Quantifying the reliance on different sublexical correspondences in German and English

Abstract

The type of sublexical correspondences employed during non-word reading has been a matter of considerable debate in the past decades of reading research. Non-words may be read either via small units (graphemes) or large units (orthographic bodies). In addition, grapheme-to-phoneme correspondences may involve context-sensitive correspondences, such as pronouncing an “a” as /ɔ/ when preceded by a “w”. Here, we use an optimisation procedure to explore the reliance on these three types of correspondences in non-word reading. In Experiment 1, we use vowel length in German to show that all three sublexical correspondences are necessary and sufficient to predict the participants' responses. We then quantify the degree to which each correspondence is used. In Experiment 2, we present a similar analysis in English, which is a more complex orthographic system.

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Quantifying the reliance on different sublexical
correspondences in German and English
Xenia Schmalza, Eva Marinusa, Serje Robidouxa, Sallyanne Palethorpea, Anne
Castlesa & Max Colthearta
a ARC Centre of Excellence in Cognition and Its Disorders, Department of Cognitive
Science, Macquarie University, Sydney, NSW, Australia
Published online: 22 Oct 2014.
To cite this article: Xenia Schmalz, Eva Marinus, Serje Robidoux, Sallyanne Palethorpe, Anne Castles & Max Coltheart
(2014): Quantifying the reliance on different sublexical correspondences in German and English, Journal of Cognitive
Psychology, DOI: 10.1080/20445911.2014.968161
To link to this article: http://dx.doi.org/10.1080/20445911.2014.968161
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Quantifying the reliance on different sublexical
correspondences in German and English
Xenia Schmalz, Eva Marinus, Serje Robidoux, Sallyanne Palethorpe,
Anne Castles, and Max Coltheart
ARC Centre of Excellence in Cognition and Its Disorders, Department of Cognitive
Science, Macquarie University, Sydney, NSW, Australia
The type of sublexical correspondences employed during non-word reading has been a matter of
considerable debate in the past decades of reading research. Non-words may be read either via small
units (graphemes) or large units (orthographic bodies). In addition, grapheme-to-phoneme correspon-
dences may involve context-sensitive correspondences, such as pronouncing an “a”as /ɔ/ when preceded
by a “w”. Here, we use an optimisation procedure to explore the reliance on these three types of
correspondences in non-word reading. In Experiment 1, we use vowel length in German to show that all
three sublexical correspondences are necessary and sufficient to predict the participants’responses. We
then quantify the degree to which each correspondence is used. In Experiment 2, we present a similar
analysis in English, which is a more complex orthographic system.
Keywords: Optimisation; Reading; Sublexical processing.
How print is converted to speech is an important
question, both from a theoretical and a practical
perspective. Sublexical translation processes have
a central role in all current models of reading
aloud (Coltheart, Rastle, Perry, Langdon, & Zieg-
ler, 2001; Perry, Ziegler, & Zorzi, 2010; Plaut,
McClelland, Seidenberg, & Patterson, 1996; Sei-
denberg & McClelland, 1989). The exact nature of
this sound-to-speech conversion procedure, how-
ever, has been under considerable debate since the
1970s. In particular, the debate revolves around
the question of whether this conversion relies
predominantly on small units, such as graphemes,
or larger units, such as orthographic bodies (e.g.,
“-ord”) (Andrews, 1982; Coltheart et al., 2001;
Cortese & Simpson, 2000; Glushko, 1979; Jared,
2002). To a lesser extent, the literature has also
drawn a distinction between context-sensitive and
context-insensitive grapheme-to-phoneme corre-
spondences (GPCs) and addressed the possibility
that rather than relying purely on single-grapheme
correspondences, in some cases the preceding or
Correspondence should be addressed to Xenia Schmalz, ARC Centre of Excellence in Cognition and its Disorders, Cognitive
Science, Macquarie University, Sydney, NSW, 2109, Australia. E-mail: xenia.schmalz@mq.edu.au
We are grateful to Angela Heine and Tila Brink for collecting the Berlin data for Experiment 1B. We also thank Petra
Schienmann and Reinhold Kliegl for their help with organising data collection at Potsdam University for Experiment 1B. We thank
Johannes Ziegler for providing a list of German consistent words. Further thanks are due to Stephen Lupker, James Adelman and
three anonymous reviewers for their helpful comments on earlier versions of this paper.
This article was written as part of XS’s doctoral dissertation under supervision of EM, AC and MC. SR conducted the data
analyses and contributed to the write-up and revision of the manuscript, and SP scored the English data.
© 2014 Taylor & Francis
1
It is not always true that graphemes are smaller (i.e.,
contain fewer letters than) bodies, for example, the graph-
eme “igh”is larger than the body of the word “cat”(“-at”).
For the sake of clarity, we follow the terminology of Ziegler
and Goswami (2005) and refer to graphemes as small units
and bodies as large units.
Journal of Cognitive Psychology, 2014
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succeeding letters may provide a cue to the reader
about the correct pronunciation of a grapheme
(Perry, Ziegler, Braun, & Zorzi, 2010; Treiman,
Kessler, & Bick, 2003; Treiman, Kessler, Zevin,
Bick, & Davis, 2006).
Thus, the literature reports three different types
of correspondences that may be involved in sub-
lexical decoding: context-insensitive GPCs, context-
sensitive GPCs and body–rime correspondences
(BRCs). Here, we propose a mathematical model
based on an optimisation procedure that will allow
us to fit the degree of reliance on each of the three
types of correspondences. We begin with two
experiments in German, where the language struc-
ture allows us to assess the independent contribu-
tion of each of the three types of correspondences.
In two further experiments, we apply the same
methodology to the English grapheme “a”, which
allows us to disentangle the reliance on context-
sensitive GPCs compared to context-insensitive
GPCs.
GPCs describe the relationship between gra-
phemes and phonemes. The phoneme is the basic
unit in spoken language, and a grapheme is the
letter or letter cluster that corresponds to a single
phoneme. The definitions of GPCs are straight-
forward in some cases; for example, the grapheme
“b”always maps onto the phoneme /b/. This is an
example of a context-insensitive GPC: regardless
of the letters that precede or succeed the graph-
eme, its assigned phoneme does not change.
However, this gets more complicated when we
consider the GPC for a grapheme such as “a”.
In English, context-insensitive correspondences
would dictate that “a”should be pronounced as
in “cat”. Using this correspondence, words like
“was”and “false”would be considered irregular,
meaning that the correct pronunciation is incon-
sistent with the GPC. Yet, upon closer inspection,
the pronunciations of “was”and “false”are
entirely predictable when the context of the
grapheme “a”is taken into account: in “was”, the
“a”is preceded by a “w”, which in most cases
changes the pronunciation to /ɔ/, as in “wad”and
“swan”.
2
This context-sensitive correspondence
can be written as “[w]a”→/ɔ/. The pronunciation
of the vowel in “false”can be similarly predicted
by a complex context-sensitive GPC, namely
“[C]a[l][C]”→/o:/, where an "a" is pronounced
as in “bald”when preceded by a consonant,
and followed by an “l”and another consonant.
It is worth noting that these context-sensitive
correspondences (CSCs) are still GPCs, as they
relate a single grapheme (in this case, “a”) to the
pronunciation of a single phoneme. Thus, GPCs
can be subdivided into context-sensitive GPCs
(“[w]a”→/ɔ/) and context-insensitive GPCs (“a”
→/æ/).
The concept of GPCs is important for the
classical computational model of the dual-route
framework, the DRC (Coltheart et al., 2001). This
model has a sublexical route which converts print
to speech via a set of GPCs that are explicitly
specified. The sublexical route contains some
CSCs (N= 28—although the exact numbers vary
according to the version of the DRC), but oper-
ates mostly on single-letter (e.g., “b”→/b/; N= 40)
and multi-letter (e.g., “th”→/θ/; N= 165) context-
insensitive GPCs.
There is also experimental evidence that stres-
ses the importance of CSCs. One study reported
the case of a patient with acquired surface dyslexia
(Patterson & Behrmann, 1997): since this patient
could not correctly read irregular words like
“colonel”and “yacht”, it was thought that her
lexical system was heavily damaged. However, not
all irregular words were a problem: she was
unimpaired with words that could be resolved by
the context-sensitive “[w]a”→/ɔ/ correspondence,
such as “wad”or “swan”. This demonstrates the
presence of such a context-sensitive correspond-
ence in the sublexical system. Furthermore, studies
of non-word reading have shown that there is
psychological reality to CSCs (Treiman et al.,
2003,2006): both adults and children tend to
pronounce non-words such as “twamp”with the
vowel as in “swan”, whereas control items such as
“glamp”are pronounced via the context-insensit-
ive GPC, →/æ/. This further suggests that the
context-insensitive correspondence “a”→/æ/ does
not fully reflect the strategies used during non-
word reading.
In addition to context-insensitive and context-
sensitive GPCs, readers have been shown to rely
on BRCs. BRCs are the sublexical links between
bodies and rimes, where bodies are defined as the
vowel and optional final consonant(s) of a mono-
syllabic word (e.g., “-ark”in the word “bark”). The
rime is the phonological equivalent to the ortho-
graphic body. A linguistic analysis has shown that
bodies are a reliable predictor of vowel
2
There are some differences associated with dialects.
Here, we use the pronunciations given by the DRC’s
vocabulary and the Macquarie Essential Dictionary (5th
edition) as representative of Australian English, and the
IPA as illustrated by Cox and Palethorpe (2007).
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pronunciation in English (Treiman, Mullennix,
Bijeljac-Babic, & Richmond-Welty, 1995).
Full reviews of the psychological reality of
BRCs can be found elsewhere (Goswami &
Bryant, 1990; Ziegler & Goswami, 2005). Most
relevant in the current context are non-word
reading studies addressing this issue because these
allow for a systematic exploration of the non-
lexical correspondences that participants rely on
when lexical information is not available. In
English, non-words can be created that would
yield different responses depending on whether
GPCs or BRCs are used. This is done by manip-
ulating the regularity and consistency of the base
word. A base word that conforms to the context-
insensitive GPCs is said to be regular, whereas
words that violate the correspondences are con-
sidered to be irregular. The concept of regularity
only matters if reading occurs at least in part via
GPCs. If non-lexical reading occurs only via
BRCs, then the reliability (or lack thereof) of the
GPC information should not influence reading at
all; rather, only inconsistency of BRCs should
affect reading latencies and accuracy (e.g., the
two ways of pronouncing “-ave”in “have”and
“save”, see Ziegler, Stone, and Jacobs 1997).
Non-word reading studies that aim to estimate
the reliance on GPCs versus BRCs can use the
regularity and consistency of a base word to
generate non-words that predict different
responses depending on the types of correspon-
dences that are used by the participant. Such
studies are important, because non-word reading
data can shed light on processing underlying
sublexical information, while minimising con-
founds from lexical processing. Understanding
this process has strong theoretical implications
because sublexical print-to-speech conversion
mechanisms play an important role in all promin-
ent models of reading.
In order to disentangle the different sublexical
processes that take place during reading, the first
step is to create non-words for which different
types of correspondences make different predic-
tions. For example, from a regular and consistent
word such as “fact”, the onset can be changed to
create a non-word, for example, “ract”. In this
case, both large and small correspondences make
the same predictions for pronouncing this non-
word. However, if we take an irregular, but
consistent word, such as “talk”, and change the
onset to create the non-word “ralk”, we can use
the readers’pronunciations of this non-word to
determine whether they relied on context-
insensitive GPCs (in which case the item would
be pronounced to rhyme with “talc”) or BRCs
(where it would rhyme with “talk”). Such studies
have shown that GPCs cannot fully account for the
types of pronunciations that participants give to
such non-words, but neither do BRCs (Andrews &
Scarratt, 1998; Brown & Deavers, 1999; Perry,
Ziegler, Braun, & Zorzi, 2010; Pritchard,
Coltheart, Palethorpe, & Castles, 2012).
Thus, there is evidence for reliance on the three
different types of print-to-speech correspondences,
but there are still questions that remain to be
answered. First, previous studies do not distinguish
between the reliance on context-sensitive GPCs
and BRCs. For example, if a participant pro-
nounces the non-word “palse”to rhyme with
“false”, it may be that a context-sensitive corres-
pondence, “a[l]”→/o:/ has been used to derive the
pronunciation, rather than the BRC that “-alse”→
/o:ls/. As will be discussed later, this is a problem
in the English language, as BRCs and CSCs are
confounded.
Second, even though such studies can establish
the psychological reality of certain types of corre-
spondences, examining between-item differences
does not allow estimation of the relative degree to
which each type of correspondence plays a role. As
previous research has demonstrated the psycholo-
gical reality of context-insensitive GPCs, context-
sensitive GPCs and BRCs, it is likely that all three
correspondence types help the sublexical route to
determine the pronunciation of a non-word. How
such a conflict between different types of corre-
spondences may be resolved by the cognitive
system is addressed in detail in the General
Discussion. The possibility of parallel activation of
several sublexical correspondences raises the ques-
tion of whether it is possible to quantify the degree
to which each plays a role in determining the
pronunciation of a novel word, which is a natural
next step after demonstrating a sublexical corre-
spondence’s psychological reality. As discussed
later, more sophisticated analyses are needed to
estimate the relative importance of each type of
correspondence.
In addition to establishing the psychological
reality of different types of sublexical correspon-
dences, a considerable body of research has
explored cross-linguistic differences in the reliance
on GPCs versus BRCs (Goswami, Gombert, & De
Barrera, 1998; Goswami, Porpodas, & Wheel-
wright, 1997; Goswami, Ziegler, Dalton, & Schnei-
der, 2003; Ziegler, Perry, Jacobs, & Braun, 2001;
Ziegler, Perry, Ma-Wyatt, Ladner, & Schulte-
SUBLEXICAL CORRESPONDENCES 3
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Körne, 2003). The psycholinguistic grain-size the-
ory, a cross-linguistic theory of reading develop-
ment and skilled reading, proposes that the degree
of reliance on sublexical correspondences of dif-
ferent types varies across languages (Ziegler &
Goswami, 2005). In particular, the reliance on
BRCs has been reported to be stronger in English
than German (Ziegler et al., 2001,2003). This is
argued to be because in English, large units (i.e.,
bodies) are a better predictor of the pronunciation
of a word than GPCs (Treiman et al., 1995): for a
word like “calm”, the pronunciation is inconsistent
with the GPCs (“kælm”) but can be derived from
its body neighbours (palm, balm, etc.). In German,
on the other hand, the GPCs are highly reliable,
meaning that there are few exceptions to the
correspondences (Ziegler, Perry, & Coltheart,
2000); therefore, smaller units are the preferred
grain size of German readers. In other words,
there is a theoretical framework which predicts
differences in the reliance on the units across
languages. Therefore, it is desirable to develop a
mathematical model quantifying the degree of
reliance in different languages.
In summary, previous literature has shown reli-
ance on three different types of correspondences in
English: Context-insensitive GPCs, context-sensitive
GPCs and BRC. The psycholinguistic grain-size
theory proposes that the reliance on the different
types of correspondences differs across languages
(Ziegler & Goswami, 2005). In the present experi-
ments, we introduce a new method of quantifying
the reliance on each type of correspondence. In the
first two experiments (1A and 1B), we used Ger-
man non-words to assess the degree of reliance on
each type of correspondence. In Experiments 2A
and 2B, we extend the procedure to a more complex
orthographic system, namely English.
EXPERIMENT 1A
The German language allows us to neatly assess
the independent contributions of context-insensit-
ive GPCs, context-sensitive GPCs and BRCs in a
non-word reading paradigm: It is possible to
create a set of items which generate different
predictions for vowel pronunciation, depending
on which strategy is used.
In German, there is relatively little ambiguity in
print-to-sound correspondences, compared to
English. What little ambiguity there is stems
mostly from vowel pronunciation (Ziegler et al.,
2000): Each vowel can be pronounced as either
long or short (e.g., “Schal”/ʃa:l/ versus “Schall”
/ʃal/). In monosyllabic words, vowel length is often
signalled by context. Some CSCs allow the reader
to unambiguously determine vowel length; for
example, any vowel followed by an “h”is pro-
nounced long (”V[h]”→long vowel). Other CSCs
are less transparent. These correspondences are
described by a German implementation of
Coltheart et al.’s(2001) DRC (Ziegler et al.,
2000). To allow the sublexical route to determine
vowel length, it contains a set of context-sensitive
super-rules: any vowel which is followed by only
one consonant elicits a long vowel response (e.g.,
“Wal”) and a vowel which is followed by two or
more consonants is pronounced short (e.g.,
“Wald”). These two rules can be summarised as
follows: “V[C]”→long vowel and “V[C][C]”→
short vowel.
Although these super-rules capture the overall
statistical distribution, there are also some excep-
tions or words that would be irregular according to
the German DRC (Ziegler et al., 2000). The word
“Magd”, for example, is pronounced with a long
vowel; conversely, the word “Bus”is pronounced
with a short vowel. The presence of several bodies
which consistently break the super-rules allows us
to orthogonally manipulate the number of con-
sonants in the body of a non-word and the
pronunciation of the base words. Thus, we create
a situation where the different types of correspon-
dences (i.e., super-rules and body analogy) make
different predictions about the pronunciation of
the vowel.
For the present experiment, we can make a set
of simple predictions if we assume that readers
generally use only one type of correspondence: If
only context-insensitive GPCs are used for Ger-
man non-word reading, we expect that the likeli-
hood of a short vowel pronunciation should be
independent of any other orthographic features of
the non-word. Such a GPC would predict many
more short than long vowels, as the majority of
vowels in German have the short pronunciation
(Perry, Ziegler, Braun, & Zorzi, 2010). If a
context-sensitive super-rule is used, vowel length
should be solely determined by the number of
consonants following the vowel. In this case, even
a non-word based on the irregular but consistent
word such as “Magd”(e.g., “blagd”) should be
pronounced with a short vowel. These irregular-
base word items can distinguish between reliance
on super-rules compared to BRCs: if BRCs are
4 SCHMALZ ET AL.
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used, non-words based on irregular consistent
words should be pronounced to rhyme with their
real-word counterparts.
Methods
Participants were 12 German native speakers who
were staff or postgraduate students at Macquarie
University, or members of the university’s Ger-
man society. As they lived in Australia, they were
also fluent in English—a point which we will
discuss in a later section. With one exception, all
participants had completed secondary education in
Germany and 10 had also attended German
tertiary education. One participant had moved to
Australia at the age of 5, but had attended a
German-speaking school for seven years.
The non-words that were used for this experi-
ment are listed in Appendix A. There were 30
non-words in each of three conditions. The non-
words were created by changing the onsets of real
words. All base words were taken from a list of
consistent German words (J. Ziegler, personal
communication, January 26, 2012). The first con-
dition used base words with V[C] bodies which
were pronounced with a long vowel (“Jod”→
“FOD”); the second condition was based on
V[C][C] words with a short vowel (“Saft”→
“BLAFT”). The third condition was derived from
irregular words, which had either a V[C] body but
a short vowel (“mit”→“GIT”) or a V[C][C]
structure and a long vowel (“Jagd”→“BAGD”).
The three conditions were matched on ortho-
graphic N(the number of real words that can be
created by substituting one letter): V[C] items had
an average orthographic N-size of 1.73 (SD =
1.46), V[C][C] items had a mean of 2.10 (SD =
1.69) and items with irregular base words had a
mean of 1.83 (SD = 1.90). The mean body-N
(number of real words with the same body) for the
three conditions is 1.93 (SD = 1.87), 2.40 (SD =
1.98) and 1.37 (SD = 1.00) respectively.
Participants were tested individually in a quiet
room. Instructions were given in German by a
native speaker. The participants were told that
they would be asked to read non-words which
were created using German orthographic rules.
The instructions emphasised that accuracy was
more important than speed to discourage quick
lexical processing, which might result in lexicalisa-
tion errors.
The items were presented using the DMDX
software package (Forster & Forster, 2003) in
random order. Each trial consisted of a fixation
cross, which remained in the centre of the screen
for 500 ms, followed by the item, which remained
on the screen until the voice key was triggered.
Ten practice non-words preceded the experiment.
As all nouns in German are spelled with capital
initial letters, presenting non-words in all lower-
case would provide an indication of word class of a
non-word. Previous research has shown that
information on the likely word class of a non-
word affects its pronunciation (Campbell & Bes-
ner, 1981). Therefore, all items were presented in
upper case.
Results
Six trials (0.6%) were excluded due to poor sound
quality or premature voice key triggering. The rest
of the trials were scored by a German native
speaker as pronounced with a long vowel, a short
vowel or incorrectly. For identifying incorrect
responses, we used a lenient marking criterion: if
a participant’s response was consistent with a
possible pronunciation of the GPCs, it was marked
as correct (e.g., “spic”was marked as correct
regardless of whether it was pronounced as /spik/
or as /ʃpik/—whereas, in German, “s”is typically
pronounced as /ʃ/ before “p”or “t”, there are a few
instances, such as loanwords, where it is assigned
as the pronunciation /s/). Overall, 1.1% of all
responses were classified as incorrect and
excluded from subsequent analyses. Of primary
interest were the proportions of long and short
vowel responses and how they differed across
condition. We split the irregular-base word condi-
tion by whether the bodies had one (hereafter
referred to as V[C] Irregular; N= 17) or two
(V[C][C] Irregular, N= 13) consonants. Note that
the two “irregular”conditions did not differ dra-
matically on any item characteristics: the mean
number of letters was 3.88 (SD = 0.34) and 4.36
(SD = 0.63) for the V[C] and V[C][C] conditions,
respectively, orthographic Nwas 1.88 (SD = 2.19)
and 1.79 (SD = 1.58), respectively, and body-
Nwas 1.56 (SD = 1.15) and 1.29 (SD = 0.61),
respectively. The proportions of short vowel
responses for each of the four item types (V[C]
Regular, V[C][C] Regular, V[C] Irregular and
V[C][C] Irregular) are listed in Table 1, along
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with the predictions according to each of the three
types of correspondences.
In order to make the predictions more specific,
we can use a corpus analysis to determine the
percentage of times a vowel is pronounced as long
or short under certain circumstances. For example,
overall, 78.02% of all monosyllabic words are
pronounced with a short vowel (Perry, Ziegler,
Braun, & Zorzi, 2010); therefore, if German read-
ers rely on context-insensitive GPCs, we expect
them to give around the same percentage of short
vowel responses. Among words with a single-
consonant coda, 24.53% are pronounced with a
short vowel, so we expect about the same percent-
age of short vowel responses to V[C] non-words, if
only super-rules are used to determine vowel
length. In Table 1, we present the predicted vowel
lengths for each of the four conditions and by each
of the three types of correspondences. For the
context-insensitive GPCs and super-rules, these
are calculated from the analyses presented in
Perry, Ziegler, Braun, and Zorzi (2010). The
predictions of the BRCs depend on the consist-
ency ratio of the body. In the current study, we
used only consistent items, where the body has
only one pronunciation in real words. This means
that if participants rely solely on BRCs, 100% of
the pronunciations should be consistent with the
base word vowel length.
The obtained percentages of long and short
vowels (Table 1) are not consistent with the
predictions of any one strategy we described
earlier: vowel length responses are neither pre-
dominantly short in all four conditions, nor com-
pletely dependent on the number of consonants
following the vowel, nor the vowel length of the
base word. This is a clear indication that German
readers rely on more than one type of correspond-
ence for reading non-words. Moreover, a closer
look at Table 1 shows that no combination of two
types of correspondences can account for the
results, either: If context-insensitive GPCs and
CSCs were the sole determiners of vowel length,
we would not expect to find different proportions
for the V[C] Regular and V[C] Irregular items—
but we do. If context-insensitive GPCs and BRCs
were the only predictors of vowel length, we
would find no difference between the V[C] Regu-
lar and the V[C][C] Regular items—and we do. If
only CSCs and BRCs were used, we should
observe less than 25% short vowel responses—
which is not supported by the data.
Modelling vowel pronunciations
It is not possible for a single or even a pair of types
of correspondences to adequately fit the empirical
data. It may be, however, that some combination
of all three types of correspondences provides a
good fit. Here we introduce a mathematical mod-
elling approach that allows us to uncover more
complex relationships between the types of corre-
spondences. The goal is to weight the three
strategies.
3
More formally, we are seeking a set
of βweights that best satisfy the following math-
ematical model (one pair of equations for
each item):
TABLE 1
Percentage of short vowel responses for each condition in Experiment 1 and the average predictions from
each of the three types of correspondences
Responses V[C] Regular V[C][C] Regular V[C] Irregular V[C][C] Irregular
Example “Wal”→“bral”“Wald”→“brald”“Bus”→“brus”“Magd”→“bragd”
% Short 1A 47.25 83.69 84.63 61.04
% Short 1B 37.28 86.79 72.95 62.84
Correspondence predictions
P(Short ∣GPC) 70.21 79.53 90.59 78.77
P(Short ∣CSC) 26.20 92.57 62.82 91.38
P(Short ∣BRC) 2.76 100.00 100.00 0.00
Model predictions
% Short 1A 44.68 87.04 87.83 60.53
% Short 1B 36.58 89.78 83.67 61.70
GPC, context-insensitive GPC; CSC, context-sensitive correspondences; BRC, body-rime correspondence.
3
Although we refer to the reliance on different types of
correspondences as a “strategy”, we do not mean to imply
that readers consciously choose the type of correspondence
that maximises the chance of correctly reading an unfamil-
iar word, in a way that optimally fits the empirical data.
6 SCHMALZ ET AL.
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where GPC½length";iis the probability of item ibeing
pronounced with a vowel of the corresponding
length according to the corpus analysis when using
only context-insensitive (single-letter) GPCs as a
predictor, CSC½length";iis the probability according to
context-sensitive super-rules and BRC½length";iis the
probability according to the BRCs. Table 1 provides
the average predictions for each condition, but the
predictions from each correspondence were calcu-
lated separately for each item in the experiments.
Pið½length"Þ is the empirically observed proportion
of the vowel length in Experiment 1A.
4
At a first glance, this would appear to be a
simple regression problem (with no intercept
term). Linear regression would optimally select β
values that minimised the prediction error for
Equation 1 (indexed by the residual sum of
squares). However, there are several reasons why
this should not be thought of as regression. First,
since the βvalues are thought of as the degree
to which a strategy applies in reading the items
in Experiment 1, negative values would be
uninterpretable. This means that all of our β
parameters must exceed 0. This constraint cannot
be guaranteed by standard linear regression using
ordinary least squares (Monfort, 1995).
Even with only positive βs, there are two ways
to interpret the weights. One could think of them
as the contribution of each strategy to some sort of
blending process that ultimately chooses the vowel
pronunciation. In which case, we can simply fit the
model in Equation 1 with the constraint that
bi%0;8i. Alternately, one can think of the
weights as the probabilities of adopting the vowel
prediction from a given strategy. We prefer the
latter interpretation (and discuss some evidence
for it later), but it requires two further constraints:
the βweights must fall below 1, and, since we
assume that the three strategies (GPCs, super-
rules and BRCs) are exhaustive, the three βs must
sum to 1. The model can be formalised as:
That is, we are seeking a set of probabilistic
weights on the three strategies that minimises the
prediction error of the model. The challenge here
is to both efficiently search the available para-
meter space and satisfy the Rbj¼1constraint. The
first problem is a well-studied one in computer
science and solutions are available that solve it.
The second problem is largely solved by introdu-
cing an additional equation that can only be
satisfied if Rbj¼1, and giving that equation a
strong influence on the final parameter set. The
interested reader can find a fuller discussion of the
implementation details in Appendix B.
Optimal weights in Experiment 1A
In Experiment 1A, we collected the proportion of
short and long vowel responses to 90 items, and
PiðshortÞ¼bgpc 'GPCshort;iþbcsc 'CSCshort;iþbbrc 'BRCshort;i
PiðlongÞ¼bgpc 'GPClong;iþbcsc 'CSClong;iþbbrc 'BRClong;i
where bj2½0;1"and Rbj¼1;8j2fgpc;csc;brcg
ð2Þ
PiðshortÞ¼bgpc 'GPCshort;iþbcsc 'CSCshort;iþbbrc 'BRCshort;i
PiðlongÞ¼bgpc 'GPClong;iþbcsc 'CSClong;iþbbrc 'BRClong;ið1Þ
4
In standard linear regression, only one of these two
formulae would be required, since they are entirely
dependent (i.e., PiðLongÞ¼1)PiðShortÞ, etc.). In tradi-
tional regression, the only difference between the first and
second equations would be the location of the estimated
intercept and the sign of the slope. However, by removing
the intercept term, our modelling strategy undermines this
interdependence. Since the intercept is not free to vary (it is
forced to be 0) the parameter estimates for P(short) would
not match those for P(long). As a result, we must
simultaneously fit both vowel pronunciations. Although it
is useful to use the language of regression to describe some
of the procedures, it is very important to remember that the
βs here do not represent regression slopes but weights.
Also, if this were a regression problem, it would be more
properly treated as a logistic regression problem. However,
this would be incompatible with our interpretation of the
weights as “the probability that a certain strategy is
adopted”.
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for each item we have the predicted probability of
a short or long vowel pronunciation according to
each of the three strategies. The strategy predic-
tions were obtained from the corpus analysis
undertaken by Perry, Ziegler, Braun, and Zorzi
(2010). Using the technique described earlier, the
native German readers in Experiment 1A appear
to be relying mostly on GPCs ( ^
bgpc ¼0:56), and to
a lesser extent on super-rules ( ^
bcsc ¼0:19) and
BRCs (^
bbrc ¼0:26). See Table 2 for a summary of
the modelling results across all of the present
experiments.
The previous analysis contains a theoretically
supported but strong assumption that readers use
only the three strategies described in the introduc-
tion when reading non-words. It is possible that
other sources of information are used by German
native speakers to determine vowel length. We
can provide a simple test of this possibility by
relaxing some of the constraints on the model and
observing how critical those constraints were to
the optimisation results. To do this, we removed
the Rbj¼1constraint and allowed the βs to take
on any positive weights in the fitting process. That
is, we fit the following alternative model (some
subscripts indicating length and item have been
omitted for simplicity):
PðLengthÞ¼bgpc 'GPC þbcsc 'CSC
þbbrc 'BRC;where bi>08ið3Þ
If readers are adopting other strategies that are not
well described by the GPC, super-rules and BRC
strategies, the incomplete nature of the model
should be reflected in these alternate weights. The
weights that optimise Equation (3) were ^
bgpc ¼
0:58;^
bcsc ¼0:14;and ^
bbrc ¼0:24. These values
sum to 0.96, suggesting that there is little need for
a fourth strategy to describe the data. This does not
conclusively rule out a role for any other strategies,
but provides some evidence that the three strategies
already tested are sufficient. That said, there is one
additional strategy that could be playing a role: anti-
body correspondences (ABC) or the probability of
a vowel being pronounced as long or short based on
the onset of the word. In this corpus of non-words,
the predictions from ABC and context-insensitive
GPCs are highly correlated, so it is difficult to
disentangle the two strategies entirely, but it may
be that ABC are more important than context-
insensitive GPCs and thus are a better predictor. To
test whether or not ABCs were important for
determining vowel pronunciations, we added a
component to model (2):
PðLengthÞ¼bgpc 'GPC þbcsc 'CSC
þbbrc 'BRC þbabc 'ABC
where bj2½0;1"and Rbj¼1
ð4Þ
where the addition of ABC represents the predic-
tions from ABCs, and β
abc
is the associated weight.
Fitting Equation 4 produced the same weights that
resulted from Equation 2 where the ABCs were not
included. That is, ^
babc ¼0, giving little reason to
believe that any other strategies are being used in
Experiment 1A.
Model fits. The optimisation procedure presented
here is only useful if it arrives at a model that fits
the data better than alternatives. To determine the
effectiveness of the model, we calculated the
TABLE 2
Weightings for the three types of correspondences in Experiments 1A, 1B, 2A and 2B
Correspondence type 1A (German bilingual) 1B (German monolingual) 2A (English monolingual) 2B (English bilingual)
GPC 0.56 0.38 0.05 0.03
CSC 0.19 0.35 0.69 0.61
BRC 0.26 0.27 0.26 0.36
TABLE 3
Summary of the fits between the models and the observed
response proportions. Each value is the correlation between
the predictions from the GPC, CSC, BRC or model and the
observed response pattern
Sample GPC CSC BRC Optimal (95% CI)
1A (German
bilingual)
0.714 0.681 0.540 0.844 (0.830, 0.847)
1B (German
monolingual)
0.578 0.730 0.659 0.827 (0.812, 0.832)
2A (English
monolingual)
0.522 0.630 0.385 0.729 (0.719, 0.731)
2B (English
bilingual)
0.514 0.573 0.568 0.792 (0.785, 0.793)
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correlation between the model predictions and the
observed response patterns. For comparison, we
did the same for the GPCs, CSCs and BRCs
individually. As can be seen in Table 3, the
optimisation process outperforms the other three
alternatives in all four samples presented here. In
Experiment 1A, the correlation is .844, whereas
the next best model (based on context-insensitive
GPCs) correlates at .714.
Discussion
In Experiment 1A, we successfully used an optimi-
sation procedure to quantify the degree of reliance
on three types of sublexical correspondences: con-
text-insensitive GPCs, context-sensitive GPCs and
BRCs. This can be achieved with the German
language because it is possible to create items where
different correspondence types make different pre-
dictions about the vowel length pronunciation.
Importantly, we found that all three types of
correspondences are both necessary and sufficient
to predict vowel length responses in a sample of
German native speakers. Context-insensitive cor-
respondences appear to be the strongest predictor.
This is in line with the psycholinguistic grain-size
theory, which argues that the smallest unit size
is favoured by readers of a language with predict-
able GPCs, such as German (Ziegler & Goswami,
2005).
Experiment 1A has some limitations. It could
be argued that the results are unreliable, first due
to the small sample size and second because the
participants were bilingual, and very fluent in
English. It is unclear how fluency in English may
affect the reliance on different types of correspon-
dences in German. Even though we took care to
only include German participants who learned to
read and write in German from a young age, there
is a possibility that their exposure to German
reading material has been diminished by residing
in an English-speaking country. It is also possible
that their knowledge of English would change the
preferred unit in their native language: for
example, psycholinguistic grain-size theory pre-
dicts that readers of English rely more heavily on
larger grain sizes than readers of German (Ziegler
& Goswami, 2005), although it does not make any
statements about sublexical processing in bilin-
guals. We address these concerns in Experi-
ment 1B.
EXPERIMENT 1B
In Experiment 1B, we collected data with two
different samples of German native speakers who
live in Germany and are not exposed to English
on an everyday basis. We hereafter refer to them
as monolingual Germans, even though they are
not strictly monolingual: due to globalisation, it
would be difficult if not impossible to find Ger-
mans who have no knowledge of English. Having
collected data with two different samples of
monolingual Germans allows us to test the reliab-
ility of the modelling method described here. If
our model arrives at similar weights for two
independent samples from the same population,
we can be more confident that our modelling
procedure is stable and reliable.
Methods
The methods were almost identical to Experiment
1A. One item was replaced (due to a typo, the
original item set contained an inconsistent item,
“blen”, which was changed to “blem”in Experi-
ment 1B).
The first sample consisted of 10 German native
speakers who were staff or students at the Freie
Universität in Berlin. All had completed their
schooling in Germany. The second sample con-
sisted of 26 undergraduate students at Potsdam
University. Again, all were native German speak-
ers and had completed their education in
Germany.
Results
The scoring procedure was identical to Experiment
1A. For the Berlin sample, there were two non-
responses (0.22%) and 15 errors (1.67%). The
Potsdam sample made 2.3% errors. A series of
t-tests showed that the percentages of long and
short vowel responses did not differ significantly for
any of the conditions across the two samples, all
p> 0.4. Furthermore, fitting each sample separately
using the model described in Equation 2 produced
very similar weights. For the participants from
Berlin, the weights were ^
bgpc ¼0:40;^
bcsc ¼0:33;
and ^
bbrc ¼0:27. For the participants from Potsdam
they were ^
bgpc ¼0:37;^
bcsc ¼0:35;and ^
bbrc ¼0:28.
This result is comforting, suggesting that the
method introduced here is reliable across different
samples from similar populations. Since there was
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little difference between the two samples, we
collapsed across them yielding a sample of 36 native
German monolinguals. Using this collapsed sample,
our model produces ^
bgpc ¼0:38;^
bcdc ¼0:35;
and ^
bbrc ¼0:27. As in Experiment 1A, the optimal
parameter set outperforms the alternatives in fitting
the observed data (Table 3).
German/English bilingual VS. German mono-
lingual readers. Since Experiments 1A and B are
based on the same set of items, we have the
opportunity to compare how the bilingual readers
differed from the monolingual readers. The critical
question is whether or not the smaller ^
bgpc and
larger ^
bcsc for monolinguals represents a real
difference, or simply random variation. In the
usual context of a linear regression model, this
would be a simple matter of including the lan-
guage status of the participants (bilingual vs.
monolingual) in the model, and testing for an
interaction between language status and the GPC
and/or CSC estimates. However, our modelling
strategy violates many of the assumptions that
allow for straightforward t-tests of the parameter
estimates (given the constraints of our model, the
parameter estimates are unlikely to be well
behaved, statistically). Instead, we turn to a boot-
strapping methodology to allow us to use the data
to conduct non-parametric tests of the variability
in our estimates.
To establish the reliability of the difference in
the ^
bgpc and ^
bcsc estimates, we repeatedly
resampled 90 items (with replacement) from the
data-set, and estimated the ^
bis for both the
bilingual and monolingual participants with each
sample of items. Of 10,000 such samples, 9890
(98.9%) produced a larger GPC weight for the
bilingual subjects than for the monolingual sub-
jects (95% CI of the difference: 0.019–0.327).
Similarly, 9634 (96.3%) samples produced a larger
CSC weight for the monolingual participants than
for the bilingual participants (95% CI: –0.011 to
0.317). This suggests that the difference in the
GPC weights is robust, whereas the difference in
the CSC weights is slightly more tenuous. The
difference in the BRC weights was not at all
significant: 3454 (34.5%) of the samples produced
larger BRC weights for bilinguals than for mono-
linguals (95% CI: –.058 to .089). We also took
advantage of these bootstrap samples to estimate
the variability in the correlations from the optimal
parameters in Table 3.
To summarise the results so far, the reliance on
BRCs did not differ between monolingual and
bilingual readers, but there was a very stable
difference in the reliance on context-insensitive
GPCs and a somewhat stable difference in the
role of context-sensitive super-rules. Monolinguals
relied less on context-insensitive GPCs and some-
what more on super-rules than bilinguals.
Individual differences. There is some ambiguity in
interpreting the weights: as we collapsed across
participants, the weightings do not give us any
information about inter-individual participant vari-
ability. Theoretically, it is possible that all partici-
pants rely on the same strategies to the same
extent, or that the weightings are reflective of the
percentage of participants who rely on a particular
strategy only. To address this, we generated the
weightings for each individual participant in
Experiments 1A and B. These are summarised in
Figure 1. This figure shows that there is individual
variability, but most participants rely on a com-
bination of the three strategies.
Discussion
As in the previous experiment, we were able to
quantify the degree of reliance on each of the
three types of correspondences in two samples of
monolingual German native speakers. Even
though there is individual variation, we found, on
average, almost identical reliance on the three
strategies in two independent samples of German
readers, suggesting that the procedure we intro-
duced is reliable. The overall pattern of results was
also broadly consistent with the findings from
Experiment 1A, showing that reliance on all three
types of correspondences is both necessary and
sufficient to explain the vowel length pronuncia-
tions in German, and that context-insensitive
correspondences are the major predictor of the
vowel responses.
Although the bilingual and monolingual partici-
pants’response patterns were similar, we did find
some significant differences in terms of reliance on
context-sensitive versus context-insensitive corre-
spondences: bilingual participants show stronger
reliance on context-insensitive correspondences
and less reliance on CSCs. Two possible causes of
the difference between German/English bilinguals
and German monolinguals are the influence of
English proficiency on reading in the bilingual
sample, or a general difference in German reading
proficiency. According to the psycholinguistic
grain-size theory, if the difference in weights is
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due to the influence of English (L2) on the choice
of correspondences in German (L1), we would
expect bilinguals to rely more on larger correspon-
dences (CSCs or BRCs as opposed to context-
insensitive correspondences). Developmental stud-
ies have shown that reliance on larger units differs
as a function of reading efficiency, as younger
children rely to a greater extent on context-sensit-
ive rules (Treiman et al., 2006). In Experiment 1B,
we found that bilingual participants rely more on
context-insensitive rules, which is more in line with
a proficiency explanation—bilinguals may be less
proficient in reading German than monolinguals,
as they are less exposed to German texts. As a
result, they rely to a greater extent on the context-
insensitive correspondences.
5
EXPERIMENT 2A
The majority of prior research on the use of GPCs,
context-sensitivity and BRCs has been conducted
in English. In contrast to German, the English
letter-to-sound correspondence system is highly
complex, as a large set of correspondences on
different levels are required to describe the rela-
tionship between print and speech (Venezky,
1970). In Experiment 2, we aimed to explore
whether it is possible to apply the methodology
which we introduced in Experiment 1 to quantify
the degree of reliance on the same three strategies
in a more complex system.
English, like German, contains some CSCs.
However, there are no super-rules, or correspon-
dences which apply to all vowels, as in German.
Therefore, we concentrated solely on the graph-
eme “a”, as its correct pronunciation can often be
disambiguated by taking into account its context.
By default, “a”is pronounced as in “cat”in
Australian English, but there are several context-
sensitive and multi-letter GPCs that can modify its
pronunciation. The context-sensitive correspond-
ence of interest here is the correspondence that an
“a”preceded by a “qu”or “w”is pronounced as /ɔ/.
We chose this correspondence to assess reliance
Figure 1. Weightings for each individual participant, sorted by degree of reliance on GPC. GPC = context-insensitive rules, CSR =
context-sensitive rules, AN = body-rime correspondences. M = monolingual participant (Experiment 1B), B = bilingual participant
(Experiment 1A)
5
It is noteworthy that Perry, Ziegler, Braun, and Zorzi
(2010) report data with a similar set of non-words to the
current study (although the study was conducted with
different aims): the authors manipulated the number of
consonants in the coda, but rather than controlling for the
consistency of the base word, their non-words differed in
terms of the existence of the body in real words: the body
either occurred in real German words or it did not. In other
words, they did not independently manipulate the predic-
tions of BRCs and CSCs, and predictions of super-rules
and body analogy were heavily correlated, rð39Þ¼0:78,
p<0:001, as were the predictions of super-rules and
GPCs, rð39Þ¼0:51,p<0:001. This means that the Perry
et al.’s data is unsuitable for our purposes: The analysis
would be unreliable, as it is impossible to disentangle
reliance on bodies versus super-rules and super-rules
versus GPCs.
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on context-sensitivity for two reasons: First, previ-
ous research has shown that there is some psycho-
logical reality to this correspondence (Patterson &
Behrmann, 1997; Treiman et al., 2003). Second,
unlike other context-sensitive GPCs (e.g., “a[l]”→
/o:/), this correspondence is not confounded with
body–rime analogy, as the modifier is located in
the onset, before the vowel. This is therefore one
of the few English CSCs that allows us to
independently assess effects of context-sensitivity.
In order to create an item set equivalent to the
German non-words used in Experiment 1, we
isolated English bodies with the vowel grapheme
“a”which are consistently pronounced irregularly
(Ziegler et al., 1997). There are five such bodies:
“-alse”,“-att”,“-alk”,“-alt”and “-ald”. With one
exception, they are confounded with the “a[l]”→/o:/
correspondence: the body “-att”only occurs in the
word “watt”and therefore only has the /ɔ/ pronun-
ciation. As a result, and in contrast to the German
experiment, the degree of reliance on BRCs cannot
be assessed using this paradigm because it is almost
perfectly confounded with reliance on the “a[l]”
context-sensitive correspondence.
In short, there are three possible pronuncia-
tions indicative of reliance on different types of
correspondences. If English participants rely on
context-insensitive GPCs, we should find that the
majority of non-words are pronounced with the /æ/
vowel. If CSCs are used, then in the conditions
where a “qu”or “w”precedes the vowel we should
find many /ɔ/ responses. If either BRCs or the
“a[l]”correspondence are used, the conditions
with the consistently irregular bodies should be
pronounced with an /o:/.
Methods
The participants were 19 undergraduate students
at Macquarie University who were all native
speakers of English.
We created four conditions of 18 words each
(listed in Appendix A). All were monosyllables
containing the single vowel grapheme “a”. The
first condition was created by taking consistently
regular bodies (Ziegler et al., 1997) and adding an
onset which does not change the pronunciation of
the vowel (i.e., any onset that does not contain “w”
or “qu”), resulting in non-words like “hact”(this
condition is hereafter referred to as CS+BR+, as
both the CSCs, CS, and the BRCs, BR, agree with
the context-insensitive GPC “a”→/æ/). The second
condition (CS+BR–, e.g., “halse”) was based on
bodies where the “a”is consistently pronounced as
/o:/ (or /ɔ/ for the body “-att”) and “normal”
onsets, as in the first condition. Here, the BRCs
predict an /o:/ pronunciation, and therefore disag-
ree with the context-insensitive correspondence.
The items in the third condition (CS–BR+, e.g.,
“wact”) were based on regular bodies and onsets
containing “w”or “qu”, meaning that the context-
sensitive “[qu,w]”a-correspondence contradicted
the context-insensitive GPC, whereas the BRCs
did not. The fourth condition (CS–BR–, e.g.,
“qualse”) had items with irregular bodies and
onsets with “w”or “qu”—here both the context-
sensitive correspondence and the body disagree
with the context-insensitive GPC. As filler items,
we used a set of unrelated non-words.
The presentation was identical to Experiment 1,
with items presented in random order and in upper
case letters. As with Experiment 1, participants
were instructed to read the items as accurately as
possible, without putting them under time pressure.
Results
The results were scored by the fourth author (SP),
a native Australian English speaker and an experi-
enced transcriber, with the aid of spectral analysis
using the EMU speech database system and
associated speech analysis tools (Cassidy & Har-
rington, 2001). SP was unaware of the aims of the
experiment as she was transcribing the data.
Unlike the German data, scoring the responses
as correct or incorrect was more complicated. For
the grapheme “a”, there are at least five plausible
pronunciations: as in “cat”, as in “false”, as in
“what”, as in “cake”and as in “car”. We consid-
ered only the first three responses, as they were
predicted either by the context-insensitive GPC,
“a”→/æ/, the context-sensitive GPC, “[qu,w]a”
→/ɔ/ or the BRC “a[l]”→/o:/ context-sensitive
correspondence. Other responses and errors
made up 4.09% of the CS+BR+ condition,
24.85% of the CS+BR–condition, 6.43% of the
CS–BR+ condition and 20.76% of the CS–BR–
condition, and were excluded from the subsequent
analyses. The percentage of “other”responses is
particularly high for the BR–conditions, partly
because in English, a post-vocalic “l”creates
ambiguity in the pronunciation of the vowel, such
that a long /o:/ may become indistinguishable from
the phoneme /əʉ/. The percentages of /æ/, /o:/ and
/ɔ/ responses are presented in Table 4, with the
results from Experiment 2B for comparison.
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Modelling vowel pronunciations in
English
The modelling strategy for Experiments 2A and B
required a small modification from that employed
in Experiments 1A and B. In German, there are
only two available vowel pronunciations for “a”:
short and long. In Australian English, there are
three pronunciations available for items of Experi-
ment 2. This means that we now need three
equations per item (item indices are omitted):
Pð!Þ¼bgpc 'GPC!þbcsc 'CSC!þbbrc 'BRC!
PðɔÞ¼bgpc 'GPCɔþbcsc 'CSCɔþbbrc 'BRCɔ
Pðo:Þ¼bgpc 'GPCo:þbcsc 'CSCo:þbbrc'BRCo:
where bj2½0;1"and Rbj¼1
ð5Þ
where each of the subscripted strategies indicates
the likelihood of the subscripted pronunciation
under that strategy; for example, GPC
æ
indicates
the likelihood of an /æ/ response under the GPC
strategy. The end result is a set of ^
bjs that fit all
three pronunciations simultaneously.
The weightings are shown in Table 2. The role
of CSCs appears to be the most important in
predicting the pronunciation of the grapheme “a”,
with, ^
bcsc = 0.69. BRCs also appear to contribute
significantly, ^
bbrc= 0.26, whereas the reliance on
context-insensitive correspondences is very small,
^
bgpc= 0.05. Indeed, the bootstrapping procedure
produced ^
bgpc ¼0in 43.3% of the samples and
^
bgpc <0:1in 82.0% of the samples, suggesting that
the reliance on context-insensitive correspon-
dences does not differ significantly from zero.
Here again, the model is outperforming each of
the independent strategies at predicting response
patterns on an item by item basis (see Table 3),
but when considering the model’s ability to predict
cell means (Table 4), it is clear this approach is less
successful in English than it was in German.
Discussion
We quantified the reliance on different types of
correspondences for English non-words with the
grapheme “a”, using the same modelling technique
we introduced in Experiment 1 for German, with
TABLE 4
Summary of vowel responses of English monolinguals (2A) and German/English bilinguals (2B), predictions from the three types of
correspondences (context-independent GPCs; context-sensitive correspondences; body rhyme correspondences) and predictions
from the model using the weights in Table 2
Experiment Responses CS−BR−CS+BR+ CS−BR+ CS+BR−
Example “qualk”“hangst”“quadge”“hald”
Participant responses
2A—monolinguals %æ 8.12 96.20 76.04 39.18
%ɔ60.25 0.00 17.19 27.19
%o: 10.63 0.00 0.88 8.77
2B—bilinguals %æ 8.07 83.33 62.50 41.20
%ɔ38.24 0.93 19.91 27.31
%o: 52.19 0.00 0.00 7.87
Correspondence predictions
GPC P(æ ∣GPC) 72.00 72.00 72.00 72.00
P(ɔ∣GPC) 5.00 5.00 5.00 5.00
P(o: ∣GPC) 6.00 6.00 6.00 6.00
CSC P(æ ∣CSC) 29.00 77.00 29.00 77.00
P(ɔ∣CSC) 47.00 0.00 47.00 0.00
P(o: | CSC) 0.00 0.00 0.00 0.00
BRC P(æ ∣BRC) 0.00 100.00 100.00 0.00
P(ɔ∣BRC) 0.00 0.00 0.00 0.00
P(o: ∣BRC) 100.00 0.00 0.00 100.00
Model predictions
2A %æ 22.46 82.98 49.07 56.37
%ɔ33.35 0.14 33.35 0.14
%o: 26.77 0.16 0.16 26.77
2B %æ 18.88 85.34 55.39 48.84
%ɔ29.38 0.05 29.38 0.05
%o: 36.57 0.07 0.07 36.57
SUBLEXICAL CORRESPONDENCES 13
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some minor modifications. Although the results
were less clear-cut than in German, we show that
the procedure can be applied to a more complex
orthography. The model fits in Table 4 indicate
that the English orthography is not best suited for
such an analysis. In particular, the poor model fits
are due to many /ɔ/ responses, even when these
were not predicted by our model. This may be a
result of the complex phonology of English: the
phonemes /ɔ/ and /o:/ are very similar, therefore it
is possible that the participants had a tendency to
shorten /o:/ responses, which then became indis-
tinguishable from the vowel /ɔ/. The second pos-
sibility is that another source of information is
used to determine vowel pronunciations in English
which we did not take into account.
Despite these limitations, there are several
conclusions that can be drawn from the results.
First, the weightings showed that in English the
three strategies are neither necessary nor sufficient
to predict the pronunciation of the grapheme “a”.
In contrast to German, we obtained a relatively
high percentage of “other”responses for the
English data, or pronunciations that were implaus-
ible according to any of the correspondences that
we thought participants may use. Such a hetero-
geneity of non-word reading aloud responses has
also been reported elsewhere (Andrews & Scar-
ratt, 1998; Pritchard et al., 2012). Although this
would be an interesting topic to pursue in further
research, for our purposes we discarded the
unusual pronunciations as we were interested in
quantifying the reliance on the same three types of
correspondences we showed to be critical to non-
word reading in German. This high percentage of
“other”responses shows that it is likely that other
strategies, such as more complex CSCs or lexical
analogy, are used during non-word reading in
English. In other words, the three types of
correspondences we described in the introduction
are not sufficient to explain vowel responses to the
grapheme “a”in English—which is in contrast to
the findings we report for German.
Second, a striking finding is that the context-
insensitive correspondences are hardly used at all
to derive the pronunciation of the grapheme “a”.
Rather, English readers rely heavily on the con-
text-sensitive GPC, which can often be used to
derive the correct pronunciation for English
words.
These results imply that in the special case of
the grapheme “a”, it may not be necessary to rely
on all three types of sublexical correspondences to
explain the pattern of vowel responses. We
consider it highly unlikely that context-insensitive
GPCs are not used at all for reading in English.
We relied solely on non-words with the grapheme
“a”to derive the weightings in Experiment 2, and
its correct pronunciation can often be predicted by
context. Arguably, this may falsely bias the
weightings towards an apparent greater reliance
on CSCs than we would observe if we used
different graphemes for this procedure. However,
we consider it likely that context-sensitivity plays
an equally important role for other vowels in
English: as is the case for the grapheme “a”, vowel
pronunciations in English are generally inconsist-
ent, but can be often resolved CSCs (Treiman
et al., 1995). Non-word reading studies have also
provided evidence for the psychological reality of
CSCs determining vowel pronunciation in English,
other than the “[qu/w]a”correspondence (Trei-
man et al., 2003,2006). As described earlier, we
focused on the “[qu/w]a”correspondence only
because it is not confounded with
BRCs—if we used any other context-sensitive
correspondence we would be unable to distinguish
it from reliance on body analogy.
Again, we stress that the almost exclusive
reliance on CSCs in Experiment 2 is unlikely to
generalise to the processing of more consistent
graphemes in English, such as consonants. If,
linguistically, context-insensitive correspondences
are generally predictive of the correct pronunci-
ation, there is no pressure on the readers to take
into account the surrounding letters for those
particular graphemes.
As discussed in the Introduction, the BRCs of
English are confounded with CSCs. Instead of the
German super-rules, we used an English context-
sensitive correspondence that is not located in the
body, namely the “[qu,w]a”→/ɔ/ correspondence.
However, we cannot fully disambiguate the reli-
ance on BRCs and the “a[l]”correspondence.
Future studies using non-word reading should
bear in mind that BRC and CSCs are heavily
confounded, and that an apparently irregular
pronunciation of a non-word may show reliance
on either CSCs or BRCs.
EXPERIMENT 2B
In Experiment 2B, we tested a sample of German/
English bilingual speakers on the English item set.
As with Experiment 1B, this will allow us to verify
the weightings in a different sample and explore
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potential differences between mono- and bilingual
participants.
In Experiment 1, we argued that the differences
that we found between the two samples are more
consistent with an account based on reading
proficiency rather than one based on the influence
of acquiring a language with a deeper ortho-
graphy. However, it may be that an early acquired
L1 shapes the cognitive system in a way that biases
the processing of subsequently learnt languages
towards familiar types of correspondences. If so,
this would predict a difference between partici-
pants reading English non-words depending on
whether their first language was English (as in
Experiment 2A) or German.
Methods
The participants were 13 native German speakers
living in Australia (undergraduate and graduate
students at Macquarie University, academic staff,
family and friends). Eight of them had also
participated in Experiment 1A several months
earlier, but did not know that the two studies
were related. In this sample, all participants had
lived in Germany for at least 18 years before
moving to an English-speaking country. The items
and procedure were identical to Experiment 2A.
The participants were told that they would see
English non-words and were asked to pronounce
each item as if it were an English word that they
are unfamiliar with.
Results
The same scoring system was used as for Experi-
ment 2A. The proportions of /æ/, /ɔ/ and /o:/
responses for both Experiments 2A and B are
presented in Table 4. German native speakers
overall gave more “other”non-word responses or
vowel responses that were inconsistent with our
predictors, compared to the English monolinguals
in Experiment 2A: 15.74%, 23.61%, 17.95% and
8.80% for the CS+BR+, CS+BR–, CS–BR+ and
CS–BR–conditions, respectively.
We repeated the optimisation technique to
derive strategy weights for this Experiment.
Table 2 summarises the weights for each of the
three strategies in Experiments 1A and B and 2A
and B. The results of Experiment 2B mirror the
findings from Experiment 2A: Again, we find
strongest reliance on CSCs, robust reliance on
BRCs, and negligible reliance on context-insensitive
correspondences. Numerically, the reliance on
CSCs appears to be larger (^
bcsc ¼0:61) than in the
monolingual sample (^
bcsc ¼0:69). Here again, the
optimal parameters outperform the alternatives
with a correlation of .717 (see Table 3).
Comparing bilingual to monolingual English
readers. Using the same bootstrapping technique
described in Experiment 1, we confirmed that the
German-English bilingual participants relied more
on BRCs (BRCs) than did the English monolin-
guals. In 9998 (99.98%) of the samples, ^
bbrc was
larger for bilinguals than monolinguals (95% CI of
the difference: 0.046–0.150). The two samples did
not differ significantly in their reliance on context-
insensitive (GPC) rules, but there is some evid-
ence that the monolinguals may rely more on
CSCs (91.72% of the samples, 95% CI: –0.039
to 0.160).
Discussion
In Experiment 2B, we collected data on English
non-word pronunciation from German/English
bilingual participants, which we then compared to
the “a”-pronunciations of English monolinguals in
Experiment 2A. Again, we find that the fits of the
model are somewhat discrepant with the data,
suggesting that the pronunciation of the letter “a”
depends also on sources of information that are
not included in our model. As in Experiment 2A,
we found no reliance on context-insensitive GPCs
in either group, and only a non-significant trend
towards larger reliance on BRCs or the “a[l]”
→/o:/ correspondence in English monolinguals
than the German/English bilinguals.
We found broadly the same pattern among two
different groups of participants; here, we once
again demonstrate the reliability of the optimisa-
tion procedure. The significant difference in the
reliance on BRCs suggest that German native
speakers, when they are highly proficient in
English, rely more on these large units than
English monolingual participants. Thus, the native
orthography does not appear to leave noticeable
footprints in the cognitive processes underlying
reading in a second language, as in that case we
would expect diminished reliance on BRC in
German compared to English native speakers.
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GENERAL DISCUSSION
In four experiments, we explored the reliance on
three different sublexical correspondence types in
different populations. In Experiments 1A and B,
we found that German native speakers relied on
all three strategies: the greatest weighting was
found for context-insensitive GPCs, followed by
context-sensitive GPCs (super-rules) and BRCs
when reading German-derived non-words. In
Experiments 2A and B, we applied the same
procedure to quantify the types of correspon-
dences that participants rely on to derive the
pronunciation of the grapheme “a”in English.
We found strong reliance on context-sensitive
GPCs, some reliance on BRCs and little evidence
that context-insensitive GPCs play a large role in
determining the pronunciation of the graph-
eme “a”.
Cross-linguistic differences in the
choice of sublexical correspondences:
comparing Experiments 1 and 2
Previous theoretical work predicts cross-linguistic
differences in the reliance on different units in
German and English (Ziegler & Goswami, 2005).
Unfortunately, with the experiments in the current
study it is impossible to make a direct quantitative
comparison across the two languages as we are
comparing two differently structured orthographic
correspondences. An alternative approach is to
conduct the analyses within the languages and
point out the differences between them on a
descriptive level.
Our data suggest that given a grapheme where
context is very important in English (i.e., “a”),
context-sensitivity becomes very important com-
pared to German, where context-insensitive corre-
spondences are the major predictor. This is true
even for a situation where there are statistical
regularities at the level of CSCs. This is broadly in
line with the psycholinguistic grain-size theory
(Ziegler & Goswami, 2005): as the context is often
an important predictor of the correct pronunci-
ation of English words, readers are forced to rely
on larger units. Our data emphasises the import-
ance of context-sensitive GPCs in an inconsistent
orthography such as English. In German, on the
other hand, context-insensitive correspondences
are mostly sufficient to derive the correct pronun-
ciation of an unfamiliar word; therefore, this level
of correspondences is preferred.
The reality of the cross-linguistic differences
becomes more evident in a comparison of Experi-
ments 1A and 2B. This is partly a within-subject
design and involves bilingual participants reading
both the English and the German item sets. The
differences between the weightings in these two
experiments were remarkable, with the pattern of
results being more similar to that of the mono-
linguals of the respective language. This shows
that the language is the determining factor for the
reliance on different unit sizes, rather than the
language background of the participants.
From this comparison, we conclude that the
language that a participant is asked to read in
matters more than the participant’s language
background: comparing the participants in Experi-
ments 1A and 2B shows that bilinguals rely on the
three types of correspondences almost to the same
extent as monolinguals do in their respective
language. Thus, we conclude that the cross-
linguistic differences in sublexical processing are
language-specific: acquiring a deep versus shallow
orthography from childhood does not shape the
cognitive system, but rather encourages the reader
to rely on certain types of correspondences above
others in that particular orthography. Those pre-
ferences do not seem directly transferable to a
later acquired orthography; instead, a reader
develops a sensitivity to the most advantageous
combination of strategies in the new language.
Models of reading
The current study shows that both in English and
in German, several correspondence types are used
in parallel. There are multiple verbal models that
postulate such a scenario (LaBerge & Samuels,
1974; Patterson & Morton, 1985; Taft, 1991,1994;
Ziegler & Goswami, 2005). The theoretical con-
tribution of the current paper is proposing a
method to quantify the degree to which these are
used, which can be used as a benchmark for
computational models.
An open question then is whether the current
computational models can simulate the obtained
results. The parallel processing of various correspon-
dences poses a computational problem: whenever
there are conflicts between the pronunciations pre-
dicted by various correspondences, the system needs
a way to resolve these. In English, this is important
because there are often cases where different
sublexical correspondences provide conflicting
information.
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In Table 5, we provide the percentages of
regular responses from two models which have
been implemented both in English and in German,
namely the DRC (Coltheart et al., 2001; Ziegler
et al., 2000) and the connectionist dual process
(CDP+) model (Perry, Ziegler, Braun, & Zorzi,
2010; Perry, Ziegler, & Zorzi, 2007). For English,
there is a newer version of the CDP+, namely the
CDP++ (Perry, Ziegler, & Zorzi, 2010), which
differs from the CDP+ in several points: it has
been trained on a larger word set, contains some
parameter changes and can also deal with polysyl-
labic words. We provide the simulation data from
both versions of the model.
Both the CDP+/CDP++ and the DRC are dual
route models of reading, where non-words are
read purely via a sublexical procedure. Therefore,
the current data are relevant to both models, as it
concerns the nature of sublexical processing. The
distinguishing feature between the two models is
the way in which this procedure operates. The
DRC has a set of sublexical GPCs, which are
manually programmed into the sublexical route. A
GPC in the DRC is defined as the most frequent
phoneme that co-occurs with a given grapheme.
As described in the Introduction, the DRC con-
tains CSCs as well as single-letter and multi-letter
correspondences, but there is some ambiguity
when it comes to deciding which CSCs to include
in the model. The current version of the English
DRC does not contain either a “[w]a”or an “a[l]”
correspondence; therefore, it provides the
response /æ/ to all items (see Table 5). For the
second DRC simulation, we added some more
CSCs; however, this does not seem to reflect the
overall responses given by participants, either, as it
now underestimates the number of regular (i.e.,
/æ/) pronunciations given by the participants. For
the German DRC, the GPCs that are used to
determine vowel length are the super-rules (Zieg-
ler et al., 2000). It is clear, both from the present
study (see Table 5) and from Perry, Ziegler,
Braun, and Zorzi (2010) that the super-rules are
not sufficient to explain German non-word
pronunciations.
The CDP+/CDP++, like the DRC, is grapheme-
based, but it develops context-sensitivity because
the GPCs are derived via a learning algorithm,
which uses real word knowledge to obtain the
most likely correspondences between print and
speech (Zorzi, 2010). Yet, the CDP+ does not
provide an optimal fit for either the German or
the English data, as it often underestimates the
number of regular pronunciations (see Table 5). In
particular, the English CDP+ and CDP++ seem to
take CSCs into account more than the participants
do, as they underestimates the number of /æ/
responses for the CS–conditions. In German, the
biggest discrepancy between the CDP+ prediction
and the behavioural data is in the BR–conditions,
suggesting that CDP+ does not develop the same
degree of reliance on BRCs that participants do.
As neither of the computational models is
compatible with the behavioural results, these
data cannot be used to adjudicate between the
DRC and CDP+ approach. (Note that this was not
the aim of the study to begin with.) We therefore
turn to verbal models to provide a theoretical
framework that can explain our obtained results.
One such model which provides a means for the
cognitive system to resolve conflicts between
different sublexical correspondences has been
proposed by Taft (1991,1994). This interactive
activation model states that activation passes
hierarchically from the smallest units, through
subsyllabic and syllabic units and morphemes to
whole words, which then gives access to the
semantic concept. There are additional feedback
connections, which send activation from larger to
smaller units.
Taft’s(1994) model also makes some explicit
statements about cross-linguistic differences: the
salient sublexical correspondences differ depend-
ing on the orthographic and phonological proper-
ties of the language. For example, whereas English
readers parse words into orthographic-syllabic
units called BOSSes (Taft, 1979,1992), French
readers rely more on the phonological syllable
(Taft & Radeau, 1995). In our experiments, we
TABLE 5
Percentages of “Regular”responses (/æ/ in English, short
vowels in German) given by the DRC and CDP+/CDP++
Model
CS+
BR+
CS−
BR+
CS+
BR−
CS−
BR−
English
Behavioural Data
100 81 51 18
English DRC
Simulation 1
100 100 100 100
English DRC
Simulation 2
100 67 11 0
English CDP+ 100 35 57 0
English CDP++ 100 43 44 0
German
Behavioural Data
86 73 63 37
German DRC 100 0 100 0
German CDP+ 93 94 8 24
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found reliance on similar types of correspondences
in English and German. Thus, the correspon-
dences that have psychological reality in English
and German appear to be very similar. It is
noteworthy that English and German are very
similar in terms of their phonological and ortho-
graphic structure; therefore, we expect that the
salient sublexical correspondences do not differ
greatly. The situation might be different in other
languages. For example, when there is a tendency
for words to be polysyllabic and to contain fewer
consonant clusters, as is the case in languages like
Italian, Spanish or Russian, BRCs are unlikely to
play a large role in reading (Duncan et al., 2013;
Kerek & Niemi, 2012).
Limitations and future directions
The goal of the study was to identify an optimal
combination of different sources of information in
deciding which vowel pronunciation is most appro-
priate when there are two or more alternatives. A
limitation of the model is that it makes no claims
about the decision-making mechanisms that
resolve the ambiguity, only that some sources of
information are more influential than others. It
may be that on each trial, the decision is based on
a“winning strategy”in which case the weights
represent the likelihood of a particular strategy
winning. Alternately, it may be that all three
sources of information are combined in a Bayesian
sense of “what response is most likely correct
given the mix of influences”. In this case, the
model weights should be interpreted as the degree
of influence that each strategy has on the decision
process. The present study is not able to adjudic-
ate between these alternatives (or any others that
we may not have considered), so we refrain from
making strong statements favouring one or the
other. The extent to which non-word pronuncia-
tions remain stable in different situations, the
factors that influence any variability and the
mechanisms that resolve ambiguity remain ques-
tions for future research. We do note, however,
that as there is considerably variability between
subjects in terms of their strategy weights (see
Figure 1), there is some recent evidence that
readers can be grouped according to their choices
(Robidoux & Pritchard, 2014), so there may be
more structure hiding within this variability.
A limitation of the paradigm as described in
this paper is that it is better suited for across-
subject comparisons than across-item comparisons,
due to the small number of available items. This is
a general problem with this approach: There are
not many items where CSCs and BRCs can be
dissociated, as these are intrinsically correlated.
Although it would be interesting to use the same
paradigm for a different set of non-word or word
items to explore systematic changes in the weight-
ings associated with item characteristics such as
frequency (for words) or word-likeness (as meas-
ured, e.g., by orthographic N), the small number of
possible items prevents us from doing this in a
meaningful way.
Arguably, the data reported in this paper are
also limited by our focus on the grapheme “a”
only. As this criticism applies to the English data,
the German data can be generalised to predicting
vowel length across different graphemes. The
English results and our conclusions based on these
analyses are therefore weaker than those from the
German analyses. Nevertheless, understanding the
principles underlying reading in languages other
than English is essential for the long-term goal of
describing all differences and similarities between
reading in different languages, and thereby creat-
ing a universal model of reading (Frost et al.,
2012). This is especially important given the focus
of previous literature on English. English is
considered to be an “outlier”orthography; there-
fore, it is questionable to use it as a base for most
models of skilled reading, reading development
and dyslexia (Share, 2008). Although we acknow-
ledge that, in the current context, the optimisation
procedure works better for German than English,
we argue that the English data provides a strong
demonstration of the parallel use of different types
of sublexical grain sizes, and in particular CSCs in
English, new insights into cross-linguistic differ-
ences associated with the reliability of print-to-
speech correspondences and a new benchmark for
computational models of reading aloud.
We believe that this approach also has some
utility when applied to other areas of psycholin-
guistics. In future research, the same paradigm can
be used to systematically explore the sources of
individual differences that we report in the current
study. The paradigm can also be used with
children: previous literature has debated for dec-
ades whether children start learning to read using
large or small units first (Goswami, 2002; Gos-
wami & Bryant, 1990; Hulme et al., 2002). Such
explorations in group and individual differences
are of theoretical and practical value. Future
research can also apply the same mathematical
procedure to any situation in which items can be
18 SCHMALZ ET AL.
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created where different strategies yield different
predictions. Other areas in psycholinguistics to
which this paradigm can be extended could be
topics such as stress assignment for polysyllabic
words, because it has been shown that, in several
languages, different cues are used by participants
to determine the stress of a given non-word
(Arciuli, Monaghan, & Seva, 2010; Burani &
Arduino, 2004; Protopapas, Gerakaki, & Alexan-
dri, 2006;Ševa, Monaghan, & Arciuli, 2009).
Conclusions
The current study contributes to the literature on
cognitive processes underlying reading in several
aspects. We show that context-insensitive GPCs,
super-rules and BRCs are necessary and sufficient
to explain the vowel length pronunciations in
German; in English, context-insensitive GPCs
play a smaller or negligible role in assigning the
pronunciation of the grapheme “a”. We introduce
a method to quantify the degree of reliance on
each of the three different sublexical correspond-
ence types using statistical modelling. This tech-
nique can be used to test other hypotheses by
future studies.
Original manuscript received February 2014
Revised manuscript received August 2014
Revised manuscript accepted September 2014
First published online October 2014
REFERENCES
Andrews, S. (1982). Phonological recoding: Is the
regularity effect consistent? Memory & Cognition,
10, 565–575. doi:10.3758/BF03202439
Andrews, S., & Scarratt, D. R. (1998). Rule and analogy
mechanisms in reading nonwords: Hough dou peapel
rede gnew wirds? Journal of Experimental Psycho-
logy: Human Perception and Performance,24, 1052–
1086. doi:10.1037/0096-1523.24.4.1052
Arciuli, J., Monaghan, P., & Seva, N. (2010). Learning
to assign lexical stress during reading aloud: Corpus,
behavioral, and computational investigations. Journal
of Memory and Language,63, 180–196. doi:10.1016/j.
jml.2010.03.005
Brown, G. D., & Deavers, R. P. (1999). Units of analysis
in nonword reading: Evidence from children and
adults. Journal of Experimental Child Psychology,73,
208–242. doi:10.1006/jecp.1999.2502
Burani, C., & Arduino, L. S. (2004). Stress regularity or
consistency? Reading aloud Italian polysyllables with
different stress patterns. Brain and Language,90,
318–325. doi:10.1016/S0093-934X(03)00444-9
Byrd, R. H., Lu, P., Nocedal, J., & Zhu, C. (1995). A
limited memory algorithm for bound constrained
optimization. SIAM Journal on Scientific Computing,
16, 1190–1208. doi:10.1137/0916069
Campbell, R., & Besner, D. (1981). This and THAP –
Constraints on the pronunciation of new, written
words. The Quarterly Journal of Experimental
Psychology,33, 375–396. doi:10.1080/146407481084
00799
Cassidy, S., & Harrington, J. (2001). Multi-level annota-
tion in the Emu speech database management
system. Speech Communication,33(1), 61–77.
doi:10.1016/S0167-6393(00)00069-8
Coltheart, M., Rastle, K., Perry, C., Langdon, R., &
Ziegler, J. (2001). DRC: A dual route cascaded
model of visual word recognition and reading aloud.
Psychological Review,108, 204–256. doi:10.1037/
0033-295X.108.1.204
Cortese, M. J., & Simpson, G. B. (2000). Regularity
effects in word naming: What are they? Memory &
Cognition,28, 1269–1276. doi:10.3758/BF03211827
Cox, F., & Palethorpe, S. (2007). Australian English.
Journal of the International Phonetic Association,37,
341–350. doi:10.1017/S0025100307003192
Duncan, L. G., Castro, S. L., Defior, S., Seymour, P. H.,
Baillie, S., Leybaert, J., …Francisca Serrano. (2013).
Phonological development in relation to native lan-
guage and literacy: Variations on a theme in six
alphabetic orthographies. Cognition,127, 398–419.
doi:10.1016/j.cognition.2013.02.009
Forster, K. I., & Forster, J. C. (2003). DMDX: A
Windows display program with millisecond accuracy.
Behavior Research Methods,35(1), 116–124.
doi:10.3758/BF03195503
Frost, R., Behme, C., Beveridge, M. E., Bak, T. H.,
Bowers, J. S., Coltheart, M. (2012). Towards a univer-
sal model of reading. Behavioral and Brain Sciences,
35, 263–279. doi:10.1017/S0140525X11001841
Glushko, R. J. (1979). The organization and activation of
orthographic knowledge in reading aloud. Journal of
Experimental Psychology: Human Perception and
Performance,5, 674–691. doi:10.1037/0096-1523.5.
4.674
Goswami, U. (2002). In the beginning was the rhyme? A
reflection on Hulme, Hatcher, Nation, Brown,
Adams, and Stuart (2002). Journal of Experimental
Child Psychology,82(1), 47–57. doi:10.1006/jecp.
2002.2673
Goswami, U., & Bryant, P. (1990). Phonological skills
and learning to read. London: Wiley Online Library.
Goswami, U., Gombert, J. E., & De Barrera, L. F.
(1998). Children’s orthographic representations and
linguistic transparency: Nonsense word reading in
English, French, and Spanish. Applied Psycholin-
guistics,19, 19–52. doi:10.1017/S0142716400010560
Goswami, U., Porpodas, C., & Wheelwright, S. (1997).
Children’s orthographic representations in English
and Greek. European Journal of Psychology of
Education,12, 273–292. doi:10.1007/BF03172876
Goswami, U., Ziegler, J. C., Dalton, L., & Schneider, W.
(2003). Nonword reading across orthographies: How
flexible is the choice of reading units? Applied
SUBLEXICAL CORRESPONDENCES 19
Downloaded by [Macquarie University] at 19:59 28 October 2014

Psycholinguistics,24, 235–247. doi:10.1017/S014271
6403000134
Grömping, U. (2010). Inference with linear equality and
inequality constraints using R: The package ic.infer.
Journal of Statistical Software,33,1–33.
Hulme, C., Hatcher, P. J., Nation, K., Brown, A.,
Adams, J., & Stuart, G. (2002). Phoneme awareness
is a better predictor of early reading skill than onset-
rime awareness. Journal of Experimental Child Psy-
chology,82(1), 2–28. doi:10.1006/jecp.2002.2670
Jared, D. (2002). Spelling-sound consistency and regu-
larity effects in word naming. Journal of Memory and
Language,46, 723–750. doi:10.1006/jmla.2001.2827
Kerek, E., & Niemi, P. (2012). Grain-size units of
phonological awareness among Russian first graders.
Written Language & Literacy,15(1), 80–113.
doi:10.1075/wll.15.1.05ker
LaBerge, D., & Samuels, S. J. (1974). Toward a theory
of automatic information processing in reading.
Cognitive Psychology,6, 293–323. doi:10.1016/0010-
0285(74)90015-2
Monfort, A. (1995). Statistics and econometric models
(Vol. 2). Cambridge: Cambridge University Press.
Patterson, K., & Behrmann, M. (1997). Frequency and
consistency effects in a pure surface dyslexic patient.
Journal of Experimental Psychology: Human Percep-
tion and Performance,23, 1217–1231. doi:10.1037/
0096-1523.23.4.1217
Patterson, K., & Morton, J. (1985). From orthography to
phonology: A new attempt at an old interpretation.
In K. Patterson, J. Morton, & M. Coltheart (Eds.),
Surface dyslexia (pp. 1217–1231). Hillsdale, NJ:
Erlbaum.
Perry, C., Ziegler, J. C., Braun, M., & Zorzi, M. (2010).
Rules versus statistics in reading aloud: New evid-
ence on an old debate. European Journal of Cognit-
ive Psychology,22, 798–812. doi:10.1080/0954144090
2978365
Perry, C., Ziegler, J. C., & Zorzi, M. (2007). Nested
incremental modeling in the development of compu-
tational theories: The CDP+ model of reading aloud.
Psychological Review,114, 273–315. doi:10.1037/
0033-295X.114.2.273
Perry, C., Ziegler, J. C., & Zorzi, M. (2010). Beyond
single syllables: Large-scale modeling of reading
aloud with the connectionist dual process (CDP++)
model. Cognitive Psychology,61, 106–151. doi:10.10
16/j.cogpsych.2010.04.001
Plaut, D. C., McClelland, J. L., Seidenberg, M. S., &
Patterson, K. (1996). Understanding normal and
impaired word reading: Computational principles in
quasi-regular domains. Psychological Review,103(1),
56–115. doi:10.1037/0033-295X.103.1.56
Pritchard, S. C., Coltheart, M., Palethorpe, S., & Castles,
A. (2012). Nonword reading: Comparing dual-route
cascaded and connectionist dual-process models with
human data. Journal of Experimental Psychology:
Human Perception and Performance,38, 1268–1288.
doi:10.1037/a0026703
Protopapas, A., Gerakaki, S., & Alexandri, S. (2006).
Lexical and default stress assignment in reading
Greek. Journal of Research in Reading,29, 418–432.
doi:10.1111/j.1467-9817.2006.00316.x
R Core Team. (2013). R: A language and environment
for statistical computing [Computer software man-
ual]. Vienna, Austria. Retrieved from http://www.
R-project.org/
Robidoux, S., & Pritchard, S. C. (2014). Hierarchical
clustering analysis of reading aloud data: A new
technique for evaluating the performance of compu-
tational models. Frontiers in Psychology,5, 267.
doi:10.3389/fpsyg.2014.00267
Seidenberg, M. S., & McClelland, J. L. (1989). A
distributed, developmental model of word recogni-
tion and naming. Psychological Review,96, 523–568.
doi:10.1037/0033-295X.96.4.523
Ševa, N., Monaghan, P., & Arciuli, J. (2009). Stressing
what is important: Orthographic cues and lexical
stress assignment. Journal of Neurolinguistics,22,
237–249.
Share, D. L. (2008). On the anglocentricities of current
reading research and practice: the perils of overreli-
ance on an “outlier”orthography. Psychological Bul-
letin,134, 584–615. doi:10.1037/0033-2909.134.4.584
Taft, M. (1979). Lexical access-via an orthographic code:
The basic orthographic syllabic structure (BOSS).
Journal of Verbal Learning and Verbal Behavior,
18(1), 21–39. doi:10.1016/S0022-5371(79)90544-9
Taft, M. (1991). Reading and the mental lexicon. Hills-
dale, NJ: Psychology Press.
Taft, M. (1992). The body of the BOSS: Subsyllabic
units in the lexical processing of polysyllabic words.
Journal of Experimental Psychology: Human Percep-
tion and Performance,18, 1004–1014. doi:10.1037/
0096-1523.18.4.1004
Taft, M. (1994). Interactive-activation as a framework for
understanding morphological processing. Language
and Cognitive Processes,9, 271–294. doi:10.1080/
01690969408402120
Taft, M., & Radeau, M. (1995). The influence of the
phonological characteristics of a language on the
functional units of reading: A study in French.
Canadian Journal of Experimental Psychology/Revue
canadienne de psychologie expérimentale,49, 330.
Treiman, R., Kessler, B., & Bick, S. (2003). Influence of
consonantal context on the pronunciation of vowels:
A comparison of human readers and computational
models. Cognition,88(1), 49–78. doi:10.1016/S0010-
0277(03)00003-9
Treiman, R., Kessler, B., Zevin, J. D., Bick, S., & Davis,
M. (2006). Influence of consonantal context on the
reading of vowels: Evidence from children. Journal
of Experimental Child Psychology,93(1), 1–24.
doi:10.1016/j.jecp.2005.06.008
Treiman, R., Mullennix, J., Bijeljac-Babic, R., & Rich-
mond-Welty, E. D. (1995). The special role of rimes in
the description, use, and acquisition of English ortho-
graphy. Journal of Experimental Psychology: General,
124, 107–136. doi:10.1037/0096-3445.124.2.107
Venezky, R. L. (1970). The structure of English ortho-
graphy (Vol. 82). The Hague: Mouton.
Ziegler, J. C., & Goswami, U. (2005). Reading acquisi-
tion, developmental dyslexia, and skilled reading
across languages: A psycholinguistic grain size theory.
Psychological Bulletin,131(1), 3–29. doi:10.1037/
0033-2909.131.1.3
20 SCHMALZ ET AL.
Downloaded by [Macquarie University] at 19:59 28 October 2014

Ziegler, J. C., Perry, C., & Coltheart, M. (2000). The
DRC model of visual word recognition and reading
aloud: An extension to German. European Journal of
Cognitive Psychology,12, 413–430. doi:10.1080/
09541440050114570
Ziegler, J. C., Perry, C., Jacobs, A. M., & Braun, M.
(2001). Identical words are read differently in differ-
ent languages. Psychological Science,12, 379–384.
doi:10.1111/1467-9280.00370
Ziegler, J. C., Perry, C., Ma-Wyatt, A., Ladner, D., &
Schulte-Körne, G. (2003). Developmental dyslexia in
different languages: Language-specific or universal?
Journal of Experimental Child Psychology,86, 169–
193. doi:10.1016/S0022-0965(03)00139-5
Ziegler, J. C., Stone, G. O., & Jacobs, A. M. (1997).
What is the pronunciation for -ough and the spelling
for/u/? a database for computing feedforward and
feedback consistency in English. Behavior Research
Methods,29, 600–618. doi:10.3758/BF03210615
Zorzi, M. (2010). The connectionist dual process (CDP)
approach to modelling reading aloud. European
Journal of Cognitive Psychology,22, 836–860.
doi:10.1080/09541440903435621
APPENDIX A: GERMAN AND ENGLISH
NON-WORDS USED IN
EXPERIMENTS 1 AND 2
German
V[C] Reg.
blaf blen (blem in Exp. 1B) blod breg brel brul flom flüb
fryp grät grem grom grul klid klur knul krel kril krön
pflyp pid plät plön prod schmün schraf schwüb speg
zwül zwun
V[C][C] Reg.
bamt birt blaft bling boft brals chrolf falb flarg flerk
gärm ginn gralb gunt kall kaxt kerv kluns knell pals peld
pfern pulk purf schern spalf stelf sturg zeng zwurt
V[C] Irreg.
bax blex blig bres flim flis git glef glip krex krin krip pfis
spic stef zwix zwok
V[C][C] Irreg.
bags blags füst gleks kagd kagt kets pagt pard peks poks
schagd stard
English
CS+BR+.
hangst kazz mact phadge phamb phangst phants plact
sangst slangs slazz stract stramb tamb tazz tradge trazz
zants
CS+BR–.
clatt hald halse kalk kalse kalt phalk phaltz slaltz strald
stralk stralse straltz tald taltz tralse tralt tratt
CS-BR+.
quadge quamb quangst quapse quazz squact squazz
swact swangst swants swazz twadge twangst twants
twazz wact wamb wangst
CS-BR–.
qualk qualse qualtz squald squalk squalse squaltz swalk
swaltz twald twalk twalse twalt twaltz wald walse walt
whald
APPENDIX B: IMPLEMENTING THE
FITTING PROCESS IN R
While fitting the models described in the text has a
certain flavour of regression to it, there are some
important differences. Most critically are the two
constraints that we have placed on the parameters: β
j
∊
[0,1] and Rbj¼1. Considerable work has been done to
develop and implement estimation methods for models
with inequality constraints such as β
j
∊[0,1] (Grömping,
2010). However, we know of no such work that has
solved the problems presented by the Rbj¼1. To
address this problem, we turned to the optim function
that is part of the base statistical analysis package in R
(R Core Team, 2013). optim is a very general
optimisation package that allows the user to minimise
any specified function, while also placing bounds on the
returned values. That is, we can define a function, place
upper and lower bounds on the returned weights and
optim will efficiently search the allowed parameter
space to minimise our function. To satisfy (2), we
defined the minimising function to be the residual sum
of squares, and restricted the βweights to fall between 0
and 1. This ensures that ^
bj2½0;1"is satisfied.
In all of the optimisation analyses, we used the following
command in R:
optim (par=runif(3, .2, .8), fn=…,…,
method='L-BFGS-B’, control=list(factr=1e5),
lower=0, upper=1). The parameters for optim operate
as follows: “par=runif(3, .2, .8)”initialises the β
I
s
to random values between .2 and .8. “fn=…,…” specifies
the function to be minimised along with any parameters it
requires. In our case we used a simple function that cal‐
culates the residual sum of squares. “method='L-BFGS-
B’” instructs optim to use an optimisation algorithm that
allows for upper and lower bounds on the returned values
(Byrd, Lu, Nocedal, & Zhu, 1995). “factr=1e5”sets the
convergence tolerance, and “lower=0, upper=1”set the
bounds on the returned values.
∑bj¼1Constraint. There is no way to explicitly tell
optim to meet the constraint that the βs must sum to 1
(∑β
j
= 1). One way to ensure that the constraint is met
is to simply scale the weights returned by optim using
the formula:
bj0¼bj=Rbj
where bj0are the new scaled weights, and are guaran‐
teed to sum to 1. However, since this adjustment
follows the optimisation process, there is little reason
to believe that the resulting bj0s would remain an
optimal solution to (2). An alternative to simply scaling
the β
j
s is to make use of the influence of outliers on
parameter estimation. For example, according to (2)
optim is trying to satisfy the following 180 equations
(two per item) simultaneously, by minimising the
residual sum of squares (while also meeting the β
j
∊
[0,1] constraint):
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The introduction of a new data point that can only be
met by satisfying the constraint that the will put some
pressure on optim to select appropriate parameters.
For example,
1¼bgpc '1þbcsc '1þbbrc '1ð7Þ
Equation (7) is equivalent to creating an artificial data
point where all of the dependent and independent
variables [P(Short), GPC, CSC, and BRC] are set to
1. Though (7) provides some pressure to satisfy
R^
bj¼1, it is unlikely to have a very large influence
since it is only a single equation with roughly equal
weight to the other 180. However, dramatically
increasing the weight of this data point will exert a
much stronger influence on the final parameter
selection. For example
10;000 ¼bgpc '10;000 þbcsc '10;000
þbbrc '10;000 ð8Þ
Equation 8 would put enormous pressure on optim
to arrive at a set of weights that satisfy R^
bj¼1
without putting any further constraints on how the
weights are apportioned to the strategies. Though
Equation (8) does not guarantee R^
bj¼1precisely, it
is sufficiently strong for the present purposes. Other
applications may require a larger multiplier.
Finally, because the number of items is not equal across
all conditions in our studies, the sums of squares were
weighted by item to ensure each condition contributed
equally. For example in Experiment 1, items in the V[C]
Irregular and V[C][C] Irregular conditions received
relatively more weight than items in the V[C] Regular
and V[C][C] Regular conditions. If this isn't done, there
is a tendency for the Regular items to have a stronger
influence on the eventual parameters. The weights
applied to each item were determined as follows:
xtype ¼:25
ntype
where type is one of the four item types (e.g., V[C][C]
Irregular in Experiment 1), xtype is the weight assigned
to items of that type, and n
type
is the total number of
items of that type. As this formula implies, each item
contributes equally to the influence of its category, but
items in smaller categories have more influence than
items in larger categories. These weights are then used
in the usual weighted sum of squares formula that optim
is trying to minimise:
SSresid ¼X
i
^
Yi)"
Yi
!"
2xtypei:
P1ðShortÞ¼bgpc 'GPCshort;1þbcsc 'CSCshort;1þbbrc 'BRCshort;1
P1ðLongÞ¼bgpc 'GPClong;1þbcsc 'CSClong;1þbbrc 'BRClong;1
...
P90ðShortÞ¼bgpc 'GPCshort;90 þbcsc 'CSCshort;90 þbbrc 'BRCshort;90
P90ðLongÞ¼bgpc 'GPClong;90 þbcsc 'CSClong;90 þbbrc 'BRClong;90
ð6Þ
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