the age-length-onset problem in research on second language acquisition among immigrants

Language Learning 56:4, December 2006, pp. 671–692C© 2006 Language Learning Research Club, University of Michigan

The Age-Length-Onset Problem in Researchon Second Language Acquisition

Among Immigrants

Gillian StevensUniversity of Illinois at Urbana-Champaign

Studies investigating the possible effects of age at immi-gration (a proxy for age at onset of second language learn-ing) on second language acquisition among immigrantsoften explicitly take the effect of length of residence in thedestination country (a measure of exposure to opportuni-ties to learn the second language) into account. A thirdvariable, age at testing, recently has caught the atten-tion of some scholars. However, the three variables “ageat immigration,” “length of residence,” and “age at test-ing” are linearly dependent. The easiest and most commonresponse to this problem is to ignore one or two of the vari-ables. In this article I show that this strategy can result inpotentially misleading conclusions and then suggest somestrategies for dealing with the problem.

Because of the strong interest in the possibility of criticalperiods in language learning, numerous studies have investigatedthe possible effects of age at immigration (a proxy for age at onsetof second language [L2] learning) on second language acquisition(SLA) among immigrants. Because language learning takes at

I am grateful to A. R. Gillis, Hiromi Ishizawa, Tim F. Liao, Michael Long,Mary McKillip, Jennifer Ortman, Ilana Redstone Akresh, Gray Swicegood,and the journal reviewers for helpful comments in the preparation of thismanuscript. This research was supported by NICHD grant HD047299-01.

Correspondence concerning this article should be addressed to GillianStevens, Department of Sociology, University of Illinois at Urbana-Champaign, 702 S. Wright St., Urbana, IL 61801. Internet: [email protected]

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least some amount of time, studies take into account the effectof immigrants’ length of residence in the destination country inorder to isolate the effects of age at onset of L2 learning. Somescholars are also beginning to consider the possibility that age attesting is related to proficiency in an L2. The three variables “ageat immigration,” “length of residence,” and “age at testing” are,however, linearly related. I show that studies considering onlyone or two of these variables might yield ambiguous conclusions.I then suggest several ways of dealing with the problem.

The Identification Problem: Age-Length-Onset

There are numerous trios of variables involving the dimen-sion of time in which values on two of the variables determine thevalue on the third. One example consists of a respondent’s age atmarriage, length of marriage, and age at observation; a secondexample consists of date of labor force entry, years of experiencein the labor force, and date of exit from the labor force. The gen-eral problem of linear dependence among trios of variables suchas these is often referred to as the “age-period-cohort” problem.The label was applied because demographers, who are often con-cerned about cohort-related phenomena, were among the first todiscuss the general problem and because knowing a person’s age(say, 40 years) in a particular time period (say, the year 2000)yields the information that the person is a member of the 1960birth cohort. In SLA research among immigrants, the analogoussituation could be called the “age-length-onset” problem. Know-ing the age of an immigrant (say, 40 years) and the length of timethe immigrant has lived in the L2 environment (say, 15 years)yields the conclusion that the person’s age at immigration, andthus age of onset of L2 learning, is 25. More formally, if A refers tochronological age, L to length of residence, and O to age at onsetof L2 learning and all three are measured in the same metric ofyears, then

A = L + O (1)

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Because the three variables are linearly related, the covari-ances between the three variables and a dependent variable, suchas a measure of L2 proficiency (SLP), are also linearly related:

Covariance(SLP, A) = Covariance(SLP, L) + Covariance(SLP, O)(2)

One result of this linear dependence is that it is impossibleto estimate all three of the slopes in an ordinary least-squares re-gression equation in which � refers to the intercept, the �’s to thepartial slopes associated with each of the independent variables,and i to the error term,

SLPi = � + �1(Li) + �2(Oi) + �3(Ai) + εi (3)

because this equation simplifies to

SLPi = � + (�1 + �3)(Li) + (�2 + �3)(Oi) + εi (4)

Equations 2 and 4 illustrate the potential pitfall in attempt-ing to sidestep the problem and estimating only two of the slopes(or correlations or covariances) in multivariate regression analy-ses. If there are theoretical reasons to believe that all three vari-ables have unique influences on the dependent variable, then theestimates of the two slopes incorporate the third in a way thatcannot be directly disentangled. Thus, the estimated effects ofthe independent variables explicitly considered in the analysismight be biased.

The age-length-onset problem persists if the data are ar-rayed and then analyzed in tabular form. Table 1 shows theskeleton of the linear dependence among the three variables. Thecell entries show the values of the variable “length of residence”for each possible combination of age at onset (when measuredthrough age at immigration) and chronological age. For example,a respondent age 40 who entered the country of destination at


Table 1

A two-way table of age at onset and chronological age showing thevalues of length of residence in the table cells

Chronological ageAge at

onset 10 20 30 40 50 60

0 10 20 30 40 50 60

10 10 20 30 40 50

20 10 20 30 40

30 10 20 30

40 10 20

age 20 has been living in the country for 20 years. A respondentage 40 who entered at age 30 has been living in the country for10 years. The shaded cells on the diagonals show two groups ofrespondents, those who have been in the country for 10 years andthose who have been in the country for 20 years.

In Table 2, the cell entries represent the hypothetical scoreson a test of L2 proficiency arrayed by the respondent’s chrono-logical age and age at onset of L2 learning. The L2 proficiencyscores were constructed to show “pure” age-at-onset effects oc-curring because of a negative association between age at onsetand L2 proficiency. Thus, every respondent reporting a specifiedage at onset of L2 learning has the same score regardless of theirchronological age (or their length of residence in the destinationcountry). Those entering at age 20, for example, achieve a scoreof 70 on the hypothetical test regardless of their age at the timethat they took the test or how many years they have resided inthe country. In a parallel fashion, respondents who entered thecountry at age 40 achieve a score of 50 regardless of their age atthe time of the test or how many years they have resided in thecountry. Although the dimension “length of residence” is no longerreadily apparent, the shading of the cells on two diagonals showsthe 10- and 20-year length of residence groupings, respectively,just as in Table 1.

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Table 2

Array of L2 proficiency scores showing pure age-at-onset effects by ageat onset of L2 learning and age at time of observation

Chronological ageAge atonset 10 20 30 40 50 60

0 90 90 90 90 90 9010 80 80 80 80 8020 70 70 70 7030 60 60 6040 50 50

Analyses of L2 proficiency among immigrants commonly fo-cus on a limited age group (such as respondents in their thirtiesand forties, or in their twenties and thirties) for several reasons.First, the emphasis on ultimate attainment in the L2 (Birdsong,2005) leads scholars to focus on adults rather than children. Sec-ond, the practicalities associated with recruiting respondents of-ten shapes the sampling frame (e.g., immigrant adults affiliatedwith an educational institution) and thus the age range of thesample. A focus on a limited age range makes it particularly easyfor several possible relationships to appear to emerge in the data.Consider the cells contained in the interior rectangle of Table 2.The average proficiency of respondents in their forties is lowerthan that of respondents in their thirties, so it looks like theremight be a negative relationship between L2 proficiency and age.In addition, those respondents who have lived longer in the des-tination country (the lighter diagonal cells) have higher scoresthan those who have lived a shorter length of time (the darkerdiagonal cells), suggesting a positive relationship between lengthof residence and L2 proficiency. This interpretation emerges eventhough the data array was originally constructed to show onlypure age-at-onset effects. Focusing on only one age group (say,respondents in their forties) to eliminate any possibility of ob-serving a spurious relationship between age and L2 proficiency


still leaves two possible conclusions: L2 proficiency is related toage at onset or L2 proficiency is related to length of residence.

In summary, the age-length-onset problem in research onSLA among immigrants cannot be addressed by correlationalanalyses because it is impossible to estimate covariances, correla-tions, or slopes for the three independent variables (age, length ofresidence, and age at immigration) and a dependent variable suchas L2 proficiency that are independent of one another. More im-portantly, if one variable is omitted, the covariances and thus thecorrelations or slopes involving the other two independent vari-ables incorporate the omitted one in a way that cannot be disen-tangled. Tabular analyses, especially two-way analyses, hide thethird variable from view, but conclusions about the presence ofrelationships between one or more of the variables and L2 profi-ciency remain ambiguous.

Age, Length of Residence, and Age at Onset in L2 Research

Because of the strong interest in the possibility of criticalperiods or maturational constraints in language acquisition, nu-merous studies have investigated the effects of age at immigrationon some facet of L2 proficiency among adult immigrants. In gen-eral, these studies focus on only one or two of the three variables:age, age at arrival, and length of residence. For example, Johnsonand Newport’s (1989) classic study considers only age at arrivaland length of residence.

Johnson and Newport’s (1989) study clearly demonstrates,if implicitly, how difficult it is to reach unambiguous conclusionswhen investigating the relationship between age at arrival andL2 proficiency among adult immigrants. (The article also hasthe virtue of including enough data to replicate part of their re-sults.) Johnson and Newport’s study showed a negative correla-tion of −.77 between age at arrival and scores on a test of Englishgrammar skills among a sample of foreign-born Chinese and Ko-rean faculty and students who had lived in the United States atleast 5 years and whose ages at time of arrival ranged from 3to 39 years. Johnson and Newport therefore concluded that the

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substantial and statistically significant negative relationship be-tween age at immigration and test scores among this sample ofadults suggested a decline in language learning skills over child-hood and into adolescence, thus supporting the idea of matura-tional constraints.

Johnson and Newport (1989) did consider length of residencein their analysis. They checked the correlation between length ofresidence in the United States and test scores; it was only .16.They also checked the correlation between length of residence andage at immigration; it was only −.09. They therefore concludedthat length of residence seemed immaterial. They also pointedout that this conclusion was in accord with those of other studiesshowing no significant effect of the number of years of exposureon language performance for learners beyond the first few yearsof exposure (p. 82).

Let us look at their data in a slightly different way. Figure 1graphs the scores on the test of English proficiency (ELP) by age

160

190

220

250

280

0 5 10 15 20 25 30 35 40 45

Age at Immigration

r = -0.76

Figure 1. ELP scores by age at immigration (redrawn from Johnson &Newport, 1989).


at immigration for Johnson and Newport’s (1989) sample. I readthe data points from their Figure 2 and so the data points shownin our Figure 1 are only approximate rather than precise. Never-theless, the correlation is almost exact, r = −.76 instead of r =−.77, and the overall shape of the figure is quite close to theirs(see Johnson & Newport, 1989, Figure 2).

I then assigned each of the subjects a value on the variable“length of residence” using a random number generator and calcu-lated each subject’s age as the sum of the values on the variables“length of residence” and “age at immigration.” I ran 30 simu-lations. In the simulation of Johnson and Newport’s (1989) datareported here,1 the correlation between length of residence andELP is −.03 (rather than .16), and as in their data, the correlationbetween length of residence and age at immigration was mini-mal (−.06 rather than −.09). However, the correlation betweenage and ELP, which was unreported in their article, was −.63(see Figure 2).

Although it is true that the data here were partially simu-lated, it is noteworthy that they replicate the strong relationship

160

190

220

250

280

15 20 25 30 35 40 45 50 55 60

Age

r = -.63

Figure 2. ELP scores by age.

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between age at immigration and English proficiency and stillsuggest, as in Johnson and Newport’s (1989) landmark article,that the effects of length of residence are trivial. Moreover, thestrong negative relationship between ELP and age shown inFigure 2, which is present in all of the 30 simulations (and which ispredicted on the basis of the interdependence between age, lengthof residence, and age at onset; refer back to Equation 2), providesgrounds for some ambiguity about the conclusion concerning theimportance of age at onset.

Still, because of the strong theoretical expectations concern-ing the effect of age at onset on L2 proficiency, the ambiguity aboutthe interpretation of the strong relationship in the data would beinconsequential if there were no compelling or plausible explana-tions for a negative relationship between chronological age andthe respondents’ proficiency in their L2. However, Johnson andNewport’s (1989) respondents consisted of faculty and studentsat the University of Illinois. As Johnson and Newport noted, theolder subjects were more likely to be faculty and the younger onesto be students. Students, especially undergraduate students, en-counter a heavily English language dominated environment atthe University of Illinois. Every semester, undergraduate stu-dents take classes taught in English, read and write intensivelyin English, and often live on campus in English language dormi-tories. Students also have recent and extensive practice in takingtests. Faculty members, on the other hand, usually teach two orfewer classes in English, generally live off-campus with their fam-ilies, and rarely, if ever, take tests. Bialystok and Hakuta’s (1994)concerns about the differing experiences of the faculty versus stu-dent respondents in Johnson and Newport’s study thus seem verypertinent; the relationship between age at immigration and suc-cess in L2 acquisition found in the study might have been at leastpartly attributable to age/life-cycle stage effects. Moreover, themore successful performances of students versus nonstudents ontests of L2 proficiency have been observed in other studies of L2proficiency among immigrants (e.g., Flege & Liu, 2001).

Other studies have used multivariate regression analysis toanalyze the relationship between age at onset and L2 proficiency


among immigrants. Hakuta, Bialystok, and Wiley (2003), for ex-ample, used 1990 U.S. census data to analyze levels of Englishproficiency among immigrants who entered the country in the1960s and 1970s.2 The immigrants had therefore lived in theUnited States between 10 and 29 years. This sample could be rep-resented in Table 2 by the two shaded diagonals showing lengthof residence of 10 years (or, more precisely, 10–19 years for the1970s entry cohort) and 20 years (or 20–29 years for the 1960s en-try cohort). The patterned values of L2 proficiency in the shadeddiagonals suggest a strong negative relationship between L2 pro-ficiency and age at onset (or age at immigration) or between L2proficiency and chronological age. In their discussion and con-clusions, Hakuta et al. considered only the possibility that theirresults showed a strong negative relationship between L2 profi-ciency and age at onset.

Birdsong and Flege’s (2001) study focused on the relation-ship between age at arrival among three groups (those arrivingin childhood, in adolescence, and in adulthood) and measures ofL2 proficiency in English among college-educated native speak-ers of Korean or Spanish. They carefully took length of residenceinto account by holding it constant through judicious samplingprocedures. However, although the summary statistics presentedin their article (Birdsong & Flege, 2001, Table 1) clearly show thatall of the respondents arriving as children were younger at thetime of the study than those arriving in adulthood, the authorssidestepped any discussion of the relationship between chrono-logical age and the measures of L2 proficiency.

Should the Linear Dependence Be Ignored?

The default response to the age-length-onset problem in SLAresearch has been to ignore the linear dependence by omittingconsideration of one (or two) of the three variables: chronologicalage, age at onset, and length of residence. This approach works iftwo of the three variables can be regarded as indexing the samecausal phenomena or if one of the variables is unrelated to the

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dependent variable. However, if there are distinct causal interpre-tations of each of the three variables, then an analysis omittingone of them is subject to spurious findings because the relation-ships between the dependent variable and the independent vari-able(s) explicitly included in the analysis might be misspecified orbiased (refer back to Equation 4). The question about whether thethree variables (age, length of residence, and age at onset) haveunique effects on SLA among immigrants thus becomes particu-larly important.

Age at Onset of Learning an L2/Age at Immigration

Of the three variables, “age at onset” has excited the mostattention; thus, there is little need to re-review the theories pre-dicting a strong relationship between age at onset of SLA andultimate attainment in an L2 here (see, e.g., extended discus-sions in Hyltenstam & Abrahamsson, 2003, and Birdsong, 2005).In studies based on immigrants, age at onset of L2 acquisitionis usually measured by age at immigration (or age at arrival) inthe destination country. It is often considered a better measure ofthe age at onset of learning an L2 than the age at which lessonsbegan, because age at immigration marks the respondent’s be-ginning of participation in social settings effectively dominatedby the L2 (Birdsong & Molis, 2001; Johnson & Newport, 1989).

One useful way to think of age-at-onset effects is to viewthem as cohort-specific effects that linger over the cohort’s life-time because of the relevant experiences shared by all or mostof the individuals at a specified age in their individual lifetimes.These shared experiences might include biological processes re-lated to physical maturation; they might also include age-gradedsocial experiences such as intensive elementary schooling in anL2 that are available to or experienced only by those beginningL2 learning at that particular age.

It is easy, however, to conflate potential “age-at-onset” effectswith “aging” effects. Hakuta et al. (2003), for example, arguedthat their analysis of 1990 census data suggests that success in


L2 acquisition steadily declines throughout the life span, fromaround age 5 up to age 60 (p. 37). Because the decline in successwas steady with no obvious disjunctures in the negative slope overthe entire life span, Hakuta et al. argued that their results did notsupport the idea of a critical period in L2 acquisition.3 They thenoffered biological processes associated with aging, such as cogni-tive declines, as possible explanations for the negative relation-ship between success in SLA and age at immigration. However,age or aging effects can (and should) be considered as separatefrom “age-at-onset” effects.

Length of Residence

Linguists have generally considered length of residence asa measure of the time available for immigrants to have learnedthe L2. Often, a span of 5 years (e.g., Johnson & Newport, 1989)or a more generous 10 years (Birdsong, 2005) is presumed to suf-fice for the achievement of ultimate attainment in the L2 and soimmigrants’ L2 proficiency is presumed to asymptote after thistime period. Sociologists and demographers, on the other hand,have long viewed length of residence in the receiving society asalso measuring immigrants’ extent of exposure to opportunities tolearn an L2. Length of residence might index the ongoing effectsof processes of selectivity as well. Migrants might see little reasonto invest in L2 learning if they anticipate returning to their homecountry after a short time. Thus, selection processes could alsoproduce a positive relationship between length of residence andL2 acquisition in cross-sectional studies because migrants whohave been in the country for a longer time have been selected onthe basis of motivation or facility in L2 learning (Lindstrom &Massey, 1994; Stevens, 1994).

Large-scale empirical analyses almost uniformly show thatlength of residence is strongly and positively related to measuresof ELP (e.g., Espenshade & Fu, 1997; Stevens, 1999) among adultimmigrants in the United States and that the relationship ex-tends well beyond 5 or 10 years of residence. The fact that the

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relationship between length of residence and L2 proficiency mightextend well after a decade is important because it suggests thatthe common practice of left-sample censoring (i.e., excluding re-spondents who have lived fewer than 5 or 10 years in the countryof destination) does not effectively control for length of residencein analyses focusing on L2 proficiency among immigrants.

Age

The third variable, “age,” is the one most often omitted inanalyses of SLA among immigrants. What theoretical conceptsor processes might chronological age (operationalized as the ageof the respondent at the time of observation) measure? Chronolog-ical age marks individuals’ current statuses in a set of the ongoingbiological processes propelled by senescence. Processes related tosenescence usually produce predictable changes in outcomes overtime. Age-related processes of cognitive decline in later adult-hood (Li et al., 2004), for example, might affect demonstrationsof L2 proficiency (Obler, Fein, Nicholas, & Albert, 1991). “Age”effects such as these suggest changes in L2 proficiency occurringwithin individuals’ life spans. Thus, longitudinal studies wouldshow that individuals’ mastery of some aspect of L2 proficiencychanging over time—probably declining over the latter part ofthe life span. In cross-sectional data, lower levels of L2 proficiencywould therefore be observed among older immigrants than amongyounger immigrants. On the other hand, studies have also sug-gested that age among adults is positively associated with someaspects of language proficiency, such as vocabulary (e.g., Wilson& Gove, 1999), presumably because of the accumulation of ex-posure and experiences. Which process predominates probablyvaries according to the feature of L2 proficiency that is the focusof the study and possibly the age range under consideration.

Chronological age, however, is more than an indicator of bi-ological processes associated with senescence. It is also an excel-lent indicator of life-cycle stage because many societies, such asthe United States, are heavily age-graded. Chronological age is


strongly related to family and marital statuses, as well as ongo-ing or past participation in numerous social institutions such aselementary, secondary, or postsecondary schools, and participa-tion in the labor force. Skills in an L2 (and in test-taking) mightbe augmented by participation in educational institutions or la-bor force settings dominated by that language. Attrition in L2skills among older adults could reflect the diminished opportuni-ties to use English in formal social spheres following life-coursetransitions such as retirement from the labor force. Among L2speakers, different life-cycle stages and, thus, chronological agemight therefore be strongly associated with motivations and op-portunities to speak and to maintain (or to improve) proficiencyin an L2.

Dealing With the Age-Length-Onset Problem

One solution to the age-period-cohort problem, in general,and the age-length-onset problem, in particular, consists of statis-tical techniques that lift the linear dependence linking the threevariables. One methodological approach is constrained multipleregression (Mason, Mason, Winsborough, & Poole, 1973), some-times referred to as “multiple classification analysis.” In this ap-proach, the dependent variable is considered to be the result ofeffect parameters that are associated with the specific levels ofeach independent variable:

Yijk = � + �i + �j + �k + εij

(i = 1, . . . , r; j = 1, . . . , s; k = 1, . . . , r + s − 1) (5)

If applied to the age-length-onset problem in L2 acquisition,the grand mean of the dependent variable in Equation 5 is rep-resented by �, the effect of the ith age group is given by �i, theeffect of the jth length of residence group by �j , the effect of thekth age-at-onset group by �k, and the random error by εij. Becauseit is impossible to obtain best linear unbiased estimates for thecoefficients in this model (it is underidentified), it is necessary

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to assume that several age groups, several length-of-residencegroups, or several age-at-onset groups have identical effects onthe dependent variable. It is also necessary to assume that theeffects of the variables are additive or depart from additivity in asystematic way.

This general methodological approach has been criticized onthe grounds that it is mechanical and atheoretical (Glenn, 1976)and that even small errors in the model specification (with re-spect to which and how many parameters are constrained) canhave large effects on the estimates (Rodgers, 1982). Thus, themethodological assumptions in studies relying on this approachhave led to heated discussions about the omitted variables or theparameterization of the model (see, e.g., Greeley & Hout, 1999,2001; Stolzenberg, 2001).

A variant of this approach sidesteps the difficulties of decid-ing which of the age, length-of-residence, or age-at-onset groupshave the same effects. The “age period cohort-characteristic”model substitutes an aggregate-level characteristic for one of thedimensions (O’Brien, 2000). In the case of SLA research, it mightbe appropriate to substitute the aggregate variable “proportionof respondents living in a household with a native speaker ofthe second language” for length of residence. This substitutioncould be made on the grounds that the longer immigrants livein their country of destination, the more likely they are to livewith a spouse or children who are native speakers of the respon-dent’s L2 and, thus, the more intense the exposure to the op-portunities to learn and to improve in the L2. Alternatively, theeffect of age could be modeled through an aggregate measure ofschool enrollment (or educational achievement) because numer-ous studies suggest that educational characteristics are stronglyassociated with L2 proficiency (e.g., Flege & Liu, 2001; Flege,Yeni-Komshian, & Liu, 1999; Hakuta et al., 2003).

A second solution lies in the gathering of more data.Gathering more data points on the same respondents acrosstime, for example, can help break the linear dependence. More-over, longitudinal data can eliminate confounding betweensubject-level factors and time-varying exposure to the effects of


treatments or selection into the study sample. “Fixed-effects”models, for example, identify an effect for each individual, thusallowing each subject to act as his or her own control (Yaffee,2003). A simple fixed-effects model with observations gathered att time points for each individual is shown in Equation 6. In thisequation, �i refers to the time-invariant effect for individual i,the �’s are the slopes for the three variables “age at onset,” “age,”and “length of residence (LOR),” respectively, and ε it refers to theerror term for each individual at time point t:

Yit = [�i + �1Onseti] + �2 Ageit + �3LORit + εit (6)

Fixed-effects models such as these can also be extended to in-clude additional variables that are linearly dependent with thoseincluded in the equation. Because the characteristics of immi-grants entering the United States (or any other destination coun-try) can vary strongly across the calendar year, it might be ap-propriate to also include the effects of year of immigration andyear of observation, which are linearly dependent on length ofresidence, in the model. (For an example of a complex analysis in-vestigating the effects of three overlapping trios of linearly depen-dent variables on coital frequency, see Jasso, 1985). However, it isnecessary to impose some constraints on even the simple modelpresented in Equation 6 to estimate separate coefficients for ageand length of residence. In addition, because the variable “age atonset” is time-invariant, the estimates of the true individual-leveleffects (the �i) are merged with the effects of age at onset, which iswhy they are shown bracketed together in Equation 6. The resultsof the model specification thus yield age and length-of-residenceeffects that are not confounded with age-at-onset effects, but itdoes not yield age-at-onset effects.

Another option is to gather better data. The usual mea-sures of age, age at immigration, and length of residence in re-search on L2 acquisition are only surrogates for more fundamen-tal and meaningful concepts and processes. More direct measure-ment of those concepts and processes would provide more valid

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explanations. The rapidly growing archives of brain images pro-vide a window into neurobiological changes within the brain thatappear to be associated with age at acquisition of the L2 and thelevel of L2 proficiency (e.g., Mechelli et al., 2004; Perani et al.,2003). More detailed data-gathering about the nature and tim-ing of the early exposure to the L2 both before immigration andafter arrival in the destination country could also help providemore precise measures of age at onset of L2 learning than thesurrogate “age at arrival.”

Length of residence is usually taken as a measure of theextent of a respondent’s opportunities to learn and practicethe L2. Flege and Liu’s (2001) study clearly shows, however, thatthe effects of length of residence on measures of L2 proficiencyvary according to the respondents’ social roles. In particular, L2proficiency increases with length of residence only if the respon-dent is participating in social settings, such as schools, in whichthey receive a substantial amount of input from native speakersof the L2. In another example of the importance of settings, L2proficiency appears to atrophy if immigrants move to a minoritylanguage community even for just a few years (Chiswick & Miller,1998), a setting in which levels of exposure to native L2 speakersare lower. More detail about the extent and intensity of the oppor-tunities in various settings to learn and practice the L2 over timecould therefore release the reliance on length of residence as themain measure of opportunities respondents have had to acquirethe L2.

A third general approach to dealing with the linear de-pendence among the three independent variables is to posittheoretically grounded nonlinear relationships between L2 profi-ciency and one or more of chronological age, length of residence,and age at onset. The theoretical parameters governing the na-ture of the relationship between age at onset of L2 learning andproficiency in adulthood, for example, include (a) the averagecritical age, (b) the degrees of certainty of nativelike success inlearning the language before and after the age, and (c) the shapeof the relationship (also see Bornstein, 1989). In a more practicalvein, the nature of the relationship between age at onset and


proficiency in the data also incorporates details about the testitems, such as the range of linguistic features in the L2 that aretested or observed (e.g., Flege et al., 1999), the variation acrosstest items in the degree of difficulty, and the numbers of test itemsexhibiting each degree of difficulty.

When investigating complex relationships, it is always dif-ficult to select the most appropriate curve or relationship. Still,unlike scholars dealing with other substantive research issueswrestling with some version of the age-period-cohort problem,scholars investigating SLA have developed theoretical stancesabout the major concepts and the nature of the relationships be-tween (various aspects of) L2 proficiency and chronological age,length of residence, and, especially, age at onset (e.g., Birdsong,2004, 2005; Birdsong & Flege, 2001; DeKeyser & Larson-Hall,2005; Hyltenstam & Abrahamsson, 2003; Long, 1990; Newport,1990).

Hypotheses about discontinuities in the effects of age atonset, or varying effects of length of residence among respon-dents in different life stages, for example, call for the positing ofcurvilinear relationships. Flege et al. (1999), for example, usedthe Gompertz-Makehm distribution to fit the data points de-scribing the relationship between age of arrival in the UnitedStates and scores on a test of English syntax for a sampleof Korean immigrants. Stevens (1999) modeled the relation-ship between the probability that immigrants in the UnitedStates spoke English “very well” and length of residence as anatural logarithmic curve. Hakuta et al. (2003) searched fordiscontinuities in the effects of age at arrival on immigrants’average level of English proficiency. What remains to be donein this general approach is to consider in more detail thenature of the relationships between all three variables and L2proficiency.

Summary and Conclusions

The relationship between age at onset of L2 learning andL2 proficiency in adulthood has become an important issue in

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research on L2 learning among immigrants because it speaks tothe possibility of a critical or sensitive period in SLA. Meanwhile,it is well established that length of residence in the receivingcountry strongly affects immigrants’ levels of proficiency in an L2,at least for the first several of years after arrival in the destinationcountry. Because of processes associated with senescence and life-cycle stages, immigrants’ ages at time of observation or testingmight also be implicated in L2 proficiency. However, if age atonset of L2 learning is measured through age at immigration,then chronological age, length of residence, and age at onset arelinearly dependent, making it impossible to consider all threesimultaneously. Chronological age is the variable that is mostoften not explicitly considered in the analyses and discussions.

If there are theoretical reasons to believe that all three ofthe variables index unique processes that are involved in someaspect of L2 proficiency, then researchers need to explicitly con-sider all three variables in their analyses or they run the risk ofmisspecifying the relationships between L2 proficiency and thevariables that are included in the analysis. The misspecificationor misinterpretation can run the gamut from assigning the rela-tionship observed in the data to processes associated with one di-mension (i.e., “aging” effects) to processes associated with another(e.g., “age-at-onset” effects) to just overestimating or under-estimating the importance of one or more sets of processes.

Unfortunately, there are no easy statistical techniquesthat can unambiguously untangle the linear dependency amongthe trio of variables consisting of chronological age, length ofresidence, and age at onset of SLA among immigrants. Sta-tistical approaches such as multiple-classification analysis orage-period-cohort-characteristic models require strong assump-tions that can be difficult to defend. The age-length-onset prob-lem in L2 acquisition therefore needs to be tackled by more care-fully considering the concepts and conceptual processes that thesethree variables are indexing. There are several promising pathsto dealing with the issue. One consists of gathering more detaileddata describing the major concepts, perhaps drawing from sourcessuch as biographical profiles, sociological data on life-cycle stages,


and neurobiological data on changes in the brain. Another isto use longitudinal data, observing respondents across time, tohelp break the linear dependency. A third option is to draw fromthe rich theoretical perspectives in sociolinguistics and psycholin-guistics and to posit nonlinear (rather than linear) relationshipsbetween L2 proficiency and at least one of the following: age attime of observation, length of residence, and/or age at onset of L2learning.

Revised version accepted 21 April 2006

Notes

1In 30 simulations, the correlations between English proficiency and lengthof residence ranged from −.274 to +.220, with an average of .012. The cor-relations between English proficiency and age ranged from −.760 to −.540,with an average of −.653.2Although Hakuta et al. (2003, p. 33) presented values on the variable“length of residence” that range from 13 years to 40+ years, their analy-sis was actually restricted to respondents who entered the country in the1960s or 1970s and whose length of residence therefore ranged from about10 to 29 years (E. Wiley, personal communication, April 8, 2003).3See Stevens (2004) for a critique of their methodological approach.

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the age-length-onset problem in research on second language acquisition among immigrants

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