Special Education 2 full page paper.

https://doi.org/10.1177/0014402919893931

Exceptional Children 2020, Vol. 86(3) 293 –309 © The Author(s) 2020 DOI: 10.1177/0014402919893931 journals.sagepub.com/home/ecx

Original Research

In the United States, school achievement is lower for English language learners (ELLs) who speak Spanish as their first language than for other minorities and Caucasian children (e.g., August & Hakuta, 1997; Hemphill & Vanneman, 2011; National Assessment of Educational Progress, 2011, 2017). In addi- tion, cross-sectional studies have shown that ELs disproportionately experience reading and math difficulties across various age levels (e.g., Kieffer, 2011; Martiniello, 2009). Com- pounding these aforementioned difficulties is that many of these ELL children with reading and math difficulties are not provided appropri- ate services. For example, national estimates reveal that ELL children are underrepresented overall in special education, meaning that a smaller percentage of these children are receiv- ing services than would be expected, given the

proportion of the overall population that they represent (e.g., Morgan & Farkas, 2016).

More important, confounds exist in the assessment of children with potential learning problems who are second-language learners. These confounds are due in part to attributing difficulties in second-language acquisition and reading or math achievement to the same cogni- tive processes as found in children with learning disabilities. In practice, these confounds may lead to ELLs being inappropriately diagnosed

893931ECXXXX10.1177/0014402919893931Exceptional ChildrenSwanson et al. research-article2020

1University of California, Riverside 2University of New Mexico

Corresponding Author: H. Lee Swanson, Educational Psychology, College of Education, University of New Mexico, Albuquerque, NM 87131, USA. Email: [email protected]

Can Difficulties in Language Acquisition and Specific Learning Disabilities Be Separated Among English Learners?

H. Lee Swanson1,2, Jennifer Kong1,2, Stefania D. Petcu2, and Monica Fiorella Asencio Pimentel2

Abstract This study investigated the prevalence of latent classes at risk for reading or math disabilities in elementary-age children whose first language is Spanish. To this end, children (N = 394) in Grades 1, 2, and 3 were administered a battery of vocabulary, reading, math, and cognitive measures in both Spanish and English. Three important findings occurred. First, five latent classes emerged (average achievers, poor achievers, reading disabled, English language learners, Spanish-dominant achievers) that varied in language and achievement scores. Second, probability estimates indicated that 10% of the total sample was at risk for learning disabilities (below cutoff score), and approximately 40% of the sample reflected a language acquisition group not at risk for academic difficulties. Finally, the best model for correctly predicting the odds of latent classes differing from average achievers included English measures of short-term memory, naming speed, and the executive component of working memory. The results support the notion that statistically distinct latent classes emerge under the umbrella of children identified as English learners and that children at risk for specific learning disabilities can be separated among a heterogeneous sample of children who are acquiring English as a second language.

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with learning disabilities and placed in special education. The opposite situation is also true: that children who are at potential risk for learn- ing disabilities are being overlooked and not being provided intervention. To circumvent some of these problems, it is necessary to iden- tify the processes in children with learning disabilities from other processes related to sec- ond-language acquisition. These issues under- score the need for better tools and methods for accurately identifying ELL children with seri- ous reading and math difficulties. (The terms “ELLs” and “emerging bilinguals” are used interchangeably throughout the article.)

Confounds are due in part to attributing difficulties in second- language acquisition and reading or math achievement to the same cognitive processes as found in

children with learning disabilities.

This study has two purposes. The first pur- pose was to determine if ELL children at risk for specific learning disabilities in reading or math reflect a discrete latent class of learners. Currently, children at risk for learning disabili- ties in reading or math have been defined by performing below a cutoff score on a norm- referenced standardized reading or math test (e.g., Branum-Martin et al., 2013; Geary et al., 2012; Lipka et al., 2006). However, this selec- tion process of determining children as at risk for learning disabilities has been criticized because of a reliance on artificial cutoff scores (e.g., Branum-Martin et al., 2013; Cirino et al., 2015). These artificial standards have also been exacerbated when defining risk status among ELL students because such children are not tested in their first language (e.g., Peña et al., 2016). This is unfortunate because it is commonly assumed that a certain threshold within one’s native language is necessary before the cognitive processes and academic performance in the second language can be assessed (e.g., Cummins, 1979).

To address some of these issues, method- ological advances contribute to our under- standing of children’s academic skills as it

relates to ELL children, such as modeling the development of discrete processes based on the latent class analysis (LCA; e.g., Collins & Lanza, 2010; Muthén, 2006). LCA is a statis- tical method used to identify subgroups of individuals characterized by similar multidi- mensional patterns of responses (e.g., Collins et al., 2000). In one sense, LCA is a categori- cal analog to factor analysis. Instead of defin- ing attributes to a complex covariance structure, LCA posits unobserved classes to explain complex associations in a multidimen- sional contingency table. Studies that involve the analysis of unobserved classes from a het- erogeneous sample are sometimes referred to as mixture models (e.g., Muthén, 2006). A rationale for using latent class or mixture mod- eling is that although reading or math skills can be represented as a continuous outcome vari- able, the sample may be composed of different groups (or classes) of individuals. The advan- tage of LCA when compared to other proce- dures, such as cluster analysis, is that it offers a probabilistic model of the distribution of latent classes in the data. In this study, we test the notion that discrete latent classes or mix- tures representing different states of academic proficiency exist in ELL children who may be identified as at risk or not at risk.

The second purpose of this study was to determine the cognitive processes that corre- late with the performance of ELL children at risk for achievement difficulties. Current pro- cedures to identify children with potential learning disabilities in reading or math assume that such children experience cognitive con- straints that impede their ability to perform efficiently on achievement measures (e.g., Geary et al., 2017; Lesaux et al., 2006). Thus, on the assumption that a discrete subgroup of ELL children at risk for learning disabilities in reading or math emerges, it is important to know the cognitive processes associated with these risk groups. One of the most-often- referred-to cognitive processes underlying both reading and math disabilities is working memory (WM; Cowan, 2014; David, 2012; Peng et al., 2016, 2018; Swanson & Beebe- Frankenberger, 2004), which has also been related to achievement difficulties in emerging

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bilinguals (e.g., Engle de Abreu, 2011; Engle de Abreu & Gathercole, 2012; Linck et al., 2013; Swanson et al., 2006, 2015). Although the association between WM and reading or math has been established in the literature, the processes of WM that underlie predictions of reading or math performance are unclear (see Peng et al., 2016, 2018, for review). Some studies have suggested that the storage com- ponent of WM (referred to as verbal short- term memory, or STM) plays a major role in academic performance. Other studies have noted that academic difficulties are tied to the executive component of WM (e.g., Peng et al., 2016, 2018; Swanson et al., 2015).

In summary, the purpose of this study was to identify whether ELL children at risk for learn- ing disabilities reflect a latent class. The study determined if this potential latent class could be differentiated in terms of severity of aca- demic deficiencies from other latent classes and whether this differentiation reflected quali- tatively different cognitive processes. To extend the literature in these areas, the study sought to answer two questions:

1. Can a latent classification of ELL chil- dren at risk for reading or math be identified within a heterogeneous sample of ELLs?

Traditionally, as indicated earlier, children at risk for learning disabilities in reading or math are operationally defined by performing below a cutoff point on a norm-referenced achievement measure (studies vary from the 11th to 25th percentile on norm-referenced standardized achievement measures; e.g., Murphy et al., 2007; Swanson et al., 2006; Vukovic & Lesaux, 2013). The present study determines the probability of identifying a latent class of participants at risk for learning disabilities using the 16th percentile (85 stan- dard score) as a cutoff point within a sample that includes a test battery of math, reading, and cognitive abilities. This cutoff was consid- ered a conservative cutoff point because it captures performance below what is consid- ered the average range in normative standard score distributions. As mentioned, LCA is a

model-based clustering approach that derives clusters using a probabilistic model that describes the distribution of data. Therefore, instead of finding clusters of children with low academic performance, LCA describes the dis- tribution of the data based on a model that assesses probabilities that certain cases are members of certain latent classes. Thus, with the goodness-of-fit indices, it is possible to test whether a “latent structure” underlies the data.

A further refinement in the sample selection of ELL children at risk for learning disabilities includes making sure that such children per- form above the cutoff scores (>16th percen- tile) on vocabulary measures in the first language (L1). This refinement is necessary to establish that risk status resides in the aca- demic domain and not in language (i.e., L1) per se. Likewise, further refinement in sample selection includes establishing that such chil- dren’s academic difficulties are not due to gen- eral intellectual difficulties or biased aptitude measures (e.g., Ferrer et al., 2010; Lohman et al., 2008; Lohamn & Gambrell, 2012).

2. Do specific cognitive measures pre- dict latent class membership?

On the basis of the aforementioned discussion, we determine if cognitive processes related to language acquisition (e.g., phonological stor- age or STM) can be separated from children at risk for learning disabilities. Clearly, both groups may share some processing difficul- ties, but one or two processes may be particu- larly helpful toward identifying ELL children with potential risk for learning disabilities in reading or math versus children experiencing difficulties acquiring English as a second lan- guage (L2). For example, it is commonly assumed that deficits in the phonological sys- tem (phonological storage) have been attrib- uted to reading disabilities in English (e.g., Stanovich & Siegel, 1994) and Spanish (e.g., Gonzàlez & Valle, 2000). Studies that are more recent have found that executive processes, primarily those executive processes related to WM, are also significantly related to L2 read- ing and math performance (e.g., Swanson et al., 2015, 2018). For this study, WM is

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defined as consisting of a limited-capacity sys- tem related to the preservation of information while simultaneously processing other infor- mation (Baddeley & Logie, 1999). The system reflects controlled attention because informa- tion to be recalled is presented in the context of competing information.

In addition to STM and WM, mental oper- ations related to naming speed and inhibition of the competing language may also play an important role in ELL children’s academic performance (e.g., Bonifacci et al., 2011; Cooper, 2012). For example, letter- and digit- naming speed may underlie the general pat- tern of cognitive difficulties among some emerging bilinguals. Thus, our predictions are that processes related to executive processing (WM, inhibition) or the phonological storage system (STM) play a unique role in predicting a latent class of children at risk for learning disabilities in reading or math.

In summary, the present study tested whether various latent classes emerge related to reading or math skills among ELL children. Measures used to classify children at risk for learning dis- abilities in either reading or math included norm-referenced tests of reading, math, and lan- guage in both Spanish and English. To enhance our focus beyond academic and vocabulary measures, we also include as part of the classifi- cation battery measures of classroom behavior (attention deficit hyperactivity disorder) and nonverbal reasoning (fluid intelligence). Specif- ically, we expected to find latent classes of chil- dren at risk for achievement difficulties (i.e., reading or math disabilities), children not at risk for achievement difficulties who were proficient in both languages (English and Spanish), and children not at risk who are more proficient in their first language (Spanish) than in their sec- ond language (English).

Method

Participants

Three hundred and ninety-four (N = 394) stu- dents in Grades 1 (n = 155), 2 (n = 129), and 3 (n = 110) from two large school districts in the southwestern United States participated in

this study. The children were designated as ELL or emerging bilinguals by their school and were selected from 30 classrooms.1 These children were selected from urban schools with a high poverty representation (over 98% of the children participated in a full or reduced federal lunch program) as well as a high His- panic representation (>95 %). The final sam- ple included 192 boys and 202 girls who returned signed consent forms. School records indicated that the children’s primary home spoken language was Spanish (>80%). All children were selected from dual-language classrooms in which instruction was provided in both English and Spanish. No significant differences in gender representation emerged across the grades, χ2(2, 394) = 2.88, p = .23.

Measures Used for Identifying Latent Classes

The study included group and individual administrations of a battery of tests. The series of tests were counterbalanced into one of four presentation orders. No Spanish and English versions of the same test (except for the Expressive One-Word Picture Vocabulary Test, Spanish-Bilingual Edition [EOWPVT- SBE]; Brownell, 2001) were presented simul- taneously. All participants were administered both English and Spanish versions of each measure by bilingual graduate students and staff researchers. The mean raw scores and reliabilities for all measures for the current sample described next are provided in the online supplement to this article (see Supple- ment Table 4). Because the normed standard- ized measures for establishing the latent class are commercially available, as is information on their validity and reliability, they are briefly reviewed here. Additional detail is provided later for the experimental cognitive measures.

Vocabulary: Receptive and Expressive

The Peabody Picture Vocabulary Test (PPVT; Dunn & Dunn, 2007) was administered in English. In this task, children were presented

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with four pictures and were asked to select the picture that matched the word read aloud in English. The Test de Vocabulario en Ima- genes (TVIP) was also administered. This measure is similar to the PPVT in the presen- tation and administration, except that words are read aloud in Spanish (Dunn et al., 1986). The EOWPVT-SBE (Brownell, 2001) was used as a measure of English- and Spanish- speaking vocabulary. The sample Cronbach’s alpha reliabilities for the receptive and expressive vocabulary measures were .96 and .95 for English and .92 and .96 for Spanish measures, respectively.

Reading: Word Identification and Passage Comprehension

The Woodcock-Muñoz Language Survey- Revised (WMLS-R) established a norm-refer- enced reading level in English and Spanish (Woodcock-Muñoz et al., 2005). The WMLS- R Spanish and English Word Identification and Passage Comprehension subtests were administered. The sample Cronbach’s alpha reliabilities for the word identification and comprehension subtests were .95 and .90 for English and .89 and .80 for Spanish measures, respectively.

Math: Calculation and Word Problems

The Calculation and Applied Math Problem Solving subtest from the Woodcock-John- son III (Woodcock et al., 2001) was admin- istered for the English presentation and the Calculation and Problemas Aplicados from the Batería III Woodcock-Muñoz (Muñoz- Sandoval et al., 2005) was administered to establish normed-referenced math levels in Spanish. Both of these subtests are individ- ually administered and assess children’s early mathematical operations (e.g., count- ing, addition, and subtraction) through practical problems. The sample Cronbach’s alpha reliabilities for the calculation and applied problems subtests were .78 and .78 for English and .83 and .71 for Spanish mea- sures, respectively.

Fluid Intelligence and Attention

Fluid intelligence. Fluid intelligence was assessed by administering the Raven Colored Progressive Matrices test (RCMT; Raven, 1976). The RCMT is commonly used to tap fluid intel- ligence because of its brevity in administra- tion and because of its high correlation with other nonverbal intelligence measures that are assumed to tap reasoning, thinking, or the ability to acquire new knowledge (referred to as fluid intelligence). The sample Cronbach’s alpha was .79.

Attention. The Conners’ Teacher Ratings Scales– Revised: Short Form (CTRS-R:S; Conners, 1997) were administered to evaluate problem behaviors by obtaining ratings from teachers. The homeroom teacher was selected for each child and was asked to complete the CTRS- R:S. The primary measure for this study was the ADHD index.

Cognitive Measures Used for Determining Correlates of Latent Class Membership

The cognitive measures assumed related to the latent classification assessed the storage of phonological information (STM, naming speed) and executive processing (inhibition or random generation, the executive component of WM). The convergence of the measures for the English and Spanish versions was estab- lished in an earlier study (see Swanson et al., 2015; Swanson, Kudo, et al., 2019, for further discussion), and a full description of each cognitive measure is provided in Swanson et al. (2015) and Swanson, Kong, et al. (2019).

Phonological Storage

STM. STM storage was measured using three tasks. The Forward Digit Span subtest of the Wechsler Intelligence Scale for Children– Third Edition (Wechsler, 1991) assessed STM because it was assumed that forward digit spans presumably involved a subsidiary mem- ory system (the phonological loop). The Word Span task was previously used by Swanson

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and Beebe-Frankenberger (2004) and assessed the children’s ability to recall increasingly large word lists (a minimum of two words to a maximum of eight words). The Phonetic Mem- ory Span task assessed the children’s ability to recall increasingly large lists of nonsense words (e.g., “des,” “seeg,” “seg,” “geez,” “deez,” “dez”) ranging from two to seven words per list. The sample Cronbach’s alpha reliabilities for digit span, word span, and pho- netic span were .82, .66, and .49 for English measures and .70, .75, and .50 for Spanish measures, respectively.

Naming speed. The Comprehensive Test of Phonological Processing (Wagner, Torgesen, & Rashotte, 2000) Rapid Digit and Rapid Letter Naming subtests were administered to assess speed in recalling numbers and letters in an English and a Spanish version. The sample Cronbach’s alpha reliabilities for let- ters and numbers subtests were .96 and .95 for English and .96, and .94 for Spanish mea- sures, respectively.

Executive Processing

Central executive. Three complex span mea- sures (tasks that include both a process and storage question) and an updating task were administered. The Conceptual Span, Listening Sentence Span, Digit Sentence Span, and Updating tasks were administered in English and Spanish to capture the executive compo- nent of WM (tasks described in detail in Swan- son et al., 2015). The WM tasks required children to hold increasingly complex informa- tion in memory while simultaneously respond- ing to a question about the task. Because WM tasks were assumed to tap a measure of con- trolled attention referred to as updating, an experimental updating task was also adminis- tered. The sample Cronbach’s alpha reliabili- ties for conceptual span, listening span, digit span, and update task were .84, .85, .52, and .80 for English measures and .83, .86, .52, and .70 for Spanish measures, respectively.

Visual-spatial WM. This component of WM was measured using two tasks (see Swanson

& Beebe-Frankenberger, 2004, for review of these tasks). The Mapping and Directions Span task assessed whether the children could recall a visual-spatial sequence of directions on a map with no labels. The sample Cron- bach’s alpha reliabilities for visual matrix and mapping/directions measures were .95 and .80, respectively.

Inhibition. The Random Number and Random Letter Generation tasks were administered to assess inhibition. Children were first asked to write, as quickly as possible, numbers (or let- ters) in a nonrandom sequential order to estab- lish a baseline. They were then asked to write numbers (or letters) as quickly as possible, out of order, in a 30-s period. Scoring included an index for randomness, information redun- dancy, and percentage of paired responses to assess the tendency of participants to suppress response repetitions. The sample Cronbach’s alpha reliabilities of the letters and numbers were .80 and .77 for English measures and .81 and .82 for Spanish measures, respectively.

Cutoff Point

To reduce the number of manifest variables, mean standard scores of subtests of vocabulary (receptive, expressive), reading (word identifi- cation, comprehension), and math (calculation, applied problems) were the primary measures. The manifest variables (vocabulary, reading, math, fluid intelligence, and attention) to deter- mine discrete groups were dummy coded as reflecting normative score at or below the 16th percentile (1 = at or below the 16th percentile, 2 = above the 16th percentile). The 16th per- centile (85 standard score) was based on the normative scores from the standardized vocab- ulary, math, reading, and fluid intelligence measures. The CTRS-R:S was in T-scores with high scores representing higher levels of inat- tention, and therefore the 16th percentile was a T-score of 63.

Procedures

Ten bilingual graduate students or research assistants trained in test administration tested

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all participants in their schools. One session of 45 to 60 min was required for small-group test administration, and two sessions of 45 to 60 min was required for individual test admin- istration. Test administration was counterbal- anced to control for order effects.

Statistical Analysis

To evaluate the model fit, and because LCA is an exploratory analysis, a series of models was fit, varying the number of latent classes between one and seven (Nylund et al., 2007; see Masyn, 2013, for a comprehensive review). A combination of statistical indica- tors and substantive theory were used to decide on the best-fitting model. We used Mplus (Muthén & Muthén, 2012) and SAS (Lanza et al., 2011) software to examine the manifest variables and determine the number of latent classes. The models with different numbers were compared using information criteria (i.e., Bayesian information criterion [BIC], Akaike information criterion [AIC], and adjusted BIC). Lower values on these fit statistics indicated a better model fit. Statis- tical model comparisons included likelihood ratio tests: the Lo-Mendell-Rubin test (LMR) and the bootstrap likelihood ratio test (BLRT). Both statistical procedures compared the improvement between neighboring class mod- els (i.e., comparing models with three vs. four classes, four vs. five, etc.) and provided p val- ues. P values were used to determine if there

was a statistically significant improvement in fit for the inclusion of one more latent class. A nonsignificant p value indicated for a k class that the previous k class with a significant p value fit the data better. Among the informa- tion criterion measures, the BIC is generally preferred, as is the BLRT for statistical model comparisons (Nylund et al., 2007). Table 1 shows the indices for the model fit.

Cognitive measures were reduced to latent constructs based on an earlier study (Swanson et al., 2015; Swanson, Kong, et al., 2019). Converting the measures to latent constructs eliminated measurement error and allowed for a focus on shared variance rather than isolated task variance. Latent scores were computed by multiplying the z score of the target vari- able by the standardized factor loading weight based on the total sample (see Nunnally & Bernstein, 1994, p. 508, for calculation proce- dures). Latent variables were specified as indicators of speed (naming speed for num- bers and letters), inhibition (random genera- tion of numbers and letters), STM (Digit Forward Span, Word Span, and Phonetic Memory Span), executive processing (Con- ceptual Span, Listening Sentence Span, Digit Sentence Span, updating), and visual-spatial WM (matrix, mapping and directions).

Finally, we used a multilevel logistic model, via SAS PROC GLIMMIX software, to analyze differences between latent classes. The reference group was the latent class con- sidered as average achievers (LC1).

Table 1. Fix Indices for Seven Latent Class (LC) Models.

Variable LC1 LC2 LC3 LC4 LC5 LC6 LC7

Log-likelihood −1616.41 −1523.45 −1498.3 −1478.96 −1467.77 −1457.87 −1454.9 AIC 474.3 306.38 274.08 253.41 249.02 247.21 259.27 BIC 506.11 373.97 377.46 392.58 423.98 457.96 505.8 CAIC 514.11 390.97 403.46 427.58 467.98 510.96 567.8 Adjusted BIC 480.73 320.03 294.96 281.53 284.37 289.79 309.08 Entropy 1 0.78 0.67 0.72 0.79 0.75 0.78 Degrees 247 238 229 220 211 202 193 LMR (p value) — 0 .056 .049 .70 .53 .09 BLRT (p value) — 0 0 0 .012 .051 .17

Note. Bold indicates the best fitting model. AIC = Akaike information criterion; BIC = Bayesian information criterion; CAIC = Bozdon AIC; LMR = Lo-Mendell-Rubin test; BLRT = bootstrap likelihood ratio test. CAIC and adjusted BIC corrected for sample size.

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Results

LCA

The indices for determining the number of latent classes are reported in Table 1. Given the indices reported in Table 1, the five- and six-class models were studied for interpret- ability. Both the LMR and BLRT yielded non- significant p values for the six-class model, indicating that the five-class model provided an excellent fit to the data. The BIC was lower for the five- than for the six-class model. In addition, adequate sample proportionality and item probabilities for the five-class model were more easily interpreted than for the six- class model. The entropy for the five-class model was .79, an acceptable value (Nylund et al., 2007). The online supplement to this article reports tables related to the proportion

of the sample in each latent class (gamma esti- mates) as well as the probabilities (rho esti- mates) for each measure (manifest variable) for each response category as a function of each latent class for the total sample (Supple- ment Table 2). Also reported in the supple- ment are the item probabilities for performance at or under the cutoff threshold of the 16th percentile (standard score of 85).

Sample Distribution of Latent Classes

Means and standard deviations for each of the normed classification measures as a function of the five latent classes are shown in Table 2. Effect sizes (ESs) comparing each latent class across all measures are shown in Table 3, and those ESs at or greater than .80 were considered

Table 2. Normative Descriptive Scores as a Function of Latent Class (LC).

LC1 (n = 224) LC2 (n = 13) LC3 (n = 30) LC4 (n = 66) LC5 (n = 61)

Variable M SD M SD M SD M SD M SD

Manifest variablesa

E vocabulary 105.56 14.50 82.14 5.38 94.50 11.89 72.96 8.65 79.74 15.96 S vocabulary 83.74 14.07 81.87 9.80 73.30 9.00 90.68 13.31 82.85 11.6 E reading 105.70 12.13 77.36 12.37 85.74 13.42 98.24 9.34 78.52 10.12 S reading 107.16 12.13 78.23 9.02 79.30 5.09 114.22 12.62 100.91 13.99 E math 103.55 10.14 77.84 8.52 99.85 8.69 95.95 9.54 87.73 11.99 S math 100.28 9.34 80.25 6.18 90.22 13.42 103.54 8.90 94.00 10.67 Fluid

intelligence 105.63 14.78 87.45 8.50 97.90 15.74 93.33 16.18 88.32 14.73

Inattentionb 50.05 9.26 59.30 3.87 54.68 11.11 48.60 7.81 56.15 11.54 Correlated variablesc

E STM 0.49 1.54 −0.67 1.30 −1.37 1.36 −0.26 1.63 −0.88 1.38 S STM 0.36 1.61 −0.65 1.42 −1.43 1.59 −0.01 1.71 −0.51 1.4 E speed −0.51 1.00 1.57 1.61 0.88 2.13 0.27 1.55 1.07 2.19 S speed −0.16 1.28 1.04 2.53 1.19 2.42 −0.48 1.09 0.50 1.74 E inhibition 0.14 0.97 0.09 0.78 −0.24 0.98 −0.18 1.05 −0.15 0.82 S inhibition 0.10 0.72 −0.25 0.82 −0.29 0.64 −0.20 0.71 0.03 0.59 E exec WM 0.50 1.48 −0.86 0.51 −0.61 1.00 −0.68 0.93 −0.75 1.09 S exec WW 0.20 1.61 −1.33 1.26 −1.37 1.11 0.47 1.68 −0.48 1.32 Visual-spatial

WM 0.21 1.16 −1.23 0.50 −0.30 0.87 0.03 1.27 −0.37 1.01

Note. LC1 = average achiever; LC2 = poor achiever; LC3 = reading disability; LC4 = high Spanish achiever; LC5 = average Spanish achiever; E = English; S = Spanish; STM = short-term memory or phonological loop; speed = naming speed; inhibition = random generation tasks; exec = executive component; WM = working memory. aStandard normed scores. bT-score. cz scores.

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of large magnitude. The percentage distribution of gender representation across the five latent class groups for males was 47.77%, 66.67%, 56.67%, 40.91%, and 52.49%, respectively. No significant effects were found for gender representation among the five latent classes, χ2(4, 394) = 4.33, p =.36.

As shown in Table 3, LC1 exceeded (ESs > .80) Latent Class 2 (LC2) on seven of the eight measures. Performance weaknesses for LC2 emerged in all domains except for Spanish vocabulary. Based on these comparisons, we characterized this latent class group (LC2) as “poor achievers.” As shown in Table 2, none of the average mean scores for this latent class (LC2) exceeded the 19th percentile (standard score of 87).

For Latent Class 3 (LC3), large ES differ- ences emerged in three out of the eight manifest variables when compared to LC1. Two of the largest ESs were the area of reading for both the English and Spanish languages. As shown in

Table 2, the mean reading scores for LC3 were 85.74 and 79.30 in English and Spanish, respec- tively. In contrast, their average math scores were 99.55 and 90.22 in English and Spanish, respectively. These differences in math scores parallel the discrepancy in vocabulary scores between the two language systems. As shown in Table 2, performance LC3 on the English vocabulary measures (M = 94.50) clearly exceeded measures on Spanish vocabulary (M = 73.30) measures. Because fluid intelli- gence (Raven) scores were in the normal range, this profile fits an operational definition of read- ing disabilities commonly found in the litera- ture (e.g., Stanovich & Siegel, 1994). We label this latent class as “reading disabilities.” In gen- eral, researchers use the term “reading disabili- ties” to identify children with average intelligence but with performance below a cer- tain percentile (e.g., 25th percentile) on norm- referenced standardized reading measures (e.g., Cirino et al. 2015; Stanovich & Siegel, 1994).

Table 3. Effect Size Comparisons Among Latent Classes (LC).

Variable LC1 vs.

LC2 LC1 vs.

LC3 LC1 vs.

LC4 LC1 vs.

LC5 LC2 vs.

LC3 LC2 vs.

LC4 LC2 vs.

LC5 LC3 vs.

LC4 LC3 vs.

LC5 LC4 vs.

LC5

Manifest measures E vocabulary 1.65 0.78 2.43 1.74 −1.19 1.12 0.16 2.21 1.00 −0.53 S vocabulary 0.13 0.77 −0.50 0.07 0.93 −0.69 −0.09 −1.43 −0.88 0.63 E reading 2.33 1.62 0.65 2.32 −0.64 −2.11 −0.11 −1.16 0.64 2.03 S reading 2.41 2.41 −0.58 0.50 −0.16 −2.97 −1.71 −3.21 −1.82 1.00 E math 2.55 0.37 0.76 1.50 −2.55 −1.93 −0.86 0.42 1.10 0.76 S math 2.18 1.02 −0.35 0.65 −0.85 −2.73 −1.37 −1.27 −0.32 0.97 Fluid intelligence 1.25 0.52 0.81 1.17 −0.75 −0.39 −0.06 0.28 0.64 0.32 Inattention −1.02 −0.49 0.16 −0.62 0.48 1.46 0.30 0.68 −0.13 −0.77 Cognitive measures E STM 0.76 1.22 0.48 0.91 0.52 −0.26 0.15 −0.72 −0.36 0.41 S STM 0.63 1.11 0.23 0.55 0.51 −0.38 −0.10 −0.85 −0.63 0.32 E speed −2.00 −1.17 −0.68 −1.18 0.35 0.83 0.24 0.35 −0.09 −0.42 S speed −0.87 −0.93 0.26 −0.47 −0.06 1.07 0.29 1.03 0.35 −0.68 E inhibition 0.05 0.39 0.32 0.31 0.36 0.27 0.30 −0.06 −0.10 −0.03 S inhibition 0.48 0.55 0.42 0.10 0.06 −0.07 −0.44 −0.13 −0.53 −0.35 E exec WM 0.94 0.77 0.86 0.89 −0.28 −0.21 −0.11 0.07 0.13 0.07 S exec WM 0.96 1.01 −0.17 0.44 0.03 −1.11 −0.65 −1.20 −0.71 0.63 Visual-spatial WM 1.27 0.45 0.15 0.51 −1.19 −1.06 −0.91 −0.28 0.07 0.35

Note. Values in bold are effect sizes (Hedges g) >.80 when compared to LC1. LC1 = average achiever; LC2 = poor achiever; LC3 = reading disability; LC4 = high Spanish achiever; LC5 = average Spanish achiever; E = English; S = Spanish; STM = short-term memory or phonological loop; speed = naming speed; inhibition = random generation tasks; exec = executive component ; WM = working memory.

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Based on the magnitude of ESs, Latent Class 4 (LC4) yielded weak performance rela- tive to average achievers (LC1) on two of the eight measures. This relatively weaker perfor- mance of LC4 versus LC1 was primarily on the English vocabulary and fluid intelligence measures. However, it is important to note that LC4 exceeded (negative ESs) the average achievers (LC1) on Spanish vocabulary, Span- ish reading, and Spanish math. Thus, we label this latent class “high Spanish achievers.”

Relative to LC1, Latent Class 5 (LC5) yielded weaker performance (ESs > .80) on four of the eight manifest variables. The weaker performances of LC5 children were in the domains of English vocabulary, English reading, English math, and fluid intelligence. It is important to note, however, that this par- ticular latent class was comparable to average achievers (LC1) in Spanish vocabulary (ES = .07). Thus, we label this group “average Span- ish achievers.”

Correlates of Latent Classes

A multilevel logistic model determined the cognitive variables that uniquely predicted latent classes. Because the choice of the refer- ence category for generalized logit models affects the results, Brown and Prescott (1999, p. 160) recommended choosing the category with the highest frequency as the reference. The estimates for the multilevel logistic unconditional and conditional models in pre- dicting the odds of being classified in one of the latent classes when compared to average achievers (LC1) as a function of variables external to the classification (cognitive vari- ables) are shown in Table 4. Thus, the four intercept values LC2, LC3, LC4, and LC5 shown in Table 4 are the latent class compari- sons to the average achievers (LC1). For all the conditional models, we have four esti- mates of the intercept but only one slope asso- ciated with the covariate. Thus, covariates

Table 4. Estimates for Two-Level Generalized Linear Polytomous Model (N = 394).

Unconditional Model 1 Model 2 Model 3 Model 4

Fixed Effect Estimate SE Estimate SE Estimate SE Estimate SE Estimate SE

Intercept LC2 −3.59*** 0.33 −5.36*** 0.80 −5.96*** 0.66 −6.23*** 0.72 −5.92*** 0.65 Intercept LC3 −2.29*** 0.23 −3.32*** 0.63 −3.73*** 0.45 −4.11*** 0.52 −3.70*** 0.43 Intercept LC5a −1.06*** 0.30 −1.80** 0.60 −2.31*** 0.42 −2.62*** 0.48 −2.27** 0.39 Intercept LC4 −0.26 0.19 −1.04 0.60 −1.54*** 0.42 −1.86*** 0.47 −1.43** 0.39 Grade 0.26 0.29 0.46* 0.20 0.58** 0.22 0.42* 0.18 Gender −0.02 0.12 −0.08 0.12 −0.06 0.13 E STM −0.38** 0.15 −0.42* 0.18 −0.42** 0.14 S STM −0.51*** 0.16 −0.09 0.17 E speed 0.51*** 0.15 0.48* 0.20 0.50*** 0.14 S speed 0.23 0.14 0.04 0.12 E inhibition −0.13 0.14 −0.006 0.16 S inhibition −0.21 0.14 −0.22 0.15 E exec WM −0.79*** 0.19 −0.87*** 0.21 −0.79*** 0.18 S exec WM −0.16 0.15 0.14 0.16 Visual-spatial WM −0.02 0.12 0.03 0.12 0.07 0.13 Error variance 0.67** 0.30 0.98* 0.46 0.12 0.15 0.16 0.19 0.09 0.13 Model fit Deviance 933.80 680.71 664.53 593.28 697.69 AIC 943.80 704.71 688.53 625.28 715.69 BIC 950.81 720.70 704.94 646.60 728.30

Note. LC2 = poor achiever; LC3 = specific reading disability; LC4 = high Spanish achiever; LC5 = average Spanish achiever; E = English; S = Spanish; STM = short-term memory or phonological loop; speed = naming speed; inhibition = random generation tasks; exec = executive component; WM = working memory; deviance = chi-square value for the correspondence between model and data; AIC = Akaike information criterion; BIC = Bayesian information criterion. aLogistic output was organized by cell size and therefore the intercept to LC5 was reported before LC4. *p < .05. ** p < .01. *** p < .001.

Swanson et al. 303

remained constant across the logits/intercepts within each model. This allowed for the inter- pretation that the increase in log odds of fall- ing into a latent class (e.g., LC2) versus LC1 resulted from a one-unit increase in the covari- ate, holding the others covariates constant across all intercepts. Indices for model com- parisons included the deviance values, AIC, and BIC. The AIC allowed for a comparison of models that were not nested, and the BIC allowed for a comparison of nested models. In general, models with lower AIC, BIC, and deviance values fit better than models with higher values.

The unconditional model in Table 4 was assumed to have no error at Level 1 (Snijders & Bosker, 1999). That is, the Level 1 residual follows a logistic distribution with a mean of 0 and a variance of 3.29 (Snijders & Bosker, 1999, p. 227). Thus, only the intercept vari- ance is considered relevant for the analysis. The intraclass correlation was computed as .17 (.67/.67 + 3.29), suggesting that approxi- mately 17% of the variability was accounted for by children nested in classrooms, leaving approximately 83% of the variability to be accounted for by the latent measures (or other unknown factors).

As shown in Table 4, three intercepts for the unconditional model indicated a signifi- cant amount of variability in the log odds of being classified as one of the three latent classes relative to average achievers (LC1). As shown, the LC4 (high Spanish achiever) intercept was not significantly different when compared to LC1, suggesting potential differ- ences were related to random effects. A shown in Table 4, Conditional Model 1 entered only Spanish cognitive measures as well as the centered measures of grade and gender. The intercepts were significant for comparisons between LC2, LC3, and LC5 when compared with LC1. As shown, when only Spanish mea- sures were in the analysis, an intercept advan- tage was found for LC4 relative to LC1. The only significant cognitive measure to emerge for Model 1 was Spanish STM.

Conditional Model 2 entered English cog- nitive measures into the model. All intercepts

were significant, as were the measures of English STM, English naming speed, and English executive WM. All intercepts were significant and negative, suggesting an advan- tage for average achievers (LC1) relative to the other latent classes. Model 3 entered all the cognitive variables along with grade and gender. All the intercept values were signifi- cant, as were measures of English STM, English naming speed, and English WM. In addition, grade level was significant, suggest- ing that increases in grade level were signifi- cantly related to the intercept differences.

Model 4 tested whether a parsimonious model that included only the significant parameters in the full model (Model 3) pro- vided a better fit to the data than the previous models. As shown, this model substantially reduced the error variance when compared to Model 1 and the unconditional model. The intercept variance for the random effect was reduced by approximately 86% (.67 –.09/.67). As shown, all intercepts were significantly in favor of average achievers, and all intercepts were significantly related to measures of English STM, English naming speed, and the English executive component of WM. Previ- ous studies have found that cross-language differences that emerged on these cognitive measures (in this case, English over Spanish measures) are best interpreted as related to ease of access within the preferred language and not a language-specific cognitive system (Swanson et al., 2015). That is, previous stud- ies have shown L1 and L2 cognitive mea- sures load on the same latent factors (Swanson et al., 2011; Swanson, Kudo, et al., 2019), suggesting that preferred access with a spe- cific language system underlies cross-lan- guage differences.

When comparing the fit indices, the devi- ance, AIC, and BIC values were lower for Model 3 when compared to the other models. However, the parsimonious model (Model 4) reduced the intercept variance related to chil- dren nested within classrooms when com- pared to Models 1 and 2. Model 2 reduced the intercept variance when compared to Model 1.

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Discussion

The purpose of this study was to identify whether a discrete class of ELL children at risk for achievement difficulties emerged within a heterogeneous sample of elementary school children that varied in L1 and L2 vocabulary, math, and reading as well as attention and non- verbal reasoning (fluid intelligence) measures. The results yielded three important findings. First, five latent classes emerged (average achievers, poor achievers, children at risk for reading disabilities, high Spanish achievers, and average Spanish achievers) when setting cutoff scores at or below the 16th percentile on the manifest variables. As expected, the latent class referred to as average achievers outper- formed the other latent classes on a host of measures besides achievement. Second, the results showed that children with specific problems in reading (LC3) could be separated for high Spanish achievers (LC4) and average Spanish achievers (LC5). Finally, when the influence of the various predictors was held constant in a logistic regression analysis, the cognitive variables that uniquely predicted these latent classes were English measures of naming speed, STM, and the executive com- ponent of WM. Given these general findings, the results related to two questions that directed this study are now addressed.

Question 1: Can a Latent Classification of ELL Children at Risk of Specific Learning Disabilities Be Identified Within a Heterogeneous Sample of Learners?

The results show that five latent classes emerged related to Spanish and English mea- sures of vocabulary and achievement within a heterogeneous sample of English learners. The latent status membership probabilities for students at risk for specific learning disabili- ties in L1 and L2 reading were approximately 7% of the total sample. These results are in line with current estimates of reading disabili- ties. Although the incidence of reading dis- abilities in public schools has been reported to vary between 5% and 17% (McCandliss &

Noble, 2003), more conservative estimates indicate prevalence rates range from 5% to 7% of the general population. Our results also suggested that approximately 10% of the sample (i.e., LC2 and LC3) showed serious achievement difficulties, whereas approxi- mately 38% of the sample was identified by weaknesses only in English language acquisi- tion (English vocabulary, i.e., LC4 and LC5). Thus, the results were able to separate chil- dren in latent classes that were primarily related to language acquisition from those with serious achievement difficulties.

Question 2: Do Specific Cognitive Measures Predict Latent Class Membership?

In terms of cognitive models that predict latent class status, two were considered. As reviewed in the introduction, these models considered whether STM storage or executive processing within the Spanish or English lan- guage system played a major role in predictions of latent class status. The results suggested that none of the models in isolation provided a parsimonious account of the findings. The significant loadings from the full logistic regression model were measures of English STM, naming speed, and the executive com- ponent of WM. These findings fit the litera- ture attributing ELL children’s academic difficulties to problems of both storage and executive processing (Engel de Abreu & Gathercole 2012; Swanson et al., 2015). This finding was also supported in recent meta- analyses of the literature on cognition and reading and math disabilities (Peng et al., 2016, 2018) identifying components of WM as playing a key role in separating children with reading or math disabilities from chil- dren without achievement difficulties.

The results also suggested that when com- pared to average achievers, ELL children at risk for reading disabilities (LC3) perform poorly on measures of storage (English STM, Spanish STM, English naming speed, Spanish naming speed) and executive process- ing (Spanish executive component of WM), whereas the English executive processing

Swanson et al. 305

measure (English executive component of WM) captured the performance of ELLs not at risk for achievement difficulties (LC = 4). Thus, we were able to separate the groups on measures of storage and executive processing. In general, the results suggest that within a het- erogeneous sample of ELL elementary chil- dren, an identifiable group of ELL children with L1 and L2 reading problems was identi- fied at the 16th percentile cutoff point. Thus, this study contributes to the emerging litera- ture that ELL children with reading disabilities represent an identifiable group.

Thus, this study contributes to the emerging literature that ELL

children with reading disabilities represent an identifiable group.

Practical Implications

There are two practical implications related to our findings. First, L1 (Spanish) measures administered in isolation of L2 (English) mea- sures were not particularly well suited to identify children at risk for specific learning disabilities (reading in this case). Second, dif- ferent cognitive processes separate the latent classes. This finding is particularly important because confounds exist in the assessment of children with potential special needs who are second-language learners. These confounds are due in part to attributing difficulties in second- language acquisition and reading or math dis- abilities to the same cognitive processes that are involved in second-language acquisition.

Limitations

There are at least five limitations to this study. First, although we used conservative cutoff points in identifying children at risk for spe- cific learning disabilities, we have not shown that the identification of latent classes vali- dates a specific cutoff point. Rather, the results suggest the measures were able to identify subgroups at the cutoff to which they were applied. Second, we did not establish the sta- bility of reading or math performance at the

upper middle grades. Although we used a variety of norm-referenced measures normed at Grades 1 to 3 to capture consistency in low achievement performance, performance across the upper elementary grades was not assessed. Third, we have an absence of inter- vention and language home-usage informa- tion. Thus, our study is limited to discussing the risk classification within a heterogeneous sample and not whether a particular interven- tion program would later influence the classi- fication of children at risk.

Fourth, the design of the study was cross- sectional instead of longitudinal. In order to investigate language dominance and language shift in ELL children, longitudinal studies in which the development of linguistic skills is monitored in the course of time are necessary. Finally, the sample yielded minimal variance in socioeconomic status (98% of the sample was on full federal assistance programs), and therefore the influence of high versus low socioeconomic status could not be evaluated.

Conclusion

In summary, this study yielded three important findings. First, latent classifications of chil- dren with learning disabilities and children with difficulties in second-language acquisi- tion could be identified among a sample of elementary school ELL children. The results provide support for the notion that children at risk for special education needs within a het- erogeneous ELL sample reflect a discrete class of learners. Second, approximately 10% of the sample would be considered eligible for spe- cial education (LC2 and LC3), and approxi- mately 40% of the children would be at risk of being misdiagnosed. Finally, English cogni- tive measures related to storage and executive processing were the only cognitive measures that consistently predicted latent class status. Overall, the results support the notion that children at risk for specific learning disabili- ties reflect a latent class group that can be separated from a heterogeneous sample of children who vary in attention, fluid intelli- gence, and L1 and L2 measures of vocabulary, reading, and math.

306 Exceptional Children 86(3)

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Authors’ Note

This research is based on a 4-year longitudinal study funded by a National Science Foundation (NSF) Division of Research on Learning grant (Award No. DRL 1660828) awarded to the first author. This study does not necessarily reflect the views of the NSF or the participating school dis- tricts. Special appreciation is given to the Lewis Center for Educational Research, participating teachers, and CEO Lisa Lamb. Special apprecia- tion is also given to Mario Del Angel Guevara, Lorena Luevano, Julianna Massa, Catherine Riskie, Tara Curtis, Christy Yan, Karen Flores, Sindy Zambrano, Karen Cruz, Bernadette Hall-Cuaron, Michael Orosco, and school district liaisons and consultants Rosie Gonzales and Erin Bostick Mason for data collection and analysis.

Supplemental Material

Supplemental material for this article is available online.

Swanson et al. 309

Note

1. Four large elementary urban schools from two large metropolitan areas in the U.S. Southwest participated in this study. Children who par- ticipated in this study were initially identified as English language learners by the school district, not by special education status. Of the total sample, only three students had indi- vidualized education programs. Data were not available to the researchers on how Tier 1 inter- vention was implemented in the schools. Two of the elementary public schools, according to a state report, yielded the lowest percentage in reading and math score proficiency within the state. Minority (Hispanic) enrollment was

95% of the study body, which was higher than the state average. In addition, the current study included two urban charter schools also with a high Hispanic (>95%) representation. State reports indicated that one of the charter schools at the time of testing (2017–2018) reported that only 35% of children were proficient in reading and 29% were proficient in math. A state report on the second charter school also indicated that only 33% of the elementary children were pro- ficient in reading and 29% proficient in math on state measures.

Manuscript received January 2019; accepted October 2019.

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