Forty-five participants (age in 16–25 years, 27 females) were recruited from adult education centers, community college, and neighborhood-gathering places. Some participants had their secondary schooling interrupted but were then seeking a high school equivalency certificate or resuming work toward a regular high school diploma. At the time of experiment, most participants were enrolled in education programs (e.g., high school, adult school, or community college) (Braze et al., 2007, 2016). All participants were English monolinguals, and had normal or corrected-to-normal vision. They were prescreened to ensure the ability of reading simple sentences with comprehension. Data from one participant were excluded due to not completing all study components.

According to the power analysis in mixed-effects models (Brysbaert and Stevens, 2018), this number of sample size, together with the rich amount of eye-movement observations obtained during reading of multiple (72) sentences containing numerous (358) word types (see section 3.3 Materials and design), is sufficient to detect reliable significant factors.

Each participant was assessed in six domains of language and literacy skills, which served as the bases for analysis. Table 1 shows the raw (and normative wherever available) scores of each measure and a key to the labels of them. The domains and the tests used to measure them were:

These individual difference measures can be grouped into two sets: those explicitly linked to reading ability (reading comprehension, decoding skill, and oral reading fluency), and those not (listening comprehension, vocabulary, and verbal working memory) (Gough and Tunmer, 1986; Hoover and Gough, 1990). They tap into abilities equally important to comprehension, no matter whether the language input arrives by ear or by eye.

In addition to these domains, we also assessed print experience by a magazine title recognition checklist (MRT) and an author recognition checklist (ART) (cf., Stanovich and Cunningham, 1992) to gauge a person’s experience with language in printed form, which for literate individuals may well be a substantial part of their overall language experience, and visual working memory based on a computerized version of the Corsi Blocks task (corsi) (Corkin, 1974) implemented in Psyscope (Cohen et al., 1993). Given the fact ART and MRT only show high validity and reliability in proficient readers (e.g., university students) in their dominant language (McCarron and Kuperman, 2021), whereas our study is based upon participants having a wide span of reading skills, we excluded print experience in the regression analyses. In addition, compared to visual working memory, verbal working memory is more relevant to our sentence reading experiment, so we also excluded visual working memory in the regression analyses.

Prior to regression modeling, we examined the distributions of raw scores for deviations from normality. Several scores showed high skewness (absolute values over .5). To them, we applied Box-Cox transformations (Box and Cox, 1964) using the bcpower function in the R package car (Fox and Weisberg, 2011). All variables, transformed or not, were standardized by converting to Z-scores. Table 2 is the correlation table of the transformed and standardized measures (cf., Braze et al., 2007, 2016).

To reduce collinearity and the total number of predictors in the regression models, we combined measures tapping into common latent constructs. This was done by (a) taking the average of the transformed and standardized scores, and then (b) converting the average scores back to Z-scores. Measures of vocabulary and listening comprehension were combined into a composite measure of oral comprehension plus vocabulary (oral.comp) (Tunmer and Chapman, 2012; Braze et al., 2016; Kukona et al., 2016). Composites were also derived for decoding (decod.comp) and reading comprehension (readcomp.comp). Table 3 shows the correlation table of the centered and transformed skill measures.

It is not surprising that the correlation between reading comprehension and oral comprehension plus vocabulary is high, since oral knowledge is an important indicator of reading comprehension (see section 2. Target skills and recent studies on them). Table 4 shows the statistics of the regression models between reading comprehension and oral comprehension plus vocabulary, decoding, and both, respectively. Consistent with early findings (Braze et al., 2007), a combination of both skills largely explains the variation of reading comprehension: R² of the model using decoding is .370, R² of the model using oral comprehension plus vocabulary is .712, and multiple R² of the regression model using both decoding and oral comprehension plus vocabulary is .738. Notably, we exclude reading comprehension from the list of predictors in the regression models.

After these preprocessing stapes, the skill measures used in our regression analyses are: (a) oral comprehension plus vocabulary (oral.comp); (b) decoding (decod.comp); (c) oral reading fluency (gort.wpm); and (d) verbal working memory (sspan.corr).

Participants were asked to read 72 individual sentences while their eye-movements were recorded. Presentation order was pseudo-random across participants. These sentences were filler items in a study of comprehension process in young adults with limited literacy skills (Braze et al., 2006). All of the sentences were grammatical and transparent in meaning. The word types in them were carefully selected among high frequent words, and common names for persons, states, or holidays. The linguistic aspects of these sentences, such as part of speech or syntactic complexity, were carefully controlled. Supplementary Table 1 shows the complete list of the sentences. Many of these sentences were simple in terms of structure; forty-six stimuli sentences (over 79%) had no embedding structures, e.g., “Most of the students will be going to the class picnic next month.”; and the other 26 had one dependent clause, e.g., “The waiter had told the customer that the pies were fresh.” There were 503 unique word types (819 word tokens) in these sentences, an average of 11.375 word tokens per sentence (range = 11–16). Note that previous studies on university students involved sentences with increasing complexity in semantics and syntax (e.g., Kuperman and Van Dyke, 2011; Kuperman et al., 2018)), we leave the investigation of the relations between sentence complexity, reading skills, and online reading behavior for future work.

Before the experiment, we asked some individuals to evaluate the understandability of these sentences, based on a scale of 5, from “easy to understand” to “hard understand”. These individuals were recruited similarly as the experiment participants, but did not participate the experiment. All of them marked the filler sentences as “easy to understand”.

For each word in a sentence, we recorded its ordinal position in the sentence (note that the sentence initial and final words were excluded), its length in characters (Len_W), and its frequency of occurrence per million words (Freq_W). Word position is a context-dependent property, but word length and frequency are independent of sentence. Lexical frequencies were obtained from the Corpus of Contemporary American English (COCA).¹ Frequency summaries for our materials exclude contractions (n = 2) and proper nouns (n = 23), both having no COCA frequencies. Possessive forms (n = 6) used the COCA frequencies of their uninflected forms. Analyses otherwise included all the remaining words found in the sentences. Most of the type frequencies showed skewed distributions, and thus log-transformed (base e). Following Kuperman and Van Dyke (2011, 2013) and other standard practice, we excluded words with a high likelihood of being skipped (i.e., highly-frequent and very short words).

Table 5 shows the lexical properties of the words contained in the sentences. Regression models targeting online reading indicators (gaze measures) at a word also included parameters for length and frequency of the previous and subsequent words. Differences between Len_W and Len_W–1 (or Len_W+1) are due to the exclusion of sentence initial and final words in the current word set (see Eye-movement measures), so are differences between Freq_W and Freq_W–1 (or Freq_W+1).

Prior to the analyses, we mean-centered lexical properties. Word length was measured in terms of number of characters. Log-transformed word frequency was standardized. Word frequencies were highly correlated with lengths of respective words: Pearson’s r between current word length and current word frequency was −0.731 (p < 0.001), −0.775 (p < 0.001) between previous word length and previous word frequency, and −0.752 (p < 0.001) between next word length and next word frequency. Following Kuperman and Van Dyke (2011), we residualized word frequencies against lengths of respective words. This was done by fitting a regression model for each of the three properties (previous, current, and next words) in which the frequency of the relevant word was predicted by its length. We took the residuals (distances between the observed and fitted values) of these models as the values of word frequency. The residualized frequencies remained strongly correlated with the original frequencies but orthogonal to the lengths of respective words: Pearson’s r between residualized and original frequencies was 0.697 (p < 0.001) for current word frequencies, 0.643 (p < 0.001) for previous word frequencies, and 0.665 (p < 0.001) for next word frequencies. The residualization (or orthogonalization) procedure does not change the result for the residualized variable, the overall explanatory power of the model, and any indices of model fit. Some scholars pointed out that such orthogonalization (Wurm and Fisicaro, 2014) could not be a useful remedy for collinearity; note that in our experiment, the significant factors reported by the regression analyses using the orthogonalized or unorthogonalized word frequency and word length values are the same.

During the test session, participants were instructed to read, one by one, a number of sentences, and to answer yes/no comprehension questions about the contents of the sentences just read (see Supplementary Table 1). Comprehension questions occurred immediately after some sentences on about a sixth of trials to ensure that participants stayed focused on the reading comprehension task throughout the session. The mean response accuracy to the comprehension questions was 0.913 (SD = 0.067).

Each sentence was presented on a single line vertically centered on a monitor, which was positioned approximately 64 centimeters from the participants’ eyes. The sentences were displayed in a monospace font (Bitstream MonoSpace 821) in black with a light background, at a screen resolution 1,280 × 1,024 and a refresh rate 85 Hz. Font size was set such that each character subtended about 17 minutes of visual arc. Participants wore an EyeLink II head-mounted eye tracker (SR Research), the sampling rate of which was set to 250 Hz. Before the test session, the accuracy of the eye tracker was calibrated based on a 9-point full-screen calibration. Over the course of the session, measurement accuracy was monitored, and if needed, the device was re-calibrated (this was rarely necessary). Data were collected binocularly. Our analyses were based primarily on the right eye data. The right eye data of one participant was problematic, and therefore, the left eye data of the participant were used.

In each trial, a fixation point appeared first at the position of the second character of the first word of the sentence (vertically centered on the screen and about 1.5 inches from the left edge). After fixating on this point, participants pressed a button to bring up a sentence and started to read it. Sentences would not show up if participants were not fixating on this point. After reading the whole sentence, participants clicked the button again. This prompted either the next trial or the display of a comprehension question. Participants gave answers to the comprehension questions by pressing the buttons denoting “yes” and “no,” respectively.

We calculated the eye-movement measures using the in-house software (Braze, 2005), which served to tally gaze measures for each word. We removed fixations shorter than 50 ms, as well as blinks and instances of track-loss. We also excluded the sentence initial and final words from analysis, as a common practice (Kliegl et al., 2004). There remained a total of 15,733 eye-movement observations, covering 358 word types in 72 sentences. The volume of the data is comparable to other eye-tracking studies of individual differences. We focused on five informative, widely-used eye-movement measures (Rayner, 1998):

Measures (1) – (3) are continuous, and (4) and (5) are binary (0/1) to capture possible effects on late stage of processing. Measures (4) and (5) are generally treated as indices of processing load associated with integration difficulty (Rayner et al., 1983, 1989).

Table 6 summarizes the gaze measures, which reflect different, but perhaps overlapping stages of word recognition, text comprehension, and integration during online sentence reading. First fixation duration and first-pass reading time reflect the early stages of print processing involving first encounter of a word by the reader following the default reading direction (left to right in English). By contrast, incidence of first-pass regression and refixation incidence reflect the later stages of print processing involving integration of word information with syntactic and/or discourse context or resolution of ambiguity whenever necessary (Vasishth et al., 2013). Total reading time is a cumulative index of “early” and “late” stages of processing. Individual differences in several components of skilled reading (e.g., decoding, oral reading fluency, vocabulary knowledge, working memory) may have different effects as gauged by these eye-movement measures (Kuperman and Van Dyke, 2011; Nelson Taylor and Perfetti, 2016).

In our dataset, 11,965 out of the total 15,733 eye-movement observations (76.050%) were first-pass eye-movements, and only 3,768 had distinct first fixation durations and first-pass reading times. This indicates that during first-pass reading, most words were fixated exactly once (many words in our simple stimuli sentences were short; see Table 5, over half of the words are shorter than 6 characters). Therefore, it is expected that if any factors can exert significant effects during first-pass reading, they might be captured mainly by first-pass reading time, not by first fixation duration. In addition, our stimuli sentences were simple in structure, which might not trigger many regressive eye-movements or second-pass reading in our participants. Therefore, incidence of first-pass regression and refixation incidence might not capture many significant effects, unlike previous studies involving more complex sentence stimuli (Kuperman and Van Dyke, 2011; Kuperman et al., 2018)).

We conducted two types of statistical analysis.

First, we used linear and logistic mixed-effects regression models (Baayen, 2008; Quené and van den Bergh, 2008) with crossed random effects to analyze respectively the continuous and categorical eye-movement measures and identify interactions between lexical properties and reading related skills. Mixed-effects models allow for simultaneous consideration of multiple covariates, while keeping the between-participants and between-items variance under statistical control (Pinheiro and Bates, 2000; Baayen et al., 2008). Unlike the random forest models used in Kuperman et al. (2018), mixed-effects models can simultaneously address multiple factors having different scales of effect sizes and directly report significance of main effects and/or interactions.

We fit five mixed-effects regression models (Quené and van den Bergh, 2008) targeting the five eye-movement measures, respectively. To reflect the collinearity of a model, we reported the condition number kappa of the model and the maximum variance inflation factor (VIF) of all predictors in the model. A condition number kappa smaller than 10 and a VIF smaller than 5 typically indicate a low degree of collinearity (Kutner et al., 2004).

Each of the five models included 23 fixed effects, consisting of seven lexical properties, four composite and single skill measures, and 12 interactions between each of the skill measures and each of the lexical properties, namely word position in a sentence, word frequency and word length. This approach provides an integrative picture of the effects of multiple skill measures on eye-movement patterns. We controlled the family-wise Type I error probability by setting the critical p value for identifying significance as 0.05/23 ≈0.00217. Given this extremely strict setting of critical p value, we focused on both the significant (p < 0.00217) and marginally significant (p is close to 0.00217) factors.

Each model included the same random effect structure, consisting of two intercepts respectively for subject and for word nested under sentence, and one slope of word frequency for subject. In principle, the slope of word length for subject should also be added in each model. However, as shown above, word length was negatively correlated with word frequency, and post-hoc analyses revealed that the separate contributions of word length to the variation in the dependent variables was <1%. Therefore, we excluded this slope in the regression models. In addition, maximal random effect structures involving other types of slopes are theoretically desirable (Barr et al., 2013) and have been applied in recent individual difference studies (e.g., Protopapas and Kapnoula, 2016). However, we did not pursue such complicated models in consideration of practical constraints on model convergence (Bates et al., 2015a).

All the mixed-effects models were implemented using the R packages lme4 (Bates et al., 2015b) and lmerTest (Kuznetsova et al., 2017).

Second, after identifying significant interactions, we continued examining the dynamics of lexical properties and eye-movement measures in individuals having different levels of target skills. Very few existing studies have investigated such dynamics. Our approach proceeded as follows. Given a two-way interaction between a lexical property and a skill measure, we first divided the participants into a high and a low group based on the medium value of the skill measure to ensure the same number of participants in each group. Then, we plotted the eye-movement measure in each group against the lexical property. A cross-group comparation of the correlations between lexical properties and eye-movement measures could reveal the effects of individual skill on online reading behavior. Instead of binary groups, quartile or quintile groups were used in some studies (e.g., Protopapas and Kapnoula, 2016), given enough participants in each group for statistical analysis. To identify correlation, we first fit a nonlinear polynomial regression (loess) between the lexical property and the eye-movement measure as the baseline, and then, used widely-adopted regression models in psychological and educational research to quantify the pattern of the correlation. For simplicity, the current study only compared simple linear regression (or logistic regression) and segmented linear regression. For each model, lexical property was treated as an independent variable, and eye-movement measure a dependent one.

Models were compared based on Akaike information criterion (AIC) and mean squared error (MSE). AIC deals with the trade-off between the simplicity and goodness of fit of a model (Akaike, 1974), but AIC alone is less informative when multiple models have similarly high or low AICs (Burnham and Anderson, 2002). In this situation, MSE is referred to, which compromises variance and bias to minimize both (see Equation 1, where obs_i is the observed essay score, pre_i is the predicted score from a model, and n is the number of data points). The best model that appropriately reflects the correlation between lexical property and eye-movement measure is the one having smaller AIC and MSE.

A recent study examining the correlation between typing speed and writing essay score has used a similar method to identify the dynamics of such correlation (Gong et al., 2022). In that study, additional models like logistic regression and ordinal categorical regression were used for model fitting, but the segmented linear regression remained the best fitting model.

In our study, the segmented regression was implemented using the R package segmented (Muggeo, 2008).

Table 7 lists one interaction between word frequency and decoding skill in determining first fixation duration. Its p value is over .00217, so it is not marked as a significant interaction.

Table 8 shows two interactions on first-pass reading time whose p values are below .01. Given their p values are smaller than (or close to) .00217, they are marked significant (or marginally significant). Figure 1 illustrates these interactions by showing that the correlation between word length and first-pass reading time is contingent on oral comprehension plus vocabulary and verbal working memory.

Figure 1 shows that the sensitivity of first-pass reading time to word length is better described as a segmented linear relation than a simple linear relation: the segmented linear curves well match the baseline loess curve and have smaller AIC and MSE than the linear curve (see Supplementary Table 2). In each panel, the segmented linear curve shows a pivot value of word length, below which the slop of the fitting curve remains small, whereas above which the slope increases, indicating that the participants showed longer first-pass reading time when reading longer words. Between the two panels in each figure, the sensitivity of first-pass reading time to word length exhibits different tendencies.

In Figure 1A, compared to the poor readers having low levels of oral comprehension plus vocabulary (the right panel), for words of the same length, the good readers having high levels of that skill (the left panel) had shorter first-pass reading time. Also, the good readers showed smaller slopes in the segmented linear curve than the poor readers (i.e., 5.585 vs. 8.938 and 19.39 vs. 29.757), indicating that the good readers were less sensitive to word length. Finally, the pivot points of word length were similar in the poor (1.652) and good (1.276) readers.

In Figure 1B, similarly, compared to the good readers having high levels of verbal working memory, the poor readers having low levels of that skill spent relatively more time in reading long words, and for both long and short words, their first-pass reading times remained more sensitive to word length (shown by the slopes of the segmented linear curves, 26.938 vs. 21.662 and 8.051 vs. 5.974). Nonetheless, the pivot points of word length in the poor and good readers were similar (1.435 vs. 1.418).

Table 9 shows three interactions on total reading time whose p values are below .01, two of which are marked as marginally significant and visualized in Figure 2.

Figure 2 illustrates a segmented linear relation between total reading time and word position in a sentence. Total reading time drops when the participants read the first few words in a sentence, and then, increases when they read the latter words in a sentence. The negative and positive slopes of the segmented linear fitting curves clearly reflect this bifurcating tendency.

In Figure 2A, compared to the good readers having high levels of oral reading fluency, the total reading time of the poor readers having low levels of that skill is generally longer, and it is more sensitive to the beginning words in a sentence, as shown by the more negative slopes (−27.098 vs. −11.428) below the pivot points of word position. However, the smaller positive slopes (3.008 vs. 17.01) above the pivot points suggest that the total reading time of the poor readers is less sensitive to the latter words in a sentence. In addition, the pivot points of word position increases from −0.715 in the poor readers to 1.375 in the good readers.

In Figure 2B, compared to the good readers having high levels of verbal working memory, the total reading time of the poor readers having low levels of that skill is less sensitive to word position in a sentence, as shown by the smaller absolute slopes both below (−15.694 vs. −19.821) and above (8.387 vs. 10.615) the pivot points of word position. In addition, the pivot points in the two panels drop from 0.684 in the poor readers to 0.250 in the good readers.

A comparison of Figures 1, 2 reveals that verbal working memory casts its influence on first-pass reading time via interaction with word length and total reading time via interaction with word position. To be specific, compared to the poor readers having low levels of verbal working memory, the first-pass reading time of the good readers is less sensitive to word length, but their total reading time is more sensitive to word position.

Table 10 shows that the interaction between decoding and word position had a p value below .00217. Figure 3 visualizes this significant interaction.

Figure 3 shows a segmented linear relation between first-pass regression and word position in a sentence. The probability of regression during the first-pass reading starts to increase when the participants read the latter words in a sentence. Compared to the poor readers having low levels of decoding, the probability of regression during the first-pass reading of the good readers increases a lot on the latter words in a sentence, as shown by bigger slopes (.042 vs. .016) above the pivot points of word position. The pivot points of word position are similar in the poor (2.108) and good (2.537) readers.

No interactions on refixation incidence have p values below .01.

Previous studies have reported significant main effects of some of the language and literacy skills discussed in this paper, or bigger effect sizes of these skills than those of lexical properties (e.g., Kuperman and Van Dyke, 2011). However, in our analyses, main effects of skill measures never reach statistical significance, though those of lexical properties often do. The effect sizes of the skill measures are also smaller than those of lexical properties. This is because that our study focused on individuals with a much wider range of language and literacy skills; only those having the highest scores of the skill measures were comparable to university students (cf. Braze et al., 2007). Such wide range of individual differences in the skill measures could result in insignificance and low effect sizes of the measures on online reading behavior. These findings can enrich existing evidence and trigger revisits on the theoretical discussions of individual differences and their roles in reading process and outcome (comprehension) (Bennink and Spoelstra, 1979; Bleckley et al., 2003).

Although lacking direct influence on online reading behavior, some of the language and literacy related skills could significantly influence online reading behavior via interactions with lexical properties. Our study showed that oral comprehension, vocabulary, verbal working memory, oral reading fluency, and decoding could predict online reading patterns via interactions with word length or position in a sentence. We also compared the effects of the interactions involving these skills on online reading patterns between the good and poor readers with respect to these skills.

To be specific, oral comprehension and vocabulary interact with word length to predict first-pass reading time (see Figure 1A); readers with good oral comprehension skill and vocabulary knowledge could efficiently process words with various lengths, thus being less troubled by long words during first-pass reading. First-pass reading time arguably reflects the duration of lexical processing, including recognition of orthographic or phonological features of a word and retrieval of semantic information from memory once attention is allocated to the word (Inhoff, 1984). This finding contributes to recent discussions on whether vocabulary knowledge could influence reading comprehension over and above the effect of language comprehension including listening comprehension (Braze et al., 2007, 2016; Tunmer and Chapman, 2012; Protopapas et al., 2013). At the early stage of print processing vocabulary knowledge already helps good readers efficiently reduce first-pass reading time on words of various lengths.

Verbal working memory presumably affects the rate at which word information is assimilated during first-pass reading, especially on long words. As shown in Figure 1B, the first-pass reading time of the good readers with high levels of verbal working memory are less sensitive to word length than the poor readers. In addition, verbal working memory helps predict total reading time via interaction with word position (see Figure 2B). Total reading time reflects the integration of early and late processing during lexical access. Word position in a sentence is a context-dependent property. A general increase in total reading time on words toward the end of a sentence reflects so-called wrap-up effects (Rayner et al., 2000; Warren et al., 2009). In our study, such effects became more explicit in readers having high levels of verbal working memory; efficient verbal working memory reduces the processing time for the first few words of a sentence but induces more wrap-up effects towards the end of a sentence.

Oral reading fluency interacts with word position to predict total reading time (see Figure 2A); a high level of this skill is associated with a less sensitivity to the first few words in a sentence, but more sensitivity to latter words in a sentence, in line with the wrap-up effects. In addition, less fluent readers generally have more difficulty in processing individual words and integrating word semantics with context, and hence spend more time reading a few words of a sentence; by contrast, more fluent readers spend less time reading words in a sentence, especially those near the beginning or in the middle of a sentence. These findings are in line with and complement the existing theories on oral and/or silent reading fluency (Fuchs et al., 2001; Tilstra et al., 2009; Kim et al., 2011; Silverman et al., 2012; Ashby et al., 2013). Furthermore, as shown in Figure 2, there is no monotonic change of the correlation between word position and total reading time. This indicates that the effects of oral reading fluency and verbal working memory on regulating online reading patterns are complex, possibly also subject to other factors.

Decoding skill interacts with word position to predict probability of first-pass regression (see Figure 3); good decoders tended to have more regressive reading when reading words towards the end of a sentence, reflecting their sentence decoding processes. Early studies have reported the effects of decoding on early (first-pass reading time) and overall (total reading time) reading and re-reading probability (Kuperman and Van Dyke, 2011; Nash and Heath, 2011; Kuperman et al., 2018). In our study, the effect of decoding on re-reading probability was fulfilled via an interaction with word position. All these are in line with the claims that decoding skill is among the key factors in lexical access (Barth et al., 2009; Hulme and Snowling, 2012) and provide evidence for VET (Perfetti, 1985; Shankweiler and Crain, 1986) and LQH (Perfetti and Hart, 2002; Perfetti, 2007) by showing how decoding influences reading processes.

In addition to confirming that language and literacy skills can influence online reading behavior indirectly via interactions with lexical properties, our study further investigated the dynamics of the correlation between lexical properties and eye-movement measures regulated by particular individual skills. Our quantitative analyses revealed that such dynamics cannot be simply described as a linear relation; instead, many of the correlations follow a segmented linear relation, with at least two distinct slopes throughout the values of the relevant lexical properties. Some of the dynamics are monotonic (see Figure 1), with positive and increasing slopes around long words, whereas others are not (see Figures 2, 3), with a transition from a negative to a positive slope. The observed segmented linear relations suggest a complex effect of key language and literacy skills on regulating reading patterns via interactions with word length or position. Between the good and poor readers based on some skills, the durations of reading time are different, so are the sensitivity of reading time or regression probability to word length or position. In addition, the pivot values of word length or position in the segmented linear correlations indicate a transition of the degree of correlation. Note that in many cases, the pivot points are not close to the mean value 0, so arbitrary binary segmentation based on word length or position (Kuperman et al., 2018) cannot clearly reveal such dynamics. This dynamics echoes the effects of interactions between lexical properties and skill measures on online reading behavior: due to individual skills, the unimodal associations between eye-movement patterns and lexical properties are broken, the degrees of associations become different when the values of lexical properties are below or above the pivot points, and the high and low levels of the skills further influence the pivot lexical property values and the degrees of associations below and above the pivot values.

The observed dynamics in all these aspects can lead to more comprehensive theories on the dynamic relations between individual skills, text properties, and reading process. For example, some theories of reading (Perfetti and Hart, 2002) and empirical studies (Johnston and Kirby, 2006; Savage, 2006) have challenged the linear assumption between decoding and reading outcomes like reading comprehension. For example, Johnston and Kirby (2006) showed that naming speed, a measure of decoding skill, had its primary effect on less able readers. A recent study of reading assessment has shown distinct relations between decoding skill and comprehension scores between good and poor decoders in Grades 5 to 10 (Wang et al., 2019). Some eye-movement studies have revealed close relations between components of decoding (e.g., phonemic awareness) and other skills (e.g., reading fluency) (Barth et al., 2009; Ashby et al., 2013). Our study enriched the findings in this line of research by visualizing the segmented linear relations between lexical properties and online reading behavior, which are manipulated by individual differences in individual language and literacy skills. This study can also inspire more empirical studies to further investigate what factors help shape the slopes and pivot values in the segmented linear models.