Some empirical tests of an interactive activation … radach 2006 some...Some empirical tests of an interactive activation model of eye movement control in reading Action editor: Erik

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Cognitive Systems Research 7 (2006) 34–55

Some empirical tests of an interactive activation model of eyemovement control in reading

Action editor: Erik D. Reichle

Ronan G. Reilly a,*, Ralph Radach b

a Department of Computer Science, National University of Ireland, Maynooth, Co. Kildare, Irelandb Department of Psychology, Florida State University, Tallahassee, FL, USA

Received 8 February 2005; accepted 1 July 2005Available online 26 September 2005

Abstract

This paper describes some empirical tests of an interactive activation model of eye movement control in reading (the ‘‘Glenmore’’model). Qualitatively, the Glenmore model can account within one mechanism for preview and spillover effects, regressions, progressions,and refixations. It decouples the decision about when to move the eyes from the word recognition process. The time course of activity in afixate centre (FC) determines the triggering of a saccade. The other main feature of the model is the use of a saliency map that acts as anarena for the interplay of bottom-up visual features of the text, and top-down lexical features. These factors combine to create a pattern ofactivation that selects one word as the saccade target. Even within the relatively simple framework proposed here, a coherent account canbe provided for a range of eye movement control phenomena that have hitherto proved problematic to reconcile. The paper examines theperformance of the model compared to data gathered in an empirical study of subjects reading a German text. The quantitative fit of themodel, while reasonable, highlighted some limitations in the model that will need to be addressed in future versions.� 2005 Elsevier B.V. All rights reserved.

1. Theoretical background: the ongoing debate about models

of eye movements in reading

Today the study of eye movement control in reading is aflourishing field of research, with many valuable contribu-tions being made from different theoretical perspectives.These viewpoints include the study of reading as a complexmental process, integrating aspects of perception and cog-nition in an ecologically valid tasks and the use of oculo-motor parameters to test specific psycholinguistichypotheses (see Radach & Kennedy, 2004; Rayner, 1998;Starr & Rayner, 2001; for overviews). Within this field,the development of computational models has assumed apivotal role, both as a tool to integrate the wealth of exist-ing empirical evidence and as a benchmark to test the mer-

1389-0417/$ - see front matter � 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.cogsys.2005.07.006

* Corresponding author.E-mail address: [email protected] (R.G. Reilly).

its of the diverse theoretical ideas on how oculomotorcontrol in reading is accomplished. When the E-Z Readermodel was published (Reichle, Pollatsek, Fisher, & Rayner,1998), it soon became clear that this particular model andwith it the class of attention based sequential processingmodels (often referred to as sequential attention shift orSAS models) would be the standard against which anyalternative models will have to compete (Underwood &Radach, 1998). Consequently, virtually all alternative mod-els have defined their theoretical scope, architectures andprinciples of operation in terms of similarities and differ-ences to E-Z Reader. Nonetheless, there are three majorlines of evidence that have led us to question key assump-tions of SAS models and we have tried to address these inour design of the Glenmore model.

First, there is an accumulating body of evidence suggest-ing that word processing in reading may be spatially dis-tributed so that more than one word within the currentperceptual span can be processed at the same time (Hyona

mailto:[email protected]

1 A similar argument can be made against the proposed division betweenthe so called labile and non-labile stages of saccade programming(McConkie & Yang, 2003; see Deubel et al., 2000, for a discussion ofanalogies between research using the double step paradigm and eyemovement control in reading).2 From a computational point of view it may be added that Engbert and

Kliegl (2001) achieved a very good fit of the Schilling, Rayner, andChumbley (1998) corpus in a model where the two phases of the wordrecognition process are replaced with an all-or-none process. Their modelalso allowed for the autonomous generation of saccades independentlyfrom lexical processing.

R.G. Reilly, R. Radach / Cognitive Systems Research 7 (2006) 34–55 35

& Bertram, 2004; Inhoff, Radach, Starr, & Greenberg,2000; Kennedy, 2000; Kennedy & Pynte, 2005; Kennedy,Pynte, & Ducrot, 2002; Pynte, Kennedy, & Ducrot, 2004;Starr & Inhoff, 2004; Underwood, Binns, & Walker,2000). The typical finding in these studies is that a charac-teristic of a parafoveal word (e.g., its lexical frequency)influences viewing time measures on the currently fixated‘‘foveal’’ word. Obviously this is in contrast to the keyassumption made by SAS models that ‘‘attention’’ is al-ways focussed on one particular word leading to a strictlyserial mode of word processing. It is important to note thatthe majority of the above references report data on parafo-vea-on-fovea effects observed in normal reading, so thatthese claims cannot easily be dismissed as stemming fromsomewhat artificial word recognition tasks. On the otherhand, there are also a couple of studies which have failedto demonstrate parafovea-on-fovea effects. One seriouscounter-argument is that part of the effects may come frommisplaced fixations (see Reichle, Rayner, & Pollatsek,2003, for a discussion of this account and Nuthmann, Eng-bert, & Kliegl, 2005, for a quantitative analysis of mis-placed fixations). However, given the weight of theavailable evidence, it appears that the question is not somuch whether they exist but whether the scope of theseparafoveal modulations is restricted to a pre-lexical levelof word processing. Moreover, a recent study by Inhoff, Ei-ter, and Radach (in press) provides direct evidence thatthere can be temporal overlap in the processing of consec-utive words. Their results indicate that parafoveal informa-tion from word n + 1 can be extracted early during afixation on word n, at a point in time when according toSAS models ‘‘attention’’ should be confined exclusively tothe currently fixated word n.

A second line of concern about a strictly sequential viewof eye movement control in reading is related to the time-line of processing events (Findlay & White, 2003). Workusing ERPs to study the time course of word recognitionsuggests that (in a single word recognition paradigm withno parafoveal preview) it takes about 130 ms for word fre-quency differences to emerge (Sereno, Rayner, & Posner,1998). Looking at the other end of the time line, McCon-kie, Underwood, Zola, and Wolverton (1985) suggestedan interval of 80–100 ms before saccade onset as the dead-line for stimulus influences during a fixation. This is in har-mony with estimates from basic research using the doublestep paradigm, indicating that the reprogramming of a can-celed saccade must be initiated at least 70–90 ms before theend of the current fixation (Deubel, O�Regan, & Radach,2000; Radach, Inhoff, & Heller, 2002). Although theremay be some dispute about the actual duration of the crit-ical time intervals for minimal word processing and saccadeinitiation (see, for example, the comments and responsesections of Pollatsek, Reichle, & Rayner, 2003), it is clearthat they exist and that the temporal window within whichcognitive influences on fixation durations have to operate isquite limited. The best example of the problems associatedwith a strictly sequential model is the scenario that SAS

models propose in order to account for ‘‘word skipping’’.It includes operations like the completion of lexical accesson word n, a shift of attention to word n + 1 plus the com-pletion of initial lexical processing on this word to initiatethe cancellation of the respective default saccade. It isclearly a challenge for SAS models to fit all these serialstages into the available time slice. We acknowledge thatin recent versions of the E-Z Reader model considerable ef-fort has been invested in accommodating these concerns,mainly by shortening the durations for some time-criticalparameters (cf. Reichle, Pollatsek, & Rayner, 2005).

A third type of criticism is concerned with the division ofword processing into an initial stage (labelled ‘‘familiaritycheck’’ in the original E-Z Reader model) and a later stageleading to full lexical access. This division is necessary froma modelling point of view, as the completion of the firststage delivers the trigger signal for saccade programming.It also provides an impressively elegant way to incorporatedifferential effects of word frequency and contextual pre-dictability (Rayner, Ashby, Pollatsek, & Reichle, 2004).However, as pointed out by Andrews (2003) and Huesteggeet al. (2003), it is not at all clear that such a division intofunctionally distinct stages is based on solid empirical evi-dence from the basic literature on word processing. Thefact that Reichle et al. (2003) prefer to ‘‘remain agnostic’’about the precise nature of the two stages prevents specu-lation but also reinforces doubts about whether the distinc-tion is in fact more than a modelling convenience1 (seehowever, Reichle & Perfetti, 2003, for a recent model ofword identification that incorporates a possible two-stagemechanism).2

In response to some of the issues discussed above, sev-eral alternative models of oculomotor control in readinghave been proposed. Engbert, Nuthmann, Richter, andKliegl (in press) refer to their SWIFT model as an examplefor ‘‘guidance by attentional gradients models’’ (GAG; seealso Engbert, Longtin, & Kliegl (2002), Richter, Engbert,& Kliegl, 2005). SWIFT extends the area of attention allo-cation to a region that includes several words (see also Inh-off et al., 2000), allowing for parallel word processing, andthus avoiding many of the problems associated with astrictly sequential view. Their model also incorporates amechanism for the autonomous generation of saccades,whose execution can be delayed via inhibition by foveallexical processing. At the same time, SWIFT retains keyelements of the architecture of E-Z Reader including the

36 R.G. Reilly, R. Radach / Cognitive Systems Research 7 (2006) 34–55

division of lexical processing into two distinct stages andthe division of saccade programming into a labile and anon-labile phase (see Kliegl & Engbert, 2003, for a recentdiscussion).

Similar to SWIFT and Glenmore, the competition/inter-action theory of Yang and McConkie (2001) is stronglyinfluenced by the theory of saccade generation by Findlayand Walker (1999). It deals explicitly with specific mecha-nisms of saccade triggering and the resulting distributionsof fixation durations which are primarily attributed tonon-cognitive factors. Another interesting line of develop-ment are ideal observer models of information processingand oculomotor control that also use a processing gradientbut attempt to simulate reading in terms of an optimalstrategy (approximated by relatively simple heuristics) forthe extraction of letter and word information (Legge, Klitz,& Tjan, 1997, 2002). Feng (2005) has recently developed anew hierarchical architecture for modeling eye-movementsin reading, referred to as SHARE, representing an ad-vanced Markov approach with model parameter estima-tion using Bayesian methods.

2. Glenmore: an outline of our theory and model

The model that will be described in this paper rests onthe general assumption that eye movements in readingare co-determined by low-level oculomotor routines andongoing cognitive processing. We believe that low-levelcontrol delivers a fairly robust trigger signal that in turnis strongly modulated by linguistic processing on the letterand word level and to some extent also by higher level pro-cessing on the sentence and discourse level (Deubel et al.,2000). One of the origins of this notion is the idea of a vi-sual scanning routine, introduced by Levy-Schoen (1981),who suggested that a routine like this ‘‘. . . does not deter-mine absolute saccade length but rather criteria accordingto which saccade length will be programmed so that theeyes move in a way relevant to the task’’ (p. 301). It is as-sumed that individual readers learn scanning patterns as away to navigate through configurations of low spatial fre-quency word units. During this process, each reader willdevelop routines that, on average, provide optimal infor-mation acquisition from the text. In the current versionof Glenmore, there are (as yet) no provisions to accommo-date individual differences. However, as will become appar-ent in the following section, our current implementationof low-level control goes far beyond the rather simpleoculomotor heuristics that were implemented in the previ-ous oculomotor control model proposed by Reilly andO�Regan (1998).

A second important route of our modelling efforts is thetheoretical framework on saccade generation developed byFindlay and Walker (1999). In harmony with a substantialbody of empirical evidence form basic oculomotor re-search, they suggested that saccade target selection isaccomplished via parallel processing and competitive inhi-bition within a two-dimensional saliency map. The actual

triggering of a saccade is controlled by a fixate centre(FC) that can accommodate input from several routes ofcognitive processing. When a saccade is triggered, it willgo to the target object that has emerged as a winner inthe saliency competition (see Findlay & Gilchrist, 2003,for a recent discussion).

As proposed by Radach (1999), in reading the saliencymap may take the form of a vector of saliency values forpositions within the current perceptual span. We followMcConkie and Zola (1984) and McConkie et al. (1988)in their assumption that during reading text is parsed intoa configuration of low spatial frequency word-objects thatsaccades are programmed to attain. The vast majority ofthese selections include the decision between very few alter-natives: to execute a saccade to one of the immediately fol-lowing words (in most cases word n + 1 or n + 2), torefixate the currently fixated word (word n), or to make aregressive saccade to the last word in the sentence (wordn � 1). Evidently, the most important low-level factors thatinfluence the decision are the eccentricity (distance to thecurrent fixation position) and the length of the respectivewords (Kerr, 1992; McConkie, Kerr, & Dyre, 1994),although a number of other factors also play a role (seeRadach & McConkie, 1998, for a review).

In Glenmore, it is assumed that at the beginning of eachfixation low-level visual information, coded as a saliencyvector, is available that allows for target selection and thetriggering of a saccade without any cognitive influence.During the fixation, the saliency values representingword-units will change in response to incoming informa-tion about linguistic processing. This mechanism canbe best illustrated for the decision about which word inthe current perceptual span will become the recipient ofthe next saccade. Suppose that a reader fixates a letterin the right half of seven-letter word, the next word(n + 1) is short (3 letters) and the word n + 2 is again sevenletters long. Given this configuration of word units, it islikely that word n + 2 will have the highest saliency valueduring most of the ongoing fixation and will be the targetfor the next inter-word saccade. If word n + 1 is easy toprocess, its saliency will decline rapidly, making its non-fixation even more likely. If however, word n + 1 turnsout to be difficult to process in the parafovea, it will gener-ate more saliency and might become the most attractivesaccade target. Alternatively, it could be that word n isexceptionally difficult, in which case its chances of beingrefixated would be increased. As will be discussed in detaillater, in this scenario there is competition between wordsfor limited processing resources, opening a route to explainfovea-on-parafovea and parafovea-on-fovea effects. Theexample also illustrates that within a spatial saliency frame-work the notion of ‘‘word skipping’’ becomes meaningless,as there is no default saccade to n + 1 requiring cancella-tion and reprogramming (see Brysbaert & Vitu, 1998, fora similar idea).

Fig. 1 illustrates the architecture of the Glenmore model.In addition to the saliency map, key elements are a visual

Fig. 1. Model overview. This figure represents the main components of the Glenmore model. The circles represent connectionist components, the rectanglea non-connectionist component. Connections with circular heads represent negative connections, those with arrows positive ones. Note that the negativeconnections from words to letters act to maintain activity in the letter units, when those units have a cumulative Gaussian transfer function. This is becausethe negative top-down values will impede the rate at which the activation values saturate as a function of their bottom-up inputs.


input module, a word processing module, a FC, and a sac-cade generator, producing the actual saccadic movement.The visual input vector is basically a representation ofthe current perceptual span and codes the visual configura-tion around the fixation position. From the input unit, vi-sual information is transferred to the saliency map and to alinguistic processing module that implements processing onthe letter and word level within an interactive activation(IA) framework (e.g., Grainger & Jacobs, 1998). In the sal-iency map representation module, saliency values for indi-vidual positions within the vector are calculated as anadditive function of bottom-up visual activation from theinput units and top-down word activation.

At the level of letter processing, the relatively sharpdrop-off in processing performance as a result of lettereccentricity is accounted for by implementing an asymmet-ric letter processing function. This is based on a study byMcConkie and Zola (1987) who used a letter substitutiontechnique to determine the likelihood of discriminating let-ters as a function of distance to the current fixation posi-tion. The time course of activation on the word level isalso a function of a word�s frequency, with high frequencywords rising and falling in activation more rapidly than lowfrequency words.

From the letter and word processing modules, informa-tion is sent in two directions. The vector of letter unit acti-vation is transmitted to the saliency map, where it is used tocontinuously modulate the saliency values of potential sac-cade targets. At the same time, feedback on the generallevel of excitation in the linguistic processing network istransferred to the FC. The actual triggering of a saccadeis based on activity in a fixate module that operates in con-junction with the dynamics of spatial saliency. Over the

course of a fixation, activity in the FC will tend to fall, aprocess that has a stochastic component and a non-spatialprocessing component, similar to autonomous saccade trig-gering in SWIFT or the random waiting time component inthe competition/interaction model. The saccade will be exe-cuted by the saccade generator module after a latencyperiod and will always be directed to the word targetwith maximum saliency at the time of commitment. Thissaccade generator effectively represents the front-end be-haviour of the eyes as described by McConkie, Kerr, Red-dix, and Zola (1988) and implemented in Reilly andO�Regan (1998) and Reichle et al. (1999). A plannedenhancement of the model is to integrate the saccade gen-erator within the saliency mechanism itself. Preliminarywork on this has indicated that it will require some addi-tional parameters.

3. Implementing the Glenmore model

Seen from a computational point of view, the develop-ment of Glenmore is an example of modelling a complexcognitive system in a non-linear dynamical systems frame-work (Port & Van Gelder, 1995; Kelso, 1995). This type ofapproach is well suited to study one of the key questions inthe field: What is the role of cognitive factors in the mo-ment-to-moment control of eye movements in reading?Rather than promoting the all-or-none style explanationsthat dominated the field over the last two decades (Radach& Kennedy, 2004; Rayner, 1998), a dynamical systems ap-proach can potentially accommodate accounts that arguefor the interplay, over time, of linguistic and oculomotorfactors. One way to implement this interplay is to providean arena for both low level and high level factors to play


their roles, perhaps with visuomotor constraints havingmore influence early in the processing of the visual input,while linguistic factors gradually come into play later dur-ing the time line of processing.

Appropriate modelling frameworks for this type of ap-proach are connectionist models, more specifically interac-tive activation (IA) models (McClelland & Rumelhart,1981; Rumelhart & McClelland, 1982). Typically, an IAmodel comprises a set of interconnected neuron-like units.Activity is transferred through the network over weightedconnections. The units in the model implement a transferfunction that combines the unit�s inputs and generates anoutput based on these combined inputs. The specific natureof the transfer function varies from model to model, butthe global design philosophy is to keep the operation itimplements relatively simple. As an example, a typicaltransfer function might take the weighted sum of inputsand perform some sort of normalising operation using,for example, the sigmoid or Gaussian function. The net-work ‘‘computes’’ by circulating activation (i.e., real valuednumbers) between units until some stopping criterion hasbeen reached (e.g., the achievement of a threshold, or thestabilising of levels of activity).

As evident in Fig. 1, the connectionist architecture of theGlenmore model is relatively simple, comprising inputunits, letter units, saliency units, and word units. In addi-tion, there is a ‘‘FC’’ module that controls the decisionwhen to execute a new saccade. During each fixation, allof the units in the network accumulate input activationover time. At the end of the fixation, some of the units havetheir activation reset to zero, while others carry activationover to the next fixation. This carryover of activation fromone fixation to the next is the mechanism whereby spilloverand preview effects are implemented. Each class of unit hasan associated transfer function determining what kind ofoutput it generates from its input activation, and how thischanges over time. More specifically, the model uses twotransfer functions: Gaussian and sigmoid. The Gaussiantransfer function allows the respective unit to generate anoutput that rises and decays over time. The specific rateof change is a function of the shape of the distribution,which in turn is determined by the two parameters of theGaussian (mean and standard deviation). These parame-ters are fixed for the version of the model described inthe present paper (m = 50, SD = 0.3m), such that the out-put of the function is 1.0 for m = 50. The sigmoid transferfunction operates in a similar way to the Gaussian, with theimportant difference that its output does not decay overtime, but instead saturates to a value of 1.0. The onlyparameters that are free to vary are the weights connectingthe units, and even here all weights of the same type (e.g.,letter-to-word weights) are given the same value. These var-iable model parameters are selected using a parameter fit-ting process based on the Alopex learning algorithm(Unnikrishnan & Venugopal, 1994).

A detailed picture of the key elements in the Glenmoremodel is presented in Fig. 2. Input from a 30 spaces wide

‘‘perceptual span’’ vector of 1s and 0s (indicating the pres-ence or absence of a letter) is fed forward to the letter units.These letter units form the nexus of the processing net-work, connecting both to the word and saliency units.The word units in turn serve as a source of top-down sup-port for the letter units, augmenting the letter activations.The saliency units preserve the spatial representation ofthe input vector and are the representational structure usedin the selection of a saccade target. A saccade is triggeredwhen activation in the FC unit exceeds an adjustablethreshold. FC activity is modulated by the global level ofactivity of the letter units which in turn are influenced byactivity in the word level. The threshold of the FC is adjust-able as a function of global strategic factors such as readingtask and difficulty of the material. In essence, variations inthis threshold permit the early or late triggering ofsaccades.

3.1. Input units

The visual input vector includes a visual field of 30 char-acter spaces with the fovea at position 11. The asymmetryin letter processing within the perceptual span is imple-mented by the probability density function of the gammadistribution centred on the fovea (see Eq. (4)). The functionis used to scale the present inputs, where the presence of acharacter is initially given a value of 1.0, and then scaleddown as a function of distance from the fovea

iðxÞ ¼ Cðx; 3:5; 4:0Þ. ð1Þ

3.2. Letter units

The units in the vector of letter processing receive bot-tom-up activation from the input units, and top-down acti-vation from the word units. The letter unit transferfunction is the probability density of a Gaussiandistribution,

gðx;m; SDÞ ¼ 1ffiffiffiffiffiffi2p

pSD

e�ðx�mÞ2

2SD2 ; ð2Þ

where x is the accumulated net input to the unit, m = 50,and SD = 0.3m. Notice that a given xi at time t + 1 is theaccumulated weighted sum of the inputs to the unit calcu-lated as

xi;tþ1 ¼ xi;t þXj

wijoj;tþ1; ð3Þ

where wij is a weight connecting unit i to unit j, and oj,t + 1

is the output from unit j at time t + 1.The presence or absence of a letter in the visual field is

indicated through the activation of a corresponding letterunit. The letter unit is in turn connected to its appropriateword unit. The determination of what letter unit is con-nected to what word units is at present done a priori bythe model. Thus, for a given fixation, the model establishesthe appropriate connections between letters and words.

Fig. 2. Model detail. This figure is a schematic representation of the Glenmore�s internal connectivity. The transfer functions of the relevant units arerepresented graphically in boxes adjacent to them. Activity in the 30 input units, scaled by the gamma function to represent variability in spatial resolution,is propagated to the saliency map (the ‘‘where’’ pathway) and to the letter units (the ‘‘what’’ pathway). Activity in the letter units feeds forward to the wordunits, which in turn feed activation back to the letter units. Note that the feedback from words to letters is negatively weighted, so that letters receiving alarge amount feedback have their activation maintained for longer. The recurrent connections on the word units are used to implement word frequencyeffects. The more familiar or frequent the word, the more rapidly its activation will rise and decay. The fixate centre unit takes input from the letter units.When that activity falls below a certain threshold, a saccade is triggered to the word with the largest peak in the saliency map. There is also a stochasticcomponent to this process that will cause the activity of the fixate centre to decay at varying times.


Consequently, the architecture of this model differs fromtraditional IA models where multiple letter units in eachcharacter position feed into multiple word candidates. Thisdesign decision was made because the focus of current ver-sion of the model is saccade target selection. The develop-ment of a more realistic word recognition module isplanned as a future extension to the model.

3.3. Saliency units

The units comprising the saliency vector receive activa-tion from both input and letter units. The input from theletter units represents a form of crosstalk between the‘‘what’’ and ‘‘where’’ processing pathways, and providesan indirect top-down ‘‘cognitive’’ contribution to the tem-poral evolution of the saliency values for specific regions ofthe visual field. The influence is indirect, as the letter unitsreceive input not only from the visual input units but alsofrom the word units, the activation of which is determinedin part by their statistical frequency. The saliency unittransfer function is the probability density of the Gaussiandistribution with parameters identical to those of the func-tion for the letter units. The saliency units accumulateactivity over time and reach a peak of activation after 50time steps, corresponding roughly to the eye-brain trans-

mission lag (McConkie, 1983; Sereno et al., 1998; Reichleet al., 2003).

The key role played by the saliency map in the model isto support the target selection process, whereby the wordunit with the highest activity at the time of triggering actsas the target for the next saccade (Findlay & Walker,1999). This can potentially be the currently fixated word,the preceding word, or one of the succeeding words. Asmentioned earlier, there is no discrete shift of ‘‘attention’’and no default saccade program to word n + 1. Once theword unit with the highest level of activity is selected, a sac-cade generator module is used to execute a saccade in away that implements the metrical properties of saccadeamplitudes in reading as described by McConkie et al.(1988). This separation of the target selection process fromthe mechanism that allows the eye to attain the target canbe argued to mirror the separation of low-level motor pro-grams from higher level processes involved in target selec-tion. Nonetheless, some (though not all) of the componentscaptured by the equations of McConkie et al. (1988) arelikely to be emergent features of the saliency mechanism it-self. As mentioned earlier, a future version of the currentmodel will aim to broaden the coverage of the saliencymechanism to include features currently modelled by theMcConkie et al. equations.


3.4. Word units

Processing units at the word level receive inputs fromtheir respective letter units, and in turn send activationback to these letter units. There are seven word units, asthis is the maximum number of words that were found tobe contained in the visual field of width 30 in the text cor-pus used in our reading experiment (see below). These unitsuse a sigmoid transfer function as follows:

sðxÞ ¼ 1

1þ e�ðx�mÞ

8

; ð4Þ

where x is the accumulated net input to the unit and m is,again, 50. This function outputs in the range 0 through 1,with 0.5 for an input of m. The divisor 8 is used to some-what linearise the S-shaped sigmoid function.

The net input, x, to this equation is a bit more complexthan for other units

xi;tþ1 ¼ xi;t þP

jwijLj;tþ1

nþXk

wikW rk;tþ1 �

Xm

wimW om;tþ1.

ð5ÞIn this equation, the terms Wr and Wo denote recurrent in-puts and inputs from other words, respectively. It is impor-tant to note that the letter input is averaged over wordlength n, so that word length itself does not affect the rateof activation accumulation, just the average activity of thecomponent letters.3 The values of the self-recurrent connec-tions are a function of the word�s statistical frequency. Thehigher the word frequency the more activation the wordreceives, and the more rapidly its output peaks. Specificvalues of the other connections are determined by theparameter search mechanism. Note again that the sameconnection value is used to for the same connection type.At this point the use of word frequency is the only linguistichigh-level factor that comes into play in the model. There isscope, however, for implementing more word propertiessuch as predictability. Importantly, the architecture of themodel also allows the implementation of top down modu-lations of the reading process using the threshold adjust-ment of the FC unit. While we have not exploited thisfeature in the current version of the model, it is intendedto use this parameter to help model reading data whereone of the independent variables is reading task difficulty.

In addition to the self-recurrent connections, the wordunits are also linked to neighbouring word units with inhib-itory connections, implementing a competition for wordprocessing resources. Words can be processed in parallelfrom a given fixation, but one word will tend to dominateat a given point in time, thus accommodating the results ofInhoff, Eiter and Radach (under revision). Generally

3 This is based on the finding by Inhoff, Radach, Eiter, and Juhasz(2003) that parafoveal word length information is not used for lexicalprocessing in reading (see also Inhoff & Radach, 2002, for a generaldiscussion).

speaking, we have a mechanism for reconciling the obviousfact that reading includes at some level the sequential left-to-right processing of words with the accumulating evi-dence in favour of simultaneous processing of more thanone word in a given fixation (see our discussion in theintroductory section).

3.5. Saccade metrics

Quantitative analyses of saccade metrics pioneered byMcConkie et al. (1988) form the basis of our current under-standing of the end-point behaviour of the eyes in reading.They demonstrated that the distributions of initial saccadelanding sites are Gaussian in shape and that the centre ofthese distributions and their standard deviations are deter-mined primarily by oculomotor factors (see also Radach &McConkie, 1998).

McConkie et al. proposed that the pattern of landingsite distributions can be accounted for by five principles:(1) The centre of the word is the functional target locationof incoming initial saccades; (2) a systematic range errorcauses the eye to be increasingly deviated from this targetas a linear function of distance from the launch site; (3) thisrange error is somewhat less, the longer the eye spends atthe launch site; (4) there is a random, Gaussian-shaped dis-tribution of landing sites around the target location; and(5) the spread of this distribution is increased as a functionof launch distance. These principles can be summarized inthree equations. The first is a linear equation (Eq. (6))describing how the mean landing site (m) on a word devi-ates as a function of launch distance (d). Note that bothm and d are defined to be zero at the centre of the targetedword. As an example, in the case of a four-letter word, thiswould be half way between the second and third letterpositions.

m ¼ 3:3þ 0:49d. ð6ÞThe second is a cubic equation (Eq. (7)) describing thespread of landing positions around m.

SD ¼ 1:318þ 0:000518d3. ð7ÞThe third is a Gaussian equation (Eq. (8)) accounting forthe random distribution of landing sites, and for which m

and SD are the parameters.

f ðx;m; SDÞ ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffi2pSD

p e�ðx�mÞ2

2SD2 . ð8Þ

In the present version of the model, once the activation ofthe FC unit reaches threshold, and a saccade is triggeredthese equations are used to determine the amplitude of asaccade aimed at the centre of the word with the highestsaliency. An alternative way to determine the functionalsaccade target would be to use the actual position of thesaliency peak at the time of saccade triggering instead ofthe centre of the target word. This could provide a wayto account for the small but significant modulations insaccade landing positions as a function of parafoveal


orthographic regularity, as suggested by Radach, Inhoff,and Heller (2004). An exploration of this potential exten-sion of the model is beyond the scope of the present paper.

Note that we have made no attempt to implementMcConkie et al.�s principle (3), suggesting a convergenceof landing positions towards the word centre. This sugges-tion was not supported by another set of corpus data re-ported by McConkie, Grimes, Kerr, and Zola (1990) andour own detailed analysis of a large corpus of individualreading data also did not find evidence in favour of thisidea (Radach & Heller, 2000).

3.6. FC unit

The FC is a single unit with connections from all of theletter units. Its level of activity is determined by a sigmoidtransfer function. The FC effectively implements an auto-matic saccade deadline mechanism with activity accumulat-ing over time, irrespective of input. As soon as thethreshold is reached, a saccade is triggered.

3.7. Dynamics of the model

The dynamics of the Glenmore model are typical of thebroad class of interactive activation models. At the start ofa fixation, the 30 element input vector of units is activatedwith values that are a function of whether there is a char-acter present in a specific location or not, and the eccentric-ity of that location. As mentioned above, a gammafunction is used to weight the inputs.

Once there is a pattern of activity on the input units,the network connections are dynamically configured toensure that the appropriate letter units connect to theappropriate word units, and vice-versa. Obviously, thisis not meant to be analogous to any biological process,and is used here as a computational convenience to re-duce the size of the network needed to run the simula-tion. The default state of the network is for everyletter unit to be connected by bi-directional connectionsto every word unit. Spaces are represented at the letterunit level as letters with zero activation. The process ofconfiguration that occurs at the beginning of each fixa-tion eliminates spurious connections. Note that the acti-vation values of word and letter units are carried overfrom one fixation to the next. By this mechanism, spill-over and preview effects are implemented. With the net-work configuration complete, the input activation is fedforward to a set of letter units and a set of saliencyunits, each of which comprises 30 units. There are one-to-one connections from the input units to the letterand saliency units. There are also feedback connectionsfrom the word units to the letter units. Because of theuse of the Gaussian probability density function asthe transfer function for the letter and saliency units,the activity of the letter units reaches a peak after anumber of cycles of activation. This has been set at 50cycles, so that the letter unit representing input from

the fovea of the visual field will peak after 50 time steps,and will then start to decline. The further one movesaway from the fovea, however, the more slowly the levelof activation accumulates. The activation of moreperipheral letters will reach the same peak value, but willtake an increasingly larger number of time steps thefurther one moves from the fovea.

The letter units receive top-down input from the wordunits whose level of activity is a function of the average

letter input from the letter units, and the frequency ofoccurrence of that word in the language. The more fre-quent is the word, the more rapidly it is activated, andthe more rapidly it asymptotes to an output value of1.0. Frequency effects are implemented by a positiveself-recurrent connection that is proportional to the fre-quency of the word. Thus the activation levels of high-frequency words rise more rapidly than lower frequencywords, but this is also a function of the activity of theletter units, which in turn is a function of the eccentricityof the letters in the visual field. Consequently, visuallyeccentric high frequency words will be more rapidly iden-tified (i.e., their activity will peak earlier) than their lowfrequency counterparts.

During the processing of words in a fixation, there iscompetition between words, mediated by inhibitory con-nections between word units. Once a word has peaked,it ceases to compete, leaving the way open for otherwords to complete their processing. In this way, severalwords can be processed simultaneously, but usually oneword draws most of the processing resources. This isthe mechanism in our model that mediates fovea-on-par-afovea effects. In contrast to parafovea-on-fovea modula-tions, the fovea-to-parafovea modulation is undisputedand well documented by studies showing that parafovealpreview effects are diminished when the foveal word is dif-ficult of process (e.g., Henderson & Ferreira, 1993). In theframework of the Glenmore model, this generally ac-cepted form of competition for processing resources isgeneralized to competition between all words within thecurrent perceptual span.

Activation from the letter units is also sent to the sal-iency units where it combines with the activation fromthe input units. Again the transfer function is a Gaussian,which models in one function the accumulation of activa-tion and its decay over time. Areas of high-activation peakand decay more rapidly. Given the varying resolution ofthe input units (modelled by the gamma function), saliencyunits receiving foveal inputs will peak and decay more rap-idly than other units. So after a certain number of itera-tions, the saliency values will drop in the foveal regionsof the saliency units, implementing a form of ‘‘inhibitionof return’’ (Gibson & Egeth, 1994).

Activity from the letter units is passed to the FC unit.This unit acts as a spatially undiscriminating summary ofnetwork unit activity. So it will, in principle, trigger a refix-ation, regressive or progressive saccade, depending onwhere the saliency maximum is located.


3.8. Parameter fitting

In order to determine an appropriate set of weights for thevarious unit connections in the simulation, a parametersearch algorithm was employed. The algorithm used wasbased on the Alopex neural network-learning algorithm(Unnikrishnan & Venugopal, 1994). Instead of using an er-ror gradient to guide the changes in weight (or parameter)values, Alopex uses local correlations between changes inindividual weights and changes in a global error measure.Unlike classical gradient descent learning algorithms suchas backpropagation (Rumelhart, Hinton, & Williams,1986) Alopex does not make any assumptions about thetransfer functions of individual units nor does it explicitly de-pend on the functional form of the error measure. For exam-ple, both transfer functions and the error functions can benon-differentiable. This makes it ideal for parameter fitting,where we might want to combine a number of factors intoa complex cost function that we wish to minimize. Thus,we can ensure the algorithm selects a set of parameters thatsatisfies the global temporal and spatial characteristics ofreading, specifically fixation duration and saccade length.

The algorithm is initially stochastic in its search, anduses a ‘‘temperature’’ parameter in a manner similar to sim-ulated annealing (Kirkpatrick, Gelatt, & Vecchi, 1983) togradually make the search more deterministic as the algo-rithm converges on a desirable set of parameters.4

The parameter search involves making small perturba-tions (e.g., ±0.01) to the parameters based on whetherthe previous change resulted in a reduction of the cost func-tion. The parameter wij(n) in Eq. (9) below refers to theconnection between units i and j at time n. This parameteris perturbed by ±d, where d is a constant value

wij nð Þ ¼ wij n� 1ð Þ þ dij nð Þ; ð9Þ

dij nð Þ ¼�d with probability pij nð Þ;þd with probability 1� pij nð Þ.

(ð10Þ

However the changes depend probabilistically on the costfunction value, as can be seen from Eq. (11)

pij nð Þ ¼ 1

1þ edDE nð ÞT nð Þ

. ð11Þ

This probability is modulated by a temperature variable(Eq. (12)), which is derived from the overall cost functionvalue. As this value decreases, the selection of parameterchange moves from being stochastic to deterministic

T nð Þ ¼ dN

Pn�1

n0¼n�NDE n0ð Þj j; if n is a multiple of N ;

T nð Þ ¼ T n� 1ð Þ; otherwise;

ð12Þ

4 The temperature term in simulated annealing has the effect ofincreasing the stochasticity of the parameter search when the error ishigh. It�s analogous to the process used in steel manufacture of heatingand slow cooling of the metal to encourage the formation of more stablecrystalline structure and thus increase the metal�s strength.

where d is the constant parameter change (usually around0.01), and DE = E(n � 1) � E(n � 2) is the change in errorbetween the two previous iterations.

The Alopex algorithm shows reasonable convergence,but is not as efficient as a gradient descent algorithm.Nonetheless, the flexibility it provides in the specificationof arbitrarily complex cost functions is worth the slowerconvergence. This is especially true when the number ofparameters to be estimated is relatively small.

In the case of the model described in this paper, therewere nine free parameters to be estimated, furthermore,the sign of four of these was constrained to be positive,and the maximum absolute value permitted was 10.0. Theparameters comprised the following connections (sign indi-cates required polarity of weight): input-to-letter (+), in-put-to-saliency (identical to input-to-letter), letter-to-word(+), letter-to-saliency (�), word-to-letter (�), word-to-word (two parameters: positive self-recurrent weight ap-plied to the word frequency and a negative connection toother words), letter-to-FC (�), FC threshold (+), and theslope of the linear FC function. The rationale for con-straining the word-to-letter parameter to be negative wasto ensure that active words maintained the level of activa-tion of their component letters. Given the Gaussian activa-tion function, negative input was necessary to counter thedecaying effect of the accumulating input from the inputunits. The letter-to-saliency weight was constrained to benegative for similar reasons.

The text used for the parameter fitting was a 7570 wordGerman text on the topic of the Inuit. The cost functionused was:

Cost ¼ n� 1ð Þ2 þ 1

m� 1

� �2

þ p � 11ð Þ � 8ð Þ2

þ t � 0:75ð Þ2 þ d� d0j j;ð13Þ

where n is the number of peaks (at a minimum for just onepeak), m is the maximum value of the peak (at a minimumwhen 1.0), p is the location of the maximum peak (at a min-imum for 8 characters to the right of the fovea), t is thethreshold for the FC unit (the desired threshold is 0.75),and the vectors d and d 0 represent desired and actual fixa-tion durations averaged over a set of word classes. In thecase of the present study, these word classes correspondedto the cells of the length · frequency design of the empiricalstudy described below. The idea behind this cost functionwas to constrain the mean saccade length and fixationduration to the values observed in the data and also toencourage the network to behave within some reasonableboundaries (i.e., to have a single saliency peak and to havethe keep the FC threshold at a workable value).

4. Qualitative evaluation

The model can deal with a variety of low-level readingphenomena in an integrated and parsimonious manner.In this section, we will demonstrate the operating principles


of the model and how they can account for such phenom-ena as preview effects, spillover effects, refixations, regres-sions, and word skipping. The advantage of this modelover others is, we believe, the variety of phenomena thatcan be accounted for with letter-level accuracy within arather simple computational framework. The followingdescription follows closely our earlier report (Reilly &Radach, 2003).

Fig. 3 illustrates how the word units, saliency units, andFC interact on a given fixation. Once the activity in the FCreaches a certain threshold, a saccade is triggered to theword with the highest saliency value, irrespective of whereit is. In this case, the word with the highest saliency is n + 1,resulting in a progressive inter-word saccade. Also illus-trated in Fig. 3 is the mechanism mediating preview effects.These effects arise through the activation value of the newword, with the rising level of activity being carried over tothe next fixation. Note that preview does not result fromthe disengagement and re-engagement of an attentionalmechanism. Rather we propose a continuous mechanismthat dynamically modulates the processing load acrossthe words in the fovea and immediate neighbourhood asa function of their relative difficulty. Thus, more than

Fig. 3. Time course of processing. This figure represents the time course of pronot shown to reduce the complexity of the figure). The top panel represents thecarried over from fixation to fixation. The vertical line down through the panactivation for the first word has asymptoted and the activation value of the secobenefit for that word when it comes to the start of the next fixation. The seconsaliency map. The bars indicate regions in saliency map that have activation valword with the highest saliency peak is the saccade target. The bottom panel is areaches an adjustable threshold, a saccade is triggered. The activity of the fixa

one word can be processed at a given time, though thereis competition for lexical processing resources betweenwords. Note that once a word reaches its asymptotic value,it no longer competes with other words.

The model is capable of accounting for the modulationof preview benefit by the difficulty (in this case, lowfrequency) of the currently fixated word (see Fig. 4). Bymodelling the processing of the words as a continuousasymptotic process, we can account for the dynamic inter-play between the processing of word n and word n + 1. InFig. 4, the frequency of word n is varied. Where word n is ahigh frequency word, the level of word activity rapidly risesto a peak, thus removing it from competition with wordn + 1, and allowing it, in turn, to be processed. When wordn is a low frequency word, less progress is made in process-ing word n + 1, thus reducing any preview benefit for it.

Spillover effects from the processing of the previousword on the currently fixated word can be accounted forin precisely the same way. In Fig. 5, we see that the process-ing of the low-frequency word has not asymptoted prior tothe fixation. Recall that the trigger for executing a saccadeis the level of activity of the FC exceeding a certain thresh-old. It bears no direct relationship to the successful, or

cessing in a number of the components of the network (the letter units aretime course of activation of two word units. The activation of word units isels indicates the time at which a saccade was triggered. At that time, thend word has started to rise. This level of activation represents the previewd panel is a spatio-temporal representation of the activity levels across theues greater than a 0.5 at a given time step. When a saccade is triggered, therepresentation of the time course of activity of the fixate centre. When thiste centre is a function of the activity of the letter units.

Fig. 4. Preview modulation by frequency of fixated word. This figure represents schematically the interaction between word frequency and peripheralpreview. The time course of word activation for two pairs of words is represented, where word nin each pair is either a low frequency word (top panel) or ahigh-frequency word (bottom panel). Because there is competition between active word units (until they reach asymptote), if word n remains active longerit will limit the processing of word n + 1. This is represented by differences in the rise time of the word n + 1, as a function of the frequency of word n.

Fig. 5. Spillover effects from preceding word. This figure schematically represents the production of spillover effects. The time course of word activation fortwo pairs of words is represented, where word n in each pair is either a low frequency word (top panel) or a high-frequency word (bottom panel). Asillustrated in the top panel, if a saccade occurs before word n reaches asymptote, its activation will carry over to the next fixation, competing for processingin the succeeding fixation. This will not happen where word n is a high frequency word (bottom panel).



otherwise, processing of the currently fixated word. If ahigh frequency word precedes the current fixation, thereis less likely to be processing of that word continuing intothe next fixation.

4.1. Refixations

In Fig. 6, we show the performance of the time course ofactivation over the letter field when an eight-letter word isfixated for the first time at its last letter. Note that there hasbeen no preceding fixation of this word or the one preced-ing it. The situation is equivalent to there having been along saccade from the right to this point in the text. Thereis a build up of activation in two competing word targetson the saliency map, with the currently fixated word (bew-eisen) marginally winning the competition. This word isthen selected as the target for the next saccade.

4.2. Regressions

In Fig. 7, we have a similar graph showing the build upof activation taking place over the location of the precedingword. Again, there was no fixation on the currently fixatedor preceding word prior to this one. The fixation position is

Fig. 6. Modelling a refixation. This figure shows two time-slices of activation inNote that neither the current nor previous word had previously been fixated. ThA saccade triggered at either 200 or 280 simulated msecs would, therefore, res

Fig. 7. Modeling a fixation before a regressive saccade. This figure shows two timthe word ‘‘zwischen’’. As in Fig. 6, neither the current nor previous word had pin a regressive fixation to word n � 1.

at the beginning of an eight letter high-frequency word.Consequently it drops in saliency fairly rapidly, leavingthe preceding word the most salient target. If a saccade istriggered at this point, the result would be a regression tothe preceding word.

4.3. Likelihood of fixating a word (‘‘word skipping’’)

Fig. 8(a) and (b) illustrates how the model can accountfor the likelihood of fixating a word as a function of its fre-quency. As mentioned above, we do not believe that thereis any default tendency to aim a saccade at each word on aline of text; therefore we put the traditional term ‘‘wordskipping’’ in quotation marks. Note that in this simulationexample, each of the graphs shows the second of two fixa-tions, the preceding fixation having been on the word toleft of the current fixation (fixation locations are indicatedby arrows). In Fig. 8(a), we can see that the high frequencyword in the right parafovea does not receive a fixation,whereas in 8(b) the low frequency word gets fixated. Thiseffect is achieved by the slower accumulation of activationfor the low frequency word, and the subsequent mainte-nance of activity in the saliency map in the region of thelow frequency word.

the saliency map for a fixation on the last letter of the word ‘‘Beweisen’’.e activation peak over the current word is marginally ahead of word n + 1.ult in a re-fixation of the current word.

e-slices of activation in the saliency map for a fixation on the first letter ofreviously been fixated. The activation peak over the preceding word results

Fig. 8. Frequency effects on word fixation likelihood. This figure shows the effect of the frequency of word n + 1 on the likelihood of it being fixated. Theblack arrow indicates the current fixation. Note that for both figures the preceding fixation was on the last letter of the preceding word, indicated by thefirst arrow. Because ‘‘nicht’’ is a higher frequency word than ‘‘Namen’’, and because saliency is influenced by word frequency, the saliency location ofthe more frequent word declines more rapidly than the less frequent word. A saccade triggered at 240 simulated msecs to the word location with the highestpeak will result in a higher frequency n + 1 not being targeted for a fixation (a), but with the opposite the case for a lower frequency n + 1 (b).

5 It should be noted that Rayner et al. (2004) recently reported a versionof their model that could accommodate frequency and predictabilityeffects obtained with target words of controlled length.


5. Quantitative evaluation

The text material used to evaluate the model was takenfrom a coherent text corpus on the history and culture ofthe Inuit people (adopted from a book by Jeier, 1977).The total corpus consists of 7570 words and is segmentedinto 108 six-line passages each including two target sen-tences. These sentences in turn include target words in-tended to be representative of the range of common wordlength and frequencies in German narrative texts. This isaccomplished by varying word length in three steps includ-ing short (4–5 letters), medium (7–8 letters) and long (10–11 letters) words. To vary word frequency, nouns weresampled form the German CELEX data base (CELEX,1995) in three ranges, between less than one per million, be-tween 10 and less than 100 per million, and equal to orgreater than 100 per million.

The simulations reported in this paper focus on the setof controlled target words, thus avoiding the well knownproblem of correlation between word length and word fre-quency in coherent text (e.g., Kliegl, Olsen, & Davidson,1982, 2004). Is has been argued that the simulation ap-proach taken by Reichle et al. (2003) is problematic, assampling word frequency over a whole corpus of text cre-ates a mixture of length and frequency effects with lengthbeing the much more powerful ingredient (Brysbaert &

Drieghe, 2003).5 Indeed numerous experimental and cor-pus studies have shown that, at least with respect to fixa-tion frequency measures, effects of word length can bemuch larger in comparison to lexical processing effects(cf. Brysbaert, Drieghe, & Vitu, 2005, for details).

Both the ‘‘experimental’’ and ‘‘statistical’’ control ap-proaches have recently been studied in detail by Kliegl,Grabner, Rolfs, and Engbert (2004), who used regressionanalysis techniques to examine effects on the target wordvs. whole corpus level. They showed that word lengthand frequency effects on viewing time and fixation fre-quency measures obtained from controlled target wordsare generally quite similar to independent effects of lengthand frequency estimated by repeated-measures multipleregression analyses over a whole corpus. Given the degreeto which experimental data can be generalized to the read-ing of whole sentences, we take our orthogonal manipula-tion of word length and frequency as a good starting pointfor simulations. In later versions of Glenmore, we willexpand the scope of the simulations to the complete Inuitcorpus, including also manipulations of reading task andformat of reading materials.


The computation of statistical word frequency for oursample of target words was supplemented with a ratingof word familiarity on a 7-point scale from ‘‘unknown’’to ‘‘ubiquitous’’ (see Juhasz & Rayner, 2003 & Williams& Morris, 2004, for recent discussions of word familiarityeffects). This lead to the exclusion of potential target wordswith mismatching frequency and familiarity values from alarger sample of candidate words. Several measures weretaken to ensure that the variation in word frequency wouldprimarily reflect the degree of processing difficulty on thelexical level. One such measure was to control for morpho-logical complexity using the respective CELEX measure,referred to as the number of morphological components(see Andrews, Miller, & Rayner, 2004; Juhasz, Starr, Inh-off, & Placke, 2003; Pollatsek, Hyona, & Bertram, 2000for evidence of effects of morpheme processing on readingtime measures). A further step in the selection of targetswas to exclude words with extreme values in overall ortho-graphic regularity, as indicated by mean positional bigramfrequencies. Table 1 lists means values of word frequency,familiarity and morphological complexity for the cells ofthe 3 (word length) x 3 (word frequency) design.

5.1. The reading experiment

5.1.1. Materials and procedure

For the present study, data from two recent experimentswere selected. One experiment investigated the effects ofreading sentences embedded in pages of coherent text vs.reading in a sentence-by-sentence fashion. The other exper-iment studied differences in silent vs. oral reading. Datafrom these manipulations will be used in later versions totailor Glenmore to different reading modes and types ofreading materials. For the present study only the data fromthe standard condition were included (108 sentences),where participants were asked to read silently at their nor-mal pace so that they would be able to understand the maincontent. Comprehension was tested using a relatively sim-ple multiple choice comprehension test.

Table 1Means and standard deviations of word frequency (top panel) and word fami

4–5 Letter words

Mean word frequency (per million)

Low frequency 0.49Medium frequency 6.41High frequency 174.87

Word familiarity rating (n = 20)

Low frequency 4.64 (0.67)Medium frequency 3.44 (0.78)High frequency 2.38 (0.54)

Mean number of morphological components

Low frequency 1.04Medium frequency 1.13High frequency 1.13

Each cell contains 24 target words. For each of the frequency ranges, means innot significantly different (p > 0.1). Bottom panel: Means and standard deviatBaayen et al., 1993). For each of the word length ranges, means for high, mea

Target words were always embedded in one-line declar-ative sentences with a line width maximum of 82. The posi-tion of the targets within the line of text was controlledsuch that they never occupied the first two or last two posi-tions. They were also evenly distributed between the left,central and right part of the line for all cells of the experi-mental design (see Vitu, Kapoula, Lancelin, & Lavigne,2004, for an analysis of line position effects). The word pre-ceding the target was always an adjective of 6–10 charac-ters in length. The word-length range for the adjectiveswas chosen on the basis of analysing a large corpus of read-ing data (Radach & McConkie, 1998) to maximize the pro-portion of cases with one fixation on the word before thetarget.

Text was presented on a 21’’ EyeQ CRT monitor at apixel resolution of 1024 · 768 in fixed-width courier font.At a viewing distance of 71 cm, each character subtendedapproximately 1/3 of a degree of visual angle. Eye move-ments were recorded using an SR Research Eyelink vi-deo-based eye tracking system, running at 250 Hz.Viewing was binocular but eye movements were recordedfrom the right eye only. Sessions consisted of a trainingblock with 8 practice trials followed by the experimentalstimuli. The experiment lasted between 45 and 60 min.

A target word was considered fixated when a fixation fellon one of its constituent letters or the blank space preced-ing it. Initial fixation durations of less than 70 ms wereadded to the subsequent fixation if the target word wasimmediately refixated. All other fixations with durationsof less than 70 ms and all fixations with more than1500 ms were removed from analyses. Excluded were alsotrials in which the first fixation on the target word wasnot preceded by a progressive saccade. Together withblinks or track losses, these restrictions resulted in therejection of about 4.8% of all observations. In the analysesof these data, first fixation durations were defined as theduration of the initial fixation on the word, irrespectiveof whether the target was subsequently refixated. Gazedurations included the time spent viewing the target word,

liarity ratings (center panel) for the cells of the 3 · 3 design

7–8 Letter words 10–11 Letter words

0.53 0.516.26 6.35

129.58 132.77

4.47 (0.90) 4.54 (0.61)3.62 (0.58) 3.40 (0.59)2.23 (0.36) 2.33 (0.35)

1.54 1.671.58 1.791.50 1.79

both word frequency and familiarity for short, medium and long words areions of the number of morphological components (according to CELEX,n and low frequency word are not significantly different (p > 0.1).

ords M

FLF

232(38)

243(34)

320(89)

383(131

)0.4(0.2)

0.5(0.2)

89.8

(14.0)

85.6

(15.1)

3.63

(0.86)

3.70

(0.78)


including the time spent refixating it during first pass read-ing, but excluding saccade durations.6 Landing positions ofincoming initial saccades were rounded to a tenth of a char-acter before averaging, with the space preceding the targetword coded as position 0.1–0.9 (see Inhoff & Radach, 1998;Inhoff & Weger, 2003 & Rayner, 1998, for discussions ofoculomotor measures). Each eye movement parameterwas subjected to a 3 (word length) · 3 (word frequency)analyses of variance, using subject (F1) variability in thecomputation of error terms.

lues)forastan

dardsetofoculomotormeasures(n

=36

)

7–8Letterwords

10–11Letterw

LF

HF

MF

LF

HF

)23

6(49)

216(41)

232(36)

252(53)

218(31)

)25

8(54)

236(57)

278(78)

331(114

)28

1(72)

)0.1(0.1)

0.1(0.2)

0.2(0.2)

0.3(0.2)

0.3(0.2)

.5)

76.4

(16.1)

79.9

(17.1)

88.2

(14.4)

88.4

(13.1)

90.3

(13.3)

50)

2.44

(0.52)

3.42

(0.73)

3.12

(0.63)

3.23

(0.71)

3.76

(0.73)

5.1.2. Results

Table 2 reports effects of word length and word fre-quency on a set of standard eye movement measures. Asexpected, both independent variables had substantial sys-tematic effects on viewing time measures. For initial fixa-tion durations, this was expressed in a highly significantmain effect of length, F(2,70) = 12.34, p < 0.01, and fre-quency F(2,70) = 44.30, p < 0.01, with no significant inter-action F(4,14) = 1.934, p = 0.11. For gaze durations, therewere again reliable main effects of word length F(2,70) =51.27, p < 0.01, and word frequency F(2,70) = 73.39, p <0.01. Here, the interaction was also significant F(4,140) =7.518, p < 0.01, indicating that frequency effects are largerin longer words. This pattern of results is closely mirroredby the data for the frequency of refixations, where we alsofound a significant main word length F(2,70) = 71.025, p <0.01, and word frequency effect, F(2,70) = 27.16, p < 0.01,and a significant interaction, F(4,140) = 3.91, p < 0.01.

Word length strongly determined the probability of fix-ating a target word, F(2,70) = 34.21, p = < 0.01. In con-trast, word frequency turned out not to have a reliableeffect, F(2,70) = 1.31, p = 0.28, while the interaction wassignificant F(4,140) = 5.42, p < 0.01. Looking at the land-ing position of initial incoming progressive saccades, therewas a substantial effect of word length F(2,70) = 95.31,p < 0.01, whereas the influence of word frequency(p > 0.5), and the interaction were both negligible,(p = 0.49).

rderrors

(SD�sforfixationfrequency

va

4–5Letterwords

HF

MF

204(33)

206(38

214(38)

212(40

cy0.1(0.1)

0.0(0.1

ty72

.2(21.1)

71.5

(19

ition

2.50

(0.54)

2.53

(0.

5.1.3. Discussion

Overall, the pattern of results reported here is ongood agreement to the literature (e.g., Kliegl et al.,2004; Rayner, Sereno, & Raney, 1996; Schilling et al.,1998). The relatively small word length effect on fixationdurations reflects the well know fact that the increase inreading time with longer words manifests itself primarilyin a larger number of fixations rather than a prolonga-tion of fixation durations (e.g., Blanchard, 1985). The ab-sence of a reliable word frequency effect on fixation

Tab

le2

Meansan

dstan

da

Fixationduration

Gazeduration

Refixationfrequen

Fixationprobab

ili

Initiallandingpos

6 We are aware of the fact that lexical processing continues during theduration of saccades (Irwin, 1998). However, reporting gaze durationswithout saccades is standard practice and used here in the interest ofcompatibility to the majority of research in the field.


probability is in line with results from some other studies(e.g., Gautier, O�Regan, & Le Gargasson, 2000; Hender-son & Ferreira, 1993; Kennison & Clifton, 1995). Look-ing at studies that have found equal or larger fixationprobabilities for more difficult words, Brysbeart et al.noted that in the 10 studies they included in theirmeta-analysis the average effect size was only 5%. Thisis consistent with the idea that a considerable amountof parafoveal lexical processing needs to be completedrelatively early during the preceding fixation to allowword frequency effects to materialize (Deubel et al.,2000). Taken together, our empirical data form a coher-ent pattern of results and therefore provide a solid basefor the simulations that will be reported in the followingsections.

5.2. Parameter fitting

The parameter fitting took place in two stages. The Alo-pex algorithm was run 500 times for a max of 10,000 fixa-tions each, with different initial conditions for each run.The best performing set of parameters was then chosenfrom these runs. A given training run of the algorithm in-volved the program repeatedly ‘‘reading’’ the Inuit textand evaluating the cost function presented earlier.

The initial best set of parameters were then analysed indetail and some of the key parameters were systematicallyadjusted in order to observe the degree to which the modelwas sensitive to specific ranges of value. In some cases, spe-cifically for values of the FC threshold parameter, therange of values for which the model gave the desired resultwas quite narrow (±0.2). We will discuss this aspect of themodelling process in more detail below.

The final set of parameters used in the simulation runsdescribed below were arrived at by a combination of auto-matic parameter search by Alopex and fine adjustment onthe basis of the sensitivity analysis described above.

Fig. 9. Fixation duration effects. Comparison of the model�s fit to fixation duraused to generate 10 simulated subjects. The general pattern of the empirical dataa decrease in frequency, an increase in fixation duration with an increase in w

5.3. Modelling word frequency and length effects on fixation

duration

For all of the simulations described here, the model wasrun on the Inuit text 60 times to generate data for 60 sim-ulated individuals. Each run consisted of the model ‘‘read-ing’’ each line of text from the corpus, but starting with adifferent initial random seed for each run. For this particu-lar model, the only significant features of the text were (1)the spatial layout of the line as determined by the combina-tion of word lengths, and (2) the word difficulty as deter-mined by its cultural frequency. For each run of themodel, a dataset was produced comprising simulated fixa-tions and saccades that could be analysed statistically inprecisely the same as way data from a conventional eyetracking experiment.

Fig. 9 is a comparison between the model and the datafor the frequency by length analysis of the Inuit data (seeTable 1). As can be seen, the model gives a reasonable,though not perfect, fit to the data. However, the keytrends are apparent: the obvious one of a decrease in fix-ation duration for an increase in frequency, as well as agradual increase in fixation duration for increasing wordlengths. The main point of deviation between the modeland the empirical data occurs for the medium frequencywords for both word lengths. It is possible to adjust thefit for a given length category by manipulating the FCthreshold, but unfortunately, this tends to reduce thegoodness of fit for the other word length categories. Ineffect, the threshold parameter demonstrates a high-de-gree of non-linearity in the way it affects the behaviourof the model. We will discuss this issue in more detailbelow.

In summary, the results of the simulation demonstratethat the simple combination of FC and an evolving sali-ency map driven, in part, by top-down lexical influencescan provide an adequate account of fixation duration

tion data from the Inuit study described in the paper. The simulation wasis captured by the model: the systematic increase of fixation duration withork length.

Fig. 10. Viewing position and fixation durations. A comparison of the effect of near and far launches (measured with respect to the space prior to the targetword) on the optimal viewing position effects on fixation duration for 7–8 letter words. The conventional U-shaped OVP is modulated by preview effects inthe model. There is, however, no evidence of the inverted OVP one finds in real reading data.


patterns without the need to invoke discrete stages of lexi-cal processing.

7 Note that the specific parameters of the saccade metric equations werederived from the Inuit corpus.

5.4. Viewing position and fixation durations

As shown by O�Regan, Vitu, Radach, and Kerr (1994),the position of fixations within a word has substantialinfluence on their duration. The duration of both firstand single fixations decreases with increasing distance fromthe word centre. This relation, termed the ‘‘inverted opti-mal viewing position effect’’ for fixation durations by Vitu,McConkie, Kerr, and O�Regan (2001), has emerged as achallenge for computational models of eye movement con-trol in reading. Why exactly we get an inverted U-shapedfunction of this kind is the subject of some debate. Onehypothesis tested by Vitu et al. was that the inversion mightbe a consequence of parafoveal preview, but this was notborne out by a post-hoc analysis of their corpus data.Fig. 10 illustrates this analysis applied to the simulationdata from the model. As is quite apparent, our simulationsdo not at all capture the inversion phenomenon. In the caseof the model, we find a U-shaped curve for long saccades,which is modified for short saccades where preview has hada chance to have an effect. In the latter case, the result is analmost positive linear function of letter position, somewhatsimilar to the result reported by Rayner et al. (1996).

We use this graph to demonstrate that there is a clearlysomething missing from the model, given its inability to ac-count for the inverted optimal viewing position phenome-non. It underlines the point that one of the benefits ofcomputational modelling is to highlight conceptual gapsin a given theory. In many cases knowing where a modelfails might be more informative than knowing where it suc-ceeds. Clearly, an additional component is necessary forour model to deal adequately with these data. One obviouspossibility examined by Nuthmann et al. (2005) is that the

effect is caused by misplaced fixations that are automati-cally corrected, leading to exceptionally short fixationdurations at word beginnings and word endings. It is verylikely that during reading some saccades have the characterof corrections (see also Radach & McConkie, 1998), a factthat will force us to add an additional mechanism to laterversions of the Glenmore model.

5.5. Landing site analysis

Fig. 11 is a comparison of the model�s performance withempirical data for mean landing site as a function of launchdistance and word length. The fit between model and datais reasonable in this case. There is a systematic overshoot-ing of the empirical landing positions which arises from thefact that the form of the equations derived from the anal-ysis of McConkie et al. (1988) assume the word centre isthe effective target, whereas for German readers the effec-tive target appears to be somewhat left of the word centre.7

In our analyses of several corpora of German eye move-ment data obtained with different text materials and read-ers, the minimum of the U-shaped refixation curve tendedto be about one letter left of the word centre. Assumingthat the refixation curve is a valid indicator of the optimalviewing position in continuous reading, this can be taken asevidence that locations slightly left of the centre are in factoptimal for word processing (see O�Regan, 1990, for a de-tailed discussion).

5.6. Discussion of quantitative fit

While Glenmore, in its present form, gives a good qual-itative account of a range of eye movement phenomena,

Fig. 11. Landing site effects. A comparison of mean landing site data for the model and Inuit study.


fitting the model to empirical data proved not an inconsid-erable challenge. A number of factors contributed to this.While limiting the model to relatively fewer free parametersthan other reading models may have had merits from thepoint of view of parsimony it made the job of the parametersearching algorithm significantly harder (both E-Z Reader 6and the recent versions of SWIFT use 13 free parameterscompared to nine in this version of Glenmore). Anyonewho has tried to train an artificial neural network with aminimal set of weights can attest to this. The parametersearch task was further compounded by the non-linearityof the transfer functions involved. While the use of theGaussian functions captured a range of complex behaviourwith a relatively simple equation, it also injected a consider-able amount of non-linearity into the overall behaviour ofthe system. In a number of cases, bifurcation-like behaviourcould be observed in the reaction of the model to smallchanges in some parameters values.

Future approaches to the parameter estimation task willneed to re-examine the current limit on parameter numbersand also explore additional search approaches such as ge-netic algorithms. These have already been successfully usedin the SWIFT model (Engbert et al., 2002) and are goodcandidate for use in our own modelling approach.

6. General discussion

In this paper we have described our theoretical ideasabout eye movement control in reading and presentedsome qualitative and quantitative tests of the Glenmoremodel. One unique feature of the model is the use of a sal-iency map that acts as an arena for the interplay of bottom-up visual processing and top-down lexical influences. Bothtypes of factors combine to create a pattern of activation asthe base for selecting one word as the saccade target. Incontrast to sequential attention-based processing models,Glenmore decouples the decision about when to movethe eyes from the word recognition process. At the sametime the model allows for substantial influence of linguistic

processing on the movement decision. More specifically,the time course of activity in a FC module determines thetriggering of a saccade as a function of ongoing processingon the letter and word levels. Hence, both spatial and tem-poral control decisions are based on low level processingwith strong cognitive modulation.

An important and so far unique feature of the Glenmoremodel is that it operates on the level of individual lettersand words both in terms of visual and linguistic processingand eye movement control. The implementation of a real-istic interactive activation network is motivated by the factthat IA models have proven especially useful for capturingthe time course of parallel activation and competitive inhi-bition between processing units on a hierarchy of levels.We believe that this component of the model is a first steptowards the necessary convergence of model developmentin the neighbouring domains of word recognition and con-tinuous reading (Grainger, 2000, 2003; Jacobs, 2000). As aconsequence of the type of word processing implemented inour model there is no need for a distinction between twoseparate stages of word processing, as it is necessary inSAS models.

We are convinced that one important advantage of ourtheory is its neuroscientific plausibility. The general archi-tecture is in harmony with neurobiological constraintsand information processing principles suggested by basicoculomotor research (see e.g., Carpenter, 2000; Wurtz,1996). As we have emphasized throughout the present pa-per, our approach is closely related to the general theoret-ical framework suggested by Findlay and Walker (1999). Inmany respects our model can be seen as an application oftheir theory to the task of reading. Consequently, we aremuch more precise with respect to a number of mechanismsregarding the interplay of visual and cognitive processingin a task as complex and specific as reading. The sugges-tions made by Findlay and Walker (1999) about descend-ing influences from higher processing centres on the FCare rather unspecific and in some respects not in agreementwith empirical data (see e.g. Radach et al., 2004, for


evidence against parafoveal ‘‘pop-out’’ of letter clusterswith low orthographic regularity). A further notable differ-ence between the original saliency map theory and ourmodel is the relation between the saliency vector and theFC. More specifically, in Glenmore there are no reciprocalconnections between these two modules due to the lack ofactive competition between potential saccade on the levelof basic visual processing (see Reilly & Radach, 2003, fora more detailed discussion). However, this is not a criticaldifference, given the fact that there is a range of opinionabout the role of a separate FC in saccade generation with-in the basic oculomotor research community (Dorris &Munoz, 1999).

As a consequence of the spatial saliency architecture,our theory of eye movement control in reading does not re-fer to the notion of attention shifts and is not related to theconcept of covert visual attention in any way. We agreewith Findlay and Gilchrist (2003) in their scepticism abouta special role for covert attention in the control of eyemovements. As discussed in the introductory section ofthe present paper, the idea that attention (seen as a lexicalprocessing beam) is at all times strictly confined to just oneof the letter strings on a line of text is highly controversial.From a theoretical point of view, it appears that the sug-gestion that ‘‘attention’’ moves in discrete steps from wordto word creates the need for explanation at another level: ifattention is an entity capable of ‘‘moving’’, this movement

will need to be controlled in some way. The question iswhether this requires another control theory and perhapsa control model on top of the mechanisms it is supposedto explain.

Obviously, Glenmore has a number of similarities to theSWIFT model developed by Engbert, Longtien & Kliegl(2002); see also (Kliegl & Engbert, 2003 and Richter, Eng-bert & Kliegl, 2005). In SWIFT the idea of a sequentiallymoving attentional spotlight is replaced with an ‘‘atten-tional gradient’’ around the point of fixation that can in-clude several words. This is combined with autonomoustiming of saccades that tend to be generated at a preferredrate and the inhibition of saccade initiation by foveal lexi-cal processing. On the other hand, SWIFT maintains somekey features of the original E-Z reader model including thedivision of lexical processing into an early versus late stage,and the distinction between a labile and a non-labile phaseof saccade programming. Another major difference is thatin Glenmore linguistic processing is implemented in a muchmore specific way at both letter and word level. Also, influ-ences of linguistic processing on the timing of saccade trig-gering are the result of the integrated processing activitywithin the perceptual span rather than exclusive processingof the foveal word. On the other hand, the SWIFT model ismore specific with respect to the time line of saccade pro-gramming, considering in detail various possibilities oftemporal overlap in the processing of successive saccades.Moreover, in SWIFT the decision which word should bethe target of the next fixation is determined as a functionof lexical activity, with the word having the largest current

lexical activity being the most likely target. In contrast, thehierarchy of potential saccade targets in Glenmore is deter-mined via combined visual information and processingdynamics in a spatial saliency map.

The competition/interaction (IC) theory by Yang &McConkie (2001); see also (McConkie & Yang 2003; Yang,2006) is another model that is related to the theoreticalframework suggested by Findlay and Walker (1999). Theirtheory is quite explicit about specific mechanisms of sac-cade triggering and the resulting distributions of fixationdurations which they primarily attribute to non-cognitivefactors. In comparison to Glenmore, the C/I theory is lessspecific about the spatiotemporal dynamics of saliencywithin the perceptual span. It also does not attempt tomodel letter level and word level linguistic processing inany explicit way. On the other hand, the C/I model also al-low for various ways in which strategic top down process-ing can modify the dynamics of oculomotor behaviour (seeReilly & Radach, 2003 for a discussion of similarities toGlenmore).

Taken together, models like C/I, SWIFT and Glenmoreare members of an emerging family of models that followsimilar principles. They all allow for a limited degree ofparallel word processing and they all attempt to implementthe idea that spatial and temporal aspects of eye movementcontrol are co-determined by visuomotor constraints andlinguistic processing. Together with the newest version ofthe E-Z Reader model (Reichle et al., 2005) the ideal obser-ver model by Legge, Hooven, Klitz, Mansfield, and Tjan(2002) and the SHARE model developed by Feng (2005),they represent a rich spectrum of opinion about the natureof eye movement control in reading. In conclusion, wewould like to emphasize our belief that all models reportedin the present special issue have their merits and their spe-cific limitations. The ongoing contest of ideas and pro-posed solutions to empirical problems continues to be achallenging intellectual endeavour. The debate on compu-tational modelling of the interplay between linguistic pro-cessing and oculomotor control is perhaps one of themain reasons why the area of research on eye movementsin reading as a whole remains particularly interesting andattractive.

Acknowledgments

This research was supported by grant 02/W/I284 fromScience Foundation Ireland to Ralph Radach. We thankGary Feng and Shun-nan Yang for helpful comments onan earlier version of the manuscript. The paper was com-pleted while the first author was a visiting professor atthe University of Wollongong in Dubai.

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