ACorpus-BasedAnalysisoftheDiscourse Functions of Ser/Estar...

Language Learning ISSN 0023-8333

A Corpus-Based Analysis of the DiscourseFunctions of Ser/Estar + Adjective in ThreeLevels of Spanish as FL Learners

Joe CollentineNorthern Arizona University

Yuly Asencion-DelaneyNorthern Arizona University

Research on the acquisition of Spanish’s two copulas, ser and estar, provides an un-derstanding of the interaction among syntax, semantics, pragmatics, morphology, andvocabulary during development (e.g., Geeslin, 2003a, 2003b; Gunterman, 1992; Ryan& Lafford, 1992). Recent research suggests that linguistic features in the surround-ing discourse influence learners’ copula choice. We present a corpus-based analysisof the lexico-grammatical features co-occurring with copula + adjective usage amongforeign-language learners of Spanish at three levels of instruction. Findings revealedthe following: (a) both ser + adjective and estar + adjective occur at all levels wherelittle linguistic complexity typically occurs; (b) ser + adjective appears in descriptiveand evaluative discourse; and (c) estar + adjective is present in narrations, descriptions,and hypothetical discourse.

Keywords second language acquisition; Spanish interlanguage; learner corpus; corpuslinguistics; grammatical development; ser and estar; copula choice

Introduction

Studying the acquisition of Spanish copulas, ser and estar, interests secondlanguage acquisition (SLA) researchers because it requires studying syn-tax, semantics, pragmatics, morphology, and vocabulary during development

We wish to thank Dr. Roy St. Laurent of the Northern Arizona University Statistical ConsultingLab for his valuable assistance in the design of the statistical analyses of this project. Any errorsreside solely with us. Our thanks also go to Dr. Vincent and Dr. Ojeda for their financial support totranscribe the texts written by the learners.

Correspondence concerning this article should be addressed to Joe Collentine, Northern ArizonaUniversity, Modern Languages, Box 6004, Flagstaff, AZ 86011. Internet: [email protected]

Language Learning 60:2, June 2010, pp. 409–445 409C! 2010 Language Learning Research Club, University of MichiganDOI: 10.1111/j.1467-9922.2010.00563.x

Collentine and Asencion-Delaney Corpus-Based Analysis of Ser/Estar + Adjective

(Leonetti, 1994). Although this might seem particular to Spanish as a secondlanguage (L2), the acquisition of these verbs shows how learners acquire oneof the two basic Indo-European sentence types (Halliday, 1970): predicative(e.g., Juan corre rapidamente “John runs quickly”) and attributive sentences(e.g., Juan es rapido “John is quick”), with the ser/estar (S/E) distinctionforming the central verbal element of the latter. Pragmatically speaking, theS/E distinction requires knowing when the relationship between the subjectand adjective involves characterization (Marıa es capaz “Mary is capable”) oridentification (Marıa es la encargada “Mary is the one in charge”; FernandezLeborans, 1999). Semantically, S/E can differ aspectually, with estar often con-noting the perfective aspect (e.g., that an event’s time frame is short and limitedin duration) and ser connoting the imperfective (e.g., the event is habitual)(Lujan, 1981). Morphologically, Spanish adjectives inflect for person and num-ber, which is especially difficult for learners whose first language (L1) has fewinflections, like English. Finally, the number of adjectives that learners must as-sociate with either ser or estar presents lexical challenges. Geeslin (2003a) andSilva-Corvalan (1986, 1994) reminded us that even native speakers of Spanishshow much variation in S/E usage with adjectives as a function of pragmaticconsiderations.

Traditionally (and in current learner textbooks), ser + adjective segmentsdescribe a subject’s permanent, seemingly unchanging characteristics. How-ever, estar + adjective segments describe temporary, dynamic characteristicsof a subject. It is for this reason that an adjective like aburrido “boring/bored”in soy aburrido, which uses ser, produces the meaning “I am boring,” whereasin estoy aburrido, which uses estar, yields roughly “I am bored”; with ser, theboredom is constant, whereas with estar, the state—and its effect on others—should pass. Nonetheless, this traditional view has come under much empiricalscrutiny, with the works of Geeslin (2003a) and Silva-Corvalan (1986, 1994)showing that this explanation only scratches the surface of the pragmatic nu-ances that native speakers consider when choosing their copula.

Studying the acquisition of S/E provides a means to address various SLAquestions (e.g., orders of acquisition, the role of study abroad), and researchershave used various methodologies (e.g., error analysis of open-ended conver-sations, raters judging the semantic intent of learner utterances). Recent S/Eresearch suggests that learner copula selection is sensitive to lexical and gram-matical features (often referred to together as “lexico-grammatical” features) inthe surrounding discourse. Corpus-linguistics methods are particularly suitedto study the interaction between a construct and its lexical and grammatical con-text. After reviewing S/E research and the potential contribution of a corpus

Language Learning 60:2, June 2010, pp. 409–445 410


analysis, we present a large-scale corpus-based analysis of learners’ use ofS/E + adjective at different instructional levels.

Ser/Estar SLA Research to Date

Initial S/E research identified developmental stages in instructed contexts, fo-cusing on accuracy and omission rates. Estar emerges in later stages, especiallyin estar + adjective segments. VanPatten (1985, 1987) studied oral interviews,grammaticality judgments, and informal class observations to propose fivestages: (a) copula absence, (b) ser as the default copula, (c) estar with progres-sive, (d) estar with locatives, and (e) estar with adjectives of condition. Sim-plification, communicative value, frequency in input, and L1 transfer influencethese stages (VanPatten, 1987). Researchers have studied whether VanPatten’sstages generalize to study-abroad and Peace Corps experiences (Gunterman,1992; Ryan & Lafford, 1992). Oral proficiency interviews in both Gunter-man’s study and Ryan and Lafford’s study confirmed most stages, with estar +adjectives of condition appearing before estar with locatives.

Although accuracy studies reveal that these two copulas develop in a pre-dictable fashion, they do not explain the variability in S/E usage. Additionally,these studies appeared when SLA research was highly concerned with the roleof input in acquisition, and explanations focused on issues such as the cop-ula’s individual frequency and communicative value/saliency (Ryan & Lafford,1992; VanPatten, 1985, 1987) in the input. Ryan and Lafford (1992) attributedthe late emergence of estar + adjective to access to naturalistic input. Nonethe-less, we know almost nothing about the input (e.g., the types of discourse)that learners process in naturalistic settings or over the course of a semesterin at-home or study-abroad settings (Collentine, 2008). SLA theory posits thatoutput (be it from instructional interventions or naturalistic experiences) playsas strong a role as input at latter stages of acquisition (Shehadeh, 2002; Swain,1985), which is when estar + adjective emerges. What type of communication,then, do learners generate that coincides with estar + adjective emergence?

Some evidence suggests that copula + adjective production improves aslearners grow in the complexity of the discourse types they generate. Copula +adjective segments help beginning learners to relate simple messages, contain-ing a subject and a verb without elaboration (e.g., accompanied by adverbs).Gunterman (1992) noted that when communication became difficult, learnersresorted to ser + adjective segments. “Because the questions typically eliciteddescriptions, explanations, and definitions, the [peace corps volunteers] wereable to build a great number of their answers around ser” (Gunterman, 1992,

411 Language Learning 60:2, June 2010, pp. 409–445


p. 1297). Descriptive discourse is structurally and semantically basic, depictinga situation’s important nouns and their states (e.g., via adjectives); descriptionslack dynamic details about events and changes of states. Estar + adjectiveappears in Gunterman’s data, where learners went beyond descriptions to com-municate narrative discourse, which entails both a situation’s states and itsevents (often chronologically). Lafford (2004) attributed copula + adjectivegains after a single semester of study abroad to “the pragmatic constraints in-herent in real-world discourse . . . and perhaps to improved overall narrative anddiscursive abilities, proficiency, and fluency” (p. 216; emphasis added). Subse-quent S/E research intimated that copula + adjective growth occurs as lexicaland grammatical choices become sensitive to what appears in the surroundingdiscourse.

In the copula + adjective segment, natives demonstrate variation in cop-ula selection because each copula affects different pragmatic and discursiveinterpretations (Geeslin, 2002; Silva-Corvalan, 1986), and so the copula +adjective context is ideal for studying how learners encode pragmatic anddiscursive information. Geeslin (2002, 2003a, 2003b) focused on differentinstructional levels while considering findings from sociolinguistic studies ofcopula + adjective language change in bilingual and monolingual communities(e.g., Silva-Corvalan, 1986) in which semantic, pragmatic, and sociolinguisticvariables such as frame of reference (i.e., comparison with group norm—Juanes alto “John is tall”—or with the referent—Juan esta alto “John’s gottentall”), susceptibility of change (i.e., inherent—Juan es inteligente “John isintelligent”—vs. changing—Juan esta viejo “John’s gotten old”), lexical classof the adjective (e.g., age, nationality), and semantic transparency (El mango esverde/El mango esta verde “The mango is green/The mango is unripe” vs. Juanes casado/Juan esta casado “John is married/John is just married”) explainedthe overuse of estar. Geeslin (2002) collected data from high school studentswith a guided interview, a picture-description task, and a contextualized ques-tionnaire, concluding that learners acquire the restriction of susceptibility ofchange earlier than the frame of reference restriction. Geeslin (2003a, 2003b)later examined copula choice with advanced learners using contextualizedquestionnaires, finding that semantic and pragmatic features interact to predictestar usage. She found that whereas advanced learners seem to overgeneral-ize pragmatic constraints such as frame of reference and experience with thereferent, native speakers favor lexical and semantic constraints (e.g., predicatetype) to decide when to use ser or estar.

Recently, Geeslin (2003b) and Geeslin and Guijarro-Fuentes (2006) sug-gested that we need to understand the context that surrounds L2 copula choice:



In the case of copula choice, advanced learners apply pragmaticconstraints, even in contexts in which native speakers do not. In contrast,native speakers choose not to apply pragmatic constraints in favor oflexical and semantic constraints. (Geeslin, 2003a, p. 751)

In copula selection, L2 Spanish learners may even be more sensitive to con-textual factors than native speakers, who appear to depend on “local” factorswithin the attributive copula + adjective segment (i.e., lexical and semanticconstraints related to the interaction of the copula and the adjective alone);learners are sensitive to a wider context, apparently attending to speaker in-tent and implicatures (as “pragmatic” considerations would imply) as well asto lexico-grammatical features in the surrounding discourse. Geeslin (2003a,p. 748) noted that words/phrases that imply change near a copula + adjectivesegment apparently cause advanced learners to select estar—the copula asso-ciated with changing states—even when the relationship between the adjectiveand the copula necessitates the use of ser—the copula associated with perma-nent states. Thus, to better understand the factors surrounding learners’ S/Eusage, we might well ask the following:

• What are the contextual features that co-occur with each copula + adjectivesegment at different levels of instruction?

• What types of discourse (e.g., narratives, descriptions) are usually associ-ated with each segment?

Corpus Techniques and the Study of Context

Geeslin’s (2002, 2003a, 2003b) research shows by way of rater judgmentsthat the pragmatic intent of copula + adjective segments influences whetherlearners use ser or estar. It is also reasonable to suspect that discourse typeinfluences copula selection in important ways. Recall that Gunterman (1992)argued that ser + adjective and estar + adjective segments are distributed withindifferent discourse types. Additionally, Lafford (2004) related learners’ copulaselection gains to the expansion of the types of discourse they can produce.Myles and Mitchell (2004) argued that SLA researchers should take note thatcorpus research examining large collections of digitized documents has had aconsiderable role in furthering the field of discourse analysis. Accordingly, thepresent study employs a variety of corpus-based techniques to understand thecontextual features that co-occur with ser + adjective and estar + adjective usein addition to the discursive functions that learners at different levels assign toser and estar. As these techniques are not widely utilized in SLA research, in



the following section we not only briefly delimit what corpus-based researchcan reveal about SLA, but we also describe important corpus assumptionsand techniques. Because our analysis compares learner data to corpus-basednative-speaker models, we also describe relevant perspectives that recent corpusresearch has uncovered about the nature of Spanish discourse.

Not only does a corpus-based approach lend itself to questions of L2 dis-course development, but the techniques also permit empirical comparisonsbetween learner behaviors and native-speaker models. For instance, using anEnglish learner corpus and two British native-speaker corpora, Siyanova andSchmitt (2007) found that, in informal speech, learners are less likely to usetwo-word verb constructs (e.g., run into, put off ) than are native English speak-ers. One advantage of comparing learner performance to native-speaker modelsis that the SLA researcher can make empirically defensible and testable assump-tions about the end state of the acquisition process, an approach we adopt inthe present study.

Myles (2005) and Myles and Mitchell (2004) lamented that SLA researchhas not been quick to embrace new technologies for collecting and analyzingdata, especially as it relates to corpus linguistics. They argued that corpus lin-guistics complements the current research by examining large amounts of datawith relative ease, thus increasing the generalizability of findings (Rutherford& Thomas, 2001). Still, some notable corpus-based SLA research has con-tributed to our understanding of the context on language development (Belz,2004; Collentine, 2004; Granger, Hung, & Petch-Tyson, 2002; Klein & Purdue,1997). Some corpus research exists on ser and estar.

Corpus-Based S/E FindingsCorpus-based S/E research provides some evidence that learner’s copula choiceis sensitive to contextual factors and that there is reason to suspect that Spanishcopula + adjective segments are distributed to different discourse types. Cheng,Lu, and Giannakouros (2008) examined a corpus of Mandarin Chinese L1learners of Spanish. They show how advanced learners’ copula choice variesaccording to the pragmatic intent of the surrounding discourse they themselvesproduce. They reported that “exploratory writing” evoked greater estar + ad-jective usage and that estar + adjective is compatible with the semantic andpragmatic goals of narratives or descriptions. Collentine (2008), in an invitedcommentary article on Cheng et al. (2008), conducted a study on whether cop-ula + adjective segments might serve discernable discourse functions in nativeSpanish discourse. His analysis uncovered a significant interaction betweencopula and text type. Ser + adjective was relatively frequent in most all types



of discourse, whereas estar + adjective was most frequent in dramas, whichentail much evaluative language and monologues containing descriptions, andnarratives. These two studies suggest that copula + adjective use by learnersand native speakers is not influenced by local features alone (which range fromwithin the copula + adjective phrase structure to the lexico-grammatical char-acteristics of the discourse) but also by communicative goals such as the typeof discourse being produced.

Techniques, Tools, and Utility of Corpus Based-ResearchCorpus linguistics ranges in complexity. Minimally, it utilizes searchable digi-tized texts sampled in a representative fashion, depending on the study’s focus.Textual information is critical for statistical procedures (just as it is for indi-vidual learners), and so files are tagged with header information, such as topic,source type, biographical information about the author, and purpose (argu-mentative essay, narrative). Concordance applications and scripting languagesallow researchers to search for specific segments and tabulate their frequenciesby text. When investigators need to search for morphosyntactic information(e.g., all adjectives, all verbs whose infinitive is either ser or estar), they oftenuse a part-of-speech tagger: a series of software modules that annotates ev-ery word with information about its major word classes (e.g., adjective, noun,verb, determiner, preposition), basic morphological information (e.g., plural,preterit), as well as its lemma (i.e., its unmarked, dictionary root, such as averb’s infinitive or a noun’s masculine, singular form).

Part-of-speech tagging requires a dictionary with lexical and grammaticalinformation about the possible words in a language (some words have morethan one entry because languages have many synonyms). For the present projectwe compiled our own dictionary and we utilized a training set (which assiststagging ambiguous forms) from samples from the Corpus del espanol (Biber,Davies, Jones, & Tracey-Ventura, 2006) as well as software routines from theNatural Language Tool Kit (NLTK; http://www.nltk.org/). After the corpus istagged in this way, the investigator must verify the accuracy of the taggingand fix errors (individual and/or systematic) through further programming.An increasingly popular technology to create search patterns (regardless ofthe tagging software) utilizes regular expressions, a sophisticated wild-card-and variable-based text-search system (e.g., \w{3,} symbolizes words of threeletters or more; \w+ing symbolizes words of any length ending in ing).

Having a tagged corpus along with the flexibility of regular expressionsprovided us with a powerful means of studying a number of lexical and/orgrammatical phenomena. For instance, the pattern \w+\"v["`]#`["`]#`["`]#`



(?:ser|estar)` (?:obvio|evidente) \"j \w+ que \" \w+ is one way to search forevery verb whose lemma is either ser or estar followed by the adjectives obvioor evidente followed by the conjunction que.

It is important to make mention of two common corpus-statistical tech-niques. The process of norming is a numerical transformation of counts toaccount for the fact that individual texts vary in length and that longer textscan have a greater influence on the numerical distribution of any phenomenon.Investigators often norm frequency counts to an arbitrary number, such as per1,000 or per 10,000 words: The count of some phenomenon in a text is di-vided by the text’s total word count, the quotient of which is multiplied by1,000 (a higher norming multiplier like 100,000 affords greater precision). Thetechnique known as normalizing involves converting the count of some phe-nomenon to its z-score value vis-a-vis its count in each document in the corpus(i.e., the difference of the phenomenon’s frequency and its mean occurrencein the corpus divided by its standard deviation). Normalizing is convenientfor measuring the relative presence of two or more linguistic features withinany given text, as one can easily sum two or more z-scores to calculate howconcentrated those features are in any texts or group of documents while takinginto account the fact that some linguistic phenomena are naturally scarce in adocument (e.g., the subjunctive), whereas others are naturally common (e.g.,articles) (cf. Biber & Conrad, 2001). For instance, the frequency of adverbs oftime and copula + adjective segments are likely to vary in different ways acrossthe texts of a corpus (e.g., adverbs of time may be generally more frequent).By summing the two segments’ z-score per document, we can find which textshave the highest concentration of the two.

Corpus-Based Native-Speaker Models of DiscourseAccording to Myles and Mitchell (2004), we now have the ability to definestructurally and statistically different discourse types. Thus, the present studynot only compares learners’ copula selection behaviors between different levelsof instruction, but it also attempts to identify the types of discourse learnersproduce when using S/E + adjective, based on a native-speaker model. Corpuslinguistics has shown through factor analyses how lexico-grammatical struc-tures bundle together to produce different types of discourse (Biber & Conrad,2001). Biber et al. (2006) provided the first comprehensive analysis of Spanish,analyzing a 20 million-word Spanish corpus with written and oral data from avariety of registers. There are four types of discourse that Biber et al. (2006)identified that learners might well produce in written texts, the features withwhich each is associated are presented in Table 1.



Table 1 Discourse dimensions and features targeted in the learner-native speaker com-parison (cf. Biber et al., 2006)

Discourse type Lexico-grammatical features

Informationally rich • Singular and plural nouns• Postnominal descriptive adjectives• Prenominal descriptive adjectives• Definite articles• Prepositions• Derived nouns• Type-token ratio• Long wordsa

• Se passives (i.e., ergative se use)

Hypothetical • Subjunctive use• Conditional use• Future use• Verbs of obligation and causation (e.g., dejar, permitir,

hacer + infinitive)• Infinitives not preceded by a verb or article• Verbs followed by an infinitive• Progressive aspect (imperfect use or present participle)• Dependent que clauses

Narrative • Clitic usage• Imperfect tense/aspect• Preterit tense/aspect• Possessives• Third-person pronouns• Reflexive se and changes of states• Infinitives not preceded by a verb or article• Verbs followed by an infinitive

Descriptive • Postnominal descriptive adjectives• Derived nouns• Absence of all narrative variables

aDefined as those that have an average number of characters in the dataset, plus thatcalculation’s standard deviation, plus one character—thus, six or more characters.

Informationally rich discourse is one that conveys large amounts of infor-mation densely. Derived nouns, adjectives, multisyllabic words, and passivesconvey information in a decidedly encyclopedic fashion. Another importanttype of discourse in Spanish—which is not found in English analyses (cf. Biber



& Conrad, 2001), perhaps because Spanish has a neatly defined mood system(with readily discernable inflections)—is hypothetical discourse, which com-municates possibilities and counterfactual information. It is characterized byfeatures such as verbs in the subjunctive and the conditional. The other twodiscourse types identified by Biber et al. (2006) are well known to most (viz.,narratives and descriptions).

Research Questions

The present study adds to our understanding of the acquisition of how contextualvariables interact with learners’ use of attributive sentences. Although the fieldhas a good idea of the communicative factors that motivate copula choice, wedo not know how each copula + adjective segment works with other lexical andgrammatical structures to communicate coherent discourse. To address this gapin the literature and to understand the discursive function that ser + adjectiveand estar + adjective segments serve over time, we provide a corpus-basedanalysis of the lexico-grammatical features that predict the use of these twosegments with foreign-language (i.e., at-home) learners in the first, second, andthird years of the university level. More specifically, we address the followingresearch questions:

1. What are the lexico-grammatical features that co-occur with ser + adjectiveusage? What are the discursive functions that these co-occurring featuresserve?

2. What are the lexico-grammatical features that co-occur with estar + ad-jective usage? What are the discursive functions that these co-occurringfeatures serve?

To address these questions, we present the results of a series of regressionanalyses predicting the occurrence of each copula + adjective segment froma variety of lexico-grammatical features (see the Corpus Description section).We predict that ser + adjective and estar + adjective segments will havedistinct lexico-grammatical associations that change over time. Specifically,we posit that ser + adjective segments appear in simple discourses (e.g., highlydescriptive and listlike discourse) and estar + adjective segments becomeincreasingly associated with discursive complexity. However, we posit that theassociation of estar + adjective with a particular discourse type will be moredifficult to identify because previous research suggests that even advancedlearners are more sensitive to contextual (i.e., pragmatic) constraints than arenative speakers with this construct.



Method

Corpus DescriptionThis study used a 432,511-word learner corpus of written Spanish, comprisingedited and nonedited compositions collected from English-speaking Spanishlearners at three levels of instruction: first year (230,270 words), second year(109,224 words), and third year (93,017 words). The compositions were notspecific tasks designed to collect the data for this study but rather writingsamples used for assessment purposes. Students wrote letters, narratives, de-scriptions, summaries, and argumentative essays both in and out of class as wellas on exams. Topics related to the textbook themes (e.g., family, childhood)and the cultural readings assigned in class. Each text was tagged for numerouslexical and grammatical features (see above).

To determine what lexico-grammatical features co-occur with ser + adjec-tive and estar + adjective usage, we considered a total of 75 potential predictorvariables, each operationalized in the form of a regular expression. In corpusstudies, variables refer to the linguistic features in the texts being analyzed. Thisstudy’s predictor variables included various lexical features, such as adjectivesother than the ones in the copula + adjective frame (e.g., derived adjectives,adjective in postnominal position), nouns (e.g., derived nouns, feminine nouns,masculine nouns), adverbs (e.g., adverbs of place, adverbs of time), and verbclasses (e.g., verb in imperfect aspect, verb in past participle), as well as mor-phosyntactic features such as dependent clauses, noun phrase configurations(e.g., article plus noun), pronoun usage (e.g., clitic—third person), as well asa variety of verb phrases (e.g., verbs of communication, verbs of knowledge).The set of variables considered involved all parts of speech, common mor-phosyntactic constructs studied by learners, as well as additional constructsstudied in Biber et al. (2006).

Data AnalysesLearner Models AnalysisTo identify the types of lexico-grammatical features that learners use withser + adjective and estar + adjective segments and to identify which vari-ables distinguish among the three levels of learners, we constructed regressionmodels of lexical-grammatical regressors predicting copula + adjective usage:a ser + adjective learner model and a estar + adjective learner model. Weconstructed regression models for each copula + adjective segment—ratherthan, for instance, a single regression model for which the choice between thetwo is the dependent variable—because the previous research suggests that thefactors motivating the use of ser + adjective usage are not the same as those



motivating estar + adjective usage (cf. Guntermann, 1992). The process in-volves screening a set of potential predictor variables for standard assumptionsof linear regression, submitting the reduced set to a best-subsets analysis—rather than a stepwise procedure—to identify the so-called “best subset,” and,finally, comparing the predictor variables’ ability to distinguish among the threelevels of learners in terms of copula + adjective usage.

We employed a standard data-screening process, identifying which of thepotential predictor variables had honest correlations with the criterion variables,thus discarding the following: (a) variables that had no correlation with a crite-rion variable (by examining correlation coefficients and scatter plots betweena potential predictor variable and the criterion); (b) variables that representedinflated correlations (i.e., where two features correlated highly with each otherand constituted too high an overlap in semantic or structural properties, so asto avoid colinearity problems in the final model selection phase);1 and (c) vari-ables that constituted deflated correlations, eliminating predictor variables thathad a highly reduced range of responses to the criterion variable (e.g., thosevariables whose frequency was very small, such as n = 2, regardless of thelevel of the participant or the genre). This screening of the data yielded a listof 58 potential linguistic variables (37 for ser + adjective and 21 for estar +adjective) that could be meaningful for the regression analyses to be performed.Table 2 shows the preliminary list of variables.

We used best-subsets analyses to derive the two regression models for ser +adjective and estar + adjective. Social scientists frequently employ stepwiseprocedures for building regression models. Although these procedures for vari-able selection work adequately for reducing a small set of potential predictorvariables to a small, more meaningful set (e.g., a subset that does not have ahigh degree of overlap), statisticians do not favor stepwise analyses when theinitial pool of predictor variables is extremely large (Miller, 2002), such as thepresent case. Following Rencher (2002), we employed instead a best-subsetsanalysis for building the two models for predicting ser + adjective and estar +adjective. The principal advantage that a best-subsets approach has over sta-tistical/stepwise regression (with a large number of predictor variables) is thatbest-subsets approaches attempt to reduce the number of predictor variablesby comparing various “combinations” of variables, whereas the stepwise pro-cedure attempts the reduction process by considering each and every potentialpredictor variable “individually.” The best-subsets approach has been shown toproduce less spurious results than stepwise procedures when reducing a largeset of potential predictor variables. With large pools of potential predictor vari-ables that have an almost infinite number of combinations, stepwise regression



Table 2 Linguistic variables used in the study after initial data screening

Variable class Ser + adjective Estar + adjective

Noun • noun - derived • noun - masculine• noun - feminine • noun - singular

Adjective# • adjective - derived • adjective - singular• adjective - feminine • adjective - type 1• adjective - masculine • adjective - type 2• adjective - plural• adjective - postnominal—Una

casa grande “a large house”• adjective - prenominal—Una

bella mansion “A beautifulmansion”

• adjective - singular• adjective - type 1—Descriptive

adjective with four inflections:masculine, feminine, singular,and plural. Blanco/a(s) “white”

• adjective - type 2—Descriptiveadjective with two inflections:singular and plural. Interesante(s),liberal(es) “interesting, liberal”

Pronoun • clitic - third person • clitic - preverbal• pronoun - subject• que subordinator

• pronoun - thirdperson

• que subordinatorOther noun phrase

elements• article noun segment—El libro

“The book”• article noun segment• possessive adjective

• definite article• possessive adjective

Verbs • SE plus third-singular verb• verb - “Gustar”-like

• SE plus 3rd-singularverb

• verb - third person • verb - “Gustar”-like• verb - communication—Decir

“say/tell,” anunciar “announce,”explicar “explain,” etc.

• verb - imperfect• verb - infinitive

• verb - third person• verb - knowledge• verb - past participle• verb - present

participle

(Continued)



Table 2 Continued

Variable class Ser + adjective Estar + adjective

• verb - infinitive 2; not precededby verb or article

• verb - knowledge—Saber“know,” recordar “recall,”entender “understand,” etc.

• verb - observation—Ver “see,”escuchar “listen,” etc.

• verb - past participle• verb - past subjunctive• verb - periphrastic future• verb - present participle• verb - preterit• verb - suasive—Querer “want,”

mandar “order”• verb aspect - progressive

• verb -suasive—Querer“want,” mandar“order,” etc.

• verb -probability—Creer“believe,” negar“deny,” dudar“doubt,” etc.

Adverbs oradverbial clauses

• adverb - place• adverb - time• adverbial clauses - contingency• adverbial clauses - time

• adverb - time• adverbial clauses -

contingency• adverbial clauses -

time

Total 37 21

Note. All adjectives in this list did not follow one of the two copulas.

may never consider combinations of predictor variables that are equally good atpredicting the occurrence of the response variable (i.e., the dependent variable)in question.2 Because this analysis is computationally intensive and not avail-able in many commercial software packages for the social sciences, we usedthe statistical package R and its best-subsets regression package to perform theanalysis (see Dalgaard, 2008).3

We employed what is termed a subgroup regression analysis to determinewhich of the variables in the two models predicting ser + adjective and estar +adjective usage distinguished among the three levels (Hardy, 1993). The pro-cess employs indicator variables (sometimes called dummy variables) to addcategorical predictor variables (into the model described earlier) called differ-ential intercept coefficients. This reveals the effect for each group for each



predictor variable (i.e., the unique contribution of each level in our study toeach coefficient calculated for the predictor variables), producing k $ 1 differ-ence (predictor) variable models, where k represents the number of groups.4

Because this group-level coefficient effect process is derived from two regres-sion models, we adjusted the alpha for significant coefficient differences via aBonferroni adjustment to 0.025 (i.e., 1 $ (1 $ .05)1/2).

Native-Speaker Model ComparisonTo objectively identify the types of discourse that the lexico-grammatical struc-tures (dis)associated with each copula + adjective segment represent (derivedfrom the best-subsets analysis), we compare the two copula + adjective learnermodels with the native-speaker discourse model described in Table 1. Ouranalysis measured the extent to which the learners’ discourse possessed indi-cators of informational richness, hypothetical discourse, narrative discourse,and descriptive discourse.

As described earlier, we calculated the normed frequency of the occurrenceof each of these variables in the learner corpus to a scale of 10,000 per text.Subsequently, we calculated the extent to which documents representing highconcentrations of each copula + adjective model correlated with high concen-trations of each of the four native-speaker discourse types in three steps: (1) Foreach document we calculated z-score totals for both the ser + adjective and theestar + adjective models; (2) for each document we calculated a z-score totalfor each of the four discourse types in Table 2; (3) we regressed the four dis-course type z-score totals against each of the copula model z-score totals alongwith subregession analyses to assess differences between the three levels. Az-score value for any document on a given variable—be it a criterion variable asin step 1 or a regressor as in step 2—represents the extent to which that variableis represented in that document vis-a-vis all other documents. Summing a setof z-scores produces a value representing to what extent any document had aconcentration of that set of variables (see Biber et al., 2006, as well as Biber andConrad, 2001, for in-depth discussions of this technique). Thus, summing thez-scores for each document for variables representing, say, narrative discourseindicated how narrative each document is. Likewise, z-score totals for the set ofregressors representing the ser + adjective model and for the set representingthe estar + adjective model for each document yields values indicating howmuch each document more or less represented each model. (Of course, allz-scores here must be weighted according to their +/$ sign in the model.) Theregression and subregression analyses answer the following question: Whendocuments reflect the ser + adjective model and the estar + adjective model,



are they more or less encyclopedic, hypothetical, narrative, or descriptive innature? Again, because we employ two regression analyses, we adjusted the al-pha for significant coefficient differences via a Bonferroni adjustment to 0.025(i.e., 1 $ (1 $ .05)1/2).

Finally, to identify documents for the qualitative analysis of the discursivenature of copula + adjective usage, we chose to concentrate on those documentsfor each learner level that most represented each regression model derived fromthe best-subsets analysis. This simply entailed identifying those documents thathad high z-score totals for the ser + adjective models and those with high z-soresfor the estar + adjective model, as described earlier in step 2.

Results

Learner Usage: Ser + AdjectiveThe best-subsets analysis identified 21 regressors predicting ser + adjective us-age across the three levels, with 16 constituting significant regressors (p % .05).This model included twice as many predictor variables as the estar + adjectivemodel did. Additionally, the amount of variation that the ser + adjective modelaccounted for was 41% in the use of the criterion variable, whereas the estar +adjective model only accounted for 5% of its criterion variable (see below).The ser + adjective model accounted significantly for ser + adjective usage,F(21, 1576) = 54.9; p = .000.

Furthermore, the subgroup regression analysis revealed that 5 of these21 regressors significantly distinguished among the three levels of learners:pronoun - subject, adverbs of place, verb - “gustar”-like, verb - observation,and verb - past subjunctive (see Table 3). In the following we discuss these21 regressors by grouping them into six lexico-grammatical regressor cate-gories: adjectives, nouns, pronouns, adverbial constructions, grammatical verbvariables, and lexical verb variables. Within the relevant lexico-grammaticalregressor categories, we discuss the five variables distinguishing among thelevels.

Seven of the regressors represented various features of descriptive adjec-tives, although none distinguished among the three levels of learners. Table 3indicates that each variable contributed significantly to the model. For the mostpart, adjectives predicted ser + copula usage, with five associating positively(i.e., their coefficient sign was positive) and two were disassociated with theconstruction (i.e., the coefficient sign was negative). The positive, adjectivalregressors reveal that, perhaps not surprisingly, a variety of adjectives represent-ing particular inflectional properties co-occur with ser + adjective, suggesting



Table 3 Best-subsets regression model for ser + adjective

Coefficient Estimate sign Estimate Std. error t test p

(Constant) $ 81.371 9.011 $9.030 .000adjective - feminine + .050 .020 2.470 .010adjective - masculine + .040 .020 2.180 .030adjective - plural + .100 .020 5.420 .000adjective - postnominal $ $.170 .020 $10.010 .000adjective - prenominal $ $.200 .020 $9.370 .000adjective - singular + .150 .020 9.680 .000adjective - type 2 + .070 .030 2.580 .010noun - derived + .020 .010 2.030 .040noun - feminine + .020 .010 2.640 .010pronoun - subjecta + .050 .010 5.800 .000adverbs of placea $ $.060 .040 $1.560 .120adverbial clauses - cause + .040 .030 1.500 .130verb - third person + .060 .010 12.380 .000verb - infinitive + .040 .010 3.730 .000verb - periphrastic future $ $.070 .050 $1.570 .120verb - past participlea $ $.040 .020 $1.530 .130verb - past subjunctive $ $.110 .060 $1.860 .060verb - “Gustar”-likea $ $.040 .020 $2.460 .010verb - communication $ $.070 .030 $2.300 .020verb - knowledge $ $.090 .040 $2.340 .020verb - observationa $ $.080 .040 $1.980 .050

aVariable distinguishing between the levels of instruction.

that at all levels in contexts/discourses where ser + adjective segments ap-pear, learners use adjectives in general in a variety of inflections. Interestingly,however, the positive correlation with type-2 adjectives (i.e., adjectives withonly two inflections: singular and plural) tempers this conclusion because theyare also significantly associated with the criterion. Finally, although variousmorphological properties of adjectives associate with ser + adjective, this con-struction is not associated with more complex uses of adjectives because ser +adjective is disassociated with adjectives that appear in either prenominal (e.g.,bella casa “beautiful house”) or postnominal position (e.g., casa grande “largehouse”).

An analysis of the two nominal regressors indicates that a certain degreeof morphological nominal complexity occurs where ser + adjective segmentspredominate, as both had a significant positive association with the criterion



variable. The association with feminine nouns shows an association with the cri-terion variable of gender-inflectional processes, whereas the association withderived nouns (which represent nouns packaging semantic information in adense fashion, as these derived forms have a base/root morpheme and an addi-tional derivational morpheme; e.g., constitu-cion, sereni-dad, procesa-miento).It is important to note, however, that this is the only indication of ser + adjectiveassociation with semantically dense forms. As with the adjectival regressors,neither of these two nominal regressors distinguished among the three levels,suggesting that the association of ser + adjective with a certain degree of mor-phological complexity occurs from the beginning to more advanced levels ofinstruction.

Subject pronouns for the most part also appeared where there was a pre-ponderance of ser + adjective segments, although the subregression analysisrevealed that this regressor significantly distinguished among the three levelsof learners. The subregression analysis revealed that for the first-year learnerssubject pronouns were positively associated with ser + adjective (beta = 0.06;std error = 0.001), that for the second-year learners there was no association atall (beta = 0.001; std error = 0.017), and that for the third-year learners therewas a disassociation with the criterion variable (beta = $0.06; std error =0.043); the analysis also revealed that the significant difference came from thefirst-year learners rather than the other two (t = 3.00; p = .003), meaning thatthe association of ser + adjective with subject pronoun use was primarily dueto the first-year-learner data.

The best-subsets analysis identified two adverbial constructions as impor-tant contributing predictors of overall ser + adjective usage: adverbs of placeand adverbial clauses of cause. Although neither of the two contributed sig-nificantly on an individual basis, adverbs of place significantly distinguishedamong the three levels of learners in terms of predicting when ser + adjectivewould occur. The subregression analysis indicated that for the first-year learn-ers, adverbs of place were disassociated with ser + adjective (beta = $0.12;std error = 0.05), whereas these adverbs were (positively) associated with thecriterion at the second (beta = 0.07; std error = 0.06) and third years (beta =0.06; std error = 0.09), with the significant difference being attributed to thedifference between the first-year and second-year individual contributions tothe model (t = 2.45; p = .015).

There were six grammatical features of verbs that predicted ser + adjectiveusage at the three levels. For the most part, verbal variables were disassociatedwith ser + adjective. Similar to the adverbial regressors, three were importantenough to be included in the ser + adjective model but did not individually



contribute significantly: Past subjunctive usage, periphrastic future usage, andpast participles—an adjectival/verbal feature—were disassociated with the useof the criterion variable. Past participles significantly distinguished among thethree levels, as the second-year coefficients (beta = $0.08; std error = 0.03)were significantly lower (t = 2.35; p = .02) than those of the first (beta = 0.04;std error = 0.13) and third year (beta = 0.09; std error = 0.06). Gustar-likeverbs were also disassociated with ser + adjective usage at a significant level;however, it is important to note that this was a regressor that the subregressionanalysis identified as one that distinguished among the three levels. For boththe first (beta = $0.04; std error = 0.02) and the second year (beta = $0.19;std error = 0.08), its coefficient was negative, meaning that it was disassociatedwith ser + adjective. For the third-year learners, this subregression coefficientwas positive (beta = 0.25; std error = 0.10), and the difference between thethird- and second-year coefficients was significant (t = 1.97; p = .05). BecauseGustar-like verbs are syntactically complex for Spanish learners, these datastrongly suggest that ser + adjective appears in general where complex verbalmorphology does not but that more complex verbal syntax begins to becomeassociated with the criterion at more advanced stages of development. Finally,simpler verbal grammatical properties were significantly and positively asso-ciated with ser + adjective usage, as verbs with third-person morphology andinfinitives reliably associated with the presence of ser + adjective segments.

The final group of variables involves various lexical classes of verbs, all ofwhich were significantly disassociated with ser + adjective usage. These in-cluded verbs of communication and knowledge, indicating that ser + adjectiveusage is not associated with discourse where epistemic stance is manifested(i.e., where one qualifies what is commented on by reporting that some as-sertion was [only] heard or is known to be true). Verbs of observation werealso disassociated with ser + adjective usage, although this regressor signifi-cantly distinguished among the three levels. The second-year (beta = $0.16;std error = 0.06) and third-year subregression coefficients (beta = $0.21; stderror = 0.10) were negative, whereas the first-year subregression coefficientswere positive (beta = 0.07; std error = 0.07), with the difference between thefirst- and the other second-year subregression coefficients (and so the third aswell) being significant (t = 2.61; p = .009).

Learner Usage: Estar + AdjectiveThe best-subsets analysis identified 10 regressors predicting estar + adjectiveusage across the three levels, with 8 constituting significant regressors (p %.05). The value of the coefficient of determination (R2) of the model, however,



indicates that only 5% of the variance in the Spanish learners’ use of estar +adjective could be explained by this regression model. This indicates that theassociation of estar + adjective with other lexical-grammatical features is weakwithin the interlanguage for all levels of learners. The model did account fora significant amount of the overall variation in estar + adjective usage, [F(10,1590) = 8.42; p < .0001].

As observed in Table 4, most of these 10 variables distinguished signifi-cantly among the three levels, with the subgroup regression analysis revealingthat four regressors significantly distinguished among the three levels of learn-ers: type-2 adjectives (i.e., adjectives with singular and plural inflection), articlenoun segments, preverbal clitics, and possessive adjectives. It is interesting tonote that this group of variables is entirely different from the group of signif-icant regressors for the ser + adjective copula. At any rate, these differencesare considered below in the interpretation of the variables, where we discussall 10 variables by grouping them into three lexico-grammatical regressor cat-egories: nominal (noun and adjectival), verbal, and syntactic variables.

In contrast to ser + adjective segments, estar + adjective is associated withdecidedly basic grammatical properties. For example, noun phrases in discoursewhere estar + adjective occurs usually comprises nouns preceded by articlesor possessive determiners (e.g., mi mama “my mother,” la universidad “theuniversity”) and adjectives that have only two inflections (e.g., inteligente “in-telligent”) or adjectives in their singular form (alta “tall” [feminine]). Three ofthe four level-distinguishing regressors identified in the subregression analysis

Table 4 Best subset regression model for estar + adjective


(Constant) $ $4.460 3.518 $1.267 .205adjective - singular + .010 .003 2.459 .014adjective - type 2a + .020 .009 2.616 .009noun - singular .000 .002 $1.716 .086article noun segmenta + .010 .002 3.544 .000possessive adjectivea + .010 .003 3.669 .000verb - “Gustar”-like $ $.020 .008 $2.419 .016verb - present participle + .030 .011 2.364 .018verb - probability + .020 .011 1.871 .062clitics - preverbala + .020 .005 3.617 .000adverbial clauses - cause + .020 .009 2.326 .020

aVariable distinguishing between the levels of instruction.



were nominal in nature. Type-2 adjectives were found to distinguish signifi-cantly between first- and third-year learners (t = 2.73; p = .006), indicatingthat the trend to associate inflectionally simple adjectives with estar + adjec-tive appears to become stronger as learners progress in their acquisition ofSpanish. This predictor variable was disassociated with the criterion variable(beta = $0.01, std error = 0.009) for the first-year students and was positivelyassociated with estar + adjective for the second (beta = 0.01, std error =0.021) and third year (beta = 0.13, std error = 0.046). The article noun seg-ment significantly distinguished only between first- and second-year learners(t = 3.30; p = .001). This regressor was weakly associated with the criterionvariable for first-year (beta = 0.002; std error = 0.003) and third-year students(beta = 0.003; std error = 0.011) and only slightly more associated with es-tar + adjective for second-year students (beta = 0.018; std error = 0.005).Finally, possessive adjectives significantly distinguished between second-yearand third-year learners (t = 2.78; p = .005). This regressor was found to beweakly associated with the criterion level for the first year (beta = 0.008; stderror = 0.003) and the third year (beta = 0.003; std error = 0.011) and onlyslightly more associated with estar + adjective for the second-year writing(beta = 0.041; std error = 0.010).

Among verbal regressors, the significant predictor variables also showedno evidence that complexity is associated with the criterion. Although Gustar-like verbs are usually associated with complex syntax, in the learners’ writingthis variable is negatively associated with the occurrence of estar + adjective.The other grammatical verb form—present participle—is expected to co-occurwith estar + adjective because it is mostly associated with estar to formthe progressive aspect. Indeed, its beta coefficient was the highest of thoseregressors included in the best-subsets analysis (0.030).

Two syntactic features were positively associated with estar + adjective.Preverbal clitics positively associated with estar + adjectives at all levels, per-haps the only indication of complexity associated with this phrase structure.The other syntactic regressor, causal adverbial clauses—which usually startedwith the conjunction porque—also predicted criterion usage. Preverbal cliticswas the only syntactic regressor variable that distinguished significantly be-tween learners use of estar + adjective at different levels. This variable wasweakly associated with the criterion for first-year learners (beta = 0.006; stderror = 0.007), which increases modestly yet significantly (t = 2.31; p = .021)into the second and third years, with the association being greater for second-(beta = 0.033; std error = 0.011) and third-year (beta = 0.056; std error =0.019) learners.



Native-Speaker Model ComparisonAs explained earlier (see the Corpus Description section), our analysis alsoincluded a measurement (via regression analysis) of the extent to which thelearners’ texts with high concentrations of each copula + adjective model re-lated with high concentrations of each of four types of native-speaker discoursetypes: informational richness, hypothetical discourse, narrative discourse, anddescriptive discourse. The native-speaker model comparison indicated thatthree native-speaker discourse types combined significantly and individually topredict where the ser + adjective learner model occurred: hypothetical, narra-tive, and descriptive (see Table 5). As observed in Table 6, three also combinedto predict where the estar + adjective learner model held: information rich,hypothetical, and narrative.

The information-rich discourse regressor indicates the extent to which doc-uments reflecting a copula + adjective model is accompanied by semanti-cally dense discourse. Considering the sign of the coefficients—specifically,whereas the encyclopedic regressor in the ser + adjective model was signifi-cantly negative—ser + adjective usage is not semantically dense. Interestingly,

Table 5 Native-speaker discourse-type predictions of documents matching ser +adjective model


(Constant) + 0.001 0.131 9.007 .995information rich $ $0.079 0.045 $1.776 .076hypothetical $ $0.303 0.039 $7.766 .000narrative + 0.376 0.124 3.030 .002descriptive + 0.350 0.114 3.060 .002

Note. F(4, 1596) = 24.38; p = .000; multiple R2: 0.06; adjusted R2: 0.06.

Table 6 Native-speaker discourse-type predictions of documents matching estar +adjective model


(Constant) + 81.371 9.011 $9.030 .000information rich + 0.129 0.026 4.954 .000hypothetical + 0.059 0.023 2.574 .010narrative + 0.550 0.072 7.592 .000descriptive + 0.135 0.067 2.025 .043

Note. F(4, 1596) = 149.3; p = .000; multiple R2: 0.06; adjusted R2: 0.06.



documents reflecting the estar + adjective model appear to be semanticallydense. Furthermore, because the subregression analysis showed no interlevelcoefficient difference, we must surmise that this association is constant for allthree levels of instruction.

The hypothetical regressor implies how much copula + adjective usageoccurs when learners conjecture and present possible scenarios. Given theirsigns and significance levels, ser + adjective discourse appears to representthe antithesis of hypothetical discourse and estar + adjective usage containshypothetical elements. The disassociation with ser + adjective discourse maybe partially explained by the observation made earlier that epistemic verbs(representing stance) are entirely disassociated with ser + adjective usageas well as the model’s exclusion of verbal entities like the subjunctive andperiphrastic future. The subregression analysis indicates that ser + adjectiveis wholly unhypothetical at the first year and that at the second and third yearsthis disassociation “raises” to the level of “no association.” The hypotheticalregressor was disassociated with the first-year learner data (beta = $0.638; stderror = 0.071), which was significantly below those of the second-year (beta =$0.167; std error = 0.098; t = 7.652; p = .000) and third-year learner ser +adjective usage (beta = 0.024; std error = 0.052; t = 3.280; p = .001).

The estar + adjective association with hypothetical discourse is supportedin the above analysis because this model was associated with verbs of proba-bility. Additionally, the learner estar + adjective regression analysis includedcausal adverbial clauses in the estar + adjective model, and cause-effect rela-tionships are an important tool for hypothesizing. This hypothetical regressorwas not associated with the first-year coefficients (beta = $0.638; std error =0.071), which were significantly below the second-year (beta = 0.055; std er-ror = 0.040; t = 4.042; p = .000) and third-year (beta = $0.029; std error =0.001; t = 3.280; p = .001) coefficients.

The narrative regressors generally indicate where learners used a cop-ula + adjective model accompanied by story-telling elements, although notnecessarily whole narrations. Both copula + adjective segments appear to besignificantly associated with the presence of narrative features. The subregres-sion analysis indicates that both the second- and third-year learners generatemore narrative features where ser + adjective occurs than first-year learners:Although the coefficients for the second-year (beta = 1.031; std error = 0.192)and third-year (beta = 1.015; std error = 0.379) data were not significantlydifferent (t = 0.030; std p = .976), the difference between the second- and first-year coefficients (beta = 0.133; std error = 0.177) was significant (t = $3.450;std p = .001). The subregression analysis indicates that the association of



estar + adjective segments with narrative features remains constant throughthe three levels, as there were no significant interlevel coefficient differences.This is consistent with the learner regression analysis, which showed thatpresent participles, which denote durative aspect—an important element ofstories—were associated with estar + adjective.

Both copula + adjective learner models were associated with descriptivefeatures, although the ser + adjective association was significant. This mightseem surprising given the operationalization of Spanish descriptive discourseoffered by Biber et al. (2006), which is almost entirely devoid of narrativefeatures. The implication here is that both copula + adjective segments operatein both narrative and descriptive contexts beyond the first year of instruction.We see a significant transition toward greater association of ser + adjectivesegments with descriptive features from first (beta = $0.154; std error =0.168), to second (beta = 0.989; std error = 0.165), to third year (beta = 1.417;std error = 0.350), with the second-year coefficients being greater than the first(t = 4.880; p = .000) as well as the third-year coefficients being greater thanthe first (t = 3.271; p = .001). Finally, It is important to note that strength ofassociation of estar + adjective segments with narrative features (beta = 0.550;std error = 0.072) is almost four times as much as with descriptive features(beta = 0.135; std error = 0.067).

Qualitative AnalysisWe contextualize the following qualitative analysis in consideration of thelearner models presented above and of their association with the precedingnative-speaker discourse models. Ser + adjective discourse serves first-yearlearners in highly descriptive discourse. The first-year documents reveal thatser + adjective segments are employed to relate descriptions containing multi-ple chained adjectives where ser tends to be the most frequently inflected verb.The following are segments from midterm-exam letters students in a first-yearcourse wrote to a Mexican friend to describe their girlfriend/boyfriend andhis/her family.

(1) yo estoy bien porque yo tengo novia. se llama jessica. ella [es] bonita,inteligente y elegante. ella tiene veinte anos. ella es de oregon. y [es] moreno,bajo y muy bonita. ella lleva camiseta verde y jeans azules. sus ropas es muchodolares. ella gusta bailar y cantar para mi. ella gusta tenıs . . . la madre dejessica [es] bonita, inteligente y bajo. se llama velerie. nosotros jugamos tenismucho. ella [es] bueno. nosotros aprendamos la universidad. ella lleva camisaverde y los jeans azul en la universidad . . . (I am well because I have a girlfriend.Her name is Jessica. She is beautiful, intelligent and elegant. She is 20 years



old. She is from Oregon and she is a brunette, short and very beautiful. Shewears a green t-shirt and blue jeans. Her clothes cost a lot of dollars. She likes todance and sing for me. She likes tennis. Jessica’s mother is beautiful, intelligentand short. Her name is Valerie. We play tennis a lot. She is good. We learn it atthe University. She wears a green shirt and blue jeans at the university . . .)

(2) yo soy bien porque yo soy amo con novia, selena. ella [es] bonita ysimpatica. ella [es] soltera y practicar. ella es alta y la ropa es mocha colores.mi muchacha lleva rojo gora, blanco jacqueta, azul jeans, y negro sandalias.ella es mi amora. selena (stays) con madre en casa grande. la familia [es] baja.la madre [es] rica y lista y soltera . . . (I am well because I am in love withmy girlfriend, Selena. She is beautiful and nice. She is single and practical.She is tall and she wears clothes in a lot of colors. My girl wears a red cap,white jacket, blue jeans, and black sandals. She is my love. Selena stays withher mother in Casa Grande. Her family is small. Her mother is rich, smart andsingle . . .)

In both of these samples we see simple discourse, grammar, and lexicon,with few verbs except for the copula and an overuse of subject pronouns.Additionally, although there are numerous adjectives in both segments, it isapparent that noun + adjective segments are scarce. These first-year samplesare nonnarrative and possess almost no conjecturing.

Among second-year learners, ser + adjective segments appear in list fashionin discourse with few conjunctions expressing interpropositional relationships(e.g., ser + adjective + que “copula + adjective + that”). Such loosely con-nected discourse not only describes people, places and concepts, but it alsodescribes evaluations and reactions to events and states. As the learner modelsuggests, there is a marked absence of epistemic verbs to demonstrate thestance (verbs of knowledge, pienso que “I think that”; verbs of perception,vemos que “we see that”; verbs of communication, se dice que “it is saidthat”). Instead, copula + adjective segments present (seemingly) indisputableassertions. Structurally speaking, we see subject pronouns omitted to markcontinuity; still, there are various referents and allusions to the things they dofrequently. This probably accounts for why ser + adjective segments are asso-ciated with a mix of descriptive and narrative features. Finally, the derivationalsophistication—and thus semantic density—of the nouns employed is slightlygreater at this level in nouns, although these are mostly cognates. The followingis an argumentative essay a second-year student wrote using short stories as thetopic.

(3) . . . este cuento es un ejemplo que muchos padres estan usando la tele-vision como ninera. pienso que esto es un problema porque los jovenes no saben



si es realidad o no. los ninos no reciben la atencion que necesitan para crecer.tambien pienso que los jovenes necesitan atencion y amor en los primerosanos mas que de cuando [son] maduros porque cuando son jovenes ellos nosaben que [es] malo o que [es] bueno. tambien, la television [es] mala paralos padres. para los adultos la puede ser un escape tan ellos no tienen hacertrabajo, o cosas diferentes que necesitan hacer durante el dıa. pero, tambienpienso que hay diferentes programas que [son] buenas. hay programas queensena como cocinar, leer (para los ninos), y que dice que esta haciendo en elmundo hoy. no todos de los programas de television [son] mala. pero yo piensoque [es] malo usar la mas de necesario. (. . . this story is an example that manyparents are using the television as babysitters. I think this is a problem becauseyoung people don’t know whether it is real life or not. Children do not receiveattention enough to grow up. I also think that young people need attention andlove in their first years of life more than when they are mature because whenthey are young they don’t know what is good or what is bad. Also, televisionis bad for parents. For adults it can be an escape because they don’t have to dotheir work or the different things they need to do during the day. But, I alsothink that there are different programs that are good. There are programs thatteach you how to cook, to read (for children) and that tell you what is beingdone in the world today. Not all the TV programs are bad, but I think it is badto use it more than necessary.)

With the third-year learners, ser + adjective is less frequent, reflected by alower overall average z-score of ser + adjective. It is now mixed among otherverbs in the third person and adjectives modifying nouns. The discourse is de-scriptive and evaluative in nature, with references to relevant events, producinga mix of descriptive and narrative elements. The following texts are expositoryessays students wrote in a third-year course about different occupations.

(4) al principio de su vida, el bebe atleta es una hija diferente de sushermanas. el grito del bebe [es] mas fuerte, el apetito mas famelico y elcuerpo pequeno mas musculoso que los otros bebes . . . de repente, en la escuelaprimaria, es la estrella de su partido de futbol y la parte necesaria entre suequipo de basquetbol. al fin, no se puede negar todos los hechos, ella esatleta. [es] seguro que hay cualidades particulares para las atletas; factoresque definen las mujeres que aman los deportes . . . mientras que la atleta estaentrenandose, se come un dietetico rico con una variedad de las frutas y lasverduras. sin las vitaminas y minerales de estas comidas, el cuerpo no funcionamejor . . . se come mucho pescado y tofu, [es] justo porque los dos son comidassaludables sin mucha grasa . . . en el concepto de la diversion, el cuerpo de laatleta es su templo. por eso, no pasan los viernes bebiendo cerveza y fumando



cigarrillas. todas las actividades giran de la salud y se mantienen la buenasalud. [es] necesario que las atletas pasen sus noches jugando los juegosactivas como escondite y jugar al corre que te pillo. (At the beginning of herlife, the baby athlete is a different daughter from her sisters. Her crying isstronger, her appetite is more ravenous. And her small frame more muscularthan the one of the other babies . . . Suddenly, in grade school, she is the star inher football game and the main player in her basketball team. At the end, youcannot deny all the facts, she is an athlete. It is sure that there are particularqualities to athletes, factors that define women that love sports . . . While theathlete is training, she has a rich diet with a variety of fruit or vegetables. Withoutthe vitamins and minerals in this food, her body couldn’t work better . . . a lotof fish and tofu is eaten. It is so because both are healthy foods without muchfat. On the entertainment side, the body of the athlete is her temple. That’s whyshe doesn’t spend her Fridays drinking beer and smoking cigarettes. All heractivities go around her health in order to keep her healthy. It is necessary thatathletes spend their nights playing active games such as hide and seek or runand catch.)

(5) los musicos es distingue por no estar religioso. muchos de ellos nocreen que haya un dios. actualmente, [es] ironico, porque los musicos vivencomo no creen en Dios, pero tan pronto como ganen un premio, lo agrade-cen . . . la dietetica no [es] similar entre musicos. unos musicos se distinguenpor su dietetica de alcohol y drogas. ellos tambien fumar cigarrillos, o otrassustancias, y asistir a fiestas todas las noches, entonces casi nunca duermen.unos musicos estan muy saludable, y estan vegetarianos estrictos . . . musicosa veces tienen su propia familia. tienen esposos y a veces hijos. tener unafamilia es muy difıcil cuando los musicos siempre estan viajando. (Musiciansare known for not being religious. A lot of them don’t believe there is a God.Actually, it is ironic because musicians live as they don’t believe in God, butas soon as they are awarded a prize, they thank God . . . The diet is not similaramong musicians. Some musicians distinguish themselves for having a dietwith alcohol and drugs. They also smoke cigarettes or other substances, andthey attend parties every night. So they almost never sleep. Some musicians arevery healthy and they are strict vegetarians. Musicians sometimes have theirown families. They have spouses and sometimes kids. Having a family is verydifficult when the musicians are always traveling.)

For the most part, however, important information is packaged into nominallexemes (adjectives and nouns) with a derivational morpheme (e.g., salud-able“healthy,” muscul-oso “muscular,” cuali-dad “quality”). Still, cognates prevailand there is creative derivation (e.g., the neologism diet-etico “diet”). Finally,



subject pronouns are scarce perhaps due to topic continuity. As with the first-year learners, we see expression of stance via epistemic verbs, and statementsare given as unqualified facts.

Regarding the estar + adjective segments, their principal discourse func-tions appear to be narrative and descriptions within narrations. In the first year,estar + adjective mostly appears with a fixed expression such as estoy feliz“I am happy” or is used in descriptive contexts where ser was required withadjectives such as bonita “pretty” and grande “large.” The following examplescome from in-class letters that learners wrote to a friend. The examples relatelife events as well as describe familiar people and places.

(6) querida maria, ¡hola! [estoy] muy feliz porque yo tengo un novio nueva.su nombre es Pete. Pete tiene veinte anos. mi novio es de indiana. Pete esmoreno y alto. mi novio es muy inteligente y optimista. (Dear Mary, Hello! I amhappy because I have a new boyfriend. His name is Pete. Pete is twenty yearsold. My boyfriend is from Indiana. Pete has dark hair and is tall. My boyfriendis very intelligent and optimist.)

(7) ¡hola aubrey! fue a costa rica para un semana. fue a un hotel en laplaya dominical de costa rica. ¡la playa dominical [estuvo] mas bonita! viajocon mis padres y mi hermano. fue en un avion y lo [estuvo] mas grande. dormıen un hotel en la playa. el mar [estuvo] muy largo y yo pesque mucho. ¡megustaron las comidas mucho! (Hello Aubrey! I went to Costa Rica for a week.I went to a hotel in the Dominical beach in Costa Rica. The Dominical beachwas very beautiful. I traveled with my parents and my brother. I went by planeand it was very big. I slept in a hotel by the beach. The ocean was very big andI fished a lot. I liked the meals very much!)

Learners couple their assessments of peoples’ states with causes embed-ded in porque “because” adverbial clauses. The semantically dense nature isattributable to the use of various cognates that are “long” words, which describeplaces, disciplines, actions, or events.

In second-year writing, estar + adjective is used in narrative and descrip-tive discourse that is detached from the writer. Writing is elicited from tasksin which students must summarize events and describe characters in readingsor audiovisual material. The description of events favors the use of the presentparticiple. The summarizing task also allows students to speculate about charac-ters’ motives or actions by using verbs of probability such as creer “to believe”and causal adverbial clauses that begin with the porque “because” causal con-junction. These are the types of behaviors that account for the hypotheticalnature identified for estar + adjective.



(8) la madre regresa de la cocina, ella piensa que el muchacho [esta]dormido. sin embargo, el muchacho [esta] despierto todavıa y esta mirando latelevision. la pantalla [esta] oscura, ası la madre le pregunta a su hijo que elhace. el hijo responde que el esta esperando la muchacha en el televisor. estoes muy triste, porque obviamente la madre no es una madre muy bien . . . el hijocree que la muchacha en el televisor es su amiga. el piensa esto porque creeque la muchacha esta hablando a el . . . (The mother returns to the kitchen, shethinks that the boy is asleep. However, the boy is still awake and he is watchingthe television. The screen is dark so she asks him what he is doing. The sonresponds that he is waiting for the girl in the television. This is very sad becauseit is obvious that the mother is not a good mother . . . The son believes that thegirl in the television is his friend. He thinks so because he thinks the girl isspeaking to him . . .)

(9) la personalidad del protagonista, juan, era tımido y tranquilo. le gustaba[estar] solo con sus pensamientos. el sonaba antes de acostarse de, todaslas peripecias de un viaje a francia, pero no pudo costearlo. no creo quejuan [estuviera] satisfecho con su vida y su trabajo porque sonaba con ir afrancia. el querıa experimentar nuevas cosas. su vida era muy rutinario y querıacambiarla. el no [estaba] satisfecho con su trabajo porque no pudo costear elviaje . . . el narrador nos sugirio que juan escribiera las cartas porque la letratuvo los mismos rasgos esenciales. creo que el narrador nos dijo eso porque eles anonimo y nos quiere hacer creer que juan [estuviera] loco y se muriera. (Thepersonality of the main character, Juan, is shy and quiet. He liked to be alonewith his thoughts. He used to dream before going to bed about his adventuresin a trip to France, but he couldn’t afford it. I don’t think that Juan was satisfiedabout his life and his work because he dreamed about going to France. Hewanted to experience new things. His life was a routine and wanted to change it.He was not satisfied about his work because he could not afford his trip . . . . Thenarrator suggested to us that Juan wrote the letters because his handwriting hadthe same main features. I think the narrator told us so because he is anonymousand he didn’t want us to believe that Juan was crazy and he died.)

Third-year students combine different discourse patterns, using estar +adjective in argumentative texts where they describe two opposing sides ofan issue, as in (10). The writer is comparing the culture or life of Americanand Hispanic cultures, which gives the text a hypothetical reading. They useestar + adjective to produce personal narratives such as what happened on abirthday. It is noteworthy that preverbal clitic forms are not only used with someGustar-like constructions but also with verbs in middle voice (e.g., infiltrarse



“to be infiltrated”) and passive constructions (e.g. ensenarse “to be taught”),making the discourse more encyclopedic-sounding.

(10) . . . . el sueno americano se infiltra desde juventud, es evidente por tele-vision, escuela, la cultura y ejemplos del gobierno y polıticos. esta influenciaes subconsciente pero fuerte y se ensena el americano que la unica cosa que senecesita hacer es trabaja fielmente y comprar las cosas correctas y eventual-mente se recibira la vida perfecta. / . . . ademas el americano siempre [esta]preocupado, consumiendo y trabajando pero viva muy poco. (The Americandream is instilled from youth, it is evident in television, school, the cultureand the examples from the government and the politicians. This influence issubconscious but strong and it is taught to the American that the only thing thathe needs to do is to work loyally and to buy the right things and eventually hewill receive a perfect life. / Moreover, the American is always busy, consumingand working but he lives very little.)

(11) mi familia recordaron mi cumpleanos! pero, en este momento mispadres [estaban] enojados conmigo. yo no querıa pelear, entonces, termino elpapel y nos sentamos a comer. mis hermanas mi desean un buen cumpleanosy me dieron un regalo bellısimo. mi padre me hablaba de un film que le habıagustado. yo pide a mi madre si a ella le a gustado y ella me respondio, no, enun tono agresivo. mientras la entera cena ella solo me dijo, no, y, si, y fue muymolestosa. no me hablo durante mi fiesta de cumpleanos! [estaba] muy tristeeste noche y la proxima dıa. (My family remembered my birthday! But, at thatmoment my parents were angry with me. I didn’t want to argue so I finishedmy paper and we sat to eat. My sisters wished me a good birthday and gave mea very beautiful present. My father was talking to me about a film he had liked.I asked my mother if she had liked it and she answered no, in an aggressivetone. During the whole dinner she told me no and yes and I was very angry.She didn’t talk to me during my birthday party! I was very sad that night andthe next day.)

Discussion and Conclusions

Studying the acquisition of the Spanish copula provides insights into the in-teraction among syntax, semantics, pragmatics, morphology, and vocabularyduring development in one of the most basic of syntactic structures—namely,attributive sentences (Leonetti, 1994). Spanish requires learners to choose be-tween two copulas in attributive sentences in accordance with a variety ofcontextual considerations and in consideration of a variety of levels of rep-resentations. Whereas relevant L2 research has examined (a) copula choice



and (b) the function of attributive sentences in terms of orders of acquisi-tion in different learning contexts (Gunterman, 1992; Ryan & Lafford, 1992;VanPatten, 1985, 1987) and (c) the contextual and semantic factors that predictlearner usage of this construct as compared to native speakers (Geeslin, 2003a,2005), the present study is the first to provide a corpus-based analysis of thelexico-grammatical features that co-occurred with the Spanish copula (i.e., serand estar) + adjective usage and so the different discursive functions that theser + adjective and the estar + adjective segments play at three learner levelsand in comparison to native-speaker models. The study delves into importantlearner issues—for example, the discourse types learners associate with copulausage (Gunterman, 1992), the strong influence of contextual cues on copulachoice (Geeslin, 2003a, 2003b)—identified in the S/E research but not fullydeveloped to date. The results overall revealed the following: (a) Both ser +adjective and estar + adjective were associated with simple discourse at alllevels; (b) ser + adjective appears in descriptive and evaluative discourse wheremuch linguistic complexity reliably occurs; (c) estar + adjective is present innarrations, descriptions, and hypothetical discourse where, nonetheless, littlelinguistic complexity typically occurs.

Specifically, findings showed that the model predicting ser + adjectiveusage identified more variables (n = 21) and accounted for more variation(41%) than the estar + adjective model, which only identified 10 predictorsand 5% of the variation. It seems that at beginning levels of instruction, learnersfind ser + adjective more communicatively productive and thus more easilyassociated with a large array of features within their interlanguage, althoughthese features are basic grammatical and lexical items. Ser + adjective is oneof the first copula segments taught and recycled during various semesters,whereas estar + adjective is primarily used at beginning levels in routinesand formulaics like estar + bien, mal, ocupado, enfermo. In this sense, theinput provided by teacher, materials, and other students in the class throughtask completion emphasizes the use of ser + adjective over estar + adjectiveconstructions and, therefore, encourages more ser + adjective usage. Thesefindings are in line with early SLA studies on ser/estar acquisition, which foundthat ser + adjective was acquired well before estar + adjective (Gunterman,1992; Ryan & Lafford, 1992; VanPatten, 1987) presumably because of thehigher frequency and saliency of ser + adjective in instructional and naturalisticinput.

It was also found that many of the lexico-grammatical predictor variables inboth models were characteristics of simple discourse and they did not differen-tiate learners’ copula + adjective usage among the three levels of instructions.



All levels seem to use copula + adjective as a discourse tool such as to commu-nicate evaluatives like es importante, lastima “it’s important, it’s a shame,” andso forth. However, when the discourse becomes more syntactically and gram-matically complex, ser + adjective segments are absent and estar + adjectivesegments become more prevalent. On the one hand, these observations contrastwith native speakers, who use ser + adjective for evaluative purposes in a widevariety of discourses, simple or complex; on the other hand, they are consistentwith natives’ propensity to use estar + adjective in more complex discourse(Collentine, 2008).

The ser + adjective model was mostly associated with adjective and gram-matical/lexical verb variables. Various morphological properties of adjectives(e.g., feminine, plural) associated with ser + adjective, whereas more com-plex adjectival syntactic processes (e.g., prenominal or postnominal adjectives)emerged as disassociated. Most of the verbal variables reflecting complex syn-tax (e.g., periphrastic future, past subjunctive, Gustar-like verbs) were disas-sociated with the copula construction and started to emerge as associated withser + adjective at advanced levels of instruction. Other features such as null sub-jects also indicated some grammatical sophistication at advanced levels whereser + adjective became less frequently used. As for the discursive functionsserved by the co-occurrence of the variables in the predictive model for ser +adjective, the disassociation of verbs of observation and communication withthe construction indicated a discourse that was nonepistemic/nonhypotheticalin nature. Comparisons with native speakers’ discourse showed that learnersused ser + adjective in discourse that is highly descriptive in nature and accom-panied by story-telling elements, especially at advanced levels of instruction.These findings corroborate those of Gunterman (1992), who examined learnersin study-abroad contexts where ser + adjective was indicative of descriptivediscourse. Spanish learners, regardless their level, associate an evaluative stancewith ser + adjective.

The estar + adjective regression analysis revealed a weak association withother lexical-grammatical features. This indicates that throughout the early tomiddle stages of acquisition, this phrase structure is weakly integrated into theinterlanguage in terms of being a productive, necessary tool for the types ofcommunication in which learners engage. In other words, the use of estar +adjective segments is not obviated—or evoked, cognitively speaking—whenlearners use their standard repertoire of lexico-grammatical tools. All told, thestory is complicated for estar + adjectives, which ultimately might accountfor its late acquisition. On the one hand, it appears where there is little as-sociated inflectional sophistication (recall that Spanish is a highly inflectional



language, both in verbal and nominal constructs.). The few variables associatedwith estar + adjective suggest that it appears in discourse lacking in overallinflectional sophistication (e.g., type-2 adjectives or adjectives with singularand plural inflections, singular nouns, negative association with Gustar-likeverbs). Its use places significant processing demands on learners, as shownby Geeslin (2003a, 2003b), who noted that learners use estar + adjectivesegments according to pragmatic factors (which require a consideration of amultitude of contextual variables) rather than according to semantic/lexicalconstraints (which are local to the copula + adjective phrase structure). Withthis in mind it is not unreasonable to conjecture that learners are more likelyto have the cognitive resources to employ it when other structural demandsare not overwhelming. On the other hand, estar + adjective segments usuallyoccurred in discourse that was semantically dense—probably because it wasbased on sources, with hypothetical elements (e.g., verbs of probability, causaladverbial clauses), narrative features (e.g., present participles), and descriptivefeatures (e.g., of adjectives type 2). Like study-abroad learners (see Gunterman,1992), in an instructional context, learners also use estar + adjective when theyneed to fulfill communicative functions that go beyond description. Learners’awareness and experience with different kinds of discourse (e.g., narration,arguments) at advanced levels of instruction might explain these associationsrather than learners’ acquisition of discrete grammatical and lexical items,given the simplicity of their interlanguage, as Lafford (2004) asserted for thegains observed for learners studying abroad. Cheng et al. (2008) concluded thatmore abstract registers can evoke greater estar + adjective usage. In this study,learners at advanced levels of instruction were asked to complete written tasksin which they summarized a story or argued in favor of a position. We haveno way of knowing if the task demands affected learners’ estar + adjectiveusage, however, the results indicate that it would be possible that weighty pro-cessing demands of discourse where referents and events were detached fromthe writer and in some cases based on reading with grammar and vocabularybeyond their linguistic knowledge could have lead to more estar + adjectiveuse. The semantic and pragmatic goals of narratives as well as hypothetical dis-course seem to entail more consideration of the states of affairs of referents andchanges in the background of a story or situation, thus being more compatiblewith estar + adjective.

The findings in our study provide evidence of the influence of the lexico-grammatical and discourse predictors in learners’ copula + adjective usage, asattested in previous studies (Cheng et al., 2008; Geeslin 2003a, 2003b, 2005).Under classroom setting conditions, learners’ written discourse in response to



tasks designed to advance their communicative abilities or testing them revealedthat copula + adjective usually co-occurred with simple linguistic features. De-velopmentally, interesting and seemingly contradictory observations emergedabout the use of the two copula + adjective segments studied here. In gen-eral, the phrase structure (ser + adjective) associated with greater linguisticcomplexity is typically associated with simple types of discourse, whereas thephrase structure (estar + adjective) associated with less linguistic complexityis typically associated with more complex discourse types. The implicationof these observations is that processing demands interact with the types ofdiscourse that learners can produce as they develop and the types of lexico-grammatical structures they produce in those types of discourse, as Chenget al. (2008) argued. The relatively simple linguistic features associated withestar + adjective may be an indication that learners hit a wall when attemptingto communicate messages within complex discourse structures. Conversely, thelearner models reported here may indicate that the simple nature of discoursestructures like descriptions may afford learners processing resources for callingup relatively complex structures. All in all, the present analysis suggests thatcopula usage and choice depends on the amount of processing resources avail-able and the discourse structure a learner produces. Consequently, we have amuch better understanding of the complex ways that pragmatic and discursivefeatures influence how learners make copula choices (in ways that are not hownative speakers make copula choices), as Geeslin (2003a, 2003b, 2005) hasargued.

The results of our study have pedagogical implications for teaching S/E +adjective. It makes sense to teach ser + adjective to beginners first becauseof its frequency and communicative value; however, estar + adjective prob-ably deserves more attention and practice in different kinds of discourse(e.g., narration and hypothetical situations). Given that there is some evi-dence that estar + adjective segments are more prominently distributed incertain kinds of discourse (cf., Collentine, 2008), exposure to input withestar + adjective-relevant types of discourse should have a positive effect.What Spanish educators might examine is whether estar emerges in learnerproduction reliably as a result of having to write estar + adjective-relevanttypes of discourse such as exploratory writing—as Cheng et al.’s (2008) studysuggests—or narratives. An interesting corollary would be whether such dis-course types emerge as a result of asking learners to produce estar + adjectivesegments.

Revised version accepted 5 March 2009



Notes

1 Screening data for inflated correlations is difficult in the linguistic sciences. Whereastwo words might represent the same part of speech (e.g., adjectives), the inflectionalmorphology of adjectives can represent important distinctions for learners, such asthose that are singular and those that are plural. Additionally, natural language isextremely redundant as communication systems go, and so our initial screeningprocess sought to balance semantic and structural collinearity considerations.

2 The analysis identifies the optimal combination of regressors for a criterion bycomparing and contrasting all possible predictor-variable combination values forMallow’s Cp, which simultaneously represents any given model’s bias (i.e., how wellit predicts the referent variable) and the variation associated with that bias. Thebest-subsets analysis compares—numerous—combinations of variables byidentifying (a) the number of and (b) which predictor variables balance bias andvariance where the mean-square error of a combination is small. The resultingmodel has a small bias with the least amount of predictor variables, such that theresulting model contains a highly reduced number of predictor variables whosecombination predicts values for the criterion variable that are closest to the observedvalues. Statisticians recommend best-subsets analysis when the potential number ofpredictor variables is large because stepwise methods tend to miss identifyingmodels that are equally good at balancing bias and variance as the resulting modelthey produce.

3 R is an open-source statistical package based on Bell’s Labs (proprietary) Sprogramming language, a standard among statisticians for statistical programming(see http://www.r-project.org/). R is gaining increasing popularity in academiccircles because of its reliability, statistical accuracy, and flexibility (it containsnumerous [tested] add-on modules) and due to the fact that it is freely available inthe public domain.

4 As a simplified example, because this process extrapolates the true coefficient foreach level, we can extrapolate individual level effects in the following fashion. Forinstance, if the X1 coefficient were 8.0 for level 1, 5.0 for level 2, and 3.0 for level 3and if the process calculates the difference coefficient for X1 between levels 1 and 2to be 3.0 (i.e., 8.0 $ 5.0 = 3.0) and between levels 2 and 3 to be 2.0 (i.e., 8.0 $5.0 = 3.0), we infer that the difference between levels 1 and 3 by summing thesetwo difference coefficients, or 5.0 (i.e., (8.0 $ 5.0) + (5.0 $ 3.0)). See Hardy(1993) for details.

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