Letters in Time and Retinotopic Space 1

Running head: LETTERS IN TIME AND RETINOTOPIC SPACE

Letters in Time and Retinotopic SpaceJames S. Adelman
University of Warwick

Main text incl. abstract: 6,335 words. Appendix: 803 words.

Model web page at: http://www.warwick.ac.uk/~pssgar/ltrs/
Correspondence:
James S. Adelman,
Department of Psychology,
University of Warwick,
Coventry,CV4 7AL,
UK.
J.S.Adelman@warwick.ac.uk

Letters in Time and Retinotopic Space 2
Abstract
Various phenomena in tachistoscopic word identification and priming (WRODS and LTRS
are confused with and prime WORDS and LETTERS) suggest that position-specificchannels are not used in the processing of letters in words. Previous approaches to thisissue have sought alternative matching rules because they have assumed that these
phenomena reveal which stimuli are good but imperfect matches to a particular word,such imperfect matches being taken by the word recognition system as partial evidence
for that word. The new Letters in Time and Retinotopic Space model (LTRS) makes thealternative assumption that these phenomena reveal the rates at which different featuresof the stimulus are extracted, because the stimulus is ambiguous when some features are
missing from the percept. LTRS is successfully applied to tachistoscopic identificationand form priming data with manipulations of duration and target-foil and prime-target
relationships.

Letters in Time and Retinotopic Space 3
Reading relies on identifying words. A word’s stored representation must beaccessed by the matching visual perceptual representation. The response to mismatchingvisual stimuli — in masked form priming and tachistoscopic identification experiments— has been extensively studied to inform theories of this representation and matching.
Contemporary theories all assume that the matching is graded: Stored representations of
mismatching words are accessed in spite of information that indicates the mismatch, butsuch access is less efficient the more severe the mismatch. The calculation of such gradedmatches is explicit in the spatial coding model (SCM; Davis, 2010), the overlap model(Gomez, Ratcliff, & Perea, 2008), SERIOL (Whitney, 2001), and other open bigram models(e.g., Schoonbaert & Grainger, 2004). Moreover, the (expected and/or normalized)
log.-likelihood plays the same role as a similarity metric in the Bayesian Reader (Norris,
Kinoshita, & van Casteren, 2010). To calculate such graded matches in a way that accords
with the data requires extensive machinery. It is my contention that the problem iscomplex because the assumption of graded matches is unnecessary, and that the data canbe more simply explained by an alternative type of theory.
The alternative theory posits — in common with a class of models of categorization(e.g., Cohen & Nosofksy, 2003; Lamberts, 1998) — that visual information is incomplete
early in processing, and incomplete visual information can match more than one stored
representation or response alternative. The posited incomplete information is composedof discrete pieces of information; it is not simply a weakened copy of the ideal
information, as in activation-based models, nor is it information contaminated with noiseor error, as in the Bayesian Reader. Indeed, the predictions can be made without
considering the possibility that visual information may be misperceived: Information has
either been perceived or not, and the system can remain wholly agnostic as to informationthat is yet to be perceived. As a consequence, all phenomena can reflect the timing of
information availability, and not its strength, so no use of graded matching is needed1 .

Letters in Time and Retinotopic Space 4
The claims of this paper are that an appropriate characterization of letter
identification processes is stochastic and piecemeal, and that phenomena attributed byother accounts to imperfect or graded matching in masked form priming andtachistoscopic identification are a consequence of these letter identification processes,
rather than the details of lexical matching processes.
The Letters in Time and Retinotopic Space model (LTRS) implements these claimsby specifying detailed assumptions about this piecemeal letter processing, but specifying
only the bare minimum of assumptions about lexical processing: that the lexical system
can distinguish a match to a particular known word from a non-match for that word(which is necessary for stimulus identification to be possible at all), and that the lexicalsystem is susceptible to a head start from additional stimulus exposure (which isnecessary for priming to be possible at all). As such, the model cannot, of course, address
phenomena that are clearly lexical, such as frequency effects or neighborhood effects, noreven lexical decision itself, only the (relative amount of) priming that occurs in that task.
Thus, all of LTRS’s explanations are that relevant information has yet to beperceived during a brief presentation; the timing of such information is a concrete
concept, measurable in identification tasks. Models that rely on some form of similarity(match score) calculation must further specify several intervening hypotheticalmechanisms: how such simliarity is calculated, its influence on lexical access, and how
the underlying representation gives rise to confusions when all information is present.
LTRS is simpler because it does not require these explanatory mechanisms. In the light ofother accounts, LTRS may appear to do little explanation, but this is because these otheraccounts interpose explanations where none are required.
This paper presents (i) a description of LTRS; (ii) discussion of some core aspects ofthe model; (iii) LTRS fits to new word tachistoscopic identification data with manipulationof target duration for transposed-letter (TL) and 1-, 2-, and 4-letter-different (1LD; 2LD;

Letters in Time and Retinotopic Space 54LD) foils; (iv) LTRS fits to nonword tachistoscopic identification data for a wide range oftarget-foil relationships; (v) LTRS fits for form priming data with a manipulation of prime
duration; and (vi) LTRS fits for priming with a range of prime-target relationships.
The Letters in Time and Retinotopic Space Model (LTRS)LTRS2 specifies letter processing in terms of the timing of initiation of processing;
the rates of processing that determining the timing of identity and approximate andprecise positional information; and specifies the inferences licenced by this positional
information in the context of the usefulness of retinotopic location and distanceinformation.
Start of processing. On a given trial, processing of all letters begins at the samerandom point in time after onset. As an approximation, this time is normally distributedwith mean α and standard deviation σ. That assumption that this time is equal for all
letters is supported by tachistoscopic identification data specifically seeking — but notfinding — time points at which identification of left-hand letters in words is above chanceand right-hand letters is at chance (Adelman, Marquis, & Sabatos-DeVito, 2010).
Processing strengths. Whilst processing begins at the same time for each letter,
positional effects (such as left-to-right trends in accuracy at intermediate durations, e.g.,
Stevens & Grainger, 2003) are accommodated in the model by processing strengths: A
letter in any position i has a processing strength β i that would be determined by theattentional gradient and the visibility of the letter (due to factors like lateral masking anddistance from fixation). As a simplification, these strengths are the same on every trial.
Identity processing. The identity of the letter in position i becomes available at an
exponentially distributed time after the start of processing, with processing rate
proportional to β i ; that is, once an amount of time t has elapsed since the start ofLetters in Time and Retinotopic Space 6
processing, the probability that the letter i has been identified is 1 − exp(−kβ i t). Without
loss of generality, k = 1. This assumption is the same as that for feature extraction in somemodels of categorization (e.g., Lamberts, 1998).
Approximate positional information. Once a letter is identified, some information
about its retinotopic location is available. This information is assumed to accurately
specify a single point or small region within the letter (because a single letter spansseveral retinotopic letter detectors). As such, if (and only if) two letters have been
identified, it is possible to (immediately) determine their order correctly, but otherinformation is not reliably diagnostic as to stimulus identity (see below). That is, theidentity/location of W in SWAN is enough to tell the word is not SCAN, but because the W
in SWAN could appear anywhere on the retina, further positional information, such as the(approximate) position of the A it is, is needed to tell SWAN from SAWN.
Precise positional information. After identification of each letter, a more precise
positioning process occurs for that letter (even if other letters remain to be identified); thisprocess has similar temporal properties to the identification process, but with a different
constant of proportionality. That is, for a letter in position i, once a duration t has elapsed
since identification of that letter, the probability that the precise positional information
has become available is 1 − exp(−λβ i t). The precise positional information is such that if
this information is available for two letters, then it is known whether the two letters are
adjacent, because this information reveals the retinotopic location of the left and rightedges of the letters3 .
Retinotopic distance information is unreliable. Although the retinotopic informationthat is posited to be available might allow estimation of the retinotopic distance between
two letters, it is assumed that this information is usually discarded as unreliable (at least
for short words). Absolute retinotopic distance information is unreliable because of size

Letters in Time and Retinotopic Space 7
constancy: The same stimuli may become larger or smaller due to font size, viewing
distance or viewing position. Relative retinotopic distance information is treated as
unreliable because it usually is; proportional fonts and handwriting are often read: For
instance — as illustrated in Figure 1 — in the word MAIL in proportional fonts, the A is
positioned largely to the right of centre, because the standard widths of these letters are inratio 10:6:3:3, whereas in the word LAMB, it is close to left edge of the word, because thewidths are in ratio 3:6:10:6, despite it being the second letter of four in both cases.
Specialization for forced-choice tachistoscopic identification
Forced-choice tachistoscopic identification involves a brief, masked presentation ofa word or nonword stimulus, following by a forced-choice alternatives for its identity, as
illustrated in Figure 2. To apply LTRS to forced-choice tachistoscopic identification,
specification must be given of the details of the consequences of masking and the absenceof the stimulus, and how responses are selected given the available information.
Loss of information. After stimulus offset, all information about each letter has asmall probability φ of being lost due to interference from the mask, or the identification of
the response alternatives; no loss can occur whilst the stimulus is present on the display.
When information is lost, all information about the relevant letter is lost; that is, identity
information about a letter cannot be spared when its precise positional information is lost.
Only stored letter information is used to determine a response; any other form of
information is ignored because it has been rendered unusable or unreliable during theidentification the response alternatives.
Response selection. Information distinguishes between the available options if (andonly if) it could have been obtained from one alternative, but not the other. If theavailable information does not distinguish between the available options, guessing
occurs. In experiments where the correct response is available (as modeled here) this canLetters in Time and Retinotopic Space 8
only occur because of missing information, because the possibility of misperception is not
used in LTRS’s predictions. When the available information does distinguish between theoptions, there is a small probability ǫ that participants make a premature guess response(or motor error)4 . Otherwise, responding is correct. Guessing produces the right-hand
response with probability ρ, modeling response bias; when trial-by-trial data is not used,
this parameter is not required, and chance accuracy is assumed.
Specialization for masked form priming
Masked form priming involves a brief (and usually forward-masked) presentationof a (typically lower-case) prime stimulus (typically a nonword) before presentation of a(typically upper-case) target word (sometimes with intervening mask or blank) on whichanother task, usually speeded lexical decision, is performed. To apply LTRS to form
priming, specification must be given of (i) how priming occurs, and (ii) the cause ofdifferences in magnitude of priming between different prime-target relationships.
2.1.1

Priming as savings. The effectiveness of the prime (compared to an unrelated primethat evokes no lexical processing of the target) is equal to the period of time for which it
evokes initial lexical processing of the target (Forster, Mohan, & Hector, 2003, call thispriming as savings), which is precisely the time for which some consistent and no
inconsistent information is available. That is, priming of a lexical entry begins if andwhen the first consistent letter is perceived; identity primes are more effective than otherprimes not because they evoke a stronger instantaneous response (higher graded match),but because they do not contain inconsistent information that would terminate priming.
That the lexical processing occurs if and only if the lexical entry is a viable match to thecurrent percept is the only assumption that is needed to generate ceteris paribus priming
predictions.
That is, priming is defined as a headstart in processing that occurs during theLetters in Time and Retinotopic Space 9
period where the target is a candidate for lexical identification of the prime. The precise
nature of the lexical processing involved could moderate the effects, but this paper
explores the extent to which phenomena in word identification can be explained byessentially perceptual aspects of letter processing; including a detailed lexical processing
mechanism would detract from this goal. A bare bones mechanism could be used to
produce lexical decision times in combination with LTRS without modifying the priming
predictions, such as a set of non-competing non-noisy accumulators with drift related tolog.-frequency. Whilst such a mechanism would produce a reasonable correlation withthe word lexical decision data5 , it would have no bearing on the priming predictions.
Most lexical mechanisms that could reasonably be posited in a priming model would be
similarly susceptible to the posited headstart, and therefore still show approximately thesame behavior if the perceptual assumptions were the same.
Termination of priming. In LTRS, the cessation of priming occurs stochastically(unlike the Forster et al., 2003, entry-opening account which posits an approximate stageof fixed duration), when (i) the target is no longer a match to the information from the
2.1.2

prime, which occurs at a random time, distributed according to the assumptions

2.4

described above; or (ii) the offset of the prime is noted — on average, some time ω after
onset — because letter processing of the target begins or an intervening mask or blank isnoted6 .
What is the representation in LTRS?
I would hope that the assumptions described so far seem neither implausible nor
counterintuitive. These assumptions do, however, lead to what may be the mostcounterintuitive aspect of LTRS, particularly in the light of the emphasis in otherapproaches on representation and similarity: LTRS’s assumptions suffice to make (good)predictions about data such as the effects of prime type on priming without specifying

Letters in Time and Retinotopic Space 10very many details of the representation. The representation needs (i) to be able to specify
which letters have been perceived without specifying anything about letters that have yet
to be perceived, (ii) to be able to specify that two letters are adjacent in a particular order,(iii) to be able to specify that two letters are non-adjacent without specifying the number
or identity of the intervening letters, (iv) to be able to specify the order of two letterswithout specifying anything about adjacency.
There are several representations that meet these criteria. I do not specify which
representation is part of the model because it has no consequences for the predictions at abehavioral level: Short of single-cell recording, differences between these representations(if the rest of LTRS is true) cannot be detected, because of the all-or-nothing nature of thecomputations. Such representations include:
Globbing. This representation consists of an ordered letter string with unknown
information indicated by a special character, as in wildcard matching for computer
filenames, such as * for any number of unknown letters, and + for at least one unknown
letter. The representation is initially unspecified, i.e. *. Thereafter, the pattern would
become more specific as more information is identified. For instance, *c*, *a*, *t*, c*, *t,*c*a*, *c*t*, *a*t*, c+t, c*a*, c*t*, *c*t, *a*t*, ca+, +at, *c*a*t*, c*a*t*, *c*a*t,
ca*t*, c*a*t, *c*at, and cat are the possible states in this representation that could be
produced by the stimulus CAT with the LTRS assumptions (though the representation
could express other states consistent with CAT). Matching could occur via a serial scan,but parallel constant-time solutions exist for these kind of problems (Chung, 1996).
Bigrams with multiple states. In this representation, there would be nodes (or otherrepresentational units) for different open bigrams (i.e., ordered pairs of letters) that could
carry additional information than just the presence of an open bigram by virtue of having
multiple states that do not correspond to strengths. One state would indicate that noLetters in Time and Retinotopic Space 11
relevant letter has been detected, the second would indicate partial satisfaction (i.e., that
one letter of the pair is present), the third the presence of the open bigram with no further
information, the fourth that the open bigram is present and is also a closed bigram (i.e.,
adjacent), and the last that the open bigram is present but is not a closed bigram (i.e.,
non-adjacent). The activation values of these states would be arbitrary as they would not
be treated as strengths, but rather treated in an all-or-none fashion.
Letters, open bigrams, adjacent bigrams, non-adjacent bigrams. In this representation,
multiple types of representational units (e.g., nodes, or a list) are taken to code theidentity of the stimulus. These are abstract, position-free units for individual letters, open
bigrams (i.e., ordered pairs of letters of any distance), adjacent bigrams (i.e., ordered pairsof letters that are adjacent) and non-adjacent bigrams (i.e., ordered pairs of letters that are
non-adjacent). This representation — as a textual list of each type of unit that is impliedby the information in the percept — is used in the implemented code for calculating mostof the predictions made here, but other representations would yield the same results. This
representation could be used in a network; this would yield a proliferation of units andconnections to the (unspecified) word level, but it does not proliferate connection
strengths that can make the model flexible: Information is combined by the logical-AND
rule; such high-threshold logic is not sensitive to strengths. In terms of input to word
units, any amount of feed-forward inhibition stops facilitation of the word unit regardlessof the amount of active facilitatory connections, and in the absence of inhibition, any
non-zero amount of active facilitatory feed-forward connections produces the maximum
effective net input to the word unit.
It bears emphasis that whilst these representations and mechanisms are complex,
such complexity is not what gives LTRS the scope to capture the data, nor does it lend themodel extra flexibility: Unlike in models based on match scores, the details of suchcomplex machinery do not form the explanation of the effects in LTRS. Instead, the coreLetters in Time and Retinotopic Space 12
explanatory mechanism in LTRS is that primes prime more if they diverge in processing
from the target on average later in processing and foils are harder to reject if they are lesslikely to have diverged in processing from the target at the time of the post-mask. I now
illustrate how effectively such an explanation can account for the data.
Tachistoscopic identification: stimulus duration
LTRS was first applied to new7 experimental data involving tachistoscopic word
identification at different display durations to demonstrate that it accounts for the timecourse of letter identity and position. The detailed method is presented in the Appendix.
Four participants performed two-alternative forced-choice word identification for masked
presentations of four-letter words that varied in duration from 0–42 ms, as illustrated in
Figure 2, with the target-foil relationship being on one of 13 major categories.
The full LTRS model for four-letter strings with 10 parameters was fitted to eachparticipant separately by maximum likelihood (exact predictions are achieved bynumerical integration); the parameter values are presented in Table 1. The data and fitted
model predictions for each participant are summarized by major target-foil relationshipcategories in Figure 3. To assess the quality of the fit, LTRS was compared to a saturated
model — a literal restatement of the data — in which any model with a guessing
component (including LTRS) is nested. For each of the 19 minor target-foil relationshipcategories that LTRS distinguishes, and for each duration, the saturated model had aparameter for the probability a guess would occur, plus one parameter parameter for the
probability that the guess would be a right-hand response; if guessing does not occur, theresponse is correct. This permitted a formal lack-of-fit test for restricting 143 parameters(153 in saturated, 10 in LTRS) for each participant. The misfit was not significant for any
participant: χ2 (143) = 156.91, 130.36, 126.54, 138.92, p = .202, .768, .835, .581. That is, there
was no evidence the model did not fit the data; it captures the functional form of theLetters in Time and Retinotopic Space 13
duration effect, the left-to-right pattern in 1LD slopes (without differing take-offs). andthe 4LD>2LD>1LD and 2LD>TL patterns.
Findings involving stimuli where letters are transposed with an adjacent letter, suchas the above 2LD vs. TL comparison, and the corresponding priming comparison (e.g.,
Perea & Lupker, 2003), have formed much of the impetus for modeling of letter position
coding. In LTRS, double-substitution foils/primes diverge from the target sooner thantransposed-letter foils/primes primarily because information about one letter suffices totell that a double-substitution prime is not the target, whilst information about two isneeded to tell that a transposed-letter prime is not the target. In particular, for theexample of 1dd4 and 1324: The identity/location of either the second or the third letter
suffices for 1dd4 (the first or second d). In contrast for 1324, one of the following sets of
information (inconsistent with 1234) is needed: (i) the identity/location of both thesecond and third letter (3 before 2); or (ii) precise location information for both (a) the firstand second letter (1 adjacent-to 3); (b) the third and fourth letter (2 adjacent-to 4); (c) the
first and third letter (1 not-adjacent-to 2); or (d) the second and fourth letter (3not-adjacent-to 4). One can have the identity/location of either the second or the third
letter without being in one of these cases, but not vice versa. Therefore, there are times atwhich 1dd4 can be distinguished from 1234 and 1324 can not be distinguished from 1234,
but there are no times when the reverse is true.
Tachistoscopic identification: target-foil relationships
LTRS was then applied to a wider range of target-foil relationships from fiveexperiments by Gomez et al. (2008) at a single presentation duration in studies they used
to support the overlap model, most of which used 5-letter nonword stimuli. In theirExperiment 1, 1LD, 2LD (both adjacent and non-adjacent) and TL (both adjacent andnon-adjacent) were used (Experiment 1b was a replication of 1a with the foils differing inLetters in Time and Retinotopic Space 14
the first letter excluded). Experiment 2 was similar to 1a but contained word-nonword
and word-word trials (but no nonword-nonword trials). In addition to 1LD and adjacent
TL foils, Experiment 3 used foils in which one letter was more than one position removed
from its location in the target and the other letters shifted (e.g., 31245) and these with anadditional letter replacement (e.g., d1245). In addition to typical 1LD, and adjacent andnon-adjacent TL foil conditions, Experiment 4 used targets and foils in which some letterswere repeated. Finally, in Experiment 5, 1LD, adjacent TL, letter insertion (6-letter foil)
and letter deletion (6-letter target) foil conditions were used.
2.3.1

This analysis was restricted to conditions where the lexical status of both options
was the same (i.e., Experiment 2 was excluded) and the stimuli were five letters long (i.e.,part of Experiment 5 was excluded) because (i) the goal of LTRS is to examine factors thatcan be explained perceptually without detailed lexical processes8 , and (ii) comparisons
between 5- and 6-letter options could be based on size relative to the mask, adding an
additional process.
Gomez et al. (2008) fitted parameters of the overlap model separately to eachexperiment; for these fitted values, the SSE for overlap is 0.192 (BIC = −538.75 with 31

2.3.3

parameters), against a total sum-of-squares of .9059 . The ten-parameter LTRS model —with parameters optimized simultaneously for all experiments — has a comparable SSE
of 0.213 for its many fewer parameters (BIC = −627.91, substantially superior). The fit
for LTRS is illustrated in Figure 4. Attempting to reduce the number of parameters in theoverlap model to seven by using the simultaneously optimized parameters for all

2.3.3

experiments — to be more comparable to LTRS — increased its SSE to 0.477(BIC = −552.84, improved, but still inferior to LTRS), suggesting the loss of parameterscompromised its ability to account for the data.
Although SCM does not have mechanisms to identify nonwords, its graded matchscores, which are controlled by 2 parameters,10 can be used in 2-parameter regression

Letters in Time and Retinotopic Space 15
equation (i.e., there is a total of 4 parameters — the other models do not require a
regression equation because they produce probabilities directly) to approximate
predictions that would result from such a mechanism. The most favorable parameters(intercept = 1.258; slope = -0.659; σ = 1.964; initial letter weight = 3.224) gave an SSE of
0.407 (BIC = −584.03, intermediate between overlap and LTRS).
Masked form priming: prime duration
Next, LTRS was applied to form priming data with variation in prime duration,
given by Forster et al. (2003) in support of the account of priming by savings.
A highly simplified version of LTRS is suitable for these data because they include
only identity and 1LD priming, and they are averaged over stimulus lengths and all
positions of difference. Only three parameters were estimated: α, ω, and B, using
β i|l = B/l for any given length l; σ was set to zero, and λ has no role in 1LD or identity
priming predictions, because letter order is irrelevant. (The remaining parameters are for
identification only.) The entry-opening account of priming — in which identity priming islinear (with slope 1) in the prime duration and 1LD priming is linear (with slope 1) in theprime duration up to the completion of the first (approximate) phase, after which it isconstant — can also be characterized by a three-parameter model; the parameters are theintercept for identity priming, the intercept for 1LD priming, and the maximum value of
1LD priming. Against a total sum of squares of 3812 ms2 , the minimum SSE for this modelis 284 ms2 (with intercept for identity 9.29 ms, intercept for 1LD -2.47 ms, and maximum
for 1LD 36.25 ms). LTRS can achieve a comparable fit (when evaluated by Monte Carlosimulation; see Figure 5) giving an SSE of 286 ms2 (with α = 11 ms, ω = 32 ms, B = .095
MHz).11 Predictions were also obtained for the SCM (see Figure 5) without changing theoriginal parameter set; optimizing the parameters to maximize the fit for the full priming
SCM would be impracticable (both in terms of time, and the type of software that isLetters in Time and Retinotopic Space 16
available to run the model) and no systematically optimized parameters were offered by
Davis12 , though some changes that improve fit have clearly occurred throughout thedevelopment of the model. The SSE for SCM was 2867 ms2 , primarily because the model
underestimated the effects by about 11 ms; without further data, it is unclear whether theslight curvature in the 1LD predictions that LTRS and entry-opening models capture issystematic or noise. The constant underestimate by SCM does not correspond to a trivial
parameter change because rescaling cycles would change the prime durations, and achange in residual time would affect both control and primed conditions.
Masked form priming: prime-target relationships
The most extensive data regarding apparent letter string similarity effects comefrom manipulation of prime-target relationships in form priming, so finally, LTRS wasapplied to these data. Davis (2010) recently reviewed such data in assessing SCM; fromhis Table 4, I extracted those (47 out of 61) results that were obtained under standard
priming conditions with manipulations of prime-target relationship in terms of letter
identity and/or position. That is, nonword-word priming was included, and word-wordpriming, sandwich priming (where a brief preview of the target precedes the prime;
Lupker & Davis, 2009), and frequency and neighborhood manipulations were excluded,
because LTRS does not model the word-specific influences involved in these phenomena.
2.5

The range of prime types covers 1–5LD conditions (index 10–14 in Davis’s table andFigure 6, and 7–9 and 51 for additional 2LD conditions), adjacent TL (21–22) andnon-adjacent TL (28 with 27 & 29 as baselines; and 54) conditions, letter addition(superset) conditions (38–45), letter deletion conditions (46–50, 52, 56–61), a combineddeletion plus TL condition (53), neighbor-once-removed conditions (23 & 24 vs. 25 & 26,
described and discussed below), and various severe disruptions of letter ordering (30–35,
55).

Letters in Time and Retinotopic Space 17
Again, to avoid excessive proliferation of β parameters for the various lengths ofstimuli, it was necessary to add an ad hoc equation constraining the β values with only afew parameters. Given the greater number of conditions to be fit, some of which were
defined by position, two were used — B and ηi — the former being the sum of the rates,
the latter reflecting increased processing strength (efficiency) for the initial position (cf.
Table 2), such that β 1|l = (1 + ηi ) B/(l + ηi ), and β i|l = B/(l + ηi ) for i 6= 1.
The observed and LTRS-predicted priming (evaluated by quadrature), with the
2.5parameters given in Table 3, are illustrated in Figure 6. The effects occurring for
substitution primes and letter-reordered primes come about for much the same reasons as
the effects for the identification task: Greater disruption of order in the prime or moreinconsistent letters in the prime give more opportunities to perceive that the prime is not
the target. Prime duration also accounts for some variability between experiments. A
couple of other important comparisons are, however, somewhat more subtle.
One of the most important comparisons comes from Davis and Bowers’s (2006;
points 23 & 24 vs. 25 & 26) examination of a type of prime they labeledneighbor-once-removed (N1R); these are generated by a transposition of adjacent lettersand a replacement of one of those letters. Contrary to certain simple open-bigram
schemes, N1R primes produced less priming than 1LD primes. According to LTRS, N1R
primes (13d45) diverge from the target sooner than 1LD primes (1d345 or, better, 12d45)
because the precise positional information about both of the two letters that should not be
adjacent (1 and 3) will sometimes be extracted before the mismatching letter (d), whilst
for both types of prime extracting the mismatching letter alone is sufficient. Consider theprime BLETS, which is a N1R of BOLTS and 1LD from BLOTS. Any pattern consistent with*e* (including, for instance, *e*s*) is sufficient to terminate priming of either BOLTS or
BLOTS , but if bl* (or bl*t* etc.) is reached, priming of BOLTS ceases, whilst priming of
BLOTS continues.

Letters in Time and Retinotopic Space 18
Superset primes are another form of prime — ones in which an extra letter isinserted relative to the target — that can distinguish between models. In particular, LTRS
predicts that when the extra letter repeats one already in the target, priming should begreater than if the extra letter is unique, because both the inserted letter and the letter it
repeats must be detected to stop priming if there is an adjacent repeat, but only the newletter needs to be detected to stop priming if it is unique. Whilst SERIOL and otheropen-bigram schemes sensitive to the distance between pairs of letters also make thisprediction, SCM makes the contrasting prediction that these conditions should beequivalent. One experiment that has examined this (Van Assche & Grainger, 2006,
Experiment 1, points 43 and 45) did not find a 2 ms difference to be significant, but thisexperiment lacked power to some extent: Other differences examined in the experiment
whose observed magnitudes were around 10 ms did not reach significance and this isroughly the size of effect LTRS predicts. In a near-replication with two inserted lettersthey (Experiment 2, not in the database) found that a 7 ms difference did not reachsignificance: Similar power issues apply, and LTRS predicts a 12 ms effect.
Against a total sum-of-squares of 12390 ms2 , LTRS’s SSE with 6 parameters was
3645 ms2 (BIC = 227.60). By comparison, the predictions from Davis’s (2010) SCM using
the default parameter settings and 55 ms prime duration (as used by Davis) obtained an
SSE of 1395 ms2 (for the 18 parameters the SCM has, BIC = 228.66). When the same
parameter settings were used with the actual prime durations of the various experiments
were used, the SSE was 2735 ms2 (BIC = 260.30); the difference suggests that mechanisms
in SCM designed to capture prime type differences between experiments might in fact be
capturing differences caused by prime duration13 . Again, parameters could notpracticably be optimized for this model. This, the probable minimal impact of someparameters on the predictions, and the exclusion of data bearing on the lexical component
mean that these BIC values have not allowed SCM to take advantage of its parametricLetters in Time and Retinotopic Space 19
flexibility and so may overpenalize SCM for its flexibility/complexity. It is therefore
difficult to assess the extent to which SCM’s advantage in SSE is due to its capturingsystematic aspects of the data, or having mechanisms that have been adapted to
idiosyncratic properties of, and noise in, some experiments; replications may go some
way to addressing this issue. I would nevertheless argue that — in terms of the necessityof the properties of perception, number of parameters, or in terms of description length— LTRS is less complex than SCM, and this should be weighed in any model assessment.
It is perhaps more telling to examine the predictions of a model for experiments ofthe type that it is designed to explain, but which were not examined in its development,
as their idiosyncrasies will not have been built into the model. Table 4 presents
predictions for 28 observations from seven experiments not examined by Davis (2010); of
these, five are from articles whose other experiments were in Davis’s Table 4, and two arefrom a more recent article (Norris et al., 2010). The overall fit for this set somewhat favors
LTRS; this could well, of course, simply reflect the selection I have made. One might also
take as important that the Norris et al. found a (significant by-subjects, marginal
by-items) 17ms difference between 1-deletion primes (acde-ABCDE) and 1LD control
primes (axcde-ABCDE) where no difference is anticipated by SCM, but some (11 ms) ispredicted by LTRS, because the deletion primes take two specific letters to be perceived(plus their adjacency) for priming to cease, but the 1LD control primes take only one
specific letter. Nevertheless, such agglomerations are likely to be misleading because of
biases in publication and selection; idiosyncratic properties of laboratories or experimentsthat models cannot capture; and the relatively poor estimation of the magnitude ofpriming effects14 . Only experiments that are designed to produce databases with a large
number of conditions in a single laboratory can truly test the detailed quantitative
assumptions in the kinds of models considered here.

Letters in Time and Retinotopic Space 20
Discussion
The Letters in Time and Retinotopic Space model accounted for effects ofmanipulations of duration and relationships between letter strings in both tachistoscopic
identification and form priming. It did so by recourse to the idea that different
information about letter strings becomes available at different times. The account asserts
neither the notion that lexical processing partially tolerates imperfect matches in thepresence of negative evidence, nor the notion that the cause of ambiguity in a percept is
contamination by noise. Other models have yet to be applied to this range of types ofdata, and there may be difficulties in doing so. For instance, the matching process in SCM
is based on word nodes, which causes difficulty in accounting for nonword identification
data, even if a decision rule to fit the effect of duration in the word identification data
were found; the overlap model has no account of the influence of exposure duration; andthe functional form of the exposure duration effect is not the half-normal cumulative
distribution that would be expected under simple signal detection accounts15 . In
contrast, in LTRS, a precise account of these duration effects is the starting point of anunderstanding of all the other effects, and a predictable link between identification andpriming is expected; indeed, some effects, such as differences between standard andsandwich priming may be attributed to differing visual properties of the prime.
3.4

Moreover, in LTRS, there is no single number that describes the relationship between atarget and a prime or foil: There is no constant graded match score, and a foil (or prime)that is more probably distinguishable than another from the target at an early time point,
may be less probably distinguishable at a later time point. For instance, in the fits plottedfor Participant 4 in Figure 4, the d234 condition is predicted to be more accurate than the1243 condition at shorter (e.g., 18 ms) durations but not at longer (e.g., 42 ms) durations.
This occurs at the level of the information available in the percept and not due to any
top-down process (as there is none). The pattern results from the distribution of timeLetters in Time and Retinotopic Space 21
taken for one piece of information having a different shape to the distribution of time
taken for two pieces of information. A similar pattern can occur with different prime
conditions, and can be exacerbated by the influence of the delay in registering the onset of
the target (i.e., ω). The predicted effects are, however, subtle, and would need carefulmanipulation of visual parameters to exacerbate them to an extent they would be
detectable in a feasible experiment.
The predictions of LTRS are derived with specification of only the most basic
properties of lexical processing relating to targets; effects of word primes, and of word
neighbors of primes, would require further specification of lexical processing (and lexicaldecision). The extent to which LTRS is successful — without reference to detailed lexical
processing — as an account of core phenomena relating to the identification, confusionand priming of letter strings over time is suggestive that priming and tachistoscopic
identification phenomena need not be understood in terms of tolerance for partial
matches, but may — in whole or in part — be explained by reference to the stochastic
timing of information extraction from the stimulus.

Letters in Time and Retinotopic Space 22
References
Adelman, J. S., & Brown, G. D. A. (2006). The time course of letter position and identity
information availability in visual word identification. Manuscript submitted for
publication.
Adelman, J. S., & Brown, G. D. A. (2008). Methods of testing and diagnosing models:Single and dual route cascaded models of word naming. Journal of Memory andLanguage, 59, 524–544.
Adelman, J. S., Marquis, S. J., & Sabatos-DeVito, M. G. (2010). Letters in words are read
simultaneously, not in left-to-right sequence. Psychological Science, 21, 1799–1801.
Chung, K.-L. (1996). O(1)-time parallel string-matching algorithm with VLDCs. Pattern
Recognition Letters, 17, 475–479.
Cohen, A. L., & Nosofksy, R. M. (2003). An extension of the exemplar-based
random-walk model to seperable-dimension stimuli. Journal of Mathematical
Psychology, 47, 150–165.
Davis, C. J. (2010). The spatial coding model of visual word identification. Psychological
Review, 117, 713–758.
Davis, C. J., & Bowers, J. S. (2006). Contrasting five different theories of letter position
coding: Evidence from orthographic similarity effects. Journal of Experimental
Psychology: Human Perception and Performance, 32, 535–557.
Forster, K. I., Mohan, K., & Hector, J. (2003). The mechanics of masked priming. In
S. Kinoshita & S. J. Lupker (Eds.), Masked priming: The state of the art (pp. 3–37).
Hove, UK: Psychology Press.
Gomez, P., Ratcliff, R., & Perea, M. (2008). The overlap model: A model of letter position
coding. Psychological Review, 115, 577–601.

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Grainger, J., Granier, J. P., Farioli, F., Van Assche, E., & Heuven, W. J. B. van. (2006). Letter
position information and printed word perception: The relative-position priming
constraint. Journal of Experimental Psychology: Human Perception and Performance, 32,
865–884.
Johnston, J. C. (1978). A test of the sophisticated guessing theory of word perception.
Cognitive Psychology, 10, 123–153.
Lamberts, K. (1998). The time course of categorization. Journal of Experimental Psychology:
Learning, Memory, and Cognition, 24, 695–711.
Lupker, S. J., & Davis, C. J. (2009). Sandwich priming: A method for overcoming thelimitations of masked priming by reducing lexical competitor effects. Journal of
Experimental Psychology: Learning, Memory, and Cognition, 35, 618–639.
Norris, D., Kinoshita, S., & van Casteren, M. (2010). A stimulus sampling theory of letter
identity and order. Journal of Memory and Language, 62, 254–271.
Perea, M., & Lupker, S. J. (2003). Transposed-letter confusability effects in masked form
priming. In S. Kinoshita & S. J. Lupker (Eds.), Masked priming: The state of the art (pp.
97–120). Hove, UK: Psychology Press.
Rumelhart, D. E. (1970). A multicomponent theory of the perception of briefly exposed
visual displays. Journal of Mathematical Psychology, 7, 191–218.
Rumelhart, D. E., & Siple, P. (1974). The process of recognizing tachistoscopicallypresented words. Psychological Review, 81, 99–118.
Schoonbaert, S., & Grainger, J. (2004). Letter position coding in printed word perception:
Effects of repeated and transposed letters. Language and Cognitive Processes, 19,
333–367.
Stevens, M., & Grainger, J. (2003). Letter visibility and the viewing position effect invisual word recognition. Perception & Psychophysics, 65, 133–151.

Letters in Time and Retinotopic Space 24
Stewart, N. (2006a). Millisecond accuracy video display using OpenGL under Linux.
Behavior Research Methods, 38, 142–145.
Stewart, N. (2006b). A PC parallel port button box provides millisecond response time
accuracy under Linux. Behavior Research Methods, 38, 170–173.
Van Assche, E., & Grainger, J. (2006). A study of relative-position priming with superset
primes. Journal of Experimental Psychology: Learning, Memory, and Cognition, 32,
399–415.
Whitney, C. (2001). How the brain encodes the order of letters in a printed word: The
SERIOL model and selective literature review. Psychonomic Bulletin & Review, 8,
221–243.

Letters in Time and Retinotopic Space 25

Appendix
Experimental Method
Participants
Four postgraduates of the Department of Psychology at the University of Warwick
acted as observers in this experiment; three were paid £100 (ca. US$170), and the fourth
was the author. All reported normal or corrected-to-normal vision, and had English as
their first language.
Stimuli
One hundred and eight four-letter English words were used to construct 432
target-foil pairings for this experiment. Each word acted as a foil for four targets, andthese were also the foils when this word acted as target. Each pairing (symmetrically)
represented one of four transformation types, their subtypes (conditions) denoted byfour-letter codes representing their relation to the string 1234: (a) replacement of four
letters (e.g., CODE vs. WASP, denoted dddd, of which there were 216 pairs (counting bothversions of a pairing as distinct); (b) replacement of two letters, either adjacent to one
another (e.g., WHIP vs. WRAP), or at the two ends (e.g., SEAL vs. TEAM), denoted dd34,
1dd4, 12dd or d23d, 20 of each subtype; (c) replacement of one letter (e.g., ABLE vs. AXLE),
denoted d234, 1d34, 12d4 or 123d, 24 of each subtype; and (d) reversal of two letters either
in adjacent positions (e.g., SAWN vs. SWAN) or at the two ends (e.g., MEAT vs. TEAM),
denoted 2134, 1324, 1243 or 4231, 10 of each subtype. The severe selection criteria were
not perfectly met, so a few of the pairings realised other relationships than thosedescribed above, due to the inclusion of the words EVER , VEER and PASS among thestimuli, and the use of ACID - DUET as a pairing. All modeling takes into account the true
relationship between the targets and foils. However, in the graphs, these pairings areLetters in Time and Retinotopic Space 26
averaged with the intended condition.
Apparatus
Stimuli were presented on a Sony CPD-G200 computer monitor driven at 166.67 Hz
by an NVidia GeForce 2 MX based graphics card. The resolution of this display was
640x480 on a 17” monitor (see Stewart, 2006a, for a description of this system). Tests witha photodiode confirmed that this system had a resolution of 6 ms. Internal monitoring ofdisplay times indicated that for approximately 1 in every 2000 trials the stimulus was
displayed one frame (6 ms) too long; these were analyzed with the actual display time(DT), not the intended display time, provided this was within the experimental range.
Responses were collected using a custom parallel-port button box (Stewart, 2006b), with
two lateral buttons, designed to be operated with both hands, and an extra central button.
DesignAccuracy was measured on two-alternative forced-choice identification of thetargets for each target-foil pairing in each of the thirteen pairing subtypes, for each ofeight display times spaced evenly from 0 to 42 ms. Six replications of each target-foil-DT
combination were tested, half associated with each response button, giving a total of
20,736 trials per observer. Over all trials, critical information was equally likely to appear
in each of the four letter positions; and given two alternatives, each was equally likely to
be correct. Every 3,456 trials observers had seen each target-foil-DT combination an equal
number of times. Every 6,912 trials, observers had seen each target-foil-DT-button
combination an equal number of times.
Procedure
Observers completed 12 sessions of approximately one hour, each containing 16
blocks of 108 trials. Before each trial a mask of ten hash (#) symbols in a 32 point Courier

Letters in Time and Retinotopic Space 27
font was displayed centrally horizontally approximately 12% from the bottom of thescreen for an inter-trial interval varying randomly between 900 and 1100 ms,
notwithstanding delays due to the parallel port failing to reset. This was then replaced by
the target word in a 24 point Courier font in lower case in the same position for a DT from0 to 42 msec (no target stimulus was shown in the 0 msec condition). The screen was thenblank for 6 msec. Then the mask was displayed again with two response options, bothtarget and foil, in lateral positions in a line below that of the mask. Observers pressed thematching lateral button of the button box to indicate their response. After this, thealternatives were removed from the display, and the mask remained for the inter-trial
interval. At the end of each block, accuracy for that block was displayed, and breaks weretaken as needed between blocks.

Letters in Time and Retinotopic Space 28
Footnotes
1 Some earlier models of tachistoscopic identification (Rumelhart, 1970; Rumelhart &Siple, 1974) also use incomplete visual information as an explanatory mechanism in
combination with a (partially) Bayesian decision. However, they give an account ofneither transposed-letter (TL) effects — such as confusions between SWAN and SAWN (aTL pair) being more frequent than those between SWAN and SCAN (a one-letter-different,or 1LD, pair) and SWAN and STUN (a 2LD pair) — which are the critical starting point for
current models, nor masked form priming, which is the most commonly used
experimental paradigm in the area.
2 Details of all the modeling and the implemented LTRS model (executable andsource code) are available at http://www.warwick.ac.uk/~pssgar/ltrs/.
3 It might be more realistic to assume that left and right edge information are

extracted independently, not simultaneously.
4 This parameter may also mimic a skew distribution of the onset of processing
5 Indeed, using log(20 + f req) for the drift would obtain a correlation of .61 for thedata considered for item-level variance by Davis (2010), to be compared with SCM’s .51.
Starting the no accumulator with an appropriate drift only when all possible words had
been eliminated would trivially produce a qualitative match to the nonword N effect, thelexicality effect and the nonword legality effect. It is possible, though not likely, that SCM
can only make good priming predictions when its frequency predictions are slightly off.
6 That is, priming is linked to prime duration, not stimulus onset asynchrony.
7 The term “new” is used loosely: The data were collected in 2003 and previously

submitted for publication by Adelman and Brown (2006).
8 In the case of these apparent context enhancement effects, a version of Johnston’s(1978) account of the effects could be based on assuming φ is higher when the percept is
2.3.1

consistent with a word, because this familiarity guards against forgetting. If all options

Letters in Time and Retinotopic Space 29
being fitted are of the same lexical status, no additional parameter is required.
9 The six parameters for Experiment 5 could have been refitted (because only 8 out

of its 18 conditions were used to calculate the SSE, whereas other experiments were
included or excluded in their entirety) but its points contribute only .011 to the SSE, andan SSE of 0.181 leads to the same conclusions.
10 In the most recent version — if only a single length (in this case, five) is considered— the adjustment to match scores considered by Gomez et al. (2008) is equivalent toadjusting the initial letter weight parameter, if regression parameters are also included.
Using σ = 1.25 and initial letter weight of 3.1 gives an SSE of 0.478.
11 Better fits could be achieved with lower values of α that would be too inconsistent

with the identification data. Using a different rate for the initial letter might fix thisproblem, but I did not explore this as the benefit would be minimal relative to the cost of
the extra parameter.
12 In the context of models of word naming, Adelman and Brown (2008) havecriticized the approach of producing models without optimized parameters (and with noeasy way to optimize them) because it creates a false barrier to falsification: The
possibility of data inconsistent with the model being attributed to a need for parameterchanges poses an unreasonable challenge for other researchers.
3.1

13 Davis (2010) suggests that the 55 ms prime duration assumption corrects somehowfor differences in display conditions. Even if there is some error in the effective prime
duration, not using the intended durations seems to me to be compounding error uponerror. Moreover, it seems to assume a systematic bias such that short prime durations areused with good viewing conditions and long prime durations are used with poor viewing
conditions; it is not clear why this should be the case.
14 This problem is often exacerbated by the re-use of a single control condition as thesubtraction for priming effects, because any misestimation in this one condition modifies

Letters in Time and Retinotopic Space 30
all the priming effects in the experiment, and it is rarely (if ever) given more trials thanthe other conditions in line with its importance.
15 Such signal detection accounts are in some cases equivalent to the Bayesian

Reader’s sensitivity to presentation duration in identification, and where they are not,they are still often good approximations to it.

Letters in Time and Retinotopic Space 31

Parameter
Onset meanαOnset s.d.
σRate 1
β 1|4Rate 2β 2|4Rate 3β 3|4Rate 4β 4|4Premature guessǫRight-hand bias
ρ
Information loss
φ
Position:identity ratio λ1
17.721
3.077
0.243
0.333
0.118
0.117
.017
.549
.092
0.021

Participant
2
3
21.767 17.343
6.491
6.126
0.475
0.106
0.472
0.096
0.171
0.080
0.071
0.081
.043
.026
.405
.540
.187
.069
0.194
3.145

Table 1
LTRS parameter values for experimental data by participant.

4
11.935
3.421
0.553
0.270
0.187
0.146
.012
.646
.038
0.068

units
ms
ms
MHz
MHz
MHz
MHz
(probability)(probability)(probability)(time−1 /time−1 )Letters in Time and Retinotopic Space 32

α
σ
β 1|5
β 2|5
β 3|5
β 4|5
β 5|5
ǫ
φ
λ

LTRS
17.663 ms
14.062 ms
0.278 MHz0.023 MHz0.023 MHz
0.018 MHz0.020 MHz0.145 (prob.)
0.061 (prob.)
0.150 (ratio)

Overlap
s1 0.473
s2 1.225
s3 1.168
s4 1.302
s5 1.201
a 4.350
arep 3.804

Table 2
Parameter values fitted to data from Gomez et al. (2008).

Letters in Time and Retinotopic Space 33

α
σ
ω
B
η
λ

21.29812.26231.086
0.198
0.362
3.530

LTRS
ms
ms
ms
MHz
(ratio: time−1 /time−1 )(ratio: time−1 /time−1 )Table 3
Parameter values fitted to data summarized by Davis (2010).

Letters in Time and Retinotopic Space 34
TargetRelatedControl

Observed

Prime
Prime
Priming (ms)Schoonbaert & Grainger (2004), Experiment 4; 53 ms
ABCDE
bacde
vwxyz
5
ABCDE
abdce
vwxyz
24
ABCDE
abced
vwxyz
8
ABCDEFG bacdefg
tuvwxyz
33
ABCDEFG abdcefg
tuvwxyz
36
ABCDEFG abcdegf
tuvwxyz36

Predicted priming (ms)LTRS

SCM (55 ms)

SCM (actual)

16
23
19
22
32
26

19
33
18
28
31
28

18
32
17
27
30
27

Norris, Kinoshita, & van Casteren (2010), Experiment 1; 53 ms
ABCDE
abcde
vwxyz
45
57
ABCDE
acbde
vwxyz
23
22
ABCDE
awxde
vwxyz
2
10
ABCDE
aadde
vwxyz
9
18

51
34
2
4

49
33
2
4

Norris, Kinoshita, & van Casteren (2010), Experiment 3b; 53 ms
ACCDE
accde
axcde
20
34
ACCDE
acde
axcde
12
18
ABCDE
abcde
axcde
36
34
ABCDE
acde
axcde
17
11

28
6
25
0

27
6
24
1

Grainger et al. (2006), Experiment 5; 33 ms
ABCDEFG abcd
wxyz
ABCDEFG defg
wxyz
ABCDEFG aceg
wxyz

16
5
17

20
16
21

13
8
6

5
5
3

Van Assche & Grainger (2006), Experiment 2; 50 ms
ABCDEFG abcdefg
rstuvwxyz
ABCDEFG abcccdefg
rstuvwxyz
ABCDEFG abeecdefg
rstuvwxyz
ABCDEFG abtucdefg
rstuvwxyz

45
43
40
36

54
31
24
19

51
34
34
34

45
30
30
30

Van Assche & Grainger (2006), Experiment 3; 50 ms
ABCDEFG abcdefg
tuvwxyz
ABCDEFG abvwefg
tuvwxyz
ABCDEFG abvdeyg
tuvwxyz
ABCDEFG abdeg/acdfg tuvwxyz

52
26
22
39

54
16
16
32

51
12
12
17

45
11
11
16

Van Assche & Grainger (2006), Experiment 4; 50 ms
ABCDEFG abcdefg
qrstuvwxyz
63
ABCDEFG abstucdefg
qrstuvwxyz
22
ABCDEFG abscudwefg
qrstuvwxyz
22

54
14
14

51
25
21

45
21
18

Sum-squared error (ms2 ):

2377

2414

2980

Table 4
Observed and predicted priming for some standard masked primed lexical decision experiments thatwere not considered by Davis (2010), with structural descriptions of the nonword primes and word
targets. SCM (55 ms) = spatial coding model with fixed prime duration of 55 ms; SCM (actual) =spatial coding model with actual prime duration used in experiment (listed).

Letters in Time and Retinotopic Space 35
Figure Captions
Figure 1. Relative position of the letter A in MAIL and LAMB in a proportional font.
Figure 2. Sequence of events on an experimental trial.
Figure 3. Data (points) and LTRS fit (lines) for brief word identification at various
durations with 1-letter-different (1LD), 2-letter-different (2LD), 4-letter-different (4LD)
and transposed-letter (TL) foils, for four participants.
2.3.2

Figure 4. Observed accuracy and LTRS fit for Gomez et al.’s (2008) Experiments 1a, 1b, 3, 4
and 5; each point is a target-foil relationship condition (both 5 letters) at 60 ms duration.
Foil generated from target by: r* or r** = 1- or 2-letters different in numbered positions; t**= transposition of numbered positions; m** = remove from first numbered position andre-insert at second numbered position (e.g., m13 = abcde → bcade); c** = remove fromfirst numbered position and insert new letter at second numbered position (e.g., c13 =abcde → bcxde); e** = duplicate letter from first numbered position in place of letter atsecond numbered position (e.g., e23 = abcde → abbde); d** = numbered positions intarget are same letter, second numbered position is replaced with new letter (e.g., d23 =abbde → abcde); b**** = duplicated letters in first two numbered positions move to last
two numbered positions (e.g., b3423 = abdde → addbe).
Figure 5. Observed (points), LTRS (solid lines), and SCM (dashed lines) priming for
Forster et al.’s (2003) priming experiments with manipulation of prime duration.
Figure 6. Observed priming and LTRS fit for nonword-word conditions considered by
Davis (2010).

lamb
mail

900−1100 ms##########
0−42 ms

lung

6 ms

until
response##########
lung

sung

1.
10
1LD

Accuracy

1.0

30
2LD

10
4LD

30
TL

0.8
0.6
0.4
10

2.

30

10
0

1LD

1.0
Accuracy

20
2LD

30

40

0

20
TL

4LD

40

0.8
0.6
0.4
0

3.

20

40

0

Accuracy10
1.0 d234
1d34
12d4
0.8 123d

1LD

dd34
1dd4
12dd
d23d

30
2LD

20

40
10

4LD
dddd

2134
1324
1243
4231

30
TL

0.6
0.4
10

4.

30

10
0

1LD

Accuracy

1.0

20
2LD

30

40

0
4LD

0.8
0.6
0.4
0

20

40

0
20
40
Display Duration (ms)

20
TL

40

Observed accuracy

1.0
r14
r13
t13 r1 r12
t14
t12
m13
b1324
c31
c13
m31 t13 r1
t12

0.9
e34e25r3
e23
r2
e45 e13
b3423
r2
r3
r2
r4e35
r5 t35
b2435
b4534
t35
b3445
e24
r2
r3c24
b3524
b2435
b2334 r4
b3423
c52t24
r3c35
m35
r5
b3524
c42 t24m52
r3
t45
d24 d25
r2
d34 d23
t24
c53
d13
d45
b2334 r4 t35
m24
r4
t45
r5
d35
m42
t23
r4
t23
m53
t34
r5
t34
t45 t23
t34
t34
t23
t34
t45

0.8

0.7

0.6

t25
t25

r25
r35
r23
r23 t12r45rr34
24 b2413
r25
r35
t12
r24
r34
r45

t25

0.5
0.5

0.6

0.7

0.8

0.9

LTRS predicted accuracy

1.0Prime Types
Identity
1LD
ModelsLTRS
SCM

Priming (ms)

60

40

20

20

30

40

50

Prime Duration (ms)

60

38

50

42

Observed Priming (ms)

20
39

56
46

43

40
57

27

45

44
48
49
47

40

30

24
23

21

50
30
28

59

41

20
22

35
13
9
7 12
34
8

0

60

51

54
55

10

52

25
26
11

10

58

32
29

61
53

31

14

0

10

20

30

40

50

LTRS Predicted priming (ms)