A Nationwide Epidemiologic Modeling Study of...

JOURNAL OF LEARNING DISABILITIESVOLUME 39, NUMBER 3, MAY/JUNE 2006, PAGES 230–251

A Nationwide EpidemiologicModeling Study of LD:Risk, Protection, and Unintended Impact

Paul A. McDermott, Michelle M. Goldberg, Marley W. Watkins, Jeanne L. Stanley, and Joseph J. Glutting

Abstract

Through multiple logistic regression modeling, this article explores the relative importance of risk and protective factors associated withlearning disabilities (LD). A representative national sample of 6- to 17-year-old students (N = 1,268) was drawn by random stratificationand classified by the presence versus absence of LD in reading, spelling, and mathematics according to ability–achievement discrepan-cies or low achievement levels. The dichotomous classifications were regressed on sets of explanatory variables indicating potentialbiological, social–environmental, and cognitive factors, problem behavior, and classroom learning behavior. Modeling revealed patternsof high risk for male students and students evincing verbal and nonverbal ability problems and processing speed problems. It was shownthat, absent controls for cognitive abilities (such as provided by the ability–achievement discrepancy definition), definitions keyed to lowachievement will substantially overidentify ethnic minority and disadvantaged students and will be confounded by significantly higherproportions of students who display oppositional and aggressive behavior problems. Alternatively, good learning behaviors uniformlyprovide substantial reduction in the risk for LD.

According to the U.S. Depart-ment of Education, NationalCenter for Learning Disabili-

ties (NCLD), 2.8 million American stu-dents are currently receiving specialeducation services for learning disabil-ities (NCLD, 2002). This represents al-most 6% of all public school children.Not included in these numbers are thechildren in private schools, who maybe receiving few, if any, learning sup-port services, and the children in bothpublic and private schools who haveserious learning difficulties but havenot been identified due to definitionalissues

Learning disabilities (LD) are con-sidered neurological deficits that inter-fere with a student’s ability to store,process, or produce information andthat create discontinuity between one’sability and performance leading to sig-nificant academic and social difficul-ties (Gettinger & Koscik, 2001; NCLD,

2002). Although a student with LDmay have performance difficulties inone or more areas, such as reading,writing, spelling, arithmetic, listening,talking, and social perception, these in-dividuals generally have normal cog-nitive abilities (Culbertson & Edmonds,1996; NCLD, 2002). The impact of theLD on the student’s education anddaily life can range from mild to se-vere, with academic underachieve-ment or failure being the most com-mon outcome.

Due to their continued academicproblems, children with LD often expe-rience social–emotional problems, suchas low self-esteem and difficulty withmaking and maintaining friendships(Gettinger & Koscik, 2001). As thesechildren move into adolescence, theymay exhibit characteristics such aslearned helplessness, decreased confi-dence in their ability to learn or suc-ceed, low motivation, attention prob-

lems, and maladaptive behavior (Desh-ler, Ellis, & Lenz, 1996). As reported by the NCLD (2002), 35% of childrenwith LD drop out of high school. Thisis twice the dropout rate of studentswithout LD. Of the students with LDwho do graduate, fewer than 2% at-tend a 4-year college, despite being ofaverage or above-average intelligence(NCLD, 2002). The NCLD (2002) alsoreported that several studies haveshown that between 50% and 60% ofadolescents in treatment for substanceabuse have LD.

The formation of a knowledge baseregarding LD began in the early 1900s(Culbertson & Edmonds, 1996). Re-search since then has produced a com-plex array of terminology and con-ceptualizations of LD, all of whichhave led to the current issues of def-initions, subtypes, and research ap-proaches (Culbertson & Edmonds,1996). Although there seems to be a

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fairly common set of terms used in thefield, there is great controversy overand variation in the issues of defini-tions and diagnostic criteria.

These issues have been hotly de-bated in educational, behavioral, andmedical journals (Doris, 1993) duringthe past 20 to 25 years in particular. Anumber of arguments have been madethat intelligence tests have limited util-ity for the identification of childrenwith LD and that the traditional IQ–achievement discrepancy criterion forLD should be abandoned (Bryan, 1989;Dombrowski, Kamphaus, & Reynolds,2004; Fletcher et al., 1998; Siegel, 1989,1990, 1999; Sternberg & Grigorenko,2002). Siegel (1989) argued that tests ofachievement might provide a clearerpicture of a child’s actual functioningthan IQ. Siegel (1989, 1999) also con-tended that individuals with LD oftenhave deficits in one or more of thecomponent skills that are measured by IQ tests and that their scores on thosetests are an underestimate of their abil-ity, thereby underidentifying childrenwith LD.

Despite these arguments, a dis-crepancy between ability and achieve-ment has long been the major criterionfor diagnosing LD in the United States(Gettinger & Koscik, 2001; Gregg &Scott, 2000; Mercer, Jordan, Allsopp, &Mercer, 1996), and an intelligence testis one of the primary tools used toidentify LD (Siegel, 1999). In a surveyof the 51 departments of education rep-resenting the states and the District ofColumbia, Mercer et al. (1996) foundthat 27% of the departments includedan ability–achievement discrepancycomponent in their definition of LDand 94% included the discrepancycomponent in their criteria for diag-nosing LD. Operationalization of thediscrepancy component varies some-what among the states, although re-gression analysis is the most commonprocedure for detecting such discrep-ancies (Mercer et al., 1996).

The use of a regression approachis thought to be the most psychometri-cally defensible method for determin-ing an ability–achievement discrep-

ancy (Culbertson, 1998; Heath & Kush,1991; Reynolds, 1984; Thorndike, 1963;Wilson & Cone, 1984). This methoduses a prediction equation based on thecorrelation between IQ and achieve-ment scores. The student’s IQ is usedto predict his or her expected achieve-ment test score, which in turn is com-pared to his or her actual achievementtest score. If there is a significant dif-ference between expected and actualachievement, the student is consideredto have a notable discrepancy.

Previous research on the etiologyof LD has included many studies on ge-netic and neurodevelopmental factors,particularly in regard to reading dis-abilities. A number of anatomical cor-relates have been studied, includingcerebral lateralization abnormalities,cerebral asymmetry, minor cortical mal-formations, immune disturbances, andgenetics (Culbertson, 1998). The NCLD(2002) has reported that experts do notknow what exactly causes LD and thatfactors such as heredity, problems dur-ing pregnancy or childbirth, and in-cidents after birth (e.g., poisoning,head injury) may contribute. Gallicoand Lewis (1992) have also noted thatthe cause of LD remains unclear. How-ever, they reported that affected chil-dren do not seem to have an increasedincidence of birth trauma or remark-able environmental influences andtend to develop as rapidly as childrenwithout disabilities, except in the areaof language.

Contemporary research includesstudies designed to explore the neuro-psychological processes that would ap-pear emblematic of LD and that arehoped to explain their unique mani-festations or origins. Most often, thiswork takes the form of studies thatattempt to discover subtypes of neu-rocognitive, academic, and other mea-surable performance patterns that dis-tinguish LD (Kavale & Forness, 1987;Siegel, 2003). Each child’s pattern offunctioning is represented by a profileof measured attributes. Similar profilesare grouped together through typalcluster or other structural analysis toform subtypes that are studied for their

relative prevalence among childrenwith LD and are otherwise interpretedfor their inferential value in explain-ing mediating neuropsychological pro-cesses. Although very interesting re-search has been produced in this arena,the scientific advances are seriouslylimited by methodological impedi-ments. Such studies tend to be overlyreliant on relatively small samples ofchildren who are classified a priori andby disparate criteria (Morris, 1988) ashaving LD, thereby failing to ensurethat the subtypes identified are trulyunique to LD populations and notcommonplace among non-LD popula-tions (e.g., Brewer, Moore, & Hiscock,1997; Davis, Parr, & Lan, 1997; Fletcher,Morris, & Lyon, 2003; Morris et al.,1998; Silver, Pennett, Black, Fair, & Ba-lise, 1999; Spreen & Haaf, 1986). Thesestudies also tend to construct chil-dren’s profiles based on attributes thathave no empirically established factor-ial validity or that are drawn from dif-ferent standardized test batteries. Inthe latter case, the clustering of profilesinto subtypes does not appear to ap-preciate the fact that performance ex-tracted through measures developedwith different normative samples atdifferent times will inevitably yieldvariation due to sampling error ratherthan true individual child variation.Such investigations alternatively re-quire large random samples of chil-dren drawn from the entire schoolpopulation, in which learning disabili-ties are uniformly identified post hoc,profile attributes are simultaneouslynormed and validated for factorial in-tegrity, and the resultant subtypes arefound emergent over multiple inde-pendent replication trials (see McDer-mott, 1998, on typal cluster replica-tion). Due caution is also warranted indrawing inferences about children’sinternal, mediating, neuropsycholog-ical processes as based on their psycho-metric and behavioral performances,rather than on direct neurological andbiological evidence.

According to Lyon (1996), limitedinformation exists on how race, ethnic-ity, and cultural factors may influence

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the development of LD. This lack of re-search may be due in part to the factthat all current state and federal defini-tions mandate that the deficits in LDcannot be attributed to cultural factors,including race and ethnicity (Lyon,1996). Culbertson (1998) suggested thatcultural and environmental factorshave important roles in learning acqui-sition. Children from impoverishedenvironments—both in terms of theamount of materials or toys availableto help learning and in terms of theavailability of educational or intellec-tual resources from caregivers—mayhave a distinct disadvantage (Culbert-son, 1998).

Prevalence data are difficult todiscern for male and female studentsbecause of conflicting data dependingon whether the child is research identi-fied or school identified (Culbertson,1998). Among students actually iden-tified as having LD by schools, onlyabout 50% demonstrate a significantaptitude–achievement discrepancy (Ka-vale & Forness, 2000). It seems thatschools tend to identify more boysthan girls as having LD, due to boys’more disruptive and attention-gettingbehavior in the classroom. Girls tend tomanifest attention and learning prob-lems differently from boys, without asmuch acting-out behavior, and, there-fore, do not attract as much attentionfrom their teachers (Gallico & Lewis,1992). According to the NCLD (2002),equal numbers of girls and boys havebeen found to have reading disabili-ties, but boys are 3 times more likely to be evaluated and treated. Lyon(1996) reported that schools identifyboys as having reading disabilitiesabout 4 times as often as girls, but that longitudinal and epidemiologicalstudies of clinical populations haveshown that approximately as manygirls as boys have reading disabilities.

The current educational zeitgeistis clearly calling for empirical researchthat is multicultural, is multidimen-sional, and can serve as the foundationfor educational programming aimed atensuring that every child receives a

quality education (Paige, 2002). To beinformative, such research must be rea-sonably generalizable across the nationand able to free the facts from the en-tanglement of controversies over defi-nition and disparities in the applica-tion of diagnostic criteria. Moreover,given the alarming prevalence and po-tentially detrimental outcomes of LD,new research must look for agents thatoperate to protect children from, orhelp to mitigate, LD, in addition to in-forming the relative precedence anddynamic pathways of risks that por-tend LD. Technically, this requires thatfuture research focus simultaneouslyon pertinent protective and risk factorsand that it not concentrate exclusivelyon the risk factors that are investigatedin the context of inconstant diagnosticcriteria.

Whereas extant epidemiologic re-search has been quite informative, ithas been grounded primarily in stud-ies with children who were diagnoseda priori as having LD (i.e., clinical pop-ulations; see, e.g., Blair & Scott, 2002),notwithstanding the high likelihoodthat such populations will reflect allthe definitional inconsistencies andvariations in diagnostic practice thatplague the field (MacMillan & Siper-stein, 2001). Modern epidemiologicscience offers a viable alternative to in-vestigations hampered by such irregu-larities. Rather than drawing on extantpopulations that are loosely presumedto share a common and objectivelyidentified morbidity, epidemiologistsprefer to draw on large, randomlysampled populations (community sam-ples) and thereafter apply uniform andscientifically reliable diagnostic criteriafor all individuals in the random sam-ple, thus distinguishing those individ-uals who in fact satisfy the criteriafrom those who do not. Once the diag-nostic distinctions are empirically de-fined, other common relevant factors(biological, environmental, behavioral,educational, etc.) are studied for all in-dividuals, with a special interest inthose factors that accurately differenti-ate those individuals diagnosed posi-

tive versus negative for the conditionand a special focus on the relative riskor protection afforded by such factors.Multivariate statistical modeling isused to help disentangle the factorsthat portend disease versus health. Aprimary example of such epidemio-logic modeling is the work in the na-tional mental health arena carried outin the wake of the U.S. EpidemiologicCatchment Area Survey (J. W. Swan-son, Borum, Swartz, & Monohan, 1996).Here, given the widespread inconsis-tency in the application of criteria formental disorders, the federal govern-ment funded the identification of a na-tionwide, stratified random sample ofpersons who thereafter were examinedthrough rigorous structured interviewsto diagnose the presence or absence ofmental illness and to identify the vari-ous life factors (other than the particu-lar diagnostic criteria) that constitutedrisks and protections. Similar large-population community studies haveassessed the longitudinal risk growthcurves that connect childhood expo-sure to birth anomalies, lead, and fam-ily stressors and subsequent cascadingschool failure (Tighe, McDermott, &Grim, 2001; Weiss & Fantuzzo, 2001).

Within this epidemiologic frame,our research team designed a series ofmodeling studies to investigate theconnections between uniformly andempirically defined LD in a large andrepresentative community sample ofAmerican students. We took advan-tage of the overlapping cohorts of stu-dents obtained for the nationwidenorming of several standardized in-struments—one measuring academicachievement and cognitive ability, an-other a myriad of classroom behaviorproblems, and still another focusing onstudent learning strategies and reac-tion styles. Given the national sample,we defined LD de novo as either theexistence of a relatively rare discrep-ancy between expected and observedachievement (the ability–achievementdiscrepancy rule) or the presence ofmarkedly low achievement (the lowachievement rule). For each definition,


and with respect to achievement inreading, spelling, and mathematics,multiple logistic models were con-structed to identify the specific leveland nature of risk for LD associatedwith five distinct classes of explana-tory variables. Whereas one might en-vision a nearly endless list of prospec-tive risks, we decided to concentrateon those variables that would be ex-pected to reasonably clarify the factsand that would comprise the types ofinformation that researchers or practi-tioners could easily duplicate withoutthe necessity for less accessible or com-plete archival data.

In our models, we applied a set ofpotentially biological markers. Theseincluded student age, sex, and ethnic-ity. Although one might argue that anyof these factors may well convey vari-ance that is more sociological than bio-logical, it is nonetheless clear that eachfactor carries variance linked directlyto conception or birth that cannot al-ternatively be caused by subsequentenvironmental factors. Another vari-able in this set was any major physicalimpairment that would not have pre-cluded a student’s participation in stan-dardized, individualized testing (e.g.,cardiac problems, speech impediments).

Given the rich literature on therelationships between environmentalagents and school success (Weiss & Fan-tuzzo, 2001), we hypothesized that stu-dents attending large, urban schoolswould suffer some risk for learningdifficulties, but that those raised inhouseholds with progressively moreeducated parents would obtain anadvantage, especially over studentswhose parents had relatively little for-mal education. Parent education alsoserves as a viable proxy in Americanpopulation research for social and so-cioeconomic strata (Ceci, 1991). Be-cause of the new evidence for botheducational and behavioral problemsthat may associate with single-parenthouseholds (Tighe et al., 2001; Weiss &Fantuzzo, 2001), we decided to incor-porate those factors in our models aswell.

Because cognitive ability is—atleast in the case of the ability–achieve-ment discrepancy definition of LD—apart of the identification mechanism,one might surmise that aspects of cog-nitive ability would not appear as in-dependent variables in a modeling in-quiry. However, its only direct role in definition is limited to estimatingachievement expectations, whereuponthe resultant dependent variable (un-derachievement) is actually formed insubsequent steps that incorporate dif-ferent achievement indices that, in ourmodeling routines, are further modi-fied through rubrics specifying whatconstitutes meaningful discrepancies.We believe—especially given the afore-mentioned controversies surroundingthe relevance of cognitive ability—thatno explanatory model would be com-plete were it to ignore the potential riskor protective effects attendant on gen-eral cognitive ability and performancesin major subdomains, such as verbal,nonverbal, and spatial abilities (seeMasten & Coatsworth, 1998, on theglobal protective aspects of children’scognitive ability). Also, researchersand practitioners who are interested inLD continue to contest the diagnosticor treatment relevance of peculiar orcharacteristic configurations of cogni-tive abilities presumably manifestedthrough substantial scatter of scoresamong the subtests that comprise abil-ity batteries or the appearance of pre-sumably rare and pathognomonicscore profiles for those same subtests.Indeed, ability subtest profile analysisis something of a mainstay in leadingtexts employed to prepare school psy-chologists (e.g., Kaufman, 1994), pro-moting subtest patterns that shouldcharacterize or raise the suspicion ofLD. Another cognitive capacity, thespeed of information processing, hasbecome a special focus of some re-searchers concerned about LD (Kail,2000, p. 52). Processing speed refers tothe ability to maintain a certain degreeof attention and concentration in rap-idly processing basic cognitive tasks(Sattler, 2000). Slower processing speed

has been linked with LD in general (H. L. Swanson, 1988; Weiler, Harris,Marcus, Bellinger, Kosslyn, & Walker,2000) and with reading disabilities inparticular (Aaron, Joshi, & Williams,1999).

Pervasive behavior disorders inthe classroom constitute another classof explanatory factors that we haveventured to model. It is conventionalpractice that LD not be diagnosedwhen the learning problems are a con-sequence of primary emotional or so-cial maladjustment, but it is neverthe-less also true that many students withLD suffer dispositional and behavioralproblems that are either concomitantsor sequelae of frustrating experienceswith learning activities (Roeser, Eccles,& Stroebel, 1998). The sense of frustra-tion and other perceived pressure ap-pears to drive some students to with-draw effort or feign incompetence, orto become defiant or outright violent(see, e.g., Boekaerts, 1993; Brackney &Karabenick, 1995; Furlong & Morrison,1994). Thus, we have collected stan-dardized assessments of markedlyatypical and phenotypically distinctbehavior patterns (attention-deficit/hyperactivity, aggressiveness, impul-siveness, oppositionality, diffidence,avoidance) over a 2-month period.Moreover, our assessments accommo-dated the more informed view of be-havior pathology as being not simplythe manifestation of certain intense re-actions in certain situations, but a moreconsistent pattern of similar manifesta-tions across multiple situations in theschool setting (Horn, Wagner, & Ia-longo, 1989). This perspective countersthe alternative prospect that problembehavior manifested only with certainpeople or in certain situations is farmore likely to be a reactive or randomoccurrence, and not indicative of anyreal pathology.

As noted earlier, we endeavoredto explore the relative impact of con-ceivably viable protective factors. Theseincluded indicators of successivelyhigher parent education levels, dual-parent families, and cognitive ability.


Higher cognitive ability alone has beendemonstrated to function as one of themost instrumental agents in protectingchildren from the vicissitudes of im-poverishment, maladjustment, and aca-demic failure (Mannuzza, Gittelman-Klein, Bessler, Malloy, & LaPadula,1993; Masten & Coatsworth, 1998; Weiss& Hechtman, 1993). Regrettably, afterdecades of research on aptitude–treatment interactions and learningpotential, most general cognitive abili-ties have been found to be relatively in-tractable to programmatic efforts thatwould improve them in malaffectedchildren (Brown & Campione, 1982;Ceci, 1990, 1991; Glutting & McDer-mott, 1990; Scarr, 1997; Snow, 1986;Spitz, 1986). It is this lack of successthat, in part, has led to the contempo-rary opinion that information drawnfrom cognitive ability measures is notvery useful for planning promisingeducational interventions (Gresham &Witt, 1997). In response, we haveturned to a final set of explanatory fac-tors that we believe to hold promise forinforming workable interventions. Wedrew on 20 years of empirical researchon students’ differential approaches tolearning (McDermott, 1999; McDer-mott, Mordell, & Stoltzfus, 2001; Stott,McDermott, Green, & Francis, 1988), orlearning behaviors, that underpin thesuccessful mastery of academic tasks.These behaviors are assessed throughstandardized teacher observations overtime and encompass aspects of compe-tence motivation, task planning, per-sistence, responses to error and assis-tance, flexibility, and positive attitudestoward learning. These attributes, asmanifested in classroom behavior,have been deemed keystone elementsin successful school performance, andit has been found that many of themare responsive to teaching and educa-tional programming (Barnett, Bauer,Ehrhardt, Lentz, & Stollar, 1996). In-deed, the National Education GoalsPanel (1997) of the U.S. Department ofEducation has underscored the partic-ular significance of learning behaviors:First, they have embraced them as oneof the five essential components of chil-

dren’s school readiness, making thema national strategic focus for early in-tervention with children at risk for pooracademic outcomes; second, howbeittheir apparent value as protectiveagents, they have been identified as the least understood and the least re-searched school readiness competen-cies (Kagan, Moore, & Bredekamp,1995).

Method

Participants

The cross-sample (N = 1,268) was com-posed of the overlapping portions ofthe national standardization samplesfor the Differential Abilities Scales (DAS;Elliot, 1990), Adjustment Scales for Chil-dren and Adolescents (ASCA; McDer-mott, Marston, & Stott, 1993), andLearning Behaviors Scale (LBS; McDer-mott, Green, Francis, & Stott, 1999).The cross-sample was designed to berepresentative of all noninstitutional-ized 6- through 17-year-old studentsattending school in the United Statesduring the 1990s. Participants were se-lected from 154 public school districtsand 47 private schools in 70 U.S. Cen-sus metropolitan statistical areas andassociated rural areas across the fourregions of the nation.

The cross-sample conformed tothe parameters of the 1992 U.S. Census(U.S. Department of Commerce, 1992)with matrix blocking for sex, age, andgrade level (634 boys and 634 girls withapproximately balanced distributionsof students and sexes within 1-year ageand grade intervals). Stratified randomsampling was conducted by race, par-ents’ education level, community size,and geographic region. Sampling pre-cision included simultaneous within-cellmatching across all stratification vari-ables (e.g., correct proportions for raceby parent education by region, etc.)and matching to marginal proportions.

On the basis of census parame-ters, the cross-sample consisted of 68%European American students, 16% La-tino, 13% African American, and 3%other ethnic minorities. Also in accord

with census parameters, 74% of thesample resided in two-parent families,24% in mother-only families, and 2% infather-only families. Parent educationserved as the primary index of socialclass because of its strong ability to re-flect essential class differences, as dem-onstrated in other research on youthscholastic ability (Ceci, 1991) and be-havior (Farrington, 1986; Magnuson,Stattin, & Dunner, 1983). Parent edu-cation was defined as the averagenumber of years of formal schoolingcompleted between a student’s motherand father (or the total number of years completed by a single parent orguardian) and was categorized into a 3-point scale. As per the standard clas-sification system employed by the U.S.Census Bureau (U.S. Department ofCommerce, 1992), 16% of sample stu-dents had parents who did not gradu-ate high school, 66% had parents whowere high school graduates, and 18%had parents who completed at least 4 years of college. Approximately 44%of students resided in major metropol-itan statistical areas, as characterizedby total populations ≥ 1 million. Con-sistent with the design to draw a rep-resentative sample, the resulting meanscores for the DAS, ASCA, and LBS inthe cross-sample were within 1 stan-dard score point of the respective pop-ulation means.

Instrumentation

Cognitive Ability. Various as-pects of cognitive ability were assessedwith the DAS (Elliot, 1990), an individ-ually administered, multidimensionalbattery for use with children ages 6 to17 years. The DAS is a hierarchicallystructured test in which scores on sixsubtests are combined to form mea-sures of three major cognitive subdo-mains: Verbal Reasoning, NonverbalReasoning, and Spatial Ability. Thesubdomains are combined to form theGeneral Conceptual Ability (GCA)score, which is a measure of generalintellectual functioning (i.e., Spear-man’s g). An additional three subtestsare usually administered as well, but

given their factorial divergence fromthe three subdomains and GCA, theseare considered diagnostic measuresand are interpreted separately. One ofthese subtests is Speed of InformationProcessing, constituting a sequentialseries of relatively easy comparisonand coding tasks that may be com-pleted with varying degrees of profi-ciency. In confirmatory factor analysis(Keith, 1990), this subtest has beenfound to form a specific cognitive fac-tor. Finally, the three diagnostic sub-tests and the six subtests that form thethree cognitive subdomains simultane-ously form a nine-subtest profile thatmay be examined for unique patternsof functioning.

The DAS was normed on a na-tional sample of 2,400 noninstitutional-ized students, ages 6 to 17 years, livingin the United States in 1990. The sam-ple was stratified by age, sex, race/ethnicity, parent education, geographicregion, and community size accordingto the U.S. Census (U.S. Department ofCommerce, 1990). For each sex andyear of age, the target matrix repre-sented the joint distribution of socio-economic status, race/ethnicity, andregion (Elliot, 1990).

Abundant evidence for the relia-bility and validity of the DAS has beenpresented in Elliot (1990) and McDer-mott (1999), including studies on inter-nal consistency, test–retest reliability,interrater reliability, construct validity,and criterion-related validity of theGCA and subdomains. Holland andMcDermott (1996) submitted the pro-files of the 2,400 standardizationparticipants on the nine subtests tohierarchical, agglomerative clusteranalyses with multiple replicationsand relocation. They identified sevenreliable and commonplace profiletypes in the national sample and pro-vided statistical procedures for deter-mining the degree of uniqueness ofany given profile.

Academic Achievement. The DASincludes an additional battery of threeindividually administered achieve-ment tests of word reading, spelling,

and basic mathematics. This batterywas normed and standardized on thesame national sample as the cognitiveability battery. The achievement testsare designed to be used with studentsages 6 to 17 years. Each achievementtest is age-blocked and calibrated to adistribution of standardized deviationscores (M = 100, SD = 15). Numerousstudies demonstrating the reliabilityand validity of the achievement bat-tery have been described by Elliot(1990) and McDermott et al. (2001).

Problem Behavior. Social andemotional adjustment was assessedthrough the ASCA (McDermott et al.,1993), a standardized observation in-strument for completion by classroomteachers. The ASCA was designed toassess the variability of students onspecific, multisituational syndromes ofbehavior pathology found generaliz-able across age, sex, and ethnicity.ASCA was standardized on a nationalsample (N = 1,400) of 5- through 17-year-olds attending U.S. schools, usingthe same stratified random samplingprocedure applied for the DAS (theDAS, ASCA, and LBS having beenconormed) for age, sex (equal numbersof boys and girls balanced over ages),race/ethnicity, parent education, geo-graphic region, and community size.

The ASCA contains 97 problemand 26 positive behavior indicators,each presented in 1 of 29 specific social,play, or learning situations in which a student’s adjustment to authority,peers, and various tasks may be ob-served. Examples of these situationsinclude seeking attention, assisting theteacher, accepting correction, answer-ing questions, informal or unorganizedplay, standing in line, caring for others’property, maintaining friendships, con-trolling outbursts, and activities re-lated to the use of drugs, alcohol, orweapons. ASCA requires the teacher tofocus on a youth’s behavior exclu-sively for 2 months and to rate each ofthe 123 behavioral indicators as eitherpresent or absent.

The behavioral indicators and sit-uations were drawn from the language

of teachers and were informed by thepreferences of teachers as compiledthrough interviews by ASCA’s authorsand subsequent field trials (McDer-mott, 1993). Through this process, itwas discovered that the best item con-tent was clearly stated and devoid ofclinical terminology, which reduced oreliminated the necessity for respon-dents to make inferences regarding themeaning of children’s behaviors or thenature of internal, mediating, psycho-logical processes such as thoughts orfeelings. As an additional step to com-ply with teacher preferences for lan-guage specific to gender, two versionsof the scale are used. The versions pro-vide identical behavioral descriptionsand situations that differ only in theuse of gender referents (“she” vs. “he,”etc.).

As a measure of differential psy-chopathology, ASCA yields scores forsix core syndromes: Attention-Deficit/Hyperactivity, Provocative Aggression,Impulsive Aggression, OppositionalDefiance, Diffidence, and Avoidance.Scores are presented in normalized T-score form (M = 50, SD = 10), withlow syndrome scores indicating ad-justment and high scores maladjust-ment. Validity and reliability evidencefor the ASCA is extensive (Canivez,2004; Canivez & Bordenkircher, 2002;McDermott, 1993; McDermott et al.,1995; Watkins & Canivez, 1997), andthe instrument has been applied fre-quently in nationwide epidemiologicalresearch (McDermott, 1996; McDer-mott & Schaefer, 1996; McDermott &Spencer, 1997; McDermott & Weiss,1995; Schaefer, 2004).

Learning Behavior. Differentialpatterns of classroom learning wereobtained through the LBS (McDermott,1999), a 29-item standardized ratinginstrument for use with students be-tween ages 5 and 17. The LBS stan-dardization sample (N = 1,500) con-formed to the parameters of the 1992U.S. Census (U.S. Department of Com-merce, 1992), precisely as did theASCA. It was designed for completionby a student’s classroom (or home-



room) teacher or teacher’s aide after 2 months’ observation in the naturalclassroom setting. Each item refers to a specific, learning-related behavior(e.g., “is very hesitant about giving ananswer,” “follows peculiar and inflexi-ble procedures in tackling tasks,”“shows little determination to com-plete a task, gives up easily,” or “showsa lively interest in learning activities”)and is rated on a 3-point Likert scale (1 = most often applies, 2 = sometimes ap-plies, 3 = does not apply).

Extensive exploratory and confir-matory latent structure analyses (Mc-Dermott, 1999; Worrell, Vandiver, &Watkins, 2001; Yen, Konold, & McDer-mott, 2004) resulted in four mutuallyexclusive dimensions: CompetenceMotivation, Attitude Toward Learning,Attention/Persistence, and Strategy/Flexibility. Observer ratings for the 29items are unit-weighted and summedto compute raw scores for each of thedimensions, which then are convertedto normalized T scores, where highervalues indicate better learning behav-iors.

The factor structure has beenfound invariant and the dimensions re-liable across independent, random,and mutually exclusive subsamples byage, sex, and ethnicity (McDermott,1999), whereas the dimension scoreshave been found internally consistentand stable across one month and acrossindependent observers (Buchanan,McDermott, & Schaefer, 1998; McDer-mott, 1999). Moreover, the dimensionsare relatively independent of cognitiveability constructs (< 15% redundancy),significantly increment prediction ac-curacy for achievement beyond what isafforded by cognitive ability, and pro-vide future achievement predictionsthat are free from bias against femaleor ethnic minority students (McDer-mott, 1999; Schaefer & McDermott,1999; Yen et al., 2004).

Procedure

Data Collection. Data were col-lected simultaneously as part of the re-spective standardization projects for

the DAS, ASCA, and LBS. Details arepresented elsewhere (Elliot, 1990; Mc-Dermott, 1993, 1999). In summary, amultistage process was applied forsample selection and data collection.Project central staff identified 70 U.S.Census metropolitan statistical areasacross the four regions of the nationbased on regional representativeness(in terms of stratification variables),reasonable proximity to surroundingrural communities, and availability ofuniversity professional psychology pro-grams where potential region supervi-sors and field coordinators might berecruited. Approximately 225 master’s-and doctoral-level psychologists andpsychology graduate students in schooland clinical psychology were recruitedby mail and telephone to function asfield coordinators. All field coordina-tors were formally trained and experi-enced in child psychological assess-ment and were instructed throughregional workshops in the use of theinstruments. Furthermore, 80 doctoral-level university faculty served as re-gion supervisors to direct the activitiesand schedules of field coordinatorsand to verify the integrity of data. Allpersonnel were paid for their services.

Based on census demographic es-timates for regional schools, projectstaff selected and recruited 154 publicschool districts and 47 private schoolswhose enrollments would potentiallyprovide the diversity required to sat-isfy population targets. With permis-sion of the school administration, ex-planatory letters, consent forms, anddemographic information forms weresent to all parents or (for large schooldistricts) to parents of students in rep-resentative classrooms. Demographicforms requested student birthdate, sex,and race/ethnicity, and the number ofyears of education of each parent orguardian living with the student. Proj-ect staff randomly selected studentsfrom those whose parents had givenconsent, with selection restricted onlyby stratification quotas and by a rulethat no more than two students couldhave the same classroom teacher toprovide ASCA or LBS observations.

Teacher observers were recruitedin a manner similar to that for parents,although their actual participation wasdependent on the stratification selec-tion of students in their classrooms.Participant teachers were compen-sated financially or through services,as required by local policy. ASCA andLBS forms were distributed separatelyand in counterbalanced fashion toteachers by field coordinators aftereach teacher had had at least 50 schooldays for observation of the target stu-dent. Forms were collected in a timelyfashion, verified for completeness, andforwarded for processing. Field coor-dinators and region supervisors weretrained in DAS application throughmultiple regional workshops andthrough subsequent trial administra-tions, protocol correction, and retrials.

Data Analyses. Levels of relativerisk and protection associated with LDwere derived through multiple logisticregression models. All models appliedthe same discrete response variable(LD vs. no LD) and several sets of ex-planatory factors (potential biological,social–environmental, cognitive, prob-lem behavior, or learning behavior).For half of the models, the responsevariable was based on the ability–achievement discrepancy definition ofLD and, for the other half, on the lowachievement definition. For each typeof definition, separate models wereconstructed for LD in reading, spelling,and mathematics. Similarly, undereach definition of LD for each achieve-ment area, nested models were con-structed to test the influence of risk andprotective factors in the presence andabsence of other factors.

Multiple logistic modeling is aprocedure especially suited to epide-miologic inquiry (Hosmer & Leme-show, 2000; J. W. Swanson et al., 1996).It is ideal for circumstances that entaildichotomous response variables (LD vs.no LD) and numerous sets of explana-tory variables that should be repre-sented as dichotomies (referred to asdesign variables) rather than continuousvariables. Thus, for example, the ex-


planatory variable reflecting the speedof information processing could alter-natively be represented by a continu-ous variable, corresponding to therange of standard scores ordinarilyavailable for that sort of measure. Thecrux of the problem is, however, thatone is really interested in knowingwhether a relatively poor and uncom-mon performance on that measure sig-nals a real risk for LD and what pre-cisely is the relative degree of that risk.To resolve those questions, one mustdetermine a theoretical or rational cut-point on the continuous scale that ear-marks poor and uncommon perfor-mance. The cut-point is necessary alsoto avert the inevitable distortion of in-formation caused by the use of contin-uous scales for discrete problem solv-ing (Moffitt, 1990). That is, were one todetermine that a speed of informationprocessing problem truly existed if per-formance was found to drop below the10th percentile of proficiency in thepopulation, the alternative use of thecontinuous scores would mask the prob-lem, because 90% of the active varia-tion in the data would be driven byscores in the irrelevant range above thecut-point. Instead, a dichotomous de-sign variable expressing poor and un-common performance versus other,more typical performance aptly appre-ciates the critical cut-point and con-centrates on discriminatory variationbetween the relevant sides of the di-chotomy. The necessity for dichoto-mous response variables, however,makes infeasible the use of ordinaryleast squares regression and the appli-cation of multiple dichotomous ex-planatory variables—especially the onesthat produce disproportionate dichot-omies that tend to defeat the equalityof the within-group covariance as-sumption underpinning multiple dis-criminant analysis (the most appropri-ate, ordinary least squares alternative).

In addition to tests for model fit,logistic regression produces the oddsratio, expressing the relative risk atten-dant on each explanatory factor as con-trolled for other factors in the model. Inturn, the natural logarithm of the odds

ratio tends to be normally distributedeven in smaller samples, availing a va-riety of inferential statistical tests thatassume normality, including tests thatpermit contrasts between competingmodels (Hosmer & Lemeshow, 2000;Wright, 1995). To yield the variety ofadvantages associated with multiplelogistic modeling, we formed designvariables as described in the followingsections.

Learning disability. The responsevariable defining any ability–achieve-ment discrepancy was formed by re-gressing achievement scores in a givenarea (e.g., reading) onto DAS GCAscores to estimate expected achieve-ment, subtracting the actual achieve-ment score from this value, and divid-ing by the standard error of estimatebased on the correlation between GCAand achievement (as per McDermott &Watkins, 1985). The cut-point for theresultant distribution of z scores wasthat marking the 90th percentile, where-upon the ability–achievement discrep-ancy was coded 1 = LD if it was statis-tically significant and rare enough tooccur in ≤ 10% of the population; it wascoded 0 (no LD) otherwise. LD wascoded 1 for the low achievement defi-nition whenever the standard scoresfor a given achievement area were < 15th percentile of the population,and was coded 0 if standard scores ≥ the 15th percentile level. These cut-points and others used in the studywere determined on the basis of the ne-cessity to ensure morbidity levels thatwere uncommon in the population (themost extreme 10% rule) or to abide bysimilar conventions (Stanovich, 1999)where standard score distributionswere involved (the 15% most extreme;i.e., deviation quotient < 85 or ≥ 115 orT score ≥ 60 rule), in conjunction withthe necessity that the requisite statisti-cal power demanded a minimal pro-portion of cases on the morbid side of design variables (Stokes, Davis, &Koch, 1995).

Potential biological factors. This setof variables included student age, sex,ethnicity, and serious physical impair-ment. Subsequent to numerous pilot

analyses showing that design variableversions of the age variable providedno advantage over age in a continuousform, age was allowed to vary as a con-tinuous variable in 1-year age incre-ments from 6 to 17 years. Sex wascoded male = 1, with female = 0 as thereference group, inasmuch as prior lit-erature (Grim, Tighe, & McDermott,2001) has portended higher morbiditylevels for male students. Ethnicity wasrepresented by three dichotomous va-riables, Latino (1 = yes, 0 = no, etc.),African American, and Other ethnicminority (Asian, Pacific Islander, etc.),with European American serving asthe reference group for each dichot-omy. Serious physical disability = 1 in-cluded those students who were med-ically diagnosed as having such or whosustained serious speech impairmentsthat would not preclude individual-ized testing. Speech impairments thatwere not severe enough to warrant for-mal classification by multidisciplinarychild study teams were not consideredserious. Approximately 4.7% of studentshad a serious physical impairment.

Social–environmental factors. Thisset of variables included indicators ofmajor urban residence, parent educa-tion level, and family structure. Majormetropolitan resident was coded 1 if astudent lived in a metropolitan statisti-cal area with population ≥ 1 million, orcoded 0 if not. Parent education wasmodeled with one design variable de-noting that a student’s residing parents(or guardian) graduated high school (1 = yes, 0 = no, etc.) and another de-noting that parents graduated college,with parents not graduated from highschool as the reference group. Twoadditional variables indicated familystructure: single-mother household(23.5% of the population) and single-father household (2.3%), with two-parent household as the reference con-dition.

Cognitive factors. Seven designvariables composed this set: one repre-senting general cognitive ability; threethe associated subdomains (verbal, non-verbal, spatial); and three assessingspeed of information processing, sub-


test scatter, and unique subtest pro-files, respectively. Higher general cog-nitive ability was coded 1 if the GCA≥ 115 (the 85th percentile) or 0 if GCA< 115. Cognitive subdomain perfor-mance was defined in one way formodels where LD was defined via ability–achievement discrepancy andin another way in the models featuringthe low-achievement definition. Thisprocedure, tested in pilot analyses,averted the inevitable point separationeffects associated with alternativemethods that included general andsubdomain abilities in the same model(see Note 1). Specifically, problems in a given subdomain (e.g., verbal) wererepresented in ability–achievementdiscrepancy models by markedly dis-parate and lower subdomain abilitythan GCA, where the most extreme10% of cases were coded 1 for verbalcognitive discrepancy, with others coded0 for no discrepancy. In this fashion, adesign variable was derived for verbalreasoning, nonverbal reasoning, andspatial cognitive discrepancies, respec-tively. In low-achievement LD models,subdomain problems were representedby subdomain scores > 85 (the 15thpercentile), coded 1 for low (e.g., ver-bal) cognitive ability, and 0 if not. A similar procedure was applied withrespect to levels of information pro-cessing speed. Here, for ability–achieve-ment discrepancy models, speed of in-formation processing discrepancy wascoded 1 if the speed of informationprocessing score was below the M scorefor all nine of a student’s DAS subtestsand among the most extreme 10% ofthose disparities; otherwise, it wascoded 0. With low achievement mod-els, speed of information processing =1 if the subtest score was < the 15thpercentile; otherwise coded 0. Variousmethods were piloted to effectivelyrepresent cognitive subtest scatter, in-cluding sums of variances and gener-alized distance scores. Maximum effec-tiveness in models was found for aparsimonious measure of scatter: thesum of standard score disparitiesamong the nine subtests. Thus, whenthe sum reached the most extreme

10%, high cognitive subtest scatter wascoded 1; otherwise, it was coded 0.Holland and McDermott (1996) pro-vided a mechanism for discoveringunique subtest profiles with the DASstandardization sample, in which anygiven nine-subtest profile was com-pared to the seven types commonplacein the general population. Thus, ap-plying Cattell’s rp(k) statistic (Tatsuoka& Lohnes, 1988, pp. 377–378) to dis-cover the similarity of each of the 1,268profiles in the cross-sample to theseven common types, we were able toassess the relative rarity of each profile.Profiles whose highest rp(k) values wereamong the rarest 10% were coded 1 forunique cognitive subtest profile andcoded 0 if not.

Problem behavior factors. A designvariable was constructed for each ofthe six ASCA syndromes (Attention-Deficit/Hyperactivity, etc.) and coded1 if the T score was ≥ 60, or 0 if < 60.This cut-point corresponded with the85th percentile.

Learning behavior factors. Accord-ingly, LBS T scores ≥ 60 on CompetenceMotivation were coded 1 for highercompetence motivation, or 0 if < 60;similarly forming design variables in-dicating Positive Learning Attitude,Persistent/Attentive Learning, and Dis-ciplined Learning Strategy, versus theiralternatives.

Results

Modeling proceeded in three steps: Weconstructed (a) models that includedall significantly contributing explana-tory factors; (b) models that excludedgeneral cognitive ability, its subdo-mains, and information processingspeed; and (c) models that excluded all potential biological and social–environmental factors. Because of thecausal precedence associated with po-tential biological factors, the completeset of those factors was entered firstinto those models that would examinebiological factors, whereas the entry ofall other individual factors was deter-mined by their ability to significantly

improve the fit of a model to the data.The models that included all sig-

nificant contributing factors are shownin Table 1. Inasmuch as the contribu-tion of each factor was controlled forthe effects of every other factor, thesemodels revealed the unique role of eachfactor as a risk or protective agent. Sixmodels are presented, the three on theleft side pertaining to LD as definedthrough ability–achievement discrep-ancies and the three on the right to LDas defined through low achievement.The exact number of students classi-fied as having LD, overall model sig-nificance, goodness of fit, and classifi-cation accuracy for each model areposted at the end of the table. All mod-els were found statistically significantoverall and a reasonable to excellent fitto the data. Based on classification ac-curacy (area under the ROC curve), allof the models except that for ability–achievement discrepant LD in mathe-matics (63.1% accuracy) would enablehigh to reasonable accuracy in theidentification of individual students(i.e., rates ≈ 70.0%). The models per-taining to the low achievement defini-tion are markedly stronger (≈ 80.0%) inthat respect.

Statistically significant explana-tory factors are indicated by the ap-pearance of odds ratios in Table 1 (seeNote 2). Odds ratios may vary from alower bound of 0.00 to an upper boundthat approaches infinity, with a scalecenter of 1.00. Values significantlyhigher than 1.00 indicate risk factors,whereas those significantly lower than1.00 indicate protective factors. Thus,for example, the 2.16 listed for malegender under the ability–achievementdiscrepancy definition of LD indicatesthat being male provides significantrisk for that type of LD (i.e., 2.16 boyswould be identified for every 1 girl)and, given the difference between 2.16and the scale center of 1.00 (2.16 −1.00 = 1.16), it specifies that boys face a116% increased risk over girls. More-over, to the extent that this factor is di-rectly controlled for all other factors inthe model (covariates), the risk forboys is unique and not alternatively


TABLE 1Multiple Logistic Regression Models Explaining Relative Risk of Empirically Defined Learning Disabilities (LD) in a

Representative National Sample: Models Including All Known Factors, by Type of Definition and Primary Area of LD

Ability–achievement discrepancy Low achievement

Explanatory variable Reading Spelling Mathematics Reading Spelling Mathematics

Potential biological factors

Age in years — — — — — —

Male (vs. female)Odds ratio 2.16† 2.98† 1.62* 1.73** 2.29† —95% CI 1.47–3.18 1.97–4.49 1.12–2.35 1.18–2.55 1.55–3.40 —SPE .21 .30 .13 .15 .23 —

Latinoa — — — — — —

African Americana — — — — — —

Other ethnic minoritya — — — — — —

Serious physical disability — — — — — —

Social–environmental factors

Major metropolitan residentOdds ratio — — — 0.62* — —95% CI — — — 0.41–0.94 — —SPE — — — −.13 — —

Parent(s) graduated high schoolb — — — — — —

Parent(s) graduated collegeb — — — — — —

Single mother householdc — — — — — —

Single father householdc — — — — — —

Cognitive factors

Higher general cognitive abilityd

Odds ratio 1.58* — — 0.07** 0.31* 0.05**95% CI 1.01–2.50 — — 0.01–0.50 0.12–0.79 0.01–0.38SPE .09 — — −.55 −.24 −.60

Verbal cognitive discrepancyd low verbal cognitive abilityd

Odds ratio 2.88† 2.04** — 5.32† 4.42† 2.14***95% CI 1.80–4.60 1.24–3.37 — 3.51–8.07 2.89–6.78 1.40–3.25SPE .18 .12 — .32 .28 .14

Nonverbal cognitive discrepancyd low nonverbal cognitive abilityd

Odds ratio — — 1.74* 3.73† 2.73† 3.16†95% CI — — 1.06–2.86 2.49–5.58 1.80–4.13 2.13–4.67SPE — — .09 .26 .20 .22

Spatial cognitive discrepancyd low spatial cognitive abilityd —

Speed of information processing low speed of information processinge

discrepancye

Odds ratio 2.32***— — 1.85** 2.37† 1.96**95% CI 1.42– 3.82— — 1.17–2.92 1.54–3.63 1.28–3.00SPE .14— — .12 .16 .13

High cognitive subtest scatter — — — — — —

Unique cognitive subtest profile — — — — — —

Behavior problem factors

Attention-deficit/hyperactivity — — — — — —

Provocative aggression — — — — — —

(table continues)


explained by other factors in themodel. Similarly, the odds ratio en-tered for higher competence motiva-tion (0.48) marks a protective factorthat expresses (1.00 − 0.48 = 0.52) a 52%reduction in the risk for LD if a studentdisplays higher competence motiva-

tion, irrespective of the other factors inthe model that signal significant risk.

A general examination of Table 1reveals several clear trends. With theexception of low achievement in math-ematics, boys were at substantiallyhigher risk for all types of LD than

girls, the risk increments ranging from62% for an ability–achievement dis-crepancy in mathematics to 198% for asimilar disability in spelling. Studentage or ethnicity, existence of seriousphysical impairments, parent educa-tion level, and presence of one or two

(Table 1 continued)



Impulsive aggressionOdds ratio — — — — 1.92* —95% CI — — — — 1.14–3.25 —SPE — — — — .10 —

Oppositional defianceOdds ratio — — — — — 2.21†95% CI — — — — — 1.47–3.33SPE — — — — — .16

Diffidence — — — — — —

Avoidance — — — — — —

Learning behavior factors

Higher competence motivationOdds ratio 0.48** 0.48** — 0.39** 0.40* 0.40**95% CI 0.28–0.81 0.28–0.82 — 0.19–0.79 0.20–0.83 0.20–0.79SPE −.17 −.17 — −.22 −.21 −.21

Positive learning attitudeOdds ratio — — 0.56** — — —95% CI — — 0.36–0.86 — — —SPE — — −.15 — — —

Persistent/attentive learning — — — — — —

Disciplined learning strategy — — — — — —

Total N 1,268 1,268 1,268 1,268 1,268 1,268

LD n f 138 134 139 165 163 168

Model chi-squareg 61.85† 70.44† 28.12*** 272.63† 220.14† 174.27†

df 9 9 8 12 12 12

Goodness of fith .10 .92 .90 .84 .65 .55

% classification accuracy i 68.8 71.3 63.1 83.8 81.1 79.1

Note. Odds ratios express relative risk associated with the respective explanatory variable and learning disability. Only statistically significant values are reported,as assessed through the Wald chi-square. 95% CI = 95% confidence interval; SPE = standardized parameter estimate for the logistic distribution.a reference group = European American, controlled for other minority groups in the model. b reference group = parent(s) not graduated from high school, controlledfor the other parent education level in the model. c reference group = two-parent household, controlled for the other single-parent household conditions in themodel. d Problems in specific cognitive subdomains (verbal, nonverbal reasoning, spatial) were represented in ability–achievement discrepancy models bymarkedly disparate and lower subdomain ability than the student’s general cognitive ability; in low achievement models, such problems were represented by subdo-main scores > 1 SD below the population mean; this procedure averted the inevitable adverse point separation effects associated with alternative methods that in-clude general and subdomain abilities in the same model. e Problems in speed of information processing were represented in ability–achievement discrepancymodels by a markedly disparate and lower speed of information processing subtest score than the mean of all of a student’s subtest scores; in low achievementmodels, such problems were represented by a speed of information processing score > 1 SD below the population mean; this procedure averted the adverse pointseparation effects associated with alternative methods that include general ability and an ability subtest in the same model. f n = number of children having LD asidentified by the respective regression discrepancy or low achievement rule; total N = 1,268. g Inferential statistic assessing the significance of the overall model. h

Probability level for the Hosmer-Lemeshow (2000) goodness of fit test, where nonsignificant values indicate plausibility of the model. i Overall accuracy for identify-ing presence and absence of LD as based on conjoint maximum sensitivity and specificity levels, corresponding to the area under the receiver operating character-istic (ROC) curve.*p < .05. **p < .01. ***p < .001. †p < .0001.


parents in the student’s householdmade virtually no difference in theidentification of any type of LD, nordid evidence of significant scatteramong cognitive subtests or the pres-ence of a unique ability subtest profile.What did uniformly make a differencewas uncommonly low performance ineither the verbal or nonverbal reason-ing subdomain of cognitive ability.Poor verbal ability marked a 104% to188% elevation in risk for ability–achievement discrepancies related tolanguage achievement (reading orspelling), whereas relatively poor non-verbal reasoning ability under theability–achievement discrepancy defi-nition translated to a 74% increase inrisk for a mathematics disability.Where any learning disability was de-fined through low achievement, bothpoor verbal ability (114%–432% riskincrement) and poor nonverbal rea-soning ability (173%–272% increment)emerged as major risk factors. Further-more, relatively low speed of informa-tion processing increased by 132% therisk for LD defined by spelling perfor-mance markedly below expectancy.Low levels of information processingspeed also increased the risk (85%–137%) for all types of low achievementdefined LD. Among the general trends,one also notes that higher general cog-nitive ability operated as a protectionfrom all areas of LD defined by lowachievement (69%–95% risk reduc-tion), but provided no protectionunder the ability–achievement dis-crepancy definition. Finally, the risk forall disabilities was reduced signifi-cantly in the presence of some mani-festation of good learning behavior(44%–61% risk reduction), usuallyhigher competence motivation.

Exceptions to these general trendsincluded the only evidence that exter-nalizing behavior problems help ex-plain LD, namely, the discovery of im-pulsive aggressive behavior as a riskcontribution (92% increase) to lowachievement in spelling and opposi-tionality as a risk (121% increase) forlow mathematics achievement. Inter-esting enough, higher general cogni-

tive ability served to elevate the risk(58%) for an ability–achievement dis-ability in reading, whereas residence inone of the nation’s large metropolitanareas reduced the risk of low readingachievement by 38% over the risk as-sociated with smaller cities and subur-ban and rural areas.

We hypothesized that the strongexplanatory presence of general cogni-tive ability and its subdomains—andpossibly its surrogate, speed of infor-mation processing—might have maskedthe underlying dynamics of high levelsof scatter amid cognitive subtests andthe importance of unique subtest pro-files. Also, we suspected, given thehigh correlations and causal paths thatcharacterized the relationships betweencognitive ability and social class, thatthe removal of the Spearman’s g-loadedfactors would potentially uncover therelevance of social–environmental fac-tors (Stone, 1993). Thus, the modelspresented in Table 2 exclude generalcognitive ability; its verbal, nonverbal,and spatial subdomains; and informa-tion processing speed.

As a preliminary measure to en-sure that the models presented in Ta-ble 2 were significantly distinct in lev-els of contribution from the models inTable 1, the chi-square statistic basedon the −2 log likelihood statistics forthe corresponding nested models (e.g.,the model for an ability–achievementdiscrepancy reading disability in Ta-ble 1 vs. Table 2) was tested, with allcontrasts statistically significant at p <.05. As hypothesized, Table 2 revealsthe emergence of factors otherwiseconcealed by the variability in stu-dents’ general cognitive abilities. First,a stronger showing of the roles playedby social–environmental factors isevident. For all LD defined by lowachievement, successively higher lev-els of parent education meant substan-tial reductions in risk for LD (43%–55%risk reduction if parents had graduatedhigh school, and a consistent and no-ticeably higher 74% reduction if par-ents had graduated college). In con-trast, the risk experienced by thereference group for each factor (i.e.,

students whose parents had not grad-uated high school) was markedlygreater. The reciprocals of the odds ra-tios appearing in Table 2 specify the in-crease in risk for students whose par-ents had not graduated high school.Thus, students whose parents had notfinished high school encountered a riskincrement of 75% over that encoun-tered by those whose parents hadgraduated high school and a risk in-crement of 285% over students whoseparents had graduated college. In con-trast, none of the social–environmentalfactors played a significant part inidentifying students whose LD weredefined via an ability–achievementdiscrepancy. Furthermore, in the ab-sence of controls for cognitive ability,disparities in risk for ethnic minoritiesemerged under the low achievementdefinition, with LD in reading andspelling more common among Latinostudents (75% and 62% risk incre-ments, respectively) and LD in readingmore common among African Ameri-can students (92% risk increment).

To some extent, the hypothesisconcerning the underlying role of cog-nitive subtest scatter was confirmed, asscatter signaled an 88% to 95% increasein risk for ability–achievement discrep-ancies in reading and spelling, respec-tively. Given that both subtest scatterand ability–achievement discrepanciesincreased with IQ level, this outcome isprobably a weak reflection of generalintelligence. However, no role in iden-tifying LD was discovered for uniquecognitive subtest profiles.

Similar to the models in Table 1,which included general cognitive abil-ities, the models in Table 2 excludingsuch abilities revealed no relevance of problem behaviors in explainingability–achievement discrepancies, butdid uncover a greater variety of prob-lem behaviors accompanying LD de-fined by low achievement. Moreover,commensurate with the models con-trolling for general cognitive abilities,better learning behaviors, in one formor another, substantially diminishedrisk for every type of LD (35%–78%risk reduction).



Representative National Sample: Models Excluding General and Subdomain Cognitive Abilities and Speed of Information Processing, by Type of Definition and Primary Area of LD



Potential biological factors

Age in years — — — — — —

Male (vs. female)Odds ratio 2.15† 2.97† 1.67** — 1.84** —95% CI 1.46–3.15 1.97–4.49 1.15–2.42 — 1.28–2.64 —SPE .21 .30 .14 — .17 —

LatinoaOdds ratio — — — 1.75* 1.62* —95% CI — — — 1.09–2.80 1.03–2.55 —SPE — — — .11 .10 —

African Americana

Odds ratio — — — 1.92** — —95% CI — — — 1.19–3.10 — —SPE — — — .12 — —

Other ethnic minoritya — — — — — —

Serious physical disability — — — — — —

Social–environmental factors

Major metropolitan residentOdds ratio — — — 0.63* — —95% CI — — — 0.44–0.92 — —SPE — — — −.13 — —

Parent(s) graduated high schoolb

Odds ratio — — — 0.45† 0.48*** 0.57***95% CI — — — 0.30–0.68 0.32–0.73 0.38–0.86SPE — — — −.21 −.19 −.15

Parent(s) graduated collegeb

Odds ratio — — — 0.26† 0.26† 0.26†95% CI — — — 0.13–0.51 0.13–0.50 0.13–0.51SPE — — — −.28 −.29 −.28

Single mother householdc — — — — — —

Single father householdc — — — — — —

Cognitive factors

High cognitive subtest scatterOdds ratio 1.88* 1.93** — — — —95% CI 1.16–3.07 1.19–3.14 — — — —SPE .11 .11 — — — —




Provocative aggressionOdds ratio — — — 1.78** 1.57* —95% CI — — — 1.19–2.64 1.02–2.42 —SPE — — — .12 .10 —

(table continues)


Table 3 displays a final set of mod-els, in which we addressed the relevantrisks and protections, if any, given the kinds of assessment informationthat psychologists or other specialistsmight more commonly collect. Thus,although the classes of potential bio-logical and social–environmental fac-tors are informative in understandingcausal and underlying aspects, they

are not ordinarily included in LD clas-sification practice because they areeither immutable or legally or politi-cally suspect. Therefore, the models in Table 3 are devoid of covariation for any potential biological or social–environmental variable.

Although risk and protection lev-els change somewhat from the fullermodels presented in Table 1, the re-

stricted models in Table 3 evince thesame overall patterns. Verbal cognitiveproblems portended risk for LD as de-fined through ability–achievement dis-crepancies, and both verbal and non-verbal problems signaled risk for low-achievement-defined LD. Speedof information processing problemssignaled ability–achievement discrep-ant disabilities in spelling and every

(Table 2 continued)



Impulsive aggressionOdds ratio — — — — 1.64* —95% CI — — — — 0.96–2.80 —SPE — — — — .08 —

Oppositional defianceOdds ratio — — — — — 2.04***95% CI — — — — — 1.37–3.04SPE — — — — — .15

Diffidence — — — — — —Avoidance — — — — — —


Higher competence motivationOdds ratio 0.56* 0.50* — 0.22† 0.25† 0.28***95% CI 0.34–0.94 0.29–0.86 — 0.11–0.45 0.12–0.50 0.14–0.55SPE −.13 −.16 — −.34 −.32 −.29

Positive learning attitudeOdds ratio — — 0.56** — — —95% CI — — 0.36–0.87 — — —SPE — — −.15 — — —


Disciplined learning strategyOdds ratio — — — — — 0.65*95% CI — — — — — 0.42–0.99SPE — — — — — −.12

Total N 1,268 1,268 1,268 1,268 1,268 1,268

LD nd 138 134 139 165 163 168

Model chi-squaree 38.34† 57.36† 22.96** 89.98† 92.75† 80.07†

df 8 8 7 11 11 11

Goodness of fit f .86 .75 .94 .23 .48 .70

% classification accuracyg 65.5 63.2 62.1 72.6 72.7 70.7

Note. Odds ratios express relative risk associated with the respective explanatory variable and learning disability. Only statistically significant values are reported,as assessed through the Wald chi-square. 95% CI = 95% confidence interval; SPE = standardized parameter estimate for the logistic distribution.a Reference group = European American, controlled for other minority groups in the model. b Reference group = parent(s) not graduated from high school, con-trolled for the other parent education level in the model. c Reference group = two-parent household, controlled for the other single-parent household conditions inthe model. d n = number of children having LD as identified by the respective regression discrepancy or low achievement rule; total N = 1,268. e Inferential statisticassessing the significance of the overall model. f Probability level for the Hosmer-Lemeshow (2000) goodness of fit test, where nonsignificant values indicate plau-sibility of the model. g Overall accuracy for identifying presence and absence of LD as based on conjoint maximum sensitivity and specificity levels, correspondingto the area under the receiver operating characteristic (ROC) curve.*p < .05. **p < .01. ***p < .001. †p < .0001.



Representative National Sample: Models Excluding Potential Biological/Physical and Social–Environmental Factors, by Type of Definition and Primary Area of LD



Cognitive factors

Higher general cognitive abilitya

Odds ratio 1.78* — — 0.07** 0.34* 0.05**95% CI 1.14–2.79 — — 0.01–0.52 0.13–0.85 0.01–0.38SPE .12 — — −.54 −.22 −.60

Verbal cognitive discrepancya low verbal cognitive abilitya

Odds ratio 2.93† 2.18** 1.91* 5.10† 3.97† 2.11***95% CI 1.84–4.65 1.34–3.55 1.16–3.12 3.43–7.59 2.65–5.95 1.40–3.17SPE .18 .13 .11 .31 .26 .14

Nonverbal cognitive discrepancya low nonverbal cognitive abilitya

Odds ratio — — — 3.91† 2.70† 3.15†95% CI — — — 2.64–5.81 1.81–4.04 2.13–4.64SPE — — — .27 .19 .22

Spatial cognitive discrepancya low spatial cognitive abilitya —

Speed of information processing low speed of information processingb

discrepancyb

Odds ratio — 2.74† — 1.86** 2.57† 2.00**95% CI — 1.70–4.42 — 1.19–2.90 1.69–3.91 1.31–3.06SPE — .16 — .12 .17 .13

High cognitive subtest scatter — — — — — —




Provocative aggression — — — — — —

Impulsive aggression — — — — — —Odds ratio — — — — 2.33*** —95% CI — — — — 1.41–3.86 —SPE — — — — .13 —

Oppositional defianceOdds ratio 1.57* — — — — 2.24†95% CI 1.02–2.43 — — — — 1.50–3.34SPE .09 — — — — .17

Diffidence — — — — — —

Avoidance — — — — — —


Higher competence motivationOdds ratio 0.47** 0.45** — 0.38** 0.38** 0.40**95% CI 0.28–0.80 0.26–0.77 — 0.19–0.77 0.19–0.78 0.20–0.79SPE −.17 −.18 — −.22 −.22 −.21

Positive learning attitudeOdds ratio — — 0.59* — — —95% CI — — 0.38–0.92 — — —SPE — — −.14 — — —

(table continues)


type of low achievement disability. Like-wise, higher general cognitive abilityprovided protection against LD de-fined by low achievement and ability–achievement discrepancies in reading.Impulsive- and oppositional-type be-havior problems increased risk for alimited number of LD, whereas goodlearning behaviors earmarked sub-stantial reductions in risk for all typesof LD.

In exploring the various logisticmodels, we incorporated into pilotanalyses a large variety of multiplica-tive interactions and exponential terms,as advised by Hosmer and Lemeshow(2000). No such effects were found tocontribute significantly to the reportedmodels. Alternatively, specific supple-mentary analyses were conducted toclarify any apparent anomalies in thereported models. Specifically, we ex-plored what might appear to be acounterintuitive risk for ability–

achievement discrepancy as deliveredby higher general cognitive ability.These analyses revealed that, depend-ing on the prevalence of LD as definedthrough ability–achievement discrep-ancies, higher IQ could pose a distinctrisk. This is due to the simple fact thatas IQ increases for students, so doesthe mathematical possibility for the oc-currence of the large discrepancies thatmust separate ability (i.e., expectedachievement) and actual achievement.As cognitive ability diminishes, lessroom is allowed within the resultantscore ranges for significantly lowerlevels of academic achievement. Alsounexpected was the appearance ofmajor metropolitan residence as a pro-tective factor against low achievementin reading. In supplementary analyses,we discovered this effect to be depen-dent on the presence in models of stu-dent ethnicity and parent educationlevel: That is, only if one controls for

student ethnicity or parent educationdoes major metropolitan residenceemerge as a protective factor. Uncon-trolled for these factors, the urban res-idence factor disappears as a signifi-cant contribution to models.

Discussion

Whereas Culbertson (1998) and Lyon(1996) have emphasized the inevitableroles that gender, ethnicity, social class,and environment play in influencingearly learning in general, and languageacquisition in particular, they also con-ceded the unsettled state of knowledgeon how these factors relate to LD. Thematter is confounded by the belief—ifnot practice—that on the one handwould defer a diagnosis of LD wheresuch exogenous factors are regarded asprimary causal agents, or on the otherhand would have such factors ignored

(Table 3 continued)




Disciplined learning strategyOdds ratio — — 0.61* — — —95% CI — — 0.40–0.93 — — —SPE — — −.13 — — —

Total N 1,268 1,268 1,268 1,268 1,268 1,268

LD nc 138 134 139 165 163 168

Model chi squared 46.18† 36.62† 20.38† 261.54† 204.03† 172.17†

df 4 3 3 5 6 6

Goodness of fit e .20 .95 .99 .57 .74 .58

% classification accuracy f 66.0 62.0 60.5 82.2 79.0 78.5

Note. Odds ratios express relative risk associated with the respective explanatory variable and learning disability. Only statistically significant values are reported,as assessed through the Wald chi-square. 95% CI = 95% confidence interval; SPE = standardized parameter estimate for the logistic distribution.a Problems in specific cognitive subdomains (verbal, nonverbal reasoning, spatial) were represented in ability–achievement discrepancy models by markedly dis-parate and lower subdomain ability than the student’s general cognitive ability; in low achievement models, such problems were represented by subdomain scores > 1 SD below the population mean; this procedure averted the inevitable adverse point separation effects associated with alternative methods that include generaland subdomain abilities in the same model. b Problems in speed of information processing were represented in ability–achievement discrepancy models by amarkedly disparate and lower speed of information processing subtest score than the mean of all of a student’s subtest scores; in low achievement models, suchproblems were represented by a speed of information processing score > 1 SD below the population mean; this procedure averted the adverse point separation ef-fects associated with alternative methods that include general ability and an ability subtest in the same model. c n = number of children having LD as identified bythe respective regression discrepancy or low achievement rule; total N = 1,268. d Inferential statistic assessing the significance of the overall model. e Probabilitylevel for the Hosmer-Lemeshow (2000) goodness of fit test, where nonsignificant values indicate plausibility of the model. f Overall accuracy for identifying pres-ence and absence of LD as based on conjoint maximum sensitivity and specificity levels, corresponding to the area under the receiver operating characteristic(ROC) curve.*p < .05. **p < .01. ***p < .001. †p < .0001.


altogether. Nonetheless, it is clear fromthe modeling studies that such extra-neous factors really do tend to dis-tinguish those students identified ashaving LD according to systematic ap-plications of popular diagnostic crite-ria. Male students are roughly twice asvulnerable as female students in thelanguage-related areas that were stud-ied here (reading and spelling), pro-vided that one controls for differencesthat are alternatively associated withcognitive ability. In the absence of suchcontrols, the vulnerability remains forlanguage problems based on ability–achievement discrepancies, but disap-pears for reading problems definedunder the low achievement rule. Thus,depending on the definition and theattention given to cognitive differ-ences, male students will tend to havenoticeably different prevalence levelsin populations of children classified ashaving LD. This may help explain theapparent contradictions in reportedprevalence rates (Culbertson, 1998;NCLD, 2002). It is likely also that, justas Gallico and Lewis (1992) have sur-mised that the higher prevalence of LDin boys identified by schools versusthose identified by researchers is duein part to teachers’ experience withsuch boys’ disruptive behavior, thedisparities are probably a function ofthe role that cognitive abilities play inweighing the importance of observedlearning problems.

The logistic models also informthe relative roles of ethnicity and so-cial class (as reflected through parenteducation levels). When learning dis-abilities are defined by regression dis-crepancies, race and class have no sig-nificant part in distinguishing studentswith LD. This finding remains whetherone chooses to control for general abil-ity level or problems in specific areas ofability. In sharp contrast, an LD defini-tion based on poor achievement in language areas will invariably signalgreater risk and higher prevalencerates for Latino and African Americanstudents and for the children of lesseducated parents, unless variations incognitive ability are systematically con-

trolled. This suggests a potentially seri-ous consequence for any identificationrubric that considers poor languagefunctioning in the absence of cognitiveability, including identification proce-dures tied to achievement test perfor-mance or to teacher-assigned grades.

The patterns for mathematics LDare somewhat distinct. Given a signifi-cant ability–achievement discrepancyin mathematics, boys remain at higherrisk than girls (≈1.6 boys per 1 girl)whether intellectual functioning iscontrolled or not. As is true in lan-guage areas, there appear to be nosignificant ethnic or social class dispar-ities in the identification process. How-ever, when learning disabilities are de-fined through low achievement, malepredominance disappears; and whendisparities in cognitive abilities are not systematically weighed, studentswhose parents are less educated be-come markedly more prevalent, al-though ethnic differences are not evi-dent.

The ability–achievement discrep-ancy definition also appears to affectthe likelihood of identifying studentswho display significant problem be-havior. Students so identified show nocomorbidity (such as oppositionalityor impulsive aggression) as long as po-tential biological and environmentalfactors are weighed. In the absence of control for such factors, ability–achievement discrepancies in readinghave a higher probability for concomi-tant oppositional behavior. However,LD defined by low math or spellingachievement are far more likely to beassociated with classroom opposition-ality and varieties of aggressive behav-ior. Once again, this trend would in-dicate that identification rules tiedprimarily to poor achievement willtend to increase the prevalence of LDidentification in students who mani-fest other distinct characteristics (inthis case, behavior disorders) that mayor may not fall within the theoreticalnetwork of LD (Hinshaw, 1992).

Thus far, the impact of cognitiveability is evident. More generally,greater cognitive ability affords sub-

stantial protection from LD viewed aslow achievement and more opportu-nity for the discovery of a significantdiscrepancy between ability and lowerachievement in the area of reading.Also revealed is the universal risk con-veyed by marked deficits in the morespecific verbal and nonverbal subareasof intellect. This discovery, althoughperhaps appealing to common sense,would seem to contradict some im-portant research showing that, oncegeneral cognitive ability is given fullconsideration, attention to cognitivesubdomains adds little useful informa-tion (Glutting, Snelbaker, & McDer-mott, 1999; Glutting, Youngstrom,Ward, Ward, & Hale, 1997; Young-strom, Kogos, & Glutting, 1999). It alsoshould be recognized that such re-search typically represents cognitiveabilities through continuously scaledvariables and ordinary least-squaresregression procedures. The epidemio-logic approach used here transformssuch variables, so that the discretepolarity of ultimate decision making(markedly poor and rare performancevs. not) more closely resembles the dis-crete decisions that must be applied in clinical practice. Furthermore, thepresent approach simultaneously ap-plies the identical decision rules for allstudents nationwide. The procedurewould operate to disclose any saliencethat factors ordinarily viewed in re-search as continua might have for theidentification of learning difficulties.

This reasoning applies also to theobservation that information process-ing speed is indeed a viable marker forLD. Notwithstanding empirical re-search demonstrating that processingspeed, in its continuous variable form,offers relatively trivial information inthe shadow of more general cognitiveability (Oakland, Broom, & Glutting,2000; Oh, Glutting, & McDermott, 1999;Riccio, Cohen, Hall, & Ross, 1997), onemay conclude from the alternative per-spective taken here that problems withinformation processing speed substan-tially increment risk for all types of lowachievement, even after controlling forthe alternative contributions of general


cognitive ability and its subdomains(see Note 3). Processing speed prob-lems play a much less prominent rolewith ability–achievement discrepan-cies, manifesting a risk only in the areaof spelling. Furthermore, the currentstudies found no significant associa-tion between problems in spatial cog-nitive ability and LD. This is consistentwith theories that anticipate that spa-tial ability will reserve its most uniquecontributions for postadolescence andprofoundly gifted students (Acker-man, 1996; Lubinski & Benbow, 2000).

As noted earlier, there are popularpractices based on the notion that cog-nitive subtest scatter and the presenceof certain unique subtest patterns aredistinct signatures of learning prob-lems and disabilities (Drummond,2004; Kaufman, 1994; Wolber & Carne,2002). Our modeling studies do notsupport this enthusiasm. Unique cog-nitive profile configurations neveremerged as LD markers, and scattersignaled a risk only when more generaland reliable aspects of ability were ig-nored. It would appear that scatter ismerely a manifestation of the cognitivesubdomains that more parsimoniouslyexplain variations among their mem-ber subtests. These findings are consis-tent with the growing body of researchdemonstrating that cognitive subtestscatter and profile analysis are ineffec-tive in differentiating childhood excep-tionality, including LD (Daley & Nagle,1996; Greenway & Milne, 1999; Ris-pens et al., 1997; Watkins, 1996, 1999;Watkins, Kush, & Glutting, 1997; Ward,Ward, Hatt, Young, & Mollner, 1995).Moreover, whereas scatter may oftenbe a faint echo of more reliable dispar-ities in cognitive functioning, the con-tinued use of profile analysis, at leastas pertains to LD, will likely increaseerrors in decision making.

Special effort was undertaken togo beyond conventional epidemiologicwork on children’s academic prob-lems. In addition to highlighting theprotective capacities afforded by highercognitive ability and family education,we tested the plausibility of goodlearning behaviors as protective agents,

while controlling for the alternativecontributions of ability, behavior prob-lems, and potential biological and en-vironmental factors. Without excep-tion, the risk of LD is markedlylessened in the presence of some aspect of better learning behavior—usuallyevidence of high competence motiva-tion—although the risk for mathemat-ics LD is offset by higher motivation,more positive attitudes toward learn-ing, and more disciplined approachesto learning tasks, depending on howLD are defined. The close connectionsamong LD, motivation, and attitudestoward learning tasks are consistentwith Gettinger and Koscik’s (2001) andTorgeson’s (1991) descriptions of chil-dren with LD whose resilience in theface of future learning challenges ishighly dependent on the motivation tosucceed and the repertoire of usefulresponses to learning difficulties. Yen et al. (2004) have demonstrated the ca-pacity of teacher-observed learning be-haviors to add substantial informationvalue beyond what is provided by cog-nitive ability as it relates to school suc-cess, and Yen et al. (2004), McDermottet al. (2001), and Schaefer and McDer-mott (1999) have shown the indepen-dence of learning behaviors from cog-nitive abilities and their freedom fromassessment bias across gender and eth-nic groups. Because of their potentialtractability through modeling, directinstruction, and programmed learn-ing, these behaviors are commonlyconsidered to be primary targets for in-tervention (Barnett et al., 1996; Kaganet al., 1995; Stott, 1981). Given theirstriking role as protective features inthe national modeling studies, it wouldbe important to assess, through ran-domized intervention studies, the com-parative power of such learned behav-iors to prevent and to vitiate the impactof LD.

Conclusion

At the time this article was undergoingeditorial review, the U.S. Congress wasplacing the final touches on dramatic

new changes to the definition of LD(Kovaleski & Prasse, 2004). The ability–achievement discrepancy definitionhas fallen into disfavor and is mori-bund. We would like to believe thatthis is the result of a solid body of em-pirical research in which students, firstsystematically identified via a uniformdefinition, were subsequently foundunresponsive to the most promisinginterventions, and not because the de-finition was inconsistently applied.Twenty years ago, it was argued that afailure to embrace a relatively invari-ant definition would ultimately leavemany of the most important questionsunanswered (McDermott & Watkins,1985). Unlike studies of pre-existinggroups (Colarusso, Keel, & Dangel,2001), these modeling studies indicatethat the discrepancy definition, not-withstanding its shortcomings, doestend to avoid the overidentification ofethnic minority students and studentsfrom disadvantaged backgrounds. Al-ternatively, a definition of LD that istied primarily to evidence of pooracademic achievement, or that is lesssystematically informed by considera-tions of cognitive ability, will over-identify minority students and disad-vantaged students. It is probable thatthe low-achievement definition of LDwill have similar effect with analogmethods of determining achievement,especially those depending on teacherevaluations of achievement. Moreover,the low achievement definition, whetherinformed by cognitive abilities or not,is likely to be confounded by signifi-cantly higher proportions of studentswho display oppositional and aggres-sive behavior problems.

The more positive perspective isfound in the utility of the epidemio-logic approach with a large, represen-tative community sample to illuminatethe pervasive and less obvious rela-tionships between definitional criteriaand the wide array of consequences,some of which are intended and someof which are not. The relative risk andprotective agency of myriad personaland environmental factors may be as-sessed simultaneously and in nested


models that unfold and highlight theless obvious facts. It is through suchpopulation studies that mental healthspecialists have discovered the morerealistic and unbiased estimates ofbasic trends for prevalence, incidence,and resource requirements (Costello &Angold, 1993; Reiss & Price, 1996). Thenew definitions of LD should be inves-tigated through the same empiricalmethods.

Promising also is the protectioncommensurate with good learning be-haviors. A similar capacity for learningbehaviors as protective agents hasbeen found in national studies focus-ing on youth psychopathology (Grimet al., 2001). This and other works havepointed to the importance of curriculadesigned especially to improve learn-ing behaviors, particularly for thosechildren at highest risk for school fail-ure. In that spirit, the National Instituteof Child Health and Human Develop-ment is currently sponsoring a series ofmultistage longitudinal field experi-ments that will attempt to effectivelyintegrate a variety of learning behaviorcurricula into field-tested curricula inearly literacy and numeracy (Fantuzzo,Gadsden, McDermott, Frye, & Culhane,2003). These field experiments are to becompleted by 2008.

ABOUT THE AUTHORS

Paul A. McDermott, PhD, is a professor inpolicy research, evaluation, and measurement atthe Graduate School of Education and professorof psychology in psychiatry in the School ofMedicine at the University of Pennsylvania. Heis a psychometrician and quantitative psycholo-gist. Michelle M. Goldberg, PhD, is a clini-cian at Children’s Crisis Treatment Center in Philadelphia, where she provides trauma-focused treatment for children and families.Marley W. Watkins, PhD, is the professor incharge of graduate programs in school psychol-ogy at the Pennsylvania State University.Jeanne L. Stanley, PhD, is an adjunct associ-ate professor at the University of Pennsylvaniain the Graduate School of Education’s AppliedPsychology and Human Development Program.Her current interests include community psy-chology and counseling issues for underservedpopulations. Joseph J. Glutting, PhD, is a pro-fessor of research, measurement, evaluation, andschool psychology at the University of Dela-

ware. He also is biostatistician for DuPont Chil-dren’s Hospital in Wilmington, Delaware. Ad-dress: Paul A. McDermott, Graduate School ofEducation, University of Pennsylvania, 3700Walnut St., Philadelphia, PA 19104-6216

NOTES

1. Categorical modeling is based on maximum-likelihood estimation of parameters for ex-planatory variables. Valid estimation isdependent on the reliable correspondence be-tween scores on the response variable andeach explanatory variables. This is termedcomplete point separation, referring to thevalid separation of the dichotomous scores ofthe response variable. If the values for agiven explanatory variable, either by itself orhaving been controlled for other explanatoryvariables already in a model, either perfectlyor near-perfectly correspond to the values of the response variable, valid estimation of maximum-likelihood parameters is pre-cluded. This is called incomplete or quasi-incomplete point separation. In the collec-tion of models for the present study, thosemodels using the ability/achievement dis-crepancy definition of learning disabilityalso apply discrepancy definitions for prob-lems in verbal, nonverbal, spatial, and in-formation processing ability. Each of thesedefinitions constitutes an intrastudent oripsative metric. Similarly, models of lowachievement learning disabilities incorpo-rate definitions of verbal, nonverbal, spatial,and information processing ability that areinterstudent or norm-referenced metrics. Inpilot analyses, it was discovered that modelswhich mixed the intra- and interstudentmetrics tended to produce incomplete orquasi-complete point separation. Per the rec-ommendations by Allison (1999), invalidmodeling was averted by application of themore parsimonious models that did not mixintra- and interstudent definitions of perfor-mance.

2. Table 1 also presents the lower and upper95% confidence limits for each odds ratioand the standardized parameter estimate foreach significant explanatory factor, wherethe within-model M and SD for parameterestimates are 0 and (π 2/3).5, respectively,under the logistic distribution.

3. As a counter prospect to the notion that in-formation processing speed problems (repre-sented in a binary fashion) are signatures ofcertain types of learning disability, it shouldbe noted that Keith’s (1990) evidence for fac-torial specificity was based on one singleDAS subtest, a singlet factor. Fabrigar, We-gener, MacCallum, and Strahan (1999) have

argued that, for both exploratory and confir-matory factoring, a viable construct must berepresented by multiple markers, not simplyone, and Watkins and Canivez (2004) havedemonstrated the unreliability of assess-ments based on deviations of cognitive sub-test scores.

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