Letters in Time and Retinotopic Space 1 Running head: LETTERS IN TIME AND RETINOTOPIC SPACE Letters in Time and Retinotopic Space

Various phenomena in tachistoscopic word identification and priming (WRODS and LTRS are confused with and prime WORDS and LETTERS) suggest that position-specific channels are not used in the processing of letters in words. Previous approaches to this issue 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 the alternative assumption that these phenomena reveal the rates at which different features of the stimulus are extracted, because the stimulus is ambiguous when some features are missing from the percept. LTRS is successfully applied to tachistoscopic identification and 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 be accessed by the matching visual perceptual representation. The response to mismatching visual 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, but such access is less efficient the more severe the mismatch. The calculation of such graded matches 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 is complex because the assumption of graded matches is unnecessary, and that the data can be 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 composed of 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 noise or 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 information that 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 by other accounts to imperfect or graded matching in masked form priming and tachistoscopic 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 claims by 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 lexical system is susceptible to a head start from additional stimulus exposure (which is necessary 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, nor even 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 be perceived 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 hypothetical mechanisms: 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 of other accounts, LTRS may appear to do little explanation, but this is because these other accounts interpose explanations where none are required. This paper presents (i) a description of LTRS; (ii) discussion of some core aspects of the model; (iii) LTRS fits to new word tachistoscopic identification data with manipulation of target duration for transposed-letter (TL) and 1-, 2-, and 4-letter-different (1LD; 2LD; Letters in Time and Retinotopic Space 5 4LD) foils; (iv) LTRS fits to nonword tachistoscopic identification data for a wide range of target-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 and precise positional information; and specifies the inferences licenced by this positional information in the context of the usefulness of retinotopic location and distance information. Start of processing. On a given trial, processing of all letters begins at the same random point in time after onset. As an approximation, this time is normally distributed with 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 not finding — time points at which identification of left-hand letters in words is above chance and 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 βi that would be determined by the attentional gradient and the visibility of the letter (due to factors like lateral masking and distance 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 βi; 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(−kβit). Without loss of generality, k = 1. This assumption is the same as that for feature extraction in some models 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 spans several retinotopic letter detectors). As such, if (and only if) two letters have been identified, it is possible to (immediately) determine their order correctly, but other information is not reliably diagnostic as to stimulus identity (see below). That is, the identity/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); this process 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(−λβit). 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 right edges of the letters3. Retinotopic distance information is unreliable. Although the retinotopic information that 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 font