Spanish stress assignment within Analogical Modeling of Language⁽¹⁾

Published in Language 2000, 76.92-109

David Eddington

Brigham Young University
Department of Linguistics and English Language
2129 JKHB
Provo, Utah
(801) 422-7452

Abstract

The advent of nonlinear phonology has resulted in an explosion of studies relating to Spanish syllable structure and stress placement. However, most of these studies claim to represent linguistic competence and language structure, not actual mechanisms which are used by speakers in speech production and comprehension.

The present study is couched within Skousen's Analogical Modeling of Language (AML)(1989, 1992, 1995). AML is a model that attempts to reflect how speakers determine linguistic behaviors such as stress placement. According to AML, when an unfamiliar word needs to be stressed, speakers access their mental lexicon and search for words that are similar to the word in question. They then apply the stress of the word(s) found to the word in question.

The 4970 most common Spanish words served as the database for the study. AML correctly assigned stress to about 94% of these words. In addition, the errors it made closely reflect the pattern of errors made by Spanish speaking children in a study by Hochberg (1988). Moreover, Aske's nonce word probe (1990) showed that native speakers are sensitive to a certain subpattern in Spanish stress assignment--a subpattern which does not receive representation in rule-models. Nevertheless, the analogical model of Spanish stress mirrors Aske's findings.

0. Introduction. Within the generative tradition, studies on Spanish stress assignment have been numerous, especially since the advent of nonlinear and autosegmental phonology (e.g. Den Os and Kager 1986; Harris 1983, 1989, 1995; Hooper and Terrell 1976; Lipski 1997; Roca 1988, 1990, 1991, 1997; Saltarelli 1997; Whitley 1976). The goal of these studies is to provide a concise representation of the linguistic structures involved in Spanish stress placement. Studies such as these usually claim to be relevant to competence--the tacit knowledge that speakers have that allows them to communicate. In this regard, Kiparsky (1975:198) states:

In phonology, the system of rules and underlying forms might be a representation of the speaker's knowledge of the systematic relationships among words in the language; not in any sense a mechanism which is applied whenever words are spoken and heard. (see also Chomsky and Halle 1968:117; Bradley 1980:38)

In other words, the formalisms, rules and derivations of phonological analyses are not usually thought to mirror psychological mechanisms.

Spanish stress is characterized by commonly occurring patterns that are considered regular, along with numerous exceptions to these patterns. Several proposals on how to account for the generalizations and exceptions have been put forth, and as Farrell (1990:37) notes, studies on the structure of Spanish stress assignment have basically taken one of two approaches:

. . . the generative approach can be summarized as follows. Either certain patterns are generated or they are not. If the basic parameters are set in too restrictive a manner, a variety of ad hoc mechanisms must be provided to allow for marginal patterns. If the basic parameters are set in such a way as to allow too much freedom, a variety of mechanisms must be provided to restrict the generation of marginal patterns.

If the formalisms of these analyses do not relate to psychological mechanisms, then the debate about which analysis is most correct is not germane to a psychological theory about how stress assignment may take place.

The present study differs quite significantly from previous analyses of linguistic competence as it relates to Spanish stress placement.⁽²⁾ It is couched within Skousen's Analogical Modeling of Language (AML)(1989, 1992, 1995). AML is a model that attempts reflect how speakers determine linguistic behaviors such as stress placement. It is not a complete model of language comprehension and production per se. Rather, it is a model of how memory tokens may be used to predict linguistic behavior. According to AML, when the need arises to stress an unknown word, speakers access their mental lexicon and search for words that are similar to the word in question. They then apply the stress of the word(s) found to the word in question. In this regard, AML has much in common with other exemplar-based models (Aha, Kibler and Albert 1991; Medin and Schaffer 1978; Riesbeck and Schank 1989; see Shanks 1995 for an overview of exemplar models; see Daelemans, Gillis, and Durieux 1994 for a comparison of AML and Aha et al.).

I will begin by outlining the basic tenets of Analogical Modeling of Language, and by presenting the facts about Spanish stress assignment. In the following section, I will describe the database and variables used in the study. In the final sections, I will show how analogy correctly assigns stress in about 94% of the instances, and how it is able to thresh out significant subpatterns in Spanish stress placement without resorting to rules or schemas.⁽³⁾ One of these subpatterns was shown to be significant for native speakers in a study by Aske (1990). However, it plays no part in any current rule-based accounts of Spanish stress. Nevertheless, it is successfully accounted for by analogy. Further evidence for analogy is found in a study of stress placement errors. A comparison of the errors made by the analogical model and those made by Spanish speaking children (Hochberg 1988) demonstrates that analogy produces outcomes consistent with actual language use.

1. Analogical Modeling of Language. Traditionally, analogy has been used to account for exceptional outcomes. When an outcome does not obey a general rule, a form that is semantically or phonetically similar to the exceptional one is sought, which is then said to influence the exceptional form in such a way that it does not develop according to the application of the general rules. What makes this sort of analogy suspicious is that it ultimately serves to patch up the inability of rules to derive all forms. In addition, no limits are set regarding what forms can serve as analogs, nor on how similar two forms must be in order for analogy to become a factor.

In contrast to the traditional notion of analogy, AML assumes that all regular as well as irregular forms may be attributed to the analogical influence of other forms. (The reader is referred to Skousen (1989, 1992) for specific details of the analogical model, and the algorithm it employs, which are beyond the scope of the present paper.) In AML, all forms are attributed to the same mechanism. For this reason it is reminiscent of connectionism. For example, neither model extracts an overall characterizations of the data in the form of rules or schemata.

There are, however, significant differences between AML and connectionist models (Chandler 1995; Skousen 1989, 1995). Connectionist networks predict only one outcome for a given context, while AML predicts the probability that one or more outcomes will be chosen. Connectionist networks require extensive training and feedback from a 'teacher,' while AML does not entail any sort of training or external teacher. In connectionism, information is stored as patterns of activation in a network of interconnected nodes; there is no representation of individual words. In AML, the information is contained in a database of exemplars representing the contents of the mental lexicon. This database may be added to at any time. In contrast, connectionist networks cannot readily accept new data without having to be completely retrained to include the new data.

In order to understand AML, it is useful to compare it to the more familiar rule model. Rule models derive surface forms from underlying forms by the application of rules. In AML, on the other hand, two things are needed: a database of fully specified words,⁽⁴⁾ and a mechanism for searching and comparing those words. The behavior of the words most similar to the word in question generally predicts the behavior, although the behavior of less similar words has a small chance of applying as well. The influence of groups of similar words which behave in the same manner is well-attested in the psycholinguistic literature(e.g. Stemberger and MacWhinney 1988), and AML provides a specific algorithm for measuring gang effects (Skousen 1989:67-71).

A concrete example should clarify the differences between AML and rule accounts. In Spanish, stem-final /k/ is retained before some suffixes beginning with front vowels, such as the diminutive: /pok+o/ + -ito > /pokito/ 'few, dim.' Other suffixes appear to cause /k/ to become a fricative: Costa Rica + ense > /kostarriense/ 'Costa Rican.' A rule-based approach can account for this by postulating a rule to the effect that k > / __ ] that applies in the strata in which -ense is affixed, but not in the strata in which -ito is affixed. In AML, in contrast, all affixed and unaffixed words are stored as wholes in a database corresponding to the mental lexicon. When the need arises to determine what the phonetic shape of word is, a search of the lexicon is conducted based on the attributes of the word in question (i.e. the given context). The basic algorithm is the following:

We first search for actual examples of that context and then move outward in contextual space looking for nearby examples. In working outward away from the given context we systematically eliminate variables, thus creating more general contexts called supracontexts. (Skousen 1995:217)

The probability that a word is chosen as an analog for the given context is dependent on three derived properties (Skousen 1995:217):

(1) proximity: the more similar the example is to the given context, the greater the chances of that example being selected as the analogical model;

(2) gang effect: if the example is surrounded by other examples having the same behavior, then the probability of selecting these similarly behaving examples is substantially increased;

(3) heterogeneity: an example cannot be selected as the analogical model if there are more similar examples, with different behavior, closer to the given context.

These derived properties are important since they constrain what examples can constitute analogs, as well as decide between competing analogs. These are precisely the factors that traditional appeals to analogy lack.

According to AML, all of the words contained in homogenous supracontexts constitute the analogical set. It is the words from this set that can serve as analogical models for a given context. The amount of influence that a word or gang of words will have on the given context is expressed in terms of the probability that the given context will adopt the behavior of one group or another. In the example given in section 1, retention of stem-final /k/ is one behavior, and its replacement by // is another.

The probability that a given context will be assigned the behavior of another word is based on the degree of similarity between the given context and the word. Each member of a group of words with similar characteristics may also affect the behavior of the given context.⁽⁵⁾ However, the members of the group affect the given context individually. No global representation of the group's collective behavior is extracted from the data, although behavior may result that appears rule- or schema-based.

Once the analogical set is determined, there are two ways in which its contents can influence the behavior of the given context (Skousen 1989:82). The first is that a word could be randomly selected from among those in the analogical set, and the behavior of that word applied to that of the given context. The other possibility would be to determine which behavior is most frequent among the words in the set, and assign that behavior to the given context. In dealing with probabilistic data, people appear to take advantage of either of these methods (Messick and Solley 1957). The latter method is assumed in the current study.

Returning to the example from Spanish, AML can predict that for any given context, /k/ will be retained before certain suffixes and replaced by // before others. This prediction is based on the simple fact that, in the words of the database, /k/ appears before some suffixes and // before others. Thus, the generalization that exists among the words of the database is applied to the given context. If we were interested in knowing what would happen to the /k/ of loco 'crazy' in its diminutive form, and the analog chosen from the set of homogenous supracontexts were poco, then the behavior of poco > po/k/ito would be extended analogically to produce lo/k/ito, instead of lo//ito from loco.

The proposal that stored exemplars of past experience determine language use may appear counterintuitive to many. Surely, a global characterization of linguistic data in the form of a rule, schema, or prototype would be more plausible given the constraints on memory. Nevertheless, there is evidence that behavior may be based on stored exemplars (Chandler 1995; Hintzman 1986, 1988; Hintzman and Ludlam 1980; Medin and Schaffer 1978; Nosofsky 1988). In addition, performing rapid searches of of memory for stored exemplars is not unfeasible. Robinson (1995) demonstrates how indexing in the form of database inversion may play a role in such searches.

Many current models of human cognition assume that the brain processes information in a massively parallel manner (Marslen-Wilson and Welsh 1978; Seidenberg and McClelland, 1989; Stemberger, 1985, 1994; see Kirchner 1999 for a discussion of how exemplars may figure into such models). A lexicon as envisioned by Bybee (1985, 1988), in which phonetically and semantically similar items are interconnected, would greatly enhance searching and processing speed. In an interactive activation model, upon hearing, seeing or saying the word fat, for example, hundreds of different words or parts of words are partially activated: words that begin with f, or that have three phonemes, or that are related to obesity, or that rhyme with fat etc. In other words, all of the attributes of a given context partially activate all the words in the lexicon that have an attribute in common. It is not necessary to individually inspect each and every word in the lexicon, only those that have been most highly activated as a result of their similarity to the given context. By means of such parallel processing and interactive activation, analogical sets could theoretically be constructed and evaluated at the speed required by comprehension and production.

Having discussed the theoretical aspects of AML, I will now focus on the issue of assigning Spanish stress placement within the framework of AML. I will begin with a description of Spanish stress placement.

2. Stress Placement in Spanish. Stress may fall on any of the last three syllables of a Spanish word. In general, penult stress on vowel-final words is the norm (e.g. tiéne 's/he has'), while consonant-final words with final stress are considered regular (e.g. mantél 'table cloth'). Antepenult stress is always regarded as irregular (e.g. crédulo 'gullible') since it runs counter to the first two more general tendencies. Preantepenult stress is rare, and only occurs when certain verbal forms are followed by two clitic pronouns (e.g. guardándoselos 'saving them for him/her').

The generalization that vowel final words are normally penult stressed, and consonant final words are normally final stressed is complicated somewhat when word final -s is considered. Hooper and Terrell (1976) observe that in nonverbal morphology, when -s functions as the plural marker, stress is normally penult not final. The same also holds true in verbal morphology when -s indicates second person singular.

The fact that penult stress is the norm in words ending in -s, is illustrated in Table 1. The data come from the 4829 most frequent polysyllabic words in the Alameda and Cuetos frequency dictionary (1995).

++Insert Table 1 here++

That penult stress is the norm for vowel final words is clearly demonstrated. However, consonant final words are almost as likely to be stressed on the penult as on the final syllable. That is, of course, until final -s words are removed, since they pattern more closely with vowel final words. In short, penult stress is viewed as the norm for words ending in -s or a vowel, while final stress is considered regular for words ending in all consonants except s.

It is important to note that Spanish stress is contrastive: sabána 'savannah,' sábana 'sheet.' This is especially evident in verbal forms: encontrára 's/he found, imp. subj.,' encontrará 's/he will find'; búsco 'I search,' buscó 's/he sought.' It is for this reason that many studies of Spanish stress consider the effects of morphology as well as those of phonology. Some even suggest that verbal and nonverbal stress assignment are governed by different rules (e.g. Roca 1988), while others strive to achieve a unified analysis (e.g. Harris 1989). I will return to this issue in section 4.

3.0. The Database.

3.1. Items Included in the Database. In order to test stress placement within AML, it was necessary to construct a database of Spanish words which would serve as the rough equivalent of a Spanish speaker's mental lexicon. Of course, whether or not regular polymorphemic words have individual representation in the mental lexicon is a hotly debated issue. Pinker and his colleagues have adduced some evidence that these words have no individual entry, but are derived online (Jaeger et al. 1996; Pinker 1991; Pinker and Prince 1994; Prasada and Pinker 1993). If this is the case, such words could not exert analogical influence as AML would require.

However, other evidence suggests that all, or at least the most frequent morphologically complex words are stored as wholes (Alegre and Gordon 1999; Baayen, Dijkstra, and Schreuder 1997; Butterworth 1983; Bybee 1995; Manelis and Tharp 1977; Sereno and Jongman 1997). Even Pinker and Prince have hedged their bets somewhat and acknowledged this possibility (1994:331). Furthermore, Chandler (1993), Chandler and Skousen (1997), and Seidenberg and Hoeffner (1998) have demonstrated that the data cited in support of Pinker's model of language may be reinterpreted to support a ruleless model as well. Perhaps the best way to reconcile the apparently conflicting evidence is to assume a lexicon in which at least the most frequently occurring morphologically complex words have individual representation, but are stored or organized in such a way that their morphological relationships are transparent (Bybee 1985, 1988; Feldman and Fowler 1987; Katz, Rexer, and Lukatela 1991). Of course, most of the evidence in favor of massive storage of morphologically complex words comes from languages with simple to moderately complex morphological systems. Future studies will need to focus on the role of storage in highly agglutinating languages such as Turkish.

Another issue which needs to be resolved is how large of a lexical database needs to be assumed in an analogical analysis. In part, the answer to this question depends on what the goal of the analysis is. If one's aim is to correctly predict the linguistic behavior of the largest number of instances, larger databases are more efficient. For example, the work by Gillis, Daelemans, Durieux, and van den Bosch (1992) on Dutch stress assignment indicates that more correct predictions are made as the size of the database increases. In addition, Baayen and his colleagues (Baayen, Lieber, and Schreuder 1997; Bertram, Baayen, and Schreuder, 1999, de Jong, Schreuder and Baayen 1999; Schreuder and Baayen 1997) found that one would have to consider a database large enough to include even the least frequently occurring words in order to account for subjective frequency ratings and reaction times to visually presented simplex words. On the other hand, extensive databases are not required in an analysis designed to model language usage. For instance, language acquisition phenomena, error prediction, and historical shifts may be modeled using databases consisting of only several hundred instances (Derwing and Skousen 1994, Skousen 1989)

In the present study, I opted for a medium-sized database, partially due to the processing restrictions of the computer program used⁽⁶⁾ which only allowed about 5000 instances. The 4970 most frequent words in the Alameda and Cuetos frequency dictionary (1995) were chosen as the database. This includes words with a frequency of 6.6 per million or more. The resulting database consisted of base forms, inflectional variants of base forms, and verb plus clitic pronoun combinations.

The most frequent words were chosen since experimentation has shown that high frequency words are accessed more rapidly than low frequency words (e.g. Allen, McNeal, and Kvak 1992; Scarborough, Cortese, and Scarborough 1977). In addition, high frequency items are less subject to error than low frequency items (e.g. MacKay 1982). This suggests that frequent forms are more readily available, and therefore, more likely to be selected as analogs.

3.2. Variables Included in the Database. The next issue that had to be dealt with was selecting which variables to use in order to encode each of the 4970 words. Skousen (1989) and Derwing and Skousen (1994) note that variable selection is one of the major challenges with AML. Nevertheless, Skousen suggests some guidelines (1989:51-53). Whenever possible, enough variables should be used so that each instance is distinct from every other. In addition, one should use the variables closest to variable whose behavior is being predicted. By encoding the phonemic content and syllable structure of the final three syllables these guidelines were largely followed. Since none of the entries contained preantepenult stress, it was not necessary to encode more than the final three syllables.

It is worth noting that the process of selecting variables in an AML analysis is not a matter of predetermining which variables are most important to the task at hand. In fact, it is desirable to include many variables which may seem irrelevant at the outset. For example, the most important variable in determining whether the indefinite article a or an will precede a given English noun or adjective is whether the word begins with a vowel or consonant. If this is the only variable in the analysis, the correct article will be always be chosen. However, if other seemingly irrelevant variables are included, such as the phonemic make up of the noun following the article, and the word preceding the article, AML begins to predict leakage toward a (Skousen 1989). That is, it correctly predicts that errors always involve the use of a in place of an (e.g. a apple), not vice-versa (e.g. an chair).

The need to include variables which may seem unimportant is further evidenced in Skousen's simulation with a group of Finnish past tense forms. For most of these verbs, the choice of the past tense morpheme appears to be dependent on what the final two phonemes of the stem are, or if the vowel of the verb stem is a. However, sorta- 'to oppress' appears to be an exceptional case. It does not become sorsi as a rule-based analysis would predict. Instead, it becomes sorti. Nevertheless, AML correctly predicts this outcome, but the prediction is made on the basis of the o in the stem which sorta- has in common with a group of other verbal stems, each of which has a past tense form ending in -ti. A stem-internal o may be an irrelevant variable for the majority of these verbs, but not for sorta-. This would not have become evident if only the variables which appeared most relevant were included in the analysis. This suggests that speakers do not make a global determination of which variables are relevant in advance, as rules imply. Instead, all variables take part in the analogical search, and the crucial variables can only be determined indirectly after the analogical set is constructed and inspected.

Returning to the issue of variable selection in Spanish, one could argue that the most relevant variable for stress assignment is a word's final phoneme, or whether the penult syllable is closed or open. Nevertheless, all of the phonemes in the final three syllables were included. Given the contrastive nature of stress, especially in verbal forms, it was also necessary to include some variables that could distinguish between phonemically equivalent forms. Therefore, variables indicating the person and the tense form of each verb were included. These also served to distinguish verbs from nonverbs. Unfortunately, the entries in the Alameda and Cuetos dictionary are not tagged for part of speech.⁽⁷⁾ As a result, I was obliged to assign the words verbal or nonverbal status by hand. In the majority of cases, the verbal status of the entries was readily apparent. In those few cases in which a word could be either a verb or a nonverb, (e.g. encuentro 'encounter,' or 'I find'), I assigned it what seemed to me to be the most common use of the word. For example, encuentro meaning 'I find' seemed to be the most common use of the word. In four cases, one meaning did not seem to be more common that another, and the assignment was made randomly.

Allowing category ambiguous words such as encuentro into the database could be viewed as problematic. It may be the case that neither encuentro as a verb, nor encuentro as a nonverb is frequent enough by itself (i.e. 6.6 words per million or above) to merit inclusion in the database. Yet, due to their combined frequency, such words are included either as a verb or a nonverb. In essence, this means is that the database may contain several items with a frequency below 6.6 words per million.

In one regard, the inclusion of a few lower frequency words in the database is not a critical problem. Since the database cannot contain all possible Spanish words, it was necessary to limit the size of this artificial mental lexicon in some principled way. This in no way implies that lower frequency items are irrelevant to the task at hand, only that frequency was chosen as the limiting factor. In reality, the only problem with including these category ambiguous words is their arbitrary assignment as either nonverbs or verbs. However, of the 13 variables used to encode encuentro as a verb and as a nonverb (see below), the nine variables that indicate the phonemic content of each syllable are identical in both forms. In other words, the word's phonological structure is frequent enough for inclusion, but not its verbal or nonverbal status.

In addition to the above mentioned variables, I also experimented with various combinations of other morphological variables. I was particularly interested in finding a way to allow vowel final preterit forms to be assigned final stress. The best results were obtained when verbal forms included three variables indicating the tense form of the verb, instead of one. This was done because repeating a variable more than once is the only way to weight one variable heavier than another. What this implies is that the tense form of the verb is considered three times more important that any single onset, nucleus or coda.

Of course, this sort of variable weighting is admittedly ad hoc, and somewhat unorthodox for an AML analysis. Nevertheless, it did produce the desired outcome. When each member of the database was removed one at a time, and AML's algorithm used to search for analogs from the remaining items in the database, the error rate to polysyllabic preterit forms was 32% (of 156) if the tense variable was included only once. It decreased to 15% when the variable was included three times. Including the variable more than three times did not result in any further decrease in the error rate. In essence, 27 fewer errors occur on preterit verbs with final stress when this variable is weighted, while none of the rest of the items in the database are affected. For this reason, these duplicate variables were allowed to remain in the analysis. The lector is invited to incorporate an additional 27 errors into the ensuing analysis if this weighting of variables is too ad hoc for his or her taste.

In sum, the encoding of each word consists of 13 variables:

++Insert Table 2 here++

4. Analogical consistency. As already noted, AML assumes that all known words are stored in the mental lexicon with their inherent stress. Therefore, if AML is asked to assign stress to a known word, the probability that the correct stress will be assigned is 100%. However, if the word is novel, or under conditions of imperfect memory, stress placement is determined on the basis of the neighbors of the word in question.

Analogical consistency involves the extent to which similarly behaving words have similar characteristics. For example, if most words that are finally stressed are also morphologically and phonemically similar, there is a high degree of analogical consistency. Where there is a high degree of consistency, the stress placement of a word can usually be determined on the basis of the stress placement of its neighbors, that is, on the basis of other items which share characteristics with the word in question. Therefore, in order to determine the analogical consistency of Spanish stress placement, a ten-fold cross-validation was performed. This consisted of dividing the database of 4970 words into ten sections of 497 words each. The members of each group were then treated as the test items, while the members of the remaining nine groups comprised the training set from which analogs were chosen.

Given the fact that the database contained several inflectional variants of many words, a possible confound exists. If the given context is the adjective rójas, its inflectional variants rójo, rója, and rójos will be included in the analogical set and influence it to receive penult stress. The idea behind determining the analogical consistency of the database is to see how analogy responds to an unknown word. If rójo, rója, and rójos are allowed to serve as possible analogs for rójas, the system is not actually treating it as a completely novel item. A simple way of controlling for the effect of items which share the same root was to alphabetize the database prior to partitioning it for the ten-fold study. In this way, inflectional variants were grouped together in the same test set, and were unable to serve as analogs for each other.

Once the database was partitioned, the stress placement of each word was determined according to AML's algorithm. Table 3 contains a sampling of outcomes computed by AML. The outcome for a given word is expressed as the probability that the word will be assigned stress on a certain syllable. As can be seen, débil 'weak' is incorrectly assigned final stress. The preterit verb preguntó 's/he asked' is correctly assigned final stress, but also shows the influence of having several neighbors with penult stress.

++Insert Table 3 here++

Under these conditions, the success rates on the 10 groups ranged from 92.2% to 96.8%. In total, 94.4% of the 4970 words tested were correctly stressed, indicating a very high degree of consistency. Penult stress was most consistent with 98.9% of penult stressed words correctly assigned stress. Word final stress followed closely at 93.6, while only 40.1% of antepenult stressed words were most heavily influenced by other words which also have antepenult stress.

Another possible objection to the study is that it considers only the highest frequency lexical items. In general, the majority of the irregularly behaving words in a language are also among the most frequent ones. In other words, there is less analogical consistency among high frequency items. As a result, they would arguably not be the optimal group to use to achieve the highest degree of accuracy in predicting stress assignment.

This becomes evident when the database is used to predict the stress of a group of low frequency items. 497 items with a frequency of one (0.2 per million) in the Alameda and Cuetos dictionary (1995) were tested against the ten training sets used in the initial ten-fold cross-validation study. The resulting success rates ranged from 91.1% to 92.6%, with an average of 91.8%. This falls slightly below the average found when testing the high frequency items alone (94.4%). The reduction in the number of items correctly stressed is probably due to the large number of irregular items in the high frequency training sets.

I concede that there are fewer irregularities among the less frequent lexical items, and that it is highly possible that the stress of a larger number of items could be correctly assigned given a training set of low frequency items, instead of high frequency items. Nevertheless, significant facts about language usage would be ignored if such a step were taken. High frequency

irregular items should be included since they play a role in linguistic cognition.

Consider the English past tense, the majority of whose irregular forms are high frequency. It may be the case that better predictions would be made regarding the phonological shape of the past tense form if only lower frequency items were analogized on. However, significant facts would be missed. For example, a common error among children is the use of brang instead of brought as the past tense of bring. This error comes about as a result of the influence of certain high frequency irregular forms such as sang. The historical move from stinged to stung is also due the analogical pressure of high frequency irregular verbs such as stunk. It is data such as these that lead me to conclude that restricting the database to the most highly frequent items is the most principled way to limit its size in order to carry out analogical simulations(see also section 3.1).

4.1 Verbal versus non-verbal stress placement. One reason for determining analogical consistency has to do with the idea that stress may be determined differently for verbs and nonverbs (e.g. Roca 1988). Of course, this opinion is not universal (e.g. Harris 1989). Therefore, it is of theoretical interest to investigate the matter more closely. If verbal and nonverbal stress assignment is processed separately, that would suggest that verbs have mainly verbal neighbors. Nonverbs, on the other hand, must be influenced mainly by nonverbs. If this is true, the analogical consistency of verbs alone should be greater than the consistency of verbs and nonverbs combined. In the same vein, the consistency of nonverbs, when considered separately, should be greater than the consistency of verbs and nonverbs combined.

In order to test this, the database was divided into two parts: one containing only verbs, and one containing only nonverbs. The words were again alphabetized and a ten-fold cross-validation was performed. This entailed randomly eliminating seven items from each new group so that they would be evenly divisible by ten. Table 4 shows that assigning verbal stress on the basis of similar verbs slightly increased the verbal error rate (i.e. the percentage of incorrectly stressed words) from 3.0% to 3.2%. However, the error rate for nonverbs decreased from 6.6% to 6.4% under the same conditions.

++Insert Table 4 here++

Therefore, if verbs and nonverbs are only allowed to influence members of their own class, the total number of errors varies very little. From an analogical perspective, there appears to be no significant benefit of considering verbal and nonverbal stress assignment as separate processes as Roca (1988) suggests. For this reason, in the remainder of this paper, the results of the corpus as a whole are considered.

5. Initial Results. As already seen, AML is able to correctly assign the stress on about 94% of the most frequent Spanish words. In addition, the words that are incorrectly assigned stress by AML are generally those that traditional analyses have treated as exceptional as well. That is, 80.1% of the errors in stress assignment occur on words that either have antepenult stress, or that have final stress and end in a vowel or s, or that have penult stress and end in a consonant other than s. What this indicates is that analogy 'recognizes' stress patterns without having to extrapolate a global generalization about the data in the form of a rule.

AML is also quite adept at fleshing out subpatterns. For example, there is a fairly large group of words, mainly adjectives, which end in -ico(s) or -ica(s) and have antepenult stress (e.g. público 'public'). In spite of the 'marked' status of antepenult stress, 99 out of 107 of these words are correctly assigned antepenult stress. On the other hand, all 7 verbal forms that end in -ica, (e.g. significa, critica, dedica) were correctly assigned penult stress.

In spite of AML's ability to correctly assign stress, a critic may argue that AML is not an accurate model of Spanish stress assignment because its success rate is not 100%.⁽⁸⁾ Rule models, on the other hand, appear to be much better suited to accounting for all the data since they can be formulated in such a way as to account for 100% of the data correctly. While this is true, one must ask what rule-based accounts must do to achieve such accuracy. In order to account for exceptional patterns and varying degrees of regularity, rule models must make use of formal mechanisms such as extrametricality, odd morphological parsings, and other abstract formalisms which in essence serve as diacritics (Farrell 1990; Gillis, Daelemans, Durieux, and Bosch 1993). The use of such formalisms is common in theories of competence and linguistic structure. Nevertheless, their status as psychological mechanisms, and whether they have actual correlates in the minds of speakers is highly questionable (Eddington 1996).

However, it would be possible to construct a rule-based account without diacritics. It would simply state that words ending in a vowel or s are stressed on the penult syllable, while those ending in a consonant, except s, receive final stress. The application of these rules to the items in Table 1 would yield 648 errors for a success rate of 86.6%. This falls far short of AML's 94.4% success rate. If antepenult words are discounted, the rate climbs to 91.8% for the rule account, and to 97.6% in the AML simulation. In either case, AML appear more adept at assigning stress correctly.

6.0. Empirical Evidence. In section 4, it was seen that the analogical consistency of Spanish stress assignment is quite high. While analogical consistency is employed as a test of performance of a language processing model, (e.g. Daelemans, Gillis and Durieux 1994), there are others. In fact, it is entirely conceivable that some linguistic behaviors have a low degree of consistency. In that case, many similarly behaving items would not have a great deal of features in common, and would not serve as analogs for each other. In other words, there would be a great deal of irregularity in the system. In AML, this is not problematic since all known items are stored as individual units in the mental lexicon. Therefore, another test of AML is whether it helps explain empirical evidence resulting from language usage such as the formation of neologisms, language acquisition data, slips of the tongue, and historical developments. Such evidence may be found for Spanish stress assignment.

6.1.0. Aske's Study. Most words ending in -n have final stress,⁽⁹⁾ which is why generative analyses derive final stress as the unmarked case for such consonant final words. However, Aske (1990:35) noticed that in Spanish, about 62% of 55 common nonverbs ending in -en have penult stress (e.g. vírgen 'virgin,' exámen 'test'). This contrasts with 135 common nonverbs that end in another vowel plus n (V_(-e)), 90% of which have stress on the final syllable (e.g. canción 'song,' según 'according to').

Aske hypothesizes that when a speaker is faced with making a decision about where to stress an unfamiliar word ending in -n, s/he may either make use of generative-type rules or analogy to determine stress placement. Generative rules would assign all -n final words final stress, since words that are unfamiliar to the speaker could not have been previously marked as exceptions. However, if speakers searched their lexicon for words similar to those in question, and applied the stress of the word(s) accessed by the search, -en words would be less likely to receive final stress than -V_(-e)n words.

In order to test his hypothesis, Aske devised 6 final -en nonce words and 6 -V_(-e)n nonce words. He then embedded them in sentences in which they appeared in a nonverbal context, and asked Spanish speakers to read them. The sentences were presented using only capital letters. Since Spanish orthography allows written accent marks to be deleted over capitals, any effect of a written accent mark was thereby controlled for.

The results clearly favor the analogical model. 96.8% of the responses to his -V_(-e)n words favored final stress, while only 55.6% of the responses to -en words received final stress (1990:37). The subjects were clearly not applying a rule which places final stress on all -n final words. The close relationship between the preferred stress patterns, and the stress patterns that exist in actual words suggests that stress assignment was determined on the basis of similar words that were known to the subjects.

6.1.1. Analogy Applied to Aske's Nonce Words. Although Aske attributes his findings to analogy, his experiment was not based on any specific model of analogy. Therefore, it is of interest to determine if his findings can be supported by an analysis based on AML. To this end, the 12 nonce items from his study were processed using the database described in section 3. The results appear in Table 5.

++Insert Table 5 here++

Words ending in -en, and those in -V_(-e)n are assigned quite different patterns as Aske hypothesized, and his experiment bore out. All -en words were assigned penult stress, while all but one of the -V_(-e)n words (seboran) received final stress.

In the AML simulation, I assume that the behavior with the highest predicted probability applies. This means that none of the nonce items ending in -en would be assigned final stress. Aske's subjects, on the other hand predicted final stress on 55.6% of the responses. On the -V_(-e)n items, AML predicts final stress for five out of six items (83.3%), while the subjects preferred final stress in 96.8% of the responses. Therefore, AML captures the subjects' preferences qualitatively, but not quantitatively. Given the variability inherent in survey data, coupled with the fact that the AML database is a limited estimation of a Spanish speaker's mental lexicon, it is sufficient that the simulation captures the major trend, and is not numerically identical.

However, there is a possible confound in the data. Aske presented the nonce words in contexts in which they could only be interpreted as adjectives or nouns, never as verbs. It is possible that seboran was assigned penult stress in the AML simulation due to the heavy influence of its verbal neighbors in the database (e.g. ponían, fuéran, tuviéron, etc.). In order to test this possibility all 12 nonce words were assigned stress using only the nonverbal items in the database. In this way, the nonverbal contexts Aske's subjects were asked to respond to were matched with the nonverbal items in the database. However, under these conditions seboran continued to receive penult stress. Furthermore, an additional item (petaben) was incorrectly stressed in comparison to the subjects' preferences. It is unclear why the stress placement given to seboran by AML does not coincide with that assigned by the subjects. However, the fact that an additional mismatch occurs when only nonverbal items are allowed as analogs, lends further credence to the hypothesis that verbal and nonverbal stress assignment should not be treated separately (section 4.1).

6.2.0. Hochberg's Study. In her study, Hochberg (1988) elicited words with different stress patterns from preschoolers. First, she had children name various objects in a picture book. Next they had to repeat nonce words that they heard, which were stressed on different syllables. Her hypothesis was that

. . .if children did in fact learn stress rules, then (a) they should find words with regular stress easier to pronounce than words with nonregular stress; and (b) they should tend to regularize stress in words with nonregular stress, but should not irregularize stress in words with regular stress. (1988:690)

Her hypothesis was partially confirmed. She found that children made significantly more structure changing errors⁽¹⁰⁾ on nonce words with irregular stress than on nonce words with regular stress patterns. In addition, more structure changing errors were made that regularized stress, compared to errors that made regular stress irregular.

The error analysis for the real words she elicited differs somewhat. As with the nonce words, more structure changing errors were made on irregularly stressed words than on regularly stressed words. However, there was no significant difference between the percentage of errors that regularized stress and the percentage of errors that converted regular stress into irregular stress. Hochberg concludes that

The most likely explanation of the difference between the imitated and spontaneous speech data is that the children had mastered both the stress system and individual exceptions to it. Thus, while they did find known irregular words somewhat harder to say than known regulars, their familiarity with these words enabled them at least to stress them correctly. In contrast, when confronted with novel words in the imitation task, the children were led by their rule knowledge to regularize irregulars. (1988:698)

An alternative explanation of her findings is possible from an analogical standpoint. Known words are stored along with their inherent stress pattern. Therefore, the fact that regularization of irregulars and irregularization of regulars was roughly equal could be attributed to the same types of retrieval problems affecting both types of words indiscriminately. Unknown words, on the other hand, have no lexical entry and would adopt the stress pattern of their neighbors. Of course, this account is only plausible if it can be proven that analogy makes errors that regularize stress more often than it assigns irregular patterns to regularly stressed words.

6.2.1. Hochberg's Acquisitional Data in an Analogical Analysis. Of the 4970 words in the database described in section 3, 277 were incorrectly stressed using AML's algorithm. According to these data, the most difficult stress to assign correctly is antepenult, since 59.9% of the antepenult words in the database were incorrectly stressed. Only 6.4% of words stressed on the final syllable were improperly stressed, while penult stress yielded the lowest error rate (1.2%). This same hierarchy of difficult is also seen in the error rates from the three- and four-year-olds in Hochberg's imitation experiment (1988:700, Figure 13).

Of the 277 errors produced by AML, 220 involved a move from an irregular to a regular stress pattern (e.g. acá to áca). This means that 33.9% of the irregularly stressed items (n=649) were regularized. In contrast, only 54 of the errors made on regularly stressed items (n=4177)⁽¹¹⁾ made them irregular (e.g. papél to pápel), yielding a 1.3% rate of irregularization. Once again, this is precisely the pattern that Hochberg found in her imitated speech study, where 53% of the errors regularized irregularly stressed words, and only 23% of the errors involved making a regular stress irregular (1988:696).

Hochberg also divided the error rates according to the age of the subjects. The error rate on regular items remained virtually unchanged for all subjects ages three to five. However, the error rate on irregular items dropped from the four- to the five-year-olds (Figure 1).

Click here to view Figure 1.

One way of approximating age differences in AML is by varying the number of items in the database (Derwing and Skousen 1994). Exactly how many words a child at a given age has learned is difficult to ascertain. Based on several different estimates, Aitchison (1994:169) assumes that a three-year-old English speaker has an active vocabulary of about 1000 words, while a five-year-old has an active vocabulary of about 3000 words. In any event, in order to determine if the analogical approach could account for the developmental phenomena, the database was divided into two halves, and the half containing the least frequent items was discarded. The remaining half was assigned stress in a ten-fold cross-validation simulation according to AML's algorithm, and the error rates were calculated. These results are also summarized in Figure 1.

The leftmost group of bars A on Figure 1 represents the error rates of Hochberg's four-year-old subjects, and the error rates that resulted when only the most frequent half of the database was included in the analogical experiment. The rightmost bars indicate the error rates for Hochberg's five-year-old subjects, and the error rates that occurred when 4970 database items were included. In both studies, error rates on regular items varied little. However the error rates on irregularly stressed items declined for older subjects. In the AML simulation, it also dropped when a larger mental lexicon was assumed. A proportions test reveals that this drop is significant (Z-statistic = 7.44, p < .01, 99% confidence interval .0676, .1384)

Hochberg concludes that her findings support the existence of rules which assign stress. Nevertheless, the analogical account mirrors her findings quite closely. The ability of an exemplar-based model to account for stress placement errors is not limited to Spanish. Gillis et al. (1994) demonstrate how stress placement errors in Dutch are better accounted for if stress is determined by analogy to known words, than it is by postulated stress rules.

7. Conclusions. The purpose of this paper was to determine to what extent Spanish stress placement could be handled within AML. The 4970 most common Spanish words served as a model of the mental lexicon, and as test cases as well. About 94% of these words were correctly stressed by analogy. Extremely low frequency words were correctly stressed in about 92% of the cases. No significant improvement was observed if verbs and nonverbs were only allowed to analogize on members of their own category.

Since AML is a model of language usage, the most important findings are those that involve actual language use. Although the results are not perfect, the analogical account of stress assignment was found to mirror the results of Aske's nonce word study and Hochberg's study of stress acquisition quite closely. Therefore, the present study lends support to AML as a plausible model of linguistic performance. Moreover, it adds to the growing body of evidence that linguistic generalizations, such as stress placement, are not embodied in rules or similar abstractions, but in exemplars which are stored in the mind.

Notes

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# of Words Ending in:	Final Stress	Penult Stress	Antepenult Stress
Vowel	178	2494	178
Consonant	798	1085	96
/s/	20	909	94
Consonant (except /s/)	778	176	2

Table 1. Stress Placement in the Most Frequent Spanish Words.

('6' indicates third person plural, and 'pt' indicates preterit tense.)

Variables:

(1) The coda of the word's final syllable, or the null symbol '-' if there is none.

(2) The nucleus of the word's final syllable.

(3) The onset of the word's final syllable or the null marker '-' if there is none.

(4) The coda of the penult syllable or the null marker '-' if there is none.

(5) The nucleus of the word's penult syllable, or the empty symbol '0' if the word is monosyllabic.

(6) The onset of the penult syllable, else '-'.

(7) The coda of the antepenult syllable, else '-'.

(8) The nucleus of the antepenult syllable, or the empty symbol '0' if the word is bisyllabic or monosyllabic.

(9) The onset of the antepenult syllable, else '-'.

(10) The verb's tense, or '0' if the item is a nonverb.

(11) The verb's tense, or '-' if the item is a nonverb.

(12) The verb's tense, or '-' if the item is a nonverb.

(13) The person the verb is conjugated for, or '-' if the item is a nonverb

Table 2. Variables Used to Encode Words in the Database.

Table 3. Probability of Stress Placement According to AML.

Table 4. Error Rates Analogizing on Entire Database and on Verbs or Nonverbs Alone.

Nonce Word	Probability of Final Stress		Probability of Penult Stress		Probability of Antepenult
	All Words	Nonverbs Alone	All Words	Nonverbs Alone	All Words	Nonverbs Alone
besoren	.006	.011	.994	.989	.000	.000
corumen	.005	.098	.995	.901	.000	.000
petaben	.006	.610	.994	.387	.000	.003
faden	.017	.298	.983	.702	.000	.000
merasen	.009	.173	.991	.827	.000	.000
gorquen	.003	.004	.998	.996	.000	.000
seboran	.003	.052	.996	.946	.001	.002
porubon	.830	.975	.169	.024	.000	.001
petamin	.614	.983	.368	.015	.018	.002
tedon	.789	.991	.211	.009	.000	.000
sorquin	.916	.822	.084	.178	.000	.000
perasun	.662	.963	.330	.035	.008	.002

Table 5. Probability of Stress Placement for Aske's Nonce Words Calculated with Entire Database and with Nonverbs Alone.

1. I express my sincerest thanks to Royal Skousen, Steve Chandler, Harald Baayen, as well as to the anonymous reviewers, for their input and help with this study. In addition, I am indebted to José Ramón Alameda for graciously allowing me access to the computerized version of his frequency dictionary. Without this, the present study would have been impossible.

2. AML has been applied to stress placement in Dutch as well (Gillis, Daelemans, and Durieux 1994).

3. Similar results were found for stress placement in Dutch using an exemplar-based model (Daelemans, Gillis, Durieux 1994; Gillis, Daelemans, and Durieux 1994; Gillis, Daelemans, Durieux , and van den Bosch 1993).

4. In this study, the phonemic attributes of words are assumed to be the relevant variables. However, AML can also incorporate other variables such as sociolinguistic variables. (Skousen 1989:97-100).

5. Prasada and Pinker (1993) provide evidence that gang effects disappear where type frequency is high, as in regular English past tense forms. In their nonce word study, no gang effects were found for regular items. The connectionist simulation of the same items, on the other hand, erroneously demonstrated gang effects. In contrast to the connectionist outcome, AML produces outcomes consistent with the nonce word study (Eddington 1999).

6. I am most grateful to Gert Durieux of the University of Antwerp for allowing me to use his version of Skousen's AML program to undertake this study. His version greatly increases the number of variables and instances in the database that may be used.

7. The frequency dictionary by Juilland and Chang-Rodríguez (1964) is tagged for part of speech, but does not include frequency information on all of the tokens that appeared in their database. In contrast, Alameda and Cuetos (1995) list the frequencies of all tokens.

8. It could be countered that people do not invariably produce the expected forms either (see Berko 1958, Schnitzer 1996).

9. For example, 60% of the polysyllabic words ending in -n in the database are stress final.

10. Structure changing errors are those that entail a stress shift or an alteration of the CV skeleton.

11. The 144 monosyllabic items were not included.