Abstract
Repetitions of letters in words are frequent in many languages. Here we explore whether these repetitions
affect word recognition. Previous studies of word processing have not provided conclusive evidence ofdifferential processing between repeated and unique letter identities. In the present study, to achieve
greater power, we used regression analyses on existing mega-studies of visual word recognition latencies.
In both lexical decision (in English, Dutch, and French) and word naming (in English), there was strong
evidence that repeated letters delay visual word recognition after major covariates are partialed out. Thisdelay was most robust when the repeated letters occurred in close proximity but not in immediateadjacency to each other. Simulations indicated that the observed inhibitory pattern of repeated letters was
not predicted by three leading visual word recognition models. Future theorizing in visual word
recognition will need to take account of this inhibitory pattern. It remains to be seen whether theappropriate adjustment should occur in the representation of letter position and identity, or in a more
precise description of earlier visual processes.

Keywords: visual word recognition; repeated letters; regression; megastudies; computational modeling;
letter processing

1. Introduction
Reading alphabetic languages requires the successful identification of letters and their position within theword. In this way, the perceptual system discriminates between lexical units that bear strong form
resemblance. It can determine the difference between two words with the same length but differing by asingle letter (“orthographic neighbors”, such as farm– form; Coltheart, Davelaar, Jonasson, & Besner,1977), have the same letters but in a different order (from-form), or have different length, but many
common letters (though - through). One of the goals of orthographic processing research has been to
explain how this discrimination is achieved and how bottom up sublexical processes such as encoding ofletter identities and their position mediate recognition of the whole word unit. The empirical results havemotivated the development and revision of visual word recognition models in which those initial
perceptual stages are implemented in their encoding schemes. These schemes determine the models’
predictions regarding the word candidates that are considered and, ultimately, the factors affecting lexical
selection. An example of such a factor that will be on focus in this work is the presence of letter
repetitions in words.
Letter repetitions are frequent in many languages, especially in words with more than one syllable.
Understanding how strings with repetitions are processed is therefore vital for understanding reading. The
exploration of repeated letter units could be informative as to how the visual system processes identicalelements in early stages of word recognition and is intrinsically related to the letter identity and letter
position encoding. In this context, repeated letter effects have received relatively little attention in theorthographic processing literature which has been more focused on the problem of letter positional
uncertainty (e.g. Kinoshita & Norris, 2009; Lupker, Perea, & Davis, 2008; Perea & Lupker, 2003; 2004;
Peressotti & Grainger, 1999; Schoonbaert & Grainger, 2004; Van Assche & Grainger, 2006; Welvaert,
Farioli, & Grainger, 2008) and the need to incorporate a mechanism for positional ambiguity in theencoding schemes of the visual word recognition models (e.g. Davis, 2010; Gomez, Ratcliff & Perea,
2008; Grainger, Granier, Farioli, Van Assche, & van Heuven, 2006; Grainger & van Heuven, 2003;
Norris & Kinoshita, 2012) .
The problems of letter repetition and positional uncertainty might be deeply intertwined: The initialambiguous location of a single letter a might well be perceived as two letters a in two distinct locationsand vice versa. Exploring the repeated letters effect in more depth might therefore have important
implications for further developing the encoding schemes of the visual word recognition models. We will
therefore first review some relevant computational models (Davis, 2010; Grainger & van Heuven, 2003;
McClelland & Rumelhart, 1981; Norris, 2006) and their encoding schemes with an emphasis on the2processing of letter repetitions and its consequences. We will further review the relatively inconsistentprevious experimental evidence for repeated letter effects. This will motivate an alternative approach tothe problem of repeated letters: regression analysis on response times from large databases of visual word
recognition tasks (megastudies). The results of the regression analysis on the empirical data will then becompared with the predictions of the discussed computational models regarding effects of letter
repetitions.
Research on letter position encoding schemes is often motivated by a comparison with the one of the mostinfluential models in visual word recognition, the Interactive-Activation (IA) model (McClelland &Rumelhart, 1981). This model explains lexical selection by means of spreading activation in a cascaded
and interactive manner between representations located in three levels of a hierarchical structure (feature,letter, word). Word nodes that are consistent with the perceptual input get activated, while inconsistentones get inhibited. Once activated, word candidates suppress each other through lateral inhibitory links
and compete until the activity of a single word reaches an activation threshold associated with lexical
selection. This model has a slot-based scheme in which every letter is assigned to a specific slot - which
defines its position within the word - and projects its activity only with regard to this slot. The letter a infirst position will activate words containing the letter a in first position and will inhibit others that startwith a different letter. It will not activate words in which a is in another position. This model could
therefore not predict any effect of letter repetition since its slot-based encoding scheme treats two
identical letters in different positions as two different letters. The IA model could explain how the reading
system could discriminate between words with equal length and different letter identities in some of thepositions but is not in accordance with evidence from the masked priming literature suggesting that theperceptual system has a considerable degree of positional tolerance.
Contrary to the prediction of the IA model (McClelland & Rumelhart, 1981), primes formed by lettertranspositions (anwser-ANSWER) produced as strong priming effects as those identical to the targets(Forster, Davis, Schoknecht, & Carter, 1987). In addition, letter strings formed by transposing letters froma base target word have been demonstrated to be orthographically more similar to the target than strings
with replaced letters in the corresponding mismatched positions. This finding has been observed withadjacent transpositions, such as jugde from the target judge, as opposed to the replaced letter control
prime jupte (Perea & Lupker, 2003), and has been extended to nonadjacent cases (e.g., caniso–CASINO;
Lupker, Perea, & Davis, 2008; Perea & Lupker, 2004). The slot-based scheme was also falsified bystudies demonstrating a priming effect with relative position primes in which the absolute order of theletters was disrupted by either letter deletions (e.g., BLCN-BALCON, Grainger et al., 2006; Peressotti &Grainger, 1999), or insertions in the primes (e.g., juastice–JUSTICE; Van Assche & Grainger, 2006;
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Welvaert, Farioli, & Grainger, 2008). These results suggest that an absolute position specific encoding inthe slot-based scheme is inaccurate and motivated the proposal of alternative letter position and identity
encoding mechanisms.
Several interactive activation framework models with different encoding schemes were later developed.
In this work, the focus will be on two of them: The relative position parallel open bigram model (Grainger& van Heuven, 2003) and the Spatial Coding Model (Davis, 2010), which are both based on theinteractive-activation architecture but have entirely different schemes with which they account for thetransposed letters and relative position priming effects. In the parallel open bigram model, the letter level
representations from the IA model are replaced by representations of open bigrams. They are in therelative position map level, at which the letter positions are encoded after letters have been initially
identified. Position encoding is achieved through activating bigram units containing information of theposition of one letter relative to the others, or more specifically, whether a letter is located to the left or to
the right of the other letters in the word (up to two intervening letters). The word SILENCE is therefore
represented by the open bigrams SI, SL, SE, IL, IE, IN, LE, LN, LC, EN, EC, EE, NC, NE, CE. In
analogy to the letter nodes in the IA model, the open bigram nodes are connected to orthographic word
representations with excitatory and inhibitory links. Bigrams consistent with the input get activated andfeed forward to the word nodes. Words containing active bigrams receive activation, while those lacking
consistent bigrams get inhibited. As in the IA model, lexical competition mechanisms are implemented byinhibitory lateral connections between the nodes at the word level. In this encoding scheme, transposed
letter and relative position primes will contain most of the targets’ constituent representations in the formof open bigrams. These primes will pre-activate targets stronger than corresponding control primes that
contain fewer consistent bigram units. In this way, the model could successfully simulate both transposed
letter and relative position priming effects. When stimuli contain letter repetitions, fewer bigrams will be
activated than with stimuli composed of unique letters, and therefore the expectation is that the open
bigram model would be likely to predict inhibitory effects of repeated letters (as noted by Schoonbaert &Grainger, 2004).
The Spatial Coding Model, unlike the relative position open bigram model (Grainger & van Heuven,2003), retains the letter representations in its architecture. Unlike the IA model, however, the letter
position and identity encoding scheme is not channel specific. In the Spatial Coding Model, a consistentletter of the input could increase the activity of a word node containing that letter, even if it appears in adifferent position. An important conceptual difference between the Spatial Coding Model and the othertwo previously described models is that the same (letter) units encode letter identities in different
positions, and so the set of letter units involved in representing from and form will be identical, unlike
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IA’s channel specific scheme, in which r in position 2 is different from r in position 3, or the open bigram
model which will encode these words with two nonidentical sets of bigram representations (FR, FO, FM,
RO, RM, OM and FO, FR, FM, OR, OM, RM, respectively). The open bigram model, therefore, has alocal-context dependent encoding scheme and uses different set of representations to encode words
containing the same letters, but in different positions (such as anagrams). Word recognition modelingwith contextual representations such as open bigrams was also implemented by Whitney in her SERIOL
model (Whitney, 2001). This model was developed independently from the relative position open bigram
model and differed in several ways. One major difference was the serial assumption of informationacquisition as opposed to the parallel one in the model of Grainger and van Heuven. In SERIOL, there isa location gradient across letter features which affects the accumulation of letter information. The
activation of the features decreases from left to right and determines the activity in the letter level. The
leftmost letters receive sufficient activation earlier and fire in a sequential manner. Letter orderinformation is thus established through the temporal firing pattern of the letters. This temporal positional
encoding is then translated into nontemporal one through the means of open bigrams. Unlike the model ofGrainger and van Heuven, in SERIOL the bigrams are generated in a serial manner in which the bigrams
containing the leftmost letters are available earlier than the ones containing the rightmost letters in thestring. Despite their differences, both SERIOL and the model of Grainger and Van Heuven have a localcontext specific encoding scheme. The Spatial Coding Model (Davis, 2010), on the other hand, has alocal-context independent encoding scheme, in which the same letter representations will be activated incases of anagrams.
In the Spatial Coding Model, the letter positions in word representations are represented by spatial
patterns. To incorporate letter position uncertainty, each letter position code of the input stimulus has theshape of a normal distribution, rather than a single value, with its spread representing positional
uncertainty. The position code of the letter in the stimulus is assigned dynamically after a rapid left toright serial scan. The spatial pattern of the input is compared to the spatial pattern of a stored word
representation, a procedure called superposition matching. The matching algorithm includes computing
the signal-weight difference functions for each letter of the word representation, sums up all thedifference functions and finally divides the obtained peak of the superposition function by the length of
the word representation. In the case of an identity prime, a perfect match score of 1 is obtained, as all thedifference functions are perfectly aligned with a mean of 0 (and peak value of 1 in the simplified case of
no identity uncertainty). In the cases of transposed letter primes, not all the difference functions are
perfectly aligned to 0, and so in the cases of the positional mismatches, the individual letter peaks do notalign with those of the other letters in the stimulus. Smaller, non-central, values will be added to thesuperposition function, resulting in a lower overall peak for the superposition function, but the total match5

score is still high. Relatively high match scores will also be calculated for primes with (few) insertions ordeletions. Separate mechanisms in the model’s architecture are responsible for the penalization in cases oflength mismatch between the word representation and the input, and for inhibition from inconsistent
stimulus letters.
The Spatial Coding Model has an explicit mechanism that deals with repeated letter cases. It uses bins ofclones of letter receptors that interact and cooperate with the final goal of achieving the maximum matchscore between the input and a word representation while not allowing for the same letter unit (repeated ornot) to contribute more than once for this calculation. With this mechanism, the Spatial Coding Modeleffectively treats repeated letters as different items and is unlikely to predict any effect of letter repetition,
unless the effect occurs due to other uncontrolled lexical or sublexical factors.
Given these models’ different mechanisms relate to repeated letters, comparing simulations of thesemodels to data on repeated letters could be informative for both repeated letter processing per se and theconceptual debate of whether the encoding of letter position and identity should have a local-context
dependent element or not. Should the encoding of additional letter a depend on whether a is alreadypresent in the string or not?
This is important, because as had been noted, although the manner at which letters can be combined toform words is quite rich, letter repetitions are common. This is particularly true for words with more than
one syllable, in which the likelihood of observing a repeated letter identity is higher, especially in thecases of vowels or high frequency consonants. Word recognition experiments targeting letter repetitions
have produced mixed and inconclusive results. Schoonbaert and Grainger (2004) used the masked primed
lexical decision task to compare nonword primes formed by deletion of either repeated or unique letters(balace vs balnce from the target BALANCE) and no difference in priming was found. Nor was arepeated letter effect found in their subsequent experiment, in which they used the items that had served
as primes as nonword targets: Items formed by deletion of a repeated letter were rejected as quickly as
those formed by deletion of a unique letter. However, the design of their masked-priming experiment also
included a between-target manipulation of letter repetition: Both words and nonwords containing letter
repetition took significantly longer time to recognize than items without repeated letters.
In another masked-priming lexical decision study, with prime manipulations using insertions, rather thandeletions in primes (Van Assche & Grainger, 2006), a difference was not found between three related
prime conditions, some of which containing repeated letters. They were constructed by doubling a letterin the target (jusstice-JUSTICE), inserting a letter already present in the target in another nonadjacentposition (justisce), and inserting a different letter in the target (juastice). These related primes all
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produced the same priming effect relative to an unrelated control. In sum, the masked-priming lexicaldecision procedure of these studies did not provide evidence of differential processing of repeated andunique letter identities within words.
Results from two other studies, however, suggest that the presence of letter repetition could affectprocessing difficulty. Gomez et al., (2008) reported a two-alternative forced choice perceptual
identification experiment in which nonword letter strings were recognized significantly less accurately
than strings without repeated letters. The authors interpreted these results as an evidence that repeatedletters were more difficult to perceive causing preference towards a foil with no repetition. Norris,
Kinoshita and van Casteren (2010) argued that an effect of letter repetition was probably not observed in
the Schoonbaert and Grainger (2004) masked-primed lexical decision study due to the lack of sensitivityof the task as well as the use of long stimuli with nonadjacent repetitions. Using shorter stimuli, Norris etal. demonstrated a stronger priming effect in the cases in which a two-replaced-letter primes wereconstructed by doubling a letter from the target (uueer-UNDER), than using two different letters (ulgerUNDER), with a masked-priming same-different task but not with lexical decision task. Again withshorter stimuli, they also showed that deletion of an adjacent repeated letter (anex-ANNEX), has asmaller disruption of the form priming effect than deletion of a unique letter (eupt-ERUPT), suggesting
differential cost of deleting a repeated versus deleting a unique letter from the target. The authorsinterpreted these results as evidence of imprecise position encoding at early stages and “leakage” of letter
identities to nearby positions, enhancing priming in cases of adjacent repetitions.
To support the identity “leakage” explanation of the obtained advantage of the repeated substitution
primes over the nonrepeated ones, Norris et al., (2010) simulated these experiments with the Bayesian
Reader model of word recognition (Norris, 2006) with an extension for positional uncertainty. The
Bayesian Reader is a model from a different class than the interactive activation framework models
described so far. Like the IA model (McClelland & Rumelhart, 1981), however, the original version of
the Bayesian Reader had a position and length-specific encoding scheme. In the Bayesian Reader, words
are represented as points in multidimensional space. Word coordinates are implemented by concatenating
vectors which encode the presence or absence of a letter in a specific position, thus effectively acting as
slots. The original model incorporates only letter identity uncertainty by adding Gaussian noise to each of
the words’ coordinates. Unlike the Interactive Activation Model and its successors, word recognition is
not achieved through spreading activation mechanisms. Rather than increasing the activation of word
representations consistent with the input, word recognition is implemented by gradual accumulation of
noisy perceptual evidence and optimal mapping of the noisy input to one of the lexical entries. In theBayesian Reader framework, readers are described as ideal observers who use Bayesian inference to7combine perceptual evidence with prior linguistic knowledge (word probabilities) to perform a word
recognition task in an optimal way. With the accumulation of evidence, word likelihoods are calculated
i.e. the probability of observing the input given that a particular word was presented. This calculation isbased on the variance of the input distributions and the distance between the mean coordinates of the
input distributions at a given time and the ideal (average) coordinates of each word in the perceptual
space. The posterior word probability, i.e. the probability that the input was generated by a particularword, is then calculated for each of the lexical entries from the prior word probabilities (their frequency)
and the likelihoods of the words.
Though recognition through accumulation of noisy evidence is one of the basic assumptions of theBayesian Reader, as a simplification, its original version implemented only identity uncertainty. The
extended version described by Norris et al., (2010) included positional uncertainty, but the model’s
encoding scheme remained length specific. The positional ambiguity in the sampling process wasachieved by randomly drawing letter positions from normal distributions centred over the real letter
positions rather than being represented as a single value (for which the authors draw parallels with Gomez
et al.’s, 2008 model). Although with this extension, the Bayesian Reader successfully simulated therepeated letter advantage in substitution primes, thus supporting the “leakage” mechanism of letter
identities described by the authors, the model could not simulate the deletion prime results from the same
study due to its length-specific encoding scheme. The length-specific limitation was later addressed by
Norris and Kinoshita (2012) who proposed a different version of the model that also included calculationsof likelihoods of letter insertions and deletions that affected the calculation of the posterior word
probabilities.
The results of Norris et al. (2010) provided evidence that the repetition of letter identity might play a rolein the recognition of the whole word unit. They also demonstrated that such an effect could be simulated
successfully with the Bayesian Reader model of word recognition (Norris, 2006) when the model
incorporates positional uncertainty. Furthermore, the study of Norris et al. (2010) raised an important
methodological concern regarding the choice of approach to problems such as repeated letters. They
could have confirmed some methodological issues in investigating repeated letter effects, such as lack ofsensitivity of the masked-primed lexical decision task for researching a phenomenon occurring at early
perceptual stages and possibly susceptibility to top-down lexical influences. It is not, however,immediately clear how the mechanism of leakage they propose could explain the results of Gomez et al.
(2008) that suggest that repeated letter targets are harder to process as well as the overall target type effectreported by Schoonbaert and Grainger (2004) also hinting at inhibitory, rather than facilitatory effect ofletter repetition. It is also not clear how such a leakage mechanism would affect nonadjacent repetitions
8with longer distances between the repeated identities and whether a repeated letter effect will still bepresent in longer items, in which it is in fact more common for a repetition to occur.
A methodology that could be effective for the investigation of repeated letter effects for several reasons isa regression approach on megastudies data containing reaction times of visual word recognition tasks inseveral languages - English, Dutch, and French (e.g., Balota et al., 2007; Brysbaert, Stevens, Mandera, &Keuleers, 2016; Ferrand et al., 2010; Keuleers, Lacey, Rastle, & Brysbaert, 2012). The English, British,
Dutch 2 and French Lexicon projects (ELP, BLP, DLP2, and FLP) contain disyllabic and multisyllabic
words in which letter repetitions occur often. The number of repeated letter observations could provide
greater power for observing a possible effect than that in previous studies exploring repeated letters using
factorial designs. The regression approach could also overcome other limitations of factorially designed
studies such as correlation problems (as factors could be covaried out), particularly problematic in visual
word recognition, experimental biases in the stimuli selection, list effects, dichotomization of continuous
variables (see Balota, Yap, Hutchison, & Cortese, 2012 for a detailed discussion of the advantages of thismethodology over factorial designs). It will also allow for a direct cross linguistic comparison of theeffect, exploring whether effects generalize across the processing of different languages or is linked to theidiosyncrasies of individual languages.
Additionally, due to the large number of items, the regression approach allows a deeper investigation of
the effect. This includes exploration of repetition effects of different distances (i.e., adjacent repetitions,nonadjacent repetitions with various number of intervening letters) by adding separate predictors
encoding the presence or absence of a repetition within each distance. Additional evidence in thisdirection could help reconcile inconsistencies in the literature, such as differential effects observed withprimes with deleted repeat vs unique letters in adjacent repetitions (Norris et al., 2010), and the absence ofthat effect in the case of nonadjacent repetitions (Schoonbaert & Grainger, 2004).
Another theoretically motivated question relates to possible dependence of the repetition effect on the
consonant-vowel status of the repeated letters. There is evidence suggesting a differential role ofconsonants and vowels in word processing and the importance of the word CV structure at initial stagesof lexical access (e.g., Acha & Perea, 2010; Chetail, Balota, Treiman, & Content, 2015; Chetail, Drabs, &Content, 2014; Chetail, Treiman, & Content, 2016; Lupker et al., 2008). Moreover, vowel letters andvowel repetitions are more common (see Table 1) and their higher frequency could modulate any letter
repetition effect. To investigate possible differences in the processing of repeated consonants and vowels,with so many items, separate variables can be constructed for each letter type.

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The present study explored whether the presence of letter repetitions affects visual word processing
difficulty and whether repetition distance and consonant-vowel status moderate this effect. The
investigation was conducted with the regression approach on response times from visual word recognition
tasks in English, Dutch and French. Simulations of the open bigram model (Grainger & van Heuven,2003), the Spatial Coding Model (Davis, 2010) and the Bayesian Reader model (Norris & Kinoshita,2012) were also included with the purpose of evaluating the models’ predictions for the effect and theplausibility of their letter position and identity encoding schemes. Norris et al. (2010) have alreadyaddressed the problem of repeated letters with adjacent repetitions and have demonstrated empirically andcomputationally facilitatory effect of repeated letters in primed word recognition tasks. More extensive
simulations on megastudy data will clarify of whether the repeated letter effect in the Bayesian Reader
could be extended to unprimed lexical decision task within different distances between the repeatedletters.

2. Method
2.1. Dependent Variables
The mean correct item latencies across participants of the lexical decision task were obtained from theEnglish Lexicon Project (Balota et al., 2007), the British Lexicon Project (Keuleers et al., 2012), theDutch Lexicon Project 2 (Brysbaert et al., 2016), and the French Lexicon Project (Ferrand et al., 2010).
Word naming latencies were acquired from the English Lexicon Project. We used the raw unscaled
response time (RT) measures to facilitate the interpretation of the results.

2.2. Independent Variables
2.2.1.

Variables of Interest (Repeated Letters)

The variables of interest were constructed with the purpose of observing the effect of repetition of letter
identity on visual word recognition. Two factors were considered while calculating the variables. These
were the consonant-vowel status of the repeated letter and the distance between the letter repetition, or
how far from each other the two letters with the same identity were. The repetition distance was measured
by the number of intervening letters between the repeated ones. There were separate variables for eachpossible repetition distance. Such a division allowed us to explore whether the letter repetition effect was10dependent on the distance between letters with same identities. The variables of interest therefore encoded
all the possible instances in which a consonant or a vowel letter could be repeated within a certain
distance. Each repeated letter variable represented the number of times a consonant or vowel repetition
within a specific distance occurs in a word. Here are several examples with English words and theircorresponding repeated letters values. The variable repetition of consonants with distance 0, summed thenumber of repeated consonant letters with no intervenor (adjacent repetition), such as c in the word accept(aCCept) and d and s in address (aDDreSS). For these words the variable had the values 1 and 2,
respectively. The variable consonant repetitions with distance 1 (one intervening letter between therepeated ones) had a value 1 for the word coconut (CoConut), as one letter, c, is repeated within that
distance, and 2 for the word suspended (SuSpenDeD), in which both s and d appear twice. The variablewith a consonant repetition with distance 2 had the values 1 for hundred (hunDreD) and 2 for accountant(accouNTaNT) and so on. The vowel repetition variables were constructed in the same way. If norepetition was present for a certain condition, the corresponding variable had a value of 0. Words inwhich one letter appeared more than twice and therefore had two or more possible distances between
repetitions of the same letter were discarded from the analyses to avoid additional complexity.
The repeated letter variables were constructed in this way for all languages under investigation, with two
variations in French. The diacritic-sensitive version took into account diacritic marks and treated letterswith and without diacritics as different. With this algorithm, there was no letter repetition in zèbre. The
diacritic-insensitive version counted letter repetitions only after all diacritic marks were removed from theitems; the rare diacritics in English and Dutch were always removed. This calculation encoded arepetition of e in zebre as it was not sensitive to the presence of the diacritic mark. The two separate
calculations were performed to provide an appropriate baseline for the evaluation of visual word
recognition models with no implementation of diacritic marks in their encoding schemes. Comparing theeffect of letter repetition in behavioral data and in models’ simulations therefore required diacritic
insensitive repeated letter measures. Apart from employing two separate algorithms that treated diacritics
differently, the repeated letters variables were constructed in the same way as for the analyses of the otherlexicon projects.
2.2.2.

Control variables

Due to the fact that the investigation was crosslinguistic and the three languages (English, Dutch, French)
had their own idiosyncrasies, the list of covariates was not identical across the different lexicons.
However, care was taken so that important control factors were included in the regression models of eachof the languages.
11English Lexicon Project. The control variables obtained from the English Lexicon Project (Balota et al.,2007) were: logarithmically transformed subtitle (SUBTLEX-US; Brysbaert & New, 2009) contextual
diversity and word frequency measures; number of letters; orthographic neighborhood size (number oforthographic neighbors, Coltheart N; Coltheart et al., 1977); phonological neighborhood size (the numberof words differing by a single phoneme); Levenshtein orthographic distance (OLD20, the averageorthographic Levenshtein distance of the 20 nearest neighbors, Yarkoni et al., 2008); Levenshtein
phonological distance (PLD20); number of morphemes; as well as two different measures of bigram
frequency: mean bigram frequency and bigram frequency by position. Apart from avoiding confounds inthe behavioral regression results, bigram frequencies were important controls as the predictions of one of
the word recognition model under evaluation could be sensitive to these measures (the relative position
open bigram model; Grainger, & van Heuven, 2003). To control for any possible effects of letter
frequency, we calculated and included in the model mean type 1-gram position specific and position
nonspecific frequencies based on the frequency of occurrence of each letter in the English Lexicon word
list. The quadratic term of the number of letters variable was also included as a predictor (New et al.,2006; Yap & Balota, 2009).
In addition to the control factors provided in the English Lexicon Project (Balota et al., 2007), several
additional phonological variables were constructed and added to the regression models, based onphonological transcriptions acquired from CELEX (Baayen, Piepenbrock, & van Rijn, 1993). Words thatwere not found in the CELEX database were excluded from the analysis. The additional variables were:first phoneme, primary lexical stress position, number of phonemes, number of syllables, and several
phonological consistency measures. The first phoneme variable was entered as a categorical variable
whose levels were each of the possible phonemes that could appear as an initial sound in English. The
primary lexical stress position variable was dummy coded and reflected the stressed syllable in a word,
primary stress on first syllable serving as a baseline. The consistency measures reflected the consistencyof mapping of print to sound and included feedforward onset, feedforward rime, feedback onset andfeedback rime consistency of the first syllable as well as four composite measures of the same type which
represented the mean consistency across all the syllables in a word (see Yap & Balota, 2009, for a
detailed discussion of consistency measures). As the construction of the consistency measurements
depended on the syllabification of the words, special care was taken so that orthographic andphonological syllabifications matched before performing the calculations. In the cases of inconsistentsyllabification between the phonological and orthographic forms, the orthographic syllable was adjusted
to the phonological one. The ratio between the orthographic Levenshtein distance (OLD20) and thephonological Levenshtein distance (PLD20) was also included as a separate measure of phonologicalconsistency (Yap & Balota, 2009). Heterophonic homograph entries such as bow that had multiple
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pronunciations for the same orthographic form and therefore multiple values of the phonological variables(phonological consistencies, phonological neighborhood, stress pattern) were not included in the analyses(N = 370).
British Lexicon Project. The control variables obtained from the British Lexicon Project were: twodifferent measures for orthographic neighborhood size (Coltheart N and OLD20), number of letters, aswell as the number of syllables in a word. The quadratic term of the number of letters variable was also
included as a predictor (New et al., 2006; Yap & Balota, 2009). The logarithmically transformed word
frequency measures in Zipf scale and the contextual diversity measures were obtained from SUBTLEXUK and were also added as control variables in the regression analyses (van Heuven, Mandera, Keuleers,& Brysbaert, 2014).
As in the English Lexicon Project (Balota et al., 2007) analyses, the additional phonological variables,
calculated based on the phonological transcription in CELEX (Baayen et al., 1993) were also included ascontrol predictors. These were first phoneme, primary lexical stress, number of phonemes, all firstsyllable and composite phonological consistency measures. In addition, the phonological neighborhood
size and the average phonological Levenshtein distance of the 20 nearest neighbors (PLD20) were
calculated using the vwr package (Keuleers, 2015) as implemented in R version 3.4.1 (R Core Team,2017). The ratio between OLD20 and PLD20 was included as an additional phonological consistency
measure (Yap & Balota, 2009). Heterophonic homographs were not included in the analyses (N = 298).
In addition, mean type-based bigram frequency was calculated by counting the number of times a bigram
appears in all English words from the CELEX database (Baayen et al., 1993), regardless of bigram
position and word length (see Westbury & Buchanan, 2002, for the description of a similar measure). For
example, the bigram frequency of ac was increased after encountering both back and act. The frequencies
of all bigrams in a word were then summed and divided by the number of word letters minus one. The
vwr package in R (Keuleers, 2015) was used for acquiring the list of words. The mean positional bigram
frequency was calculated in a similar way, the only difference being that the bigram counts were
performed for the specific bigram position, rather than for all positions. This measure was bigram
position, but not word length specific, i.e. all words that contained the bigram in the specific position(relative to the beginning of the word) contributed to its count. The bigram ac in position 1 was counted
in both act and action, but not in back, where ac in position 2 was counted instead. Mean positional andnonpositional 1-gram frequencies were calculated in an analogous manner and were included to control
for possible letter frequency effects.

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To control for possible morphological effects, two morphological variables were included in the analyses.
The first variable was constructed by counting the number of morphemes after immediate segmentation of
the lemma. The second variable represented the number of elements after the inflectional transformationof the wordform. The morphological database from CELEX (Baayen et al., 1993) was used for theconstruction of these variables.
Dutch Lexicon Project 2. The control variables obtained from the Dutch Lexicon Project 2 were numberof letters, number of syllables, SUBTLEX2 word frequency (added as a control after a logarithmictransformation), number of phonemes, orthographic Levenshtein distance (OLD20), the phonologicalLevenshtein distance provided in the lexicon (PLD30)1, Coltheart N. As this lexicon also provided ratingsof concreteness and age of acquisition, these were also added as control variables.
In addition, bigram and 1-gram frequency measures were calculated in an identical way as for the
analyses of the British Lexicon Project. Mean bigram and 1-gram frequencies and positional bigram and1-gram frequencies were therefore included in the model. The number of elements after immediatesegmentation of the lemma was added as a morphological factor. This calculation was performed on themorphological analyses provided by CELEX (Baayen et al., 1993).
French Lexicon Project. The control variables provided in the French Lexicon Project (Ferrand et al.,2010) and included in the regression model were two measures of word frequency (cfreqmovies andcfreqbooks). The logarithmically transformed sum of both frequencies and their quadratic term wereadded as suggested by Ferrand et al. (2010) as a frequency measure accounting for largest amount ofvariance. Other important controls provided by the lexicon and included in the model were number ofletters and number of syllables.2 In addition to these variables, several other important lexicalcharacteristics were obtained from the Lexique 3 database (www.lexique.org; New, Brysbaert, Veronis, &Pallier, 2007; New, Pallier, Brysbaert, & Ferrand, 2004). The phonological transcription of the words wasused to extract the identity of the first phoneme, which was entered as a categorical variable. The
orthographical Levenshtein distance (OLD20) and the phonological Levenshtein distance (PLD20) were

1

The Dutch Lexicon 2 project provided phonological neighborhood distance measure that was equal to theaverage phonological Levenshtein distance of the 30 nearest neighbors, unlike the measure in the English Lexicon
project, in which the number of neighbors was 20.
2
The are methodological differences between the lexicon projects. In the English Lexicon Project, unlike the otherprojects, the stimuli were presented in uppercase and the nonword material in most of the cases was generated bychanging one letter from a baseword. The other lexicons used a lowercase presentation and nonword generation
algorithms that were design to minimize serial scanning mechanisms for example by changing the proportions ofdifferent letters between the nonwords and the basewords as a function of the stimulus length. Methodologicaldifferences such as these might be the source of some of the observed effects, such as a stronger word length
effect in the English Lexicon Project.

14entered as measures of neighborhood densities. The number of morphemes of the word item was also
added as a predictor. In the cases in which several possible values were matched to the same orthographic
form, a preference was given to the biggest value (larger number of morphemes). In addition,
nonpositional and positional mean type bigram and 1-gram frequencies were calculated for each of theitems. The calculations were based on the Lexique 3 word list with items without spaces and dashes. The
list was generated from the vwr package in R (Keuleers, 2015).

3. Results
3.1. Lexical Decision Task
A hierarchical regression analyses was performed on the lexical decision latencies of the selected items
from each of the lexicons.3 The first step included all described control variables. The total proportion ofvariance explained in each of the regression models was R2 = 54.37% for the English Lexicon Project(ELP), R2 = 44.39% for the British Lexicon Project (BLP), R2 = 43.48% for the Dutch Lexicon Project 2(DLP2), and R2 = 42.94% for the French Lexicon Project (FLP). In the next step, the repeated letter
variables were added to the models. Their inclusion significantly improved all models: English, F(26,28202) = 10.304, p < .001; British, F(20, 24872) = 7.949, p < .001; Dutch, F(28, 18021) = 11.44, p <.001, and French, F(28, 31532) = 8.144, p < .001. These variables accounted respectively for an
additional ΔR2 = 0.43%, ΔR2 = 0.35%, ΔR2 = 0.99%, and ΔR2 = 0.41% unique variance.
3.1.1.

Adjacent repetitions

The coefficients of the repeated letter variables can be seen in Figure 1. When the repeated letters wereadjacent, there was a 5 ms significant facilitation effect for vowel repetitions and a small (3 ms)
nonsignificant facilitation effect for consonant repetitions in the ELP regression. In the BLP regressions,the 4 ms inhibitory effect was significant for consonants, while there was no effect (0 ms) for adjacentvowel repetitions. In the DLP 2 regression model, the results for the adjacent repetitions showed
dissociation between consonants and vowels, with consonants having a significant 5 ms inhibitory effect,
while vowels produced significant 7 ms facilitation effect. In the FLP regressions, the 9 ms effect ofadjacent consonant repetitions was inhibitory and significant. The effect of adjacent vowels was different,

3

Full regression tables are available as a supplementary material. There is an active clickable link on the final pageof the PDF for reviewers.

15

depending on whether diacritic marks were disregarded or not, with the variables, constructed with thediacritics sensitive algorithm having an inhibitory nonsignificant 6 ms effect, while the same variable
produced significant 29 ms facilitation when diacritics were not taken into account. Overall, the results
suggested a small facilitation effect of vowel repetitions, except for the diacritics-sensitive vowel variablein the French Lexicon project, while the effect of the adjacent consonants trended towards small
inhibition, except for in the ELP model, in which it was not significant4.
3.1.2.

Nonadjacent repetitions (1-3 intervening letters)

When the repetitions were within a 1-to-3-intervening-letters distance, all consonants and vowels
variables in all lexicons indicated a significant inhibitory effect. In ELP this effect was in the range 11 ms
to 13 ms when the distance was within 2 intervening letters and dropped to 4 ms and 8 ms for the 3intervening letters variables, vowel and consonant repetitions, respectively. In BLP, the effect size was in
the range 7 ms to 11 ms for the vowel repetitions and 4 to 12 ms for consonant repetitions. The effect wasslightly smaller in size, but quite consistent in DLP2. It ranged between 3 ms and 9 ms with a similar
pattern for vowels and consonants. In FLP, the effect of repeated letters within the 1 to 3 letters distance
was in the range from 7 ms to 12 ms for vowels and 7 ms to 9 ms for consonants.
3.1.3.

Nonadjacent repetitions (more than 3 intervening letters)

When the repetitions were within a longer than 3 intervening letters distance, the pattern of results was
not as consistent and clear as the one in the previous distance interval. However, as in the previous
distance interval, the pattern was generally inhibitory. There were some differences within the lexicons
as well as between the consonants and vowel repetitions. In ELP, 7 of the repeated letter variables withinthat distance indicated significant inhibitory effect. In this lexicon the vowel repetitions in the longer
distances peaked and indicated large effects. A similar peak was also observed in the BLP results for thevowel repetitions, while none of the consonant variables within that distance interval showed a significant
effect. In DLP2, there were significant inhibitory effects of the 4 letters distance for both letter types, aswell as for the 5 and 9 letters distance vowels repetition. In FLP, the only significant variables that4

To investigate the possible effect of the frequency of the geminates (adjacent repeated letters), a separate
analysis was performed on subsets of words containing one geminate. This frequency measure replaced thevariables encoding adjacent repetition. It represented the number of occurrences of the geminates in the wordlistsof the main regression analyses. All other variables were identical to the one in the main regression analyses. The
results indicated significant facilitation effects of geminate frequency in ELP (β = -0.018, t = -4.759, p < .001); BLP (β= -0.011, t = -2.923, p = .003), DLP2 (β = -0.004, t = -4.271, p < .001), and significant inhibitory effect in FLP (β =0.009, t = 4.110, p < .001).

16

encoded repetition within that distance interval were the consonant repetition variables with 5 and 6
intervening letters between the repetitions.
3.1.4.

Lexical Decision (up to ten-letters-long words)

Regression models were also fitted on subsets of the words from all lexicons, that were up to ten letterslong. This was done with the purpose of providing a common basis of comparison between the behavioral
data on these subsets and simulation results of computational models, where not all models accommodate
longer words in their simulators. The diacritics-insensitive variables were used for the French Lexicon
Project analyses, as diacritic marks were not implemented in two of the models under examination, andcoefficients from the Bayesian Reader did not substantially differ when diacritics were used. The
coefficients of the repeated letter variables on these subsets can be seen in Figure 2. Overall, the patterns
did not deviate from those observed with the slightly bigger datasets. The adjacent vowel repetitions were
either nonsignificant (ELP, BLP) or trended towards facilitation (DLP2, FLP with no diacritics), while theadjacent consonant repetitions had either null or small inhibitory effect. The results at the 1-3 intervening
letters distance were broadly significant and inhibitory. The pattern at longer distances was mainly
inhibitory, but not all variables were significant.

3.2. Lexical Decision Task Simulations
3.2.1.

Spatial Coding Model

Lexical decision task simulations were run with the Spatial Coding Model (SCM; Davis, 2010) on thedata sets of words up to ten letters long from ELP, BLP, DLP2 and FLP using the SCM simulator5. Prior
to each simulation, the model’s vocabulary was set to the word list of the corresponding lexicon project.
The vocabularies contained all words from the lexicon projects, except for those longer than 10 letters.
The resultant lexical decision latencies of the correctly recognized words were then entered in regression
models as the dependent variable. The control predictor variables were identical to the ones in thecorresponding regression models on behavioral data and were held constant across models’ simulations.
These variables explained R2 = 36.11%, R2 = 75.81%, R2 = 67%, R2 = 57.73% of the variance in themodel’s reaction times for ELP, BLP, DLP2 and FLP, respectively. In the next step, the repeated letter
variables were added to the models. All models were significantly improved, except for the English
Lexicon Project model: English, F(18, 25314) = 1.452, p = .097; British, F(18, 24837) = 8.887, p < .001;
5

Downloaded from http://www.pc.rhul.ac.uk/staff/c.davis/SpatialCodingModel/

17

Dutch 2, F(18, 18388) = 8.322, p < .001, and French, F(18, 26779) = 62.34, p < .001. These variables
accounted respectively for an additional ΔR2 = 0.07%, ΔR2 = 0.15%, ΔR2 = 0.27%, and ΔR2 = 1.7%
unique variance.
The effects of the repeated letter variables predicted by SCM for the four datasets can be seen in Figure 3.
The model’s predictions did not agree with the patterns observed in the empirical data. The consistentinhibitory pattern in the distance of 1-to-3 intervening letters was not present in the SCM simulation
results. The model predicted several very small significant effects in the different lexicons, many ofwhich were in the opposite direction. In FLP, SCM predicted a relatively strong inhibitory effect for
adjacent vowel repetitions (4 cycles). This effect was, however, facilitatory in the corresponding
empirical diacritics-insensitive regression model.

3.2.2.

Relative Position Open Bigram Model

Lexical decision task simulations were also run with the Relative Position open bigram Model (RPM;
Grainger, & van Heuven, 2003) on the same reference data sets as the ones used for the SCM simulations.
The RPM simulations were run with the easyNet software (http://adelmanlab.org/easyNet/). The model’s
vocabulary was set to the corresponding lexicon word list prior to each simulation. Only the correctly
recognized words were included in the analyses (see Figure 4 for number of observations in each dataset
and patterns of repeated letter effects). The control predictors explained R2 = 23.23%, R2 = 23.74%, R2 =22.82%, R2 = 19.41% of the variance of the model’s reaction times for ELP, BLP, DLP2 and FLP,
respectively. Adding the repeated letter predictors improved all four models: English, F(18, 22938) =6.853, p < .001; British, F(18, 21869) = 11.263, p < .001; Dutch 2, F(18, 17455) = 4.771, p < .001, andFrench, F(18, 21054) = 9.086, p < .001. These variables accounted respectively for an additional ΔR2 =0.41%, ΔR2 = 0.7%, ΔR2 = 0.38%, and ΔR2 = 0.62% unique variance.
As can be seen in Figure 4, RPM tended to predict inhibitory, rather than facilitatory, effects of repeatedletters. However, in most of the datasets, the effects were larger for the adjacent repetitions and were notconsistent in the 1-3-letters distance interval, therefore also failing to capture the empirical data pattern.

3.2.3.

Bayesian Reader Model

Lexical decision task simulations were run with the Bayesian Reader Model (BRM; Norris & Kinoshita,2012) on the data sets of words up to ten letters long from ELP, BLP, DLP2 and FLP. The simulation
18

software was the one provided by Norris and Kinoshita as a supplementary material to their paper. Prior
to each simulation, the model’s vocabulary was set to the word list of the corresponding lexicon. Words
longer than 10 letters were excluded from the vocabularies. The mean reaction times of the correctly
recognized words (“Yes” responses) were then entered in the regression models as the dependent
variable. The “yes” threshold was set to .90. The control predictor variables were identical to the ones in
the corresponding behavioral data regression models and the simulations with the previous two models.
These variables explained R2 = 62.29%, R2 = 84.85%, R2 = 86.76%, R2 = 79.35% of the variance in themodel’s reaction times for ELP, BLP, DLP2 and FLP, respectively. When the repeated letter variables
were added, all but the DLP2 models were significantly improved: English, F(18, 24637) = 2.419, p <.001; British, F(18, 24837) = 8.844, p < .001; Dutch 2, F(18, 18388) = 1.308, p = .171, and French, F(18,26779) = 5.093, p < .001. These variables accounted respectively for an additional ΔR2 = 0.07%, ΔR2 =0.1%, ΔR2 = 0.02%, and ΔR2 = 0.07% unique variance. As the Bayesian Reader Model has animplemented version that is diacritics-sensitive, separate French Lexicon Project simulation was also run
with items and vocabulary with preserved diacritics. The control variables explained R2 = 81.07 % of thevariance in the model's reaction times. The repeated letter variables improved the model significantly,
F(18, 28120) = 2.157, p = .003. The results of the Bayesian Reader Model simulations are displayed in
Figure 5. The model did not predict a consistent pattern of the repeated letter effects and did not capture
the inhibitory repeated letter effects in the shorter repetition distances.

3.3. Word Naming Task
A linear regression model was also fitted with the latencies from the word naming task, obtained from theEnglish Lexicon Project (Balota et al., 2007). The same control variables were entered in the model as theones in the lexical decision model for this lexicon project. These variables explained R2 = 54.52% of thevariance. The model was significantly improved after adding the repeated letters predictors, F(26, 28206)= 11.822, p < .001. They explained additional ΔR2 = 0.49% unique variance. The effects of repeatedletters can be seen in Figure 6. Overall, the pattern was the same as the one in the lexical decision data. In
the word naming results, however, both adjacent repetitions had a significant facilitation effect and wereslightly larger in size than those in the lexical decision results (10 ms for vowel repetitions and 7 ms forconsonant repetitions). This facilitation effect was followed by consistent inhibitory effects in the intervalof 1-to-3 intervening letters for both letter types. In the more than three letters distance interval, most of
the variables, especially the vowel repetitions were significant, and, as in the lexical decision data, there
was a peak of the inhibitory effect in the long-distance vowel repetitions.
19

4. Discussion
The presence of letter repetitions in words significantly predicted reaction times of lexical decision andword naming tasks, after controlling for important lexical and sublexical variables. Regressions showedthat the presence of nonadjacent letter repetition delays visual word recognition. The inhibitory repeatedletter effect was robust in the cases in which the repeated letters were intervened by one, two or threeletters. The effect was less consistent but still generally present with increasing distance between therepetitions. The effect was observed in all three languages under consideration: English, Dutch, andFrench. This replication implies that the inhibition of letter repetition might be linked to a generalmechanism in visual word recognition rather than to idiosyncrasies of a single language. The obtained
results are in accordance with the reported target type effect in the methodologically similar primed
lexical decision task in the Schoonbaert and Grainger’s (2004) study, in which targets containing
nonadjacent repetitions took longer to process. However, they disagree with the methodologically lesssimilar masked priming data, reported by these authors and by Van Assche and Grainger (2006), which
provided no evidence for differential processing between repeated and unique letter identities. The results
are also broadly consistent with Gomez et al.’s (2008) perceptual identification data that showed lower
accuracies for stimuli containing repetition in comparison to stimuli with no repetition. A difference
between their results and the results presented here is that Gomez et al. reported inhibitory repeated letter
effects in both adjacent and nonadjacent repetitions, while the inhibitory pattern in the present study ismore consistent in the cases of nonadjacent repetitions.
In the cases of adjacent repetitions, the effect had alternating patterns, suggesting that adjacent repetitions
might be a special case of letter repetitions. The results also implied possible dissociation between
consonants and vowels and double letter processing in different languages. In English, the inhibitory
effect was less consistent for consonants and trended towards facilitation in the cases of vowel repetitions.
In Dutch, the vowel-consonant dissociation was clearly observed, with repeated consonants producing asmall but significant inhibitory effect, while repeated vowels had a small but significant facilitatory effect.
In French, the adjacent consonants preserved their inhibitory pattern. It should be noted that adjacentvowel repetitions are extremely rare in French, mostly occurring in loanwords, while in Dutch they arequite common. Given the constraints of French orthography, the sensitivity of the pattern for vowels tothe processing of diacritics suggests that words with the bigram ée are read quicker than those containing
ee or oo, which are very often loanwords. The differential effects might therefore result from the adjacent
double letters idiosyncrasies of the language.
20

The different patterns of adjacent repetition might be due to counteractive processes that are notassociated with cases of nonadjacent repetition and possible benefits of the letters being in contiguous
positions. Such an interpretation is consistent with the idea that adjacent repetition (letter doubling)should be coded as an additional dimension, that is separate from letter identity and letter position. Thisidea arises in studies and models of spelling (e.g., Fischer-Baum & Rapp, 2014; Glasspool & Houghton,
2005; Tainturier & Caramazza, 1996). Tainturier and Caramazza argue that graphemic representations are
multidimensional structures and grapheme doubling is encoded separately from grapheme identity. In
their study, they reported a case of dysgraphic patient in which the presence of adjacent letter repetition
was preserved even when the letter identity and order information was severely distorted (e.g., giraffe GAFFICATE). The special status of repeated adjacent letters has also been supported by evidence fromvisual word recognition research. It has been demonstrated that participants are more likely tomisperceive the number of letters in a word and report a word with repetition (WEED instead of WED) if
it was presented with a distractor word with another double letter (WOOD) than with a distractor wordwith no repetition (WORD; Fischer-Baum, 2017).
Another possible cause of the diminished inhibitory effect in the cases of adjacent repetitions might belinked to the proposed letter identity “leakage” to nearby positions (Gomez et al., 2008; Norris et al.,2010) that could possibly be less detrimental in the cases of same adjacent identities than in the cases of
nonadjacent ones. It should also be noted that two adjacent repeated letters could differ from two uniqueones, especially in the cases of consonants, in that in most cases, in the languages considered in thisstudy, these would map into a single phoneme, rather than into two phonemes. This would lead toshortening of the phonological length (number of phonemes) relative to a case with two different adjacentletters. However, any phonological contribution to the effect due to this reason was dealt with byincluding the number of phonemes as a covariate.
The finding of inhibitory effects of letter repetitions suggests that there is a mechanism related to therapid processing of identical sublexical elements (such as letters) that has not been previously describedin the visual word recognition literature. Such a mechanism might be linked to a smaller number ofactivated abstract representations in the cases of repetitions compared to cases with no repetitions. This
explanation is conceptually consistent with the architecture of the open bigram model (Grainger & vanHeuven, 2003) as well as with the argument of Schoonbaert and Grainger (2004) that the open bigram
model would predict an inhibitory effect of repeated letters due to duplications of open bigrams andtherefore a smaller number of active representations in cases of repeated letters. In accordance with their
proposal, the open bigram model indeed predicted consistent inhibitory effects of repeated letters and in
this sense was conceptually most accurate. However, the specific prediction of the model on word lists of21

four lexicon projects did not match the observed pattern as it overestimated the inhibitory adjacentrepetition effect and underestimated the nonadjacent one, therefore depicting the wrong inhibitory pattern
than the one in the lexicon projects.
A possible explanation for the wrong predictions of the open bigram model (Grainger & van Heuven,2003) could be the encoding scheme of the model and more specifically, the manner of which open
bigrams are constructed. One factor affecting the predictions is the three-letter distance constraint on how
open bigrams are generated (silence consists of SI SL and SE but not of SN, SC and another SE). Anotherfactor affecting the model’s predictions is the left-to-right manner of open bigram construction thatprivileges internal letters as they participate in more bigrams. This tends to disadvantage of the last threeletters of the word, for example, as they appear in the first position of only two, one and zero open
bigrams, respectively (nce from silence will generate respectively NC, NE, and CE, and no bigram). In
this way, in words in which one letter does not appear more than twice, as in the present lexicon subsets, a
repeated bigram is only possible to occur either when the repeated letters are adjacent or when they areintervened by only one other letter. The latter case is further constrained on the repeated letters notappearing at external positions within the word. For these reasons, many words with nonadjacent letter
repetitions are in fact not encoded with fewer units, a possible prerequisite for a prediction of an
inhibitory effect. As the pattern of predictions of the open bigram model by Grainger and van Heuven(2003) does not agree with the nonadjacent inhibitory effects of repeated letters, a revision of theencoding scheme might be appropriate that could include some relaxation of the current constraints.
It was, perhaps, less surprising that the spatial coding scheme (Davis, 2010) also did not contribute to a
successful simulation of the repeated letter effects, as the scheme contains explicit mechanism thatprevents repeated letter identities from playing a different role than nonrepeated ones. This mechanism
comprises cooperative competitive interactions between banks of receivers (clones of receptors) for eachletter in a word representation (word template). When there are repeated letters in both the input and theword template, multiple receivers in a single bank would become active. This would force a competition
between the activated receivers for the selection of a winner. This selection is based on the signal-weight
differences between the input and the word template, which equal 0 in the cases in which the letters
appear in their expected positions. In the current implementation of the model, the resolution in cases ofmultiple activated receivers occurs immediately and without any cost. This could explain why the Spatial
Coding Model did not predict the observed inhibitory pattern of repeated letters and in cases evenpredicted effects in the opposite direction. The results obtained in this study therefore present a challenge
for the Spatial Coding Model and possibly signal the necessity of implementing a time penalization for
resolving cases with repeated letters. This solution was, in fact, already suggested by Davis (2010) for the22discrepancy between the model’s mechanisms and the reported inhibitory effect of repeated letters intargets of the study of Schoonbaert and Grainger (2004). The disambiguation and allocation to thecorresponding positions of two identical units (letters) already recognized by the system as separate
objects could therefore be another possible explanation of the observed inhibitory repeated letter effect.
Another way to approach the repeated letter problem could be in terms of the Bayesian Reader frameworkdescribed by Norris and Kinoshita (2012), in which there is graded positional uncertainty: Evidence for aletter in a given position is also (weaker) evidence for nearby positions. A Bayesian decision makerreceiving noisy data from two identical letters in different positions should therefore place somelikelihood on the source of these data being a single instance of that letter somewhere in the middle,
which will be evidence for a different string, typically a nonword, slowing responses to words in lexicaldecision. By contrast, this possibility does not need to be considered when there are no repetitions ofletters. Although the Bayesian Reader model (Norris & Kinoshita, 2012) did not predict a consistentinhibitory pattern from repeated letters, such an explanation is conceptually consistent with the broader
theoretical framework with a specific model enhanced with a more perceptually veridical likelihood
calculation.
Another possible explanation to an extent follows up from the problem of a smaller number of abstract
representations and more specifically, the shared identity of letter objects in cases of repetition. It might
be the case that repeated identities force serial processing due to functional specialization and modularityof the processing components (letter receptors) associated with each letter identity. In such a scenario,
processing of two identical elements might not be achieved in the rapid parallel manner, in which it has
been previously demonstrated that letters are perceived (Adelman, Marquis, & Sabatos-DeVito, 2010), as
the same component might be involved in encoding of two or more letters at once, therefore resulting insome processing delay, albeit not in predictable sequence. This delay differs from that considered for the
Spatial Coding Model (Davis, 2010) both in that it affects one or other of the letters, but not both, and inthat this delay is tied to an early stage of perception rather than a later stage of resolution of letter
repetition in the lexical unit.
The problem of repeated letter identities might also be approached in terms of exploring how the visualsystem establishes the numerosity of objects with similar identities. It might be the case that the inhibitory
repetition effect might result from limitations of the perceptual system in either very early low-levelstages or later more abstract levels in the form of incapability of dissociating between two identical(letter) units. The perceptual system could perceive the two identical letters but cannot perceive that they
are two, that the same letter representation is present at two different locations. In this case, the identityof both letters is recognized but it is the numerosity that is yet to be established. Such an assumption is23

consistent with the repetition blindness phenomenon and the problem of registering two different tokensof the same type. Kanwisher (1987) found that participants were unable to report the second occurrenceof a word from a word list in a rapid serial visual presentation (RSVP), when words were presented for a
117 ms followed by a mask and when the two occurrences were intervened by a small number of items.
Since the effect was larger with a smaller number of intervenors, Kanwisher argued that the effect was notdue to people forgetting the items. She also discarded the possibility that the tokens were not perceived.
In Experiment 3 of her study, she demonstrated that when the word lists were truncated after the second
occurrence of the repeated word, or its corresponding nonrepeated control word, and participants had toreport the final item in lists of various length, their accuracy was higher when the final word was repeatedthan when it was not. Kanwisher posited that the repetition blindness phenomenon is not related toinability of recognizing the type of the occurrences, but rather to “individuating” the items as two tokensof the same type.
Two apparent differences between Kanwisher’s study (1987) and the present are: the serial versus theparallel presentation of the repeated items; their scale (words vs. letters). However, the problem ofperceiving several occurrences (tokens) of the same letter (type) has also been explored with a parallel
presentation of letter strings containing repetitions. Kanwisher (1991) used word and nonword stimuli
which were displayed in the original RSVP presentation, a “moving” RSVP presentation with eachincremental letter shifted one character to the right, and a simultaneous presentation in which the wholestring was briefly flashed. The word stimuli containing repetition were chosen so that the deletion of asecond occurrence generated another genuine word (manager – manger). The repetition blindness effectwas observed in all three presentation conditions, with the simultaneous repeated condition being least
detrimental.
Another account of the repetition blindness effect was proposed by Luo and Caramazza (1996). They
argued that the recognition system might be less sensitive to a type node shortly after it has already been
perceived (a refractory period). They suggested that the processing of successive or concurrent stimuli
continues after their presentation and the recognition of two identical items might overlap in time in both
RSVP and simultaneous visual presentations. In their study, they manipulated the onset of the encoding of
two critical items in both type of presentations. The authors assumed that in the simultaneouspresentation, the distance between the repeated elements affects the temporal overlap of their processing.
In their experiment, five letters and three dollar signs were displayed in eight consecutive clocklike
positions within a circle. In the RSVP presentation, the letters appeared sequentially in a clockwise
direction and were either preceded or followed by the dollar signs. In the repeated condition, the repeatedletters appeared within a distance of one intervening letter and were either the second and the fourth or the24third and the fifth within the letter sequence. The start location of the stimuli presentation was any of theeight possible clock locations. In the simultaneous presentation, all letters and dollars were briefly
displayed at the same time. The results indicated lower accuracy in the repeated conditions in bothpresentation modes with a stronger repetition blindness effect in the RSVP condition. In a follow-up
experiment, the authors further investigated the repetition blindness effect in simultaneous presentation by
manipulating the distance between the repeated elements in terms of number of other intervening letters(0-3). The results showed that the effect was stronger within distances 1 and 2 than distances 0 and 3 andindicated an inverted U-shaped repetition blindness effect as a function of distance. The authors
explained the results in terms of a type refractory period in which the sensitivity of the recognition system
to a certain type is reduced after stimulation and is recovering to its resting levels. If two identical stimuli
are encoded with a minimal delay and the second stimulation is received shortly after the first one, theexcitation level of the type node is still peaking above its resting level, a priming facilitation effect mightoccur (repetition priming). As, however, after peaking, the activity of the node drops below its restinglevel, if the second stimulation happens while the node recovers to its resting state (the refractory period),
this will lead to a delayed encoding of the second stimuli and an inhibitory effect proportional to the
distance away from the resting level. Luo and Caramazza suggested that the effect of the repetition lag(distance) can be explained with the activity of the type node which after peaking first decreases below
resting level and then recovers back to resting level resulting in the reversed U-shape of the repetition
blindness effect. The reported repetition distance effects by these authors are consistent with the results ofthe present study, in which the adjacent repeated letter condition induces less inhibition than theimmediate nonadjacent conditions, which in turn have more consistent effect than the longer repetition
distances.
In another study related to the repetition blindness effect, Mozer (1989) showed that participants were lessaccurate when they had to report the number of letters in a briefly presented display when a string ofletters was formed by repeating the same letter (DDDD) than when it was formed by different letters(NRVT). He referred to this effect as “homogeneity effect” and argued that it is dependent on thecommon form of the items. He extended his findings and demonstrated that a repeated letter effect canalso operate on the level of abstract letter identities. When the task required recognition of the letter
identities, rather than just counting the visual objects, the number of two nonadjacent repeated lettertargets presented in different case was still harder to perceive than the number of two distinct letters.
Participants were less accurate when they reported the total number of As and Es in a display of two CVC
strings when the display contained repeated letters (BEC mes) than when the target letters were notrepeated (ner TAL). Mozer proposed a model of parallel processing of information from different visual
fields. The repeated letter (homogeneity) effect is caused by spatial uncertainty and imprecision in25

retrieving the exact location information of the two repeated objects. As the system differentiates between
the two instances of a single object by the difference in their location, in stages that have insufficientspatial information it is unable to process their number. Mozer argued that the repetition blindness
phenomenon described by Kanwisher resembles the homogeneity effect in his study. The difference in themechanisms of the two effects, according to him, were that the insufficient processing time in the rapid
serial visual presentation led to inability for the events to be tagged to a temporal serial position in asequence, while the homogeneity effect in parallel processing were caused by inefficient spatial tagging.
In both cases, the information of the number of identical objects therefore could not be retrieved. Mozer
also suggested that serial attentional scanning could decrease spatial uncertainty and weaken thehomogeneity effect.
Another possible cause of processing delay could be the increased positional ambiguity when letters arerepeated. With identical signals coming from separate locations, making it more difficult for the visualsystem to allocate two identical letters to their corresponding positions than two different letters. In thiscase, the identity of both letters is established, and it is the positional encoding that is delayed, possibly
leading to increased processing difficulty. Such an interpretation is, however, not consistent with theevidence provided by Adelman (2011) from a two-forced choice perceptual identification task showing asimilar take-off of the accuracy function in conditions in which the foils were formed by identity
substitution and a condition with transposition, suggesting that information about identity and position
gets resolved in a similar timeframe.
This evidence was considered in the design of the Letters in Time and Retinotopic Space (LTRS;
Adelman, 2011) model. Although LTRS describes perceptual timing mechanisms that could explain
effects of different prime types, it does not describe downstream lexical processing mechanisms thatwould be affected by these timings when entirely consistent information (i.e., the target alone) ispresented. The model perceives items of information at different times, so identifying one of a set of
repeated letters is ambiguous between several possibilities unless there is other disambiguating
information. So, although the model is highly sensitive to (excess) repeated letters in primes, it issensitive to repeated letters in lexical decision targets only insofar as they make some non-identicalprimes more ambiguous. The model could be extended to include less efficient processing of repeatedletters, by adjusting the attention equation so that repeated letters do not receive as high a processing rate
as unique letters. This would delay responding to these items, because the total processing rate would belower, increasing the average latency to perception of the first letter, and hence delaying the start oflexical processing. This would not provide evidence as to the nature of the delays in letter processing,although there is evidence from other paradigms that such delays exist.
26

In summary, the possible causes of the repeated letter effects include lower number of active
representations, resolution of the position of the repeated letters at later processing stages, capacity
limitations due to serial processing of repeated letters, inability of the processing system to tokenize theletter types at early perceptual stages, increased ambiguity in cases of repeated letters. It might also be thecase that multiple of the aforementioned mechanisms underly the inhibitory repeated letter effect. For
example, it might be the case that the perceptual system is indeed unable to establish the numerosity of
the letters at early stages and requires additional time to establish that the positional uncertainty for asingle identity is higher than that of other identities (even after a certain period of time) and therefore thesource of that information should come from (at least) two separate locations. There is also a possibility
that the repeated letters effects might be driven by other non-perceptual phenomenon not yet addressed in
the current literature. The control variables that were included, however, consisted of the major lexicaland sublexical factors, including but not limited to frequency and size measures in multiple levels. We,
therefore, consider it unlikely for the effect to be driven by effects such as letter frequencies or any of the
known possible factors. The clear presence of an inhibitory effect within megastudies, established here,
will require complementary experimental efforts to determine its cause.
In conclusion, the results of the present study demonstrated a robust inhibitory effect which was
replicated in all three languages under consideration. The effect was stable in the cases of one, two andthree intervening letters, it was broadly consistent in larger distances and decreased in the cases ofadjacent repetitions. The observed inhibitory pattern of repeated letter effects in the regression analyses
was not predicted by three leading computational models and it is not yet reflected in any mechanism in
the visual word recognition literature. These results have important implications for development oftheories of visual word recognition and, more specifically, for understanding letter position and identity
encoding and sublexical orthographic processes mediating lexical access. The obtained effects should
motivate additional research in that direction, as well as additional theoretical and computationalmodelling effort with the purpose of the better understanding of the processes involved in the repeatedletters effects.

Acknowledgments
This work was supported by the Leverhulme Trust (Project Grant RPG-2013-408) and an Early Career
Fellowship awarded to the first author by the Institute of Advanced Study, University of Warwick, United
Kingdom.

27

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Lexicon Project
Distance

CV

ELP

BLP

DLP2

FLP

0

C

14.5

14.6

12.3

18.9

0

V

3.7

5.1

17.9

0.1

1

C

5.4

3.9

4.4

5.4

1

V

10.2

5.0

14.0

11.3

2

C

8.5

6.9

9.3

8.4

2

V

10.6

8.0

12.3

15.2

3

C

8.0

6.4

6.9

6.6

3

V

7.5

4.8

7.0

8.9

4

C

6.7

5.3

6.9

6.3

4

V

6.6

2.4

6.2

7.1

5

C

4.8

2.9

5.1

4.5

5

V

4.0

0.8

4.5

5.0

6

C

3.0

1.7

3.4

3.1

6

V

2.5

0.2

2.4

2.8

7

C

1.6

0.7

2.2

1.9

7

V

1.3

0.0

1.3

1.4

8

C

0.9

0.3

1.2

1.1

8

V

0.7

0.0

0.5

0.7

9

C

0.5

0.1

0.4

0.5

9

V

0.4

NA

0.1

0.3

10

C

0.2

0.0

0.2

0.2

10

V

0.1

NA

0.1

0.1

11

C

0.1

NA

0.1

0.1

11

V

0

NA

0

0

12

C

0

NA

0

0

12

V

0

NA

0

0

13

C

0

NA

0

0

13

V

0

NA

NA

0

Any

Any

65.7

54.2

74.1

68.4

Table 1.
Proportions of items containing any letter repetition (at least one repeated letter) and at least one of eachof the repetition types in the English Lexicon Project (ELP), British Lexicon Project (BLP), Dutch
Lexicon Project 2 (DLP2) and French Lexicon Project (FLP) datasets. The repetition types are presented
in terms of the repetition distance (number of intervening letters between the repeated) and consonantvowel (CV) class of the repeated letter. Words in which the same letter appears more than twice areexcluded.

32

Figure 1. Repeated letter effects in English Lexicon Project (ELP), British Lexicon Project (BLP), Dutch Lexicon Project 2 (DLP2) and French Lexicon Project(FLP; with diacritics). Positive values indicate inhibition, negative values indicate facilitation. The distance is measured with the number of intervening letters
between the repeated ones. Error bars represent 95% confidence intervals.

Figure 2. Repeated letter effects in subsets of the lexicon projects with words no longer than ten letters.
Positive values indicate inhibition, negative values indicate facilitation. *** p < .001; ** p < .01; * p <.05

Figure 3. Spatial Coding Model’s predictions of repeated letter effects. Positive values indicate inhibition,negative values indicate facilitation. *** p < .001; ** p < .01; * p < .05

35

Figure 4. Relative Position Open Bigram Model’s predictions of repeated letter effects. Positive values
indicate inhibition, negative values indicate facilitation. *** p < .001; ** p < .01; * p < .05

36

Figure 5. Bayesian Reader Model’s predictions of repeated letter effects. Positive values indicate
inhibition, negative values indicate facilitation. *** p <.001; ** p <.01; * p <.0537

Figure 6. Repeated letter effects in word naming in English Lexicon Project. Positive values indicate inhibition, negative values indicate facilitation. The distanceis measured with the number of intervening letters between the repeated ones. Error bars represent 95% confidence interval