjusting saccade length in

response to processing difficulty rather than by selecting default saccade targets. We

discuss this hypothesis in relation to both what is known about saccadic targeting

during the reading of English versus Chinese and current models of eye-movement

control in reading.

Keywords: Chinese reading; eye-movement control; Landolt-C paradigm; visual

search.

Running Head: Reading Landolt-C sequences.

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Humans are remarkably adept at exploiting the environmental regularities to

optimize behavior (Anderson, 1990). It should therefore come as little surprise that, in

complex tasks like reading, we exploit regularity to allow (near) optimal performance

(e.g., see Liu, Reichle, & Gao, 2013; Reichle & Laurent, 2006). For example, because

common words are identified more rapidly than uncommon words, readers spend less

time fixating high- than low-frequency words (e.g., Inhoff & Rayner, 1986; Schilling,

Rayner, & Chumbley, 1998). And similarly, because words can be identified most

rapidly when fixated near their centers (e.g., Rayner & Morrison, 1981), readers (of

most alphabetic languages) tend to move their eyes to locations near the centers of

words (e.g., Rayner, 1979). Such eye-movement behaviors exploit the inherent

regularities of text to support rapid reading while maintaining some overall level of

comprehension. What is less clear, however, is how well such behaviors generalize

across languages and writing systems that exhibit less—or perhaps different—patterns

of regularity. One prime example that has been the focus of much recent research is

Chinese (for a review, see Yu & Reichle, 2017).

Chinese differs significantly from the European languages and writing systems

that have most often been used in experiments to understand reading. For example,

Chinese words are not comprised from letters or clearly demarcated by boundaries,

but instead consist of 1-4 equally sized, box-shaped characters comprised of 1-36

strokes (see Fig. 1) arranged into continuous sequences without spaces or other

identifiers to separate the individual words. Chinese readers must therefore use their

knowledge of the language to somehow segment character strings into their

corresponding words (e.g., Li, Rayner, & Cave, 2009) for their identification and for

deciding when and where to move their eyes during reading.

Because word segmentation/identification is a computationally difficult process,

our understanding of their relation to eye-movement control is incomplete. For

example, although early studies of Chinese reading purportedly showed that character

processing is more important (e.g., has a larger influence on fixation durations) than

word processing during Chinese reading (e.g., Hoosain, 1992), more recent studies

suggest that word processing plays a larger role, with the modulating effects of word

frequency on fixation durations, for example, often overshadowing the smaller

character-frequency effects (e.g., Li, Bicknell, Liu, Wei, & Rayner, 2014; Yan, Tian,

Bai, & Rayner, 2006).

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Figure 1

And in a similar manner, early studies of Chinese reading suggested that saccade

targeting is possibly character-based, as suggested by the means of fixation-location

distributions being approximately uniform over words (Tsai & McConkie, 2003;

Yang & McConkie, 1999). This hypothesis was partially refuted by a corpus analysis

reported by Yan et al. (2010; see also Yan & Kliegl, 2016) which indicated that the

distributions of fixations on words that were the recipients of only one fixation tended

to be centered near the centers of the words, whereas the distributions of the first

fixations on words that received multiple fixations tended to be centered near the

beginnings of the words. Yan et al. (2010) provided a default-targeting account of this

finding: Chinese readers direct their eyes towards the middle of a segmented word

because it will likely be identified from that viewing location, but direct their eyes

towards the beginning of an unsegmented word because it is less likely to be

identified and thus more likely to require a second fixation. Unfortunately, the

relationship between whether a word-segmentation success and the number of times it

will be fixated is correlational. As demonstrated using simulations in which saccade

length was fixed in length but with some random variability, fixations near the

beginning of a word are more likely than fixations near the center of a word to be

followed by a subsequent fixation on the same word (see also, Li, Liu, & Rayner,

2011).

More recent empirical evidence suggests that, instead of directing their eyes

towards specific target locations, Chinese readers dynamically adjust their saccade

lengths to reflect local difficulty with lexical processing (Liu, Reichle, & Li, 2015,

2016; Liu, Huang, Li, & Gao, 2017). A computational implementation of this

alternative account simulated a number of findings related to saccade targeting,

including how the frequency of and fixation position on wordN influence the length of

the saccade to wordN+1 (Liu, Huang, Gao, & Reichle, 2017; Wei, Li, & Pollatsek,

2013), as well as how the length of this saccade is influenced by both frequency and

predictability of wordN+1 (Liu et al., 2016; Liu, Guo, Yu, & Reichle, 2017).

Importantly, this dynamic-adjustment model provides a better quantitative account of

these findings than an implementation of Yan et al.’s (2010) default-targeting account.

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The success of the dynamic-adjustment account suggests that, in the absence of

word boundary information, readers switch from moving their eyes towards default

saccade targets (i.e., the centers of parafoveal words) to another mode of maximizing

their reading efficiency—the dynamic adjustment of saccade lengths as a function of

on-going lexical processing difficulty. But is this shift towards dynamic-adjustment of

saccades specific to reading (or perhaps specific to the reading of Chinese), or does it

instead reflect task demands that might be shared by other visual-cognitive tasks?

One paradigm that has been used to dissociate the visual and oculomotor

processes of reading from those that are language specific is the Landolt-C “reading”

task (Williams & Pollatsek, 2007; Williams, Pollatsek, & Reichle, 2014; Vanyukov,

Warren, Wheeler, & Reichle, 2012). In this task, participants are instructed to scan

through linear arrays of Landolt-Cs (i.e., ring-shaped stimuli having missing segments

or gaps of variable size and/or orientations) to search for target stimuli—rings with no

missing gaps. Because these Landolt-C stimuli can be arranged into cluster sequences

resembling “words,” the task has been used to study saccadic targeting under

conditions that resemble the reading of alphabetic languages, and that engages vision,

attention, and memory, but without the various lexical and linguistic processes that are

normally engaged during reading. Experiments using this paradigm have

demonstrated that participants direct their eyes towards the centers of Landolt-C

clusters and spend less time fixating on those that are easy to process (e.g., contain

larger gaps and/or occur more often during the course of the experiment). Such

findings again demonstrate that humans exploit regularities to optimize task

performance, and that aspects of reading-like eye-movement behavior (e.g., targeting

the centers of clusters) reflect general rather than reading-specific task demands.

What remains unclear, however, is whether the dynamic adjustment of saccade length

during Chinese reading (e.g., see Liu, Reichle, & Li, 2016) also reflects general rather

than reading-specific task demands.

This article will report the results of an eye-movement experiment in which a

variant of the basic Landolt-C paradigm (adapted to resemble Chinese reading; see

Fig. 2) was used to examine how the absence of clear word boundaries affects

saccade targeting. The main objective was to determine if, as is the case with the

actual reading of Chinese, the absence of “word” boundaries causes participants to

dynamically adjust their saccade lengths rather than moving their eyes to default

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targets (e.g., the centers of upcoming Landolt-C clusters). To discriminate between

these two possibilities, we also report the results of two simulations using

implementations of the dynamic-adjustment versus default-targeting models.

Experimental Method

Participants

Thirty native Chinese-speaking students recruited from Sun Yat-sen University

were paid for their participation. All participants had normal or corrected-to-

normal vision and were naïve about the purpose of the experiment.

Apparatus

Stimuli were displayed on a 27-inch LED monitor (ASUS, PG27AQ) with a

resolution of 2,560 × 1,440 pixels and a 144-Hz refresh rate. Stimulus presentation

was controlled using an OpenGL-based Psychophysics Toolbox 3 with EyeLink

Toolbox extensions in Matlab. Eye movements were recorded using a SR-Research

Ltd. Eyelink1000 eye tracker (1,000-Hz sampling rate) using a tower setup with

forehead and chin rests to minimize noise due to head movements. Viewing was

binocular but only the right eye was recorded.

Stimuli and Design

The stimuli were configured to resemble Chinese sentences (cf., Figs. 1 vs. 2),

with each “character” being a Landolt-C (36 pixels × 36 pixels, with a 1°, 2°, 3°, or 4°

gap in the left, right, top, or bottom of the character) and each “word” being a cluster

of 1, 2, 3, or 4 characters. The space between any two successive characters was four

pixels. Sixteen unique 2-character exemplar words were generated, with each having a

unique combination of gap size and orientation, and each being repeated 50 times

across the experiment. 1,904 other words that appeared only once across the

experiment were generated using unique combinations of character number per cluster,

gap sizes, and gap orientations, and by allowing small random permutations of gap

angle. Eight words were randomly assigned to each “sentence” string to generate 330

trials, with each sentence containing 0, 1, or 2 targets (i.e., characters without gaps)

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that could appear with equal probability within any word except the exemplars or the

first or last word within a sentence.

Figure 2

Procedure

Upon arriving, participants were given task instructions, gave informed consent,

and then seated 58 cm from the monitor (so that one character subtended ∼1° of the

visual angle). The eye-tracker was calibrated and validated using a 3-dot procedure at

the beginning of the experiment, with additional calibrations and validations being

conducted as necessary. A drift-check procedure was performed before each trial; a

sentence was displayed after participants successfully fixated a white box (1° × 1°)

located at the position of the first character in the sentence. Participants were

instructed to scan through each sentence, indicating the number of targets in each

using response buttons on a Microsoft SideWinder Game Pad. Participants completed

eight practice trials (not included in our analyses) and then completed the remaining

experimental trials in a random order.

Experimental Results

Accuracy

The mean overall target-number response accuracy was 0.86 (SD = 0.106).

Eye-Movement Results

Our primary analysis focuses on the two-character exemplars because

approximately 72% of Chinese words are composed of two characters. Fixations on

exemplars in which blinks occurred and fixations immediately preceding/following

clusters containing targets were first removed from our analyses, leaving 82.62% of

the total fixations on exemplars. (This precaution was necessary because fixations

near/on targets are not representative of fixations elsewhere; e.g., because of the

requirement to keep track of the number of targets.) To determine how cluster

processing affected fixation durations, our analyses examined how properties of the

fixated exemplar clusters and the spatially adjacent clusters influenced: (1)

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first-fixation duration (FFD), or the duration of the first fixation on the exemplar

during first-pass scanning; (2) gaze duration (GD), or the sum of all first-pass fixation

durations on the exemplar; (3) total-viewing time (TT), or the sum of all fixation

durations on the exemplar. To determine how parafovea cluster processing affected

saccade targeting, our analyses also examined how exemplar properties influenced

saccade length into the exemplars using: (4) progressive-saccade length (PSL), or the

length of the forward saccade launched from a 2-character pre-exemplar region during

first-pass scanning; and (5) incoming-saccade length (ISL), or the length of the

forward saccade launched from a 2-character pre-exemplar region during first-pass

scanning conditional upon resulting fixation being on the exemplar. These two

analyses were restricted to saccades launched from a 2-character pre-exemplar region

to ensure that the exemplars received some amount of parafoveal processing.

Linear mixed-effects models were built for each measure, using parsimonious

random structure by iterative reduction of insignificant variance and covariance

components from maximal models (see Bates, Kliegl, Vasishth, & Baayen, 2015).

For fixation-duration measures on exemplars, exemplar gap size and repetition

number, as well as the gap size and length of spatially adjacent clusters were

included as predictors. For saccade-length into exemplars, to simplify, only exemplar

gap size and repetition number were included as predictors. The models were then

fitted using the lme4 package (ver. 1.1-13) and p-values were estimated using

lmerTest package (ver. 2.0-33) in R (ver. 3.4.1).

Fixation Durations. Tables 1-3 indicate that fixation-duration measures decreased

with increasing gap size of the fixated exemplar (all ps < 0.001), the increasing gap

size of subsequent cluster (all ps ≤ 0.001), and—with one measure—the increasing

gap size of preceding cluster (GD: p = 0.031). Gaze duration and total-viewing time

decreased with exemplar repetition (GD: p = 0.048; TT: p < 0.001), but first-fixation

duration was not influenced by exemplar repetition (p = 0.574). These results are

broadly consistent with Chinese-reading experiments showing that fixation durations

on words decrease as their processing ease increases (Liversedge, Zang, Zhang, Bai,

Yan, & Drieghe, 2014; Yan et al., 2006; Yang & McConkie, 1999; see Li et al., 2014

for a corpus analysis), and with results showing that fixation durations on words can

be influenced by the orthographic processing ease of parafoveal words (Kennedy,

1998, 2000; White, 2008).

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Tables 1-3

Saccade Length. Table 4 indicates that both saccade-length measures increased

with the increasing gap size of the exemplar cluster (PSL: b = 0.12, SE = 0.02, t =

7.00, p < 0.001; ISL: b = 0.09, SE = 0.01, t = 7.92, p < 0.001), although the effect of

exemplar repetition did not reach significance (ps > 0.119). These results are broadly

consistent with Chinese-reading experiments showing that forward saccade length

increases with parafoveal processing ease (Liversedge et al., 2014; see also White &

Liversedge, 2006). Our results therefore also suggest that the dynamic adjustment of

saccade length reflects general demands (i.e., demands associated with parafoveal

processing difficulty) rather than factors specific to reading Chinese.

Table 4

Computational Modeling

The simulations reported below shed light on how the saccades moving the eyes

into the exemplar clusters were influenced by their gap size, and whether this

behavior is better explained via the default targeting of saccades or the

dynamic-adjustment of saccade length. The simulations using each model were based

on 10,000 Monte Carlo runs, each of which involved first sampling a saccade launch

site from a uniform distribution covering the pre-exemplar region so that a precise

saccade target (Simulation 1) or length (Simulation 2) could then be calculated using

Equations 1-4. (The method for finding best-fitting model parameters is described in

the Appendix.) To account for any gap-size effect, the simulations were fit separately

for each gap-size condition, compensating for the scarcity of data in each condition by

collapsing across the smaller (1-2°) and larger (3-4°) gap sizes.

Simulation 1: Default-Targeting Model

The fundamental assumption of this model is that, if an exemplar cluster is

segmented, a saccade is directed towards its center; otherwise, a saccade is directed

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towards its beginning, allowing the cluster to be refixated. The model does not specify

precisely how this happens, but instead uses Yan et al.’s (2010) assumptions about the

relationship between segmentation and fixation number to estimate the probability of

exemplar’s segmentation from how often it was fixated, using four mutually exclusive

and exhaustive saccade behaviors: (1) refixating the 2-character pre-exemplar region;

(2) fixating and then moving the eyes from the exemplar (presumably because it was

segmented in the parafovea); (3) fixating and then refixating the exemplar

(presumably because it was not segmented in the parafovea); and (4) skipping the

exemplar. Polynomial regression functions (Equation 1) were fit to each possible

saccade launch site (binned to the nearest 0.5 character), with the constraint that the

probabilities of the four types of eye-movement behaviors from each saccade site

summed to 1. To account for exemplar gap size, these functions were fit separately for

smaller and larger gap sizes. In Equation 1, x represents the distance (in character

spaces) between the pre-exemplar launch site and the leftmost edge of the exemplar,

and k0, k1, and k2 respectively represent the intercept, linear, and quadratic polynomial

coefficients.

(1) p(x) = k2 x2 + k1 x + k0

The estimated probabilities were used to specify saccade targets as follows: (1)

saccades to refixate the pre-exemplar region were directed towards this region’s center;

(2) parafoveal exemplar segmentation caused the eyes to move towards its center; (3)

unsuccessful exemplar segmentation caused the eyes to move towards its beginning

(i.e., the center of its first character); and (4) exemplar skips were directed towards the

beginning of post- exemplar cluster (i.e., the center of its first character). Because

visual acuity and the perceptual span are limited (i.e., the latter extends 2–3 characters

to the right of fixation; see Chen & Tang, 1998; Inhoff & Liu, 1998), those rare

instances where the eyes might move past (i.e., to the right of) the beginning of

post-exemplar were not simulated. Variance was added to the saccade target to

simulate saccadic error, which was sampled from a Gaussian distribution with μ = 0,

and σ values selected to fit the empirical fixation-position distributions of incoming

saccades on exemplars.

Simulation 2: Dynamic-Adjustment Model

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The fundamental assumption of this model is that readers modulate saccade

length as a function of the amount of parafoveal processing that has been completed.

The assumption was instantiated using a simplifying assumption: Saccade length is a

linear function of parafoveal preprocessing. To do this, the amount of exemplar

preprocessing completed from the pre-exemplar region was sampled from a gamma

distribution having shape, α, and scale, β, parameters as described by Equation 2.

(2) preprocessing = gamma (α, β)

Using this equation, the amount of exemplar preprocessing (as determined by the

value of α) was modulated by exemplar gap size as specified by Equation 3. In this

equation, η0 is a constant representing the minimal value of α, and η1 is a parameter

that modulates the influence of gap size on α.

(3) α = η0 + η1 condition

Saccade length (in character spaces) is then linearly related to preprocessing

using Equation 4, where λ is a free parameter scaling this relationship, and intrinsic

variability in saccade length being determined by the parameter β.

(4) length = λ preprocessing

= λ gamma (α, β)

= gamma (η0 + η1 condition, λβ)

Figure 3

Simulation Results

Figure 3 shows that, relative to the default-targeting model, the

dynamic-adjustment model provides a better quantitative fit of the observed

relationships between the saccade launch sites and the subsequent fixation landing

sites, for both progressive saccades (i.e., all saccades launched from the pre-exemplar

region, irrespective of whether they resulted in fixations on an exemplar;

default-targeting: MSE = 6.71 × 10-1; dynamic-adjustment: MSE = 6.30 × 10-3) or

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incoming saccades (i.e., only saccades launched from the pre-exemplar region that

resulted in exemplar fixations; default-targeting: MSE = 2.75×10-2;

dynamic-adjustment: MSE = 8.70×10-3). Also note that the default-targeting model

exhibited poorer performance across its full range of parameter values (see the shaded

region of Figure 3A).

Discussion

The present article examined whether the dynamic-adjustment account of

saccadic targeting during reading is specific to reading (or perhaps even the reading

of Chinese), or whether it might instead reflect the more general visual and/or

oculomotor constraints of tasks that require the rapid identification of visual patterns

embedded in continuous arrays (e.g., our Landolt-C paradigm). The results of our

experiment support the latter interpretation by demonstrating that the length of the

saccade entering Landolt-C exemplar clusters is modulated by the processing

difficulty (i.e., gap sizes) of those clusters, consistent with prior evidence that

on-going processing difficulty modulates saccade length during the reading of

Chinese (e.g., Liu et al., 2015, 2016; Liu, Huang, Gao et al., 2017; Liu, Huang, Li et

al., 2017; Liu, Guo et al., 2017). Although one might argue against this conclusion on

the grounds that our Landolt-C task does not entail two key components of reading

(i.e., word identification and linguistic processing), the fact that our task does not

engage language processing but does engage other perceptual, cognitive, and motor

processes is precisely why the observed dynamic adjustment of saccade length must

reflect general task demands rather than demands specific to reading.

Additionally, a direct comparison of the performance of explicit computational

versions of the dynamic-adjustment versus default-targeting models suggests that the

former provides a more accurate description of participants’ performance in our

experiment, lending further general support to the hypothesis that, during the reading

of Chinese text, readers modulate saccade lengths in a manner that is sensitive to the

moment-to-moment processing difficulty, rather than selecting one (of a small

possible number) or pre-defined saccade targets (e.g., the beginning or middle of the

upcoming word). Of course, it is important to consider this conclusion in relation to

the full range of possible accounts of saccade targeting during reading.

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At one extreme, readers might adopt some simple heuristic (e.g., the “fixed

saccade length” assumption used in the simulations reported by Li et al., 2011; see

also Yan et al., 2010) in deciding where to move their eyes. At the other extreme,

readers might use specific saccade targets, as posited by current models of

eye-movement control during the reading of alphabetic languages like both English

(e.g., E-Z Reader: Reichle, Pollatsek, Fisher, & Rayner, 1998; Reichle, Warren, &

McConnell, 2009; Reichle, 2011) and German (e.g., SWIFT: Engbert, Nuthmann,

Richter, & Kliegl, 2005; Schad & Engbert, 2012). Neither of these extremes provides

a plausible account of saccadic targeting in Chinese or our experiment; whereas the

former fails to predict that saccade lengths are modulated by processing difficulty

(e.g., Li et al., 2014; Liu et al., 2015; Wei et al., 2013), the latter erroneously predicts

preferred-viewing locations (which are generally absent; e.g., Li et al., 2011; Liu et al.,

2016; Liu, Huang, Gao, et al., 2017; Liu, Guo, et al., 2017). Therefore, through the

process of elimination, one is left with our preferred account: Chinese readers’

decisions about where to move their eyes are based on information other than word

boundaries. By our account, this information is the relative level of processing

difficulty being experienced at any given point in time. In the context of actual

reading, this processing is related to the segmentation and/or identification of the

upcoming words, while in the context of our Landolt-C paradigm, the processing is

related to the discrimination required to know whether an upcoming cluster is likely to

be a target.

Of course, we acknowledge that our account is incomplete, and that the

“boundary conditions” that determine when participants or readers shift from using

default saccade targets to dynamically adjusting the lengths of their saccades has not

been established. For example, although we have argued that the latter strategy

provides the best account of saccadic targeting in Chinese reader, the two leading

models of eye-movement control in reading (i.e., E-Z Reader and SWIFT) were

developed to explain the patterns of eye movements observed during the reading of

alphabetic languages, and consequently, incorporate the default-targeting assumption

to good approximation. However, evidence that this assumption is only an

approximation is provided by demonstrations that, even in the reading of English, for

example, the length of a saccade exiting a word can be modulated by its frequency

(e.g., Rayner, Ashby, Pollatsek, & Reichle, 2004; White & Liversedge, 2006). We

14

therefore suspect that, in the context of reading, the decisions about where to move

the eyes is jointly determined by the quality (i.e., regularity) of possible saccade

targets, as well as whatever difficulty the reader might currently be experiencing in

lexical processing. This perspective suggests that both factors contributed to the

decisions, with some sort of weighting being assigned to each factor (e.g., more

weight to default targets in English vs. more weight to saccade-length adjustment in

Chinese), rather than being a strict dichotomy. Future empirical work is required to

show this conclusively; future modeling work is required to demonstrate how the two

types of strategies might be integrated and how this integration might be modulated

by languages, writing systems, and possibly other variables.

15

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Table 1. LMM analyses of first-fixation durations (ms).

PredictorsModel Values4 (ms)

b SE t p Min. Max.

ClusterPosition Intercept 328.58 9.80 33.54 < 0.001 - -

Previous# Characters1 0.11 1.40 0.08 0.940 301.35 301.67

Gap Size2 -1.12 1.22 -0.92 0.363 303.19 299.83

CurrentRepetitions3 0.04 0.07 0.56 0.574 300.55 302.47

Gap Size2 -6.16 1.29 -4.77 < 0.001 310.75 292.27

Subsequent# Characters1 0.15 1.35 0.11 0.913 292.05 292.49

Gap Size2 -4.20 1.20 -3.49 0.001 298.56 285.98

Notes:1. Number of characters: min. = 1 character, max. = 4 characters.2. Gap size: min. = 1°, max. = 4°.3. Repetitions: min. = 1, max. = 50.4. Estimates of predicted variable values were calculated while fixing the values of the other variables equal to their means.

20

Table 2. LMM analyses of gaze durations (ms).


b SE t p Min. Max.


Previous# Characters1 -0.90 1.87 -0.48 0.629 348.53 345.82

Gap Size2 -3.52 1.61 -2.19 0.031 352.46 341.90

CurrentRepetitions3 -0.21 0.11 -1.98 0.048 352.29 342.06

Gap Size2 -18.29 2.25 -8.14 < 0.001 374.61 319.74

Subsequent# Characters1 -2.39 1.90 -1.26 0.209 323.33 316.16

Gap Size2 -6.87 1.79 -3.85 < 0.001 330.05 309.43


21

Table 3. LMM analyses of total-viewing times (ms).


b SE t p Min. Max.


Previous# Characters1 -1.83 2.80 -0.65 0.518 381.57 376.09

Gap Size2 -2.26 2.18 -1.04 0.307 382.21 375.45

CurrentRepetitions3 -0.56 0.12 -4.60 < 0.001 392.52 365.13

Gap Size2 -24.15 2.97 -8.13 < 0.001 415.05 342.61

Subsequent# Characters1 -2.31 2.11 -1.09 0.275 346.08 339.14

Gap Size2 -10.36 2.17 -4.78 < 0.001 358.15 327.07


22

Table 4. LMM analyses of progressive and incoming saccade length (in characters).

Saccade Type VariablesModel Values3

(characters)

b SE t p Min. Max.

Progressive Saccade

Intercept 3.02 0.22 13.70 < 0.001 - -

Repetitions1 -0.01 0.003 -1.61 0.119 3.33 3.07

Gap Size2 0.12 0.02 7.00 < 0.001 3.01 3.38

Incoming Saccade

Intercept 1.86 0.04 45.93 < 0.001 - -

Repetitions1 0.001 0.001 0.96 0.344 2.08 2.11

Gap Size2 0.09 0.01 7.92 < 0.001 1.97 2.22

Notes:1. Repetitions: min. = 1, max. = 50.2. Gap size: min. = 1°, max. = 4°.3. Estimates of predicted variable values were calculated while fixing the values of the other variables equal to their means.

23

Figure Caption

Figure 1. Examples of two Chinese sentences and their translations. In the first,

the sequence of four underlined characters correspond to two words. In the second,

the same characters correspond to a single word.

Figure 2. Examples of experimental materials, with two targets (i.e., circles) and one

exemplar cluster being rendered in gray for illustrative purposes.

Figure 3. The predicted relationship (in character spaces) between the saccade launch

site (from the pre-exemplar region) and the subsequent fixation landing site (on the

exemplar) generated by the: (A) default-targeting model (Simulation 1); and (B)

dynamic-adjustment model (Simulation 2). The symbols show the observed means

averaged within each launch-distance bin, the black and gray lines respectively

represent the simulated progressive and incoming saccades, and both launch sites and

landing sites are aligned to the beginning of the exemplar. The shaded region in panel

(A) demarcates the default-targeting model’s performance across its full parameter

domain (i.e., between the two extreme cases in which exemplars are never vs. always

segmented in the parafovea). (Notes: LE = larger gap-size exemplars; SE = smaller

gap-size exemplars; PS = progressive saccade; IS = incoming saccade.)

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Figure 1.

25

Figure 2.

26

Figure 3.

27

Appendix

Simulation 1 parameters: As Equation 1 shows, polynomial regression functions

were used to estimate the probabilities of observing the four different types of

saccades using the method of least squares. Because these probabilities summed to 1

for each saccade launch site, only the probabilities associated with three saccades

types were estimated. Finally, the values of σ, which control saccadic-error variability,

were chosen to maximize the goodness-of-fit to the empirical fixation-position

distributions of incoming saccades in the smaller and larger gap-size conditions

separately (MSE = 0.327 and 0.847, respectively). Table A1 lists the best-fitting

parameters. Figure A1 shows that these parameters accurately describe the empirical

data (i.e., probability of refixating pre-exemplar region: MSE = 1.783 × 10-5;

probability of fixating exemplar center: MSE = 3.479 × 10-4; probability of fixating

exemplar beginning: MSE = 1.951 × 10-5). Simulation 1 thus required 20 free

parameters.

Simulation 2 parameters: The expected value of Equation 4 is λβ (η0 + η1condition),

or the predicted value using the mean first progressive saccade length from the

pre-exemplar region. Thus, two groups of parameters, λβη1 and λβη0, are coefficients

for a regression equation for progressive saccade length using gap-size condition as a

predictor variable (i.e., smaller condition: 1-2°; larger condition: 3-4°). And because

the variance associated with Equation 4 (i.e., the variance associated with saccadic

error) is given by the quantityλ2β2(η0 + η1condition), the parameter pair λβ can also be

estimated using the empirical distribution of fixations on exemplars. The final

parameter values used to simulate the results were: η0 = 3.178; η1 = 0.254; and λβ =

1.166 and 0.875 for the smaller and larger gap-size conditions, respectively.

Simulation 2 thus required four (groups of) free parameters.

28

Table A1. Best-fitting parameters for default-targeting model (Simulation 1).

Exemplar Gap Size Saccade Type k2 k 1 k 0 σ

Larger

Refixate Pre-Exemplar Region 0.139 0.121 0.024

0.847Fixate Exemplar Center -0.115 -0.224 0.354

Fixate Exemplar Beginning -0.060 -0.155 -0.026

Smaller

Refixate Pre-Exemplar Region 0.137 0.093 0.018

0.327Fixate Exemplar Center -0.158 -0.289 0.372

Fixate Exemplar Beginning -0.064 -0.159 -0.004

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Figure A1. Observed (symbols) and estimated (lines) probabilities of refixating the

pre-exemplar region, fixating the exemplar center (i.e., single fixation), fixating the

exemplar beginning (i.e., first-of-multiple fixations), and skipping the exemplar, as a

function of exemplar gap size. (Notes: SE = smaller gap-size exemplars; LE = larger

gap-size exemplars.)

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