Modeling the Speeded Determinants of Adolescents’ Academic and Attentional Functioning

Abstract

The current study utilized a large, unselected sample of adolescent twins to examine whether processing speed (PS) is an important shared predictor that accounts for covariance among reading, math, ADHD, and rapid naming (RN). The best fitting model included correlated but distinguishable latent measures of PS, RN, reading, math, inattention, hyperactivity/impulsivity, and academic fluency. PS was a shared predictor across all outcomes, while RN was uniquely associated with reading, fluency, and (albeit weakly) math. The results add to a growing literature suggesting that PS and RN may be important components of comprehensive neuropsychological models of academics, ADHD, and their covariation.

Reading disability (RD, or dyslexia), math disability (MD, or dyscalculia), and attention-deficit/hyperactivity disorder (ADHD) are common neurodevelopmental disorders that each affect approximately 5–10% of children (American Psychiatric Association, 2013). Further, there are high rates of co-occurrence, or comorbidity, between these disorders, with comorbidity rates ranging from 30 – 70% between RD and MD and 25 – 40% between ADHD and either RD or MD (e.g., Badian, 1999; Willcutt et al., 2013; Kovas et al., 2007; Landerl & Moll, 2010; Willcutt & Pennington, 2000; Capano, Minden, Chen, Schacher, & Ickowicz, 2008).

Several models have been proposed to explain the mechanisms of comorbidity between neurodevelopmental disorders. One set of explanations suggest that comorbidity may occur for artifactual reasons such as referral biases or definitional overlap, but the literature thus far suggests that these artifactual reasons are unlikely to fully explain the overlap among reading, math, and attentional difficulties (e.g., Pennington, Willcutt, & Rhee, 2005; Willcutt et al., 2019). Another possible explanation is a phenocopy phenomenon, such that symptoms of one disorder (e.g., attention regulation difficulties) lead to the secondary expression of symptoms in another disorder (e.g., gleaning less from instruction and thus struggling with academic skills relative to peers) even in the absence of the causal factors that are typically associated with the second disorder when it occurs in isolation (e.g., Pennington, Groisser, & Welsh, 1993). Once again, however, most studies have not supported this hypothesis as a primary explanation of comorbidity between RD, MD, and ADHD (e.g., Willcutt, Pennington, Olson, Chhabildas, & Hulslander, 2005; Willcutt, Betjemann, et al., 2010; Willcutt et al., 2013).

A third possibility, and the theoretical model that provides the foundation for the current study, is the shared cognitive deficit model of comorbidity that emerges from multiple deficit cognitive models of developmental disorders (Pennington, 2006). This model posits that the etiology and cognitive weaknesses associated with neurodevelopmental disorders are multifactorial in nature, with outcomes determined by a constellation of risk and protective factors. Some of these risk factors may be unique to each disorder, leading to the distinctions between disorders, whereas others are shared risk factors that lead to the co-occurrence that is frequently observed between neurodevelopmental disorders.

Past studies have identified a number of possible cognitive risk factors for learning and attention problems, and several studies suggest that weaknesses in processing speed (PS) may be shared across multiple disorders (Peterson et al., 2017; McGrath et al., 2011; Shanahan et al., 2006; Willcutt et al., 2005). However, more work needs to be done to better understand PS as a construct and its role in the comorbidity between learning disorders. In the following sections, we first describe PS and related cognitive constructs, briefly summarize previous studies on the role of PS and other speeded measures in the overlap between RD, MD, and ADHD, highlight the limitations of the extant literature, and outline the specific aims for the current study.

PS and Related Constructs

PS is typically considered to be the speed at which an individual is able to process and act upon external stimuli (e.g., Shanahan et al., 2006). This cognitive process develops during childhood and adolescence such that children can process information faster as they mature (e.g., Kail, 1991; Cerella & Hale, 1994; Kail & Hall, 1994), which in turn has been shown to mediate developmental gains in working memory and fluid intelligence (Fry & Hale, 1996).

Despite the importance of PS to cognitive development, the field still lacks a strong consensus around the measurement of this construct, leading to a construct that is broad and often weakly defined. Previous studies have used both verbal and non-verbal measures to capture PS, and tasks have varied from simple tasks with little or no executive component to more complex tasks with a large working memory load. For example, measures used to represent PS have included measures of simple reaction time (e.g., Fry & Hale, 1996), perceptual discrimination tasks (e.g., Cirino, Fuchs, Elias, Powell, & Schumacher, 2015), and tasks with significant graphomotor demands such as the PS tasks on the Wechsler intelligence tests (e.g., Jacobson et al., 2011).

Some studies have also included rapid naming (RN) speed, a linguistic measure of the speed at which individuals can name highly familiar visual stimuli (e.g., letters, numbers, colors), under the umbrella of PS, and used these two terms interchangeably (e.g., Benner, Allor, & Mooney, 2008). In contrast, other studies have found that PS and RN are related but distinct constructs that may play differential roles in the overlap between neurocognitive disorders (e.g., Willcutt et al., 2013; McGrath et al., 2011). For example, one large study (N = 1,031) found that low PS was a shared cognitive weakness explaining a portion of the variance between difficulties in reading and math, whereas RN was uniquely predictive of reading difficulty (Willcutt et al., 2013). These mixed results underscore the need for additional research to clarify whether different speeded cognitive tasks measure distinct cognitive processes or the same underlying latent construct, as well as how these speeded measures relate to different aspects of academic and behavioral functioning.

The role of PS in the Comorbidity between RD, MD, and ADHD

Comorbidity between RD and MD

Difficulties in reading and math frequently co-occur, with comorbidity rates between RD and MD ranging from 30 – 70% (e.g., Badian, 1999; Willcutt et al., 2013; Kovas et al., 2007; Landerl & Moll, 2010). There is consistent evidence that this covariance is due at least in part to shared genetic influences (e.g., Light & DeFries, 1995; Plomin & Kovas, 2005). Several studies also suggest that reading and math difficulties may be associated with a shared weakness in verbal working memory or other linguistic skills such as phonological processing (Child, Cirino, Fletcher, Willcutt, & Fuchs, 2019; Willcutt et al., 2013; Cirino et al., 2015; Moll, Göbel, Gooch, Landerl, & Snowling, 2016). In addition, some studies found that slow processing speed was associated with both reading and math (i.e., multiple regression betas of .30 and .41, respectively) and accounted for a significant proportion of their covariance (e.g., Willcutt et al., 2013). However, another study found that a verbal measure of PS was associated with RD (ƞ² = .13) but not MD status (ƞ² = .00; Moll et al., 2016), and a third study found that a nonverbal measure of PS was associated with MD but not RD (least-squares means differences of .63 and .21, respectively; Cirino et al., 2015). Finally, some studies reported minimal or no association between nonverbal measures of PS and either reading or math after controlling for other cognitive variables (e.g., Child et al., 2019; Moll et al., 2016). Importantly, the measures used to examine PS have varied across these studies, suggesting that differences in measurement (e.g., differing linguistic, graphomotor, or working memory demands) may explain some of the variability in results, underscoring the need for additional research.

Comorbidity between RD and ADHD

Although comorbidity between RD and ADHD has been studied in several different ways, much of this research has been completed by one group using a single twin sample (e.g., McGrath et al., 2011; Willcutt et al., 2005; Willcutt et al., 2019). Results from this sample indicate that RD and ADHD co-occur more often than would be expected by chance (comorbidity rates between 25 – 40%; Willcutt & Pennington, 2000), and shared genetic influences account for much of the covariance between reading and inattention (e.g., Willcutt, Pennington, Olson, & DeFries, 2007; Willcutt et al., 2019). Further, individual differences in PS are largely due to the same genetic influences that contribute to individual differences in reading and inattention, and these shared genetic influences on PS account for the majority of genetic covariance between reading and both inattention and hyperactivity/impulsivity (McGrath et al., 2011; Willcutt, Betjemann, et al., 2010). Several studies have also demonstrated that slow performance on RN measures was uniquely associated with reading difficulty and not ADHD (e.g., McGrath et al., 2011; Peterson et al., 2017; Shanahan et al., 2006), though other groups have found that RN (described as verbal PS in their study) was moderately associated with both reading (ƞ² = .07) and attentional difficulties (ƞ² = .06) when both were included in the model (Moll et al., 2016). Another study of 233 second grade students also found that a single paper-and-pencil measure of PS speed was significantly associated with inattention (r = .36) and both timed (r = .26) and untimed (r = .27) measures of single word reading (Child et al., 2019). These effects were relatively modest (i.e., small to medium effects), however, only marginally significant when controlling for other cognitive variables such as working memory and phoneme awareness and explained a small portion of shared variance between reading and inattention (pr² = 0.16).

Given these measurement and analytic inconsistencies, additional samples and a broader range of measures of PS and reading would help clarify the relationship between reading and ADHD. In particular, studies that include multiple measures of PS and naming speed, a wider range of reading measures (e.g., including more complex measures of reading comprehension), and later developmental periods are needed to better understand these cognitive contributions to academic performance.

Comorbidity between MD and ADHD

Relative to the literature on RD and ADHD, few studies have examined the comorbidity between MD and ADHD. Approximately 20 – 30% of individuals with ADHD meet criteria for MD (see review by Willcutt et al., 2012), and similar rates of comorbidity have been reported in samples selected for MD (see review by Pham & Riviere, 2015). Similar to the results for RD and ADHD, the comorbidity between MD and ADHD also seems to be largely explained by shared genetic influences (Hart et al., 2010; Polderman et al., 2011; Willcutt, Pennington, et al., 2010), with results of a systematic meta-analysis indicating a stronger association between math ability and inattention (r = .34) than between math and hyperactivity/impulsivity (r = .16; Willcutt, Nigg, et al., 2012).

To our knowledge, only a few studies have examined shared cognitive risk factors for MD and ADHD (Child et al., 2019; Peterson et al., 2017; Moll et al., 2016). Similar to the results described above, Peterson and colleagues found that PS explained a significant amount of the covariance between math and inattention. In contrast, Child and colleagues (2019) found a stronger contribution of working memory and phoneme awareness to the overlap between math and attention, with a weaker prediction from PS after the other cognitive variables were added to the model. Finally, Moll and colleagues (2016) found that slower nonverbal PS had a small to moderate association with attention difficulties (ƞ² = .05) but not MD. Once again, these results underscore the need for additional research to clarify these mixed results, and to expand beyond measures of math calculations to examine higher-order aspects of math such as math fluency and word problem solving.

Comorbidity between RD, MD, and ADHD

In one of the only studies to examine the neuropsychological predictors of reading, math, and attention simultaneously, Peterson and colleagues (2017) used structural equation modeling to test unique and shared predictors of reading, math, and inattention. Their results showed that PS was a shared cognitive predictor between inattention and both reading and math, whereas the comorbidity between reading and math ability was influenced by verbal comprehension. Somewhat unexpectedly, neither PS nor any other predictor accounted for the overlap between all three symptom dimensions. Another study that examined the relation between PS and both RD and MD, including attention as a covariate, found that while attention was moderately related to PS, neither RD nor MD status were associated with lower performance on a nonverbal paper-and-pencil PS task (Moll et al., 2016). Overall, these differing results, analytic approaches, and dearth of studies, highlight the importance of further research to clarify the relations between PS, naming speed, and difficulties with reading, math, and attention.

Summary and Remaining Gaps in the Literature

Overall, the available literature provides initial evidence that slow cognitive processing speed may contribute to at least some aspects of the well-documented covariance between reading, math, inattention, and hyperactivity-impulsivity. However, results have been inconsistent, and very few studies have simultaneously examined the shared cognitive risk factors for these disorders in a single model.

Several factors may contribute to these mixed results. The definition and measurement of PS have varied across studies in several potentially important ways. Studies have included both verbal/linguistic and nonverbal PS and RN measures that also vary in their reliance on other cognitive skills such as language and executive functions. Further, most previous studies have focused on measures of single word reading and math calculations, and little is known regarding the generalization of these findings to measures of academic fluency or more complex academic skills such as reading comprehension or word problems.

Sample differences also complicate the interpretation of results across studies. The Colorado twin sample that has been used most frequently in previous studies was overselected for the presence of learning difficulties (e.g., Shanahan et al., 2006; Peterson et al., 2017). Approximately 80% of the Colorado sample was under age 13, and the study by Child and colleagues used an unselected school-based sample of second grade students (Child et al., 2019). It is plausible that the relation between PS and measures of math, reading, and ADHD may change across development as the demands of the academic achievement measures increase in complexity (Fry & Hale 1996), and no studies have examined these associations in a high school sample. Therefore, studies that focus on specific age in an unselected sample of adolescents will provide a useful extension of the existing literature to examine potential developmental or sampling effects.

The Current Study

The current study uses an unselected sample of adolescents (M_age=15.5 years; age range = 14.6 – 16.6 years) to begin to address gaps in our current understanding of the structure of PS and its role in the comorbidity between reading difficulties, math difficulties, inattention, and hyperactive or impulsive behaviors. The study extends the previous literature in the following ways:

1. Exploratory and confirmatory factor analyses were conducted to test several specific hypotheses regarding the validity and latent structure of each of the primary constructs in the study (see Figure 1).

   1. We hypothesized that the best fitting model of the speeded tasks would indicate that PS and RN are correlated but separate constructs. Additionally, we hypothesized that all measures of PS would have similar loadings on a latent processing speed factor, indicating that the three measures were equally robust manifest indicators of the latent construct of PS despite differences in task parameters.
   2. We predicted that the best fitting model of the academic tasks would include correlated but distinguishable latent measures of overall reading (i.e., single-word reading, reading comprehension, and sentence reading fluency) and math (i.e., calculation, applied problems, and math fluency). Additionally, because of the shared speeded component of the academic fluency tasks, we expected to find evidence of an additional latent factor comprised of reading and math fluency that is independent of the overall variance in the other math and reading tasks.
   3. Finally, we expected to support the well replicated finding that symptoms of ADHD reflect two separate but correlated dimensions of inattention and hyperactivity/impulsivity symptoms.
2. The latent factors identified in the measurement models were then included in structural equation models designed to test specific hypotheses about the relationships between PS, RN, and individual differences and overlap among reading, math, inattention, and hyperactivity/impulsivity (see Figure 2).

   1. We hypothesized that we would find moderate to strong associations between PS and all measures of math, reading, and inattention, and that PS would account for a significant proportion of the shared variance among these dimensions. In contrast, we expected the association between PS and hyperactivity/impulsivity to be weaker.
   2. In addition to the variance in PS that is shared across the overall measures of reading, math, and inattention, we predicted that slow PS would also be weakly to moderately associated with the latent measure of academic fluency.
   3. In contrast to the general association between PS and measures of reading, math, and inattention, we expected to replicate findings from previous studies suggesting that RN may be weakly to moderately associated with reading difficulties even when general PS is included in the model.

Figure 1.

Overall measurement model with standardized parameter estimates. All solid regression paths p < .000 and dotted paths p > .05.

Figure 2.

Full structural model with standardized parameter estimates. All solid regression paths p < .000; *p = .027; +p = .023; dotted paths p > .05.

Methods

Participants

Participants were 930 individuals drawn from the Colorado component of the International Longitudinal Twin Study of Early Reading Development (ILTSERD; e.g., Byrne et al., 2009; Becker et al., 2018; Christopher et al., 2012). This sample is separate from another Colorado twin study that has also focused on questions related to learning and attentional difficulties (e.g., McGrath et al., 2011; Peterson et al., 2017; Shanahan et al., 2006). The overall ILTSERD also includes twins from Australia and Scandinavia, but the present study only includes data from participants from Colorado because that is the only sample with data collected at the end of ninth grade.

The twins were initially recruited from the Colorado Twin Registry, a registry based on birth records that includes information on over 90% of all twin births in Colorado. All available twins were invited to participate, yielding an unselected sample in which learning and attentional difficulties were free to vary. The twins were first assessed during the summer prior to starting kindergarten (M_age=4.9 years). After the initial preschool assessment, participants were assessed again in the summers following kindergarten, first grade, second grade, fourth grade, and ninth grade (M_age=15.5 years). The current analyses focus on the assessment completed at the end of ninth grade.

Results of several analyses indicate that the current sample is generally representative of the population from which it was drawn. Approximately 85% of mothers and 83% of fathers identified as White, consistent with the demographic characteristics of the local population. Comparisons with available normative data on several of the measures of academic achievement suggest that the distributions in the current sample are consistent with the overall population (e.g., Christopher et al., 2012). Parents reported that approximately 6% of the twins had received a diagnosis of a learning disability, a rate that is consistent with the proportion of students in the overall population who receive special education services for a learning disability (National Center for Education Statistics, 2020). Finally, the rates of clinical diagnoses of ADHD (7%), anxiety disorders (6%), and major depressive disorder (5%) in the current sample are consistent with the base rates of these disorders in the population for this age range (e.g., Ghandour et al., 2019; Willcutt, 2012).

Procedures

All study procedures were approved by the Institutional Review Board. Informed consent or assent was obtained from all participants and their parents at initial enrollment and at each follow-up assessment.

Testing procedures are described in detail in previous papers (e.g., Christopher et al., 2012). Briefly, the twins completed the measures of reading, math, and processing and naming speed during an individual testing session while one parent or caregiver completed a battery of questionnaires that included the measures of ADHD symptoms described in this report.

To facilitate initial recruitment and enrollment of participants, families were given the option to complete the testing in the home or in our laboratory for the initial waves of testing in elementary school, and this procedure has been continued for subsequent assessments to maximize retention. The current assessment described in this report was completed in a single session in the twins’ home or at the university. Approximately 60% of participants completed the assessment in our laboratory, and 40% chose to complete the assessment in a quiet space in their home. A direct comparison of results by setting indicated that participants tested in the home scored significantly lower on two measures (Woodcock-Johnson III Applied Problems and ETS Identical Pictures). However, these effects were relatively small (d = 0.3), and none of the other variables differed significantly as a function of the location of testing (d = 0.0 – 0.2). Further, correlations between the measures included in this paper were nearly identical in the subset of the sample that completed the testing at home versus in the laboratory. These subsamples were therefore combined and utilized for the analyses described in this report.

Measures

Reading Achievement

Participants completed a battery of standardized measures of different components of reading achievement.

Untimed Single Word Reading.

The Word Identification subtest from the Woodcock-Johnson Tests of Achievement: Third Edition (WJ-III; McGrew & Woodcock, 2001) requires the participant to read single words with no time constraints. The WJ-III Technical Manual reports test-retest reliability correlations for the current age range = .88 – .95.

Reading Comprehension.

On the WJ-III Passage Comprehension subtest, participants silently read short passages of one or two sentences and provide a missing word to demonstrate their comprehension (test-retest r = .88 – .95; McGrew & Woodcock, 2001). The Gates-McGinitie Reading Test – IV (test-retest r = .90; MacGinitie, MacGinitie, Maria, & Dreyer, 2002) is a second measure of reading comprehension that requires the participant to read and answer questions about more extended passages, providing a measure of the ability to make inferences and draw broader conclusions that are not stated explicitly in the text.

Reading Fluency.

The WJ-III Reading Fluency subtest requires the participant to silently read simple sentences and indicate whether or not the statement in each sentence is true as quickly as possible. The dependent measure if the number of correct responses within three minutes (test-retest r = .90 – .94).

Math Achievement

Calculations.

The WJ-III Calculations subtest is an untimed paper-and-pencil measure of mathematics calculations (test-retest r = .83 – .84).

Quantitative Reasoning.

More complex higher-order mathematical understanding was assessed by two measures. The WJ-III Applied Problems subtest requires the participant to complete a series of math word problems (test-retest r = .92 – .95). Each question is presented orally by the examiner while the participants reads along silently. WJ-III Quantitative Concepts is an orally administered measure that assesses understanding of math term, symbols, and concepts (test-retest r = .90 – .93).

Math Fluency.

The WJ-III Math Fluency subtest requires participants to complete as many simple arithmetic problems as possible within three minutes (test-retest r = .89 – .91).

ADHD Ratings

The Disruptive Behavior Rating Scale (DBRS) (Barkley & Murphy, 1998) was used to obtain parent ratings of the 18 symptoms of DSM-IV ADHD (93% of ratings were completed by the mother). On the DBRS, the parent is asked to indicate how often in the last 6 months each symptom occurred on a four-point scale (0=never or rarely, 1=sometimes, 2=often, and 3=very often). Total scores on the nine inattention symptoms and nine hyperactivity/impulsivity symptoms were reverse scaled to match the scaling of the other academic domains and used as the primary measures of ADHD behaviors.

Processing Speed (PS)

The WISC-III Coding and Symbol Search subtests (Wechsler, 1991) are paper-and-pencil measures of PS that have been shown to be associated with ADHD and learning difficulties in several previous studies (e.g., Chhabildas, Pennington, & Willcutt, 2001; McGrath et al., 2011; Peterson et al., 2017; Rucklidge & Tannock, 2002; Willcutt, Betjemann, et al., 2010). The Coding subtest requires the participant to rapidly copy symbols associated with specific digits based on a key provided at the top of the page, and the dependent measure is the total number of correct items after two minutes. The Symbol Search subtest requires the participant to match a symbol to an identical target that is displayed among several distracter stimuli that share some physical features. The dependent measure is the number of correct items minus the number of incorrect items completed before the two-minute time limit. Psychometric studies indicate that these subtests have adequate reliability (test-retest r = .86 – .88), and they correlate relatively modestly with FSIQ (Wechsler, 1974; 1991), suggesting that they may tap aspects of PS that are at least partially independent of general intelligence.

In addition to the two WISC-III subtests, the Educational Testing Service Identical Pictures subtest (French, Ekstrom, & Price, 1963) requires the participant to identify as quickly as possible the one picture out of five options that is an exact match to a target picture. The primary dependent measure is the number of items completed correctly in two minutes, and the alternate forms reliability of the identical pictures score is .92.

Rapid Naming (RN)

Two measures of RN were obtained from the Comprehensive Test of Phonological Processing (CTOPP; Wagner, Torgesen, & Rashotte, 1999). In rapid letter naming, participants named 72 individual letters as quickly as possible. Rapid digit naming is identical in format but used six digits as stimuli. If a participant made more than four errors on one of the RN tasks the administration was considered invalid and the score was not included (N = 2 participants on the rapid letter naming measure). Test-retest reliability for the RN measures is .84 (Wagner et al., 1999).

Analytic Strategy

Structural equation modeling (SEM) and confirmatory factor analyses have several advantages for analyses that are designed to investigate issues of measurement and construct validity. By using unobserved (i.e., latent) constructs composed of the shared, reliable variance of measured items or symptoms rather than the simple sum or mean of related items, both internal and external relationships can be explored with reduced measurement error. The latent modeling framework also facilitates the typical progression from exploratory factor analysis – to delineate the most appropriate set of items measuring a hypothesized construct – to confirmatory factor analyses and structural equation models that examine the relationships among relevant constructs.

SEM was used to perform exploratory and confirmatory factor analyses (EFAs and CFAs) of both the endogenous and exogenous latent traits. Consistent with prior literature and EFAs of these and related constructs (e.g., Willcutt et al., 2014), primary loadings for all EFAs performed were defined as loadings of .60 or higher, and measures were considered cross-loaded if secondary loadings were greater than .30 and within .20 of the measure's primary loading. To address Aim 1a, an EFA of the PS and RN measures was conducted using Geomin rotation and either 1 or 2 latent factors in which all measures were allowed to cross-load. The latent structure of the best fitting model was then confirmed by assigning each measure to its indicated factor in a subsequent CFA. A similar approach was applied for the reading and mathematics measures in Aim 1b. However, in this case EFA models with 2 versus 3 potential factors were tested due to our hypothesis that the academic fluency measures might load on a separate factor from the rest of the reading and math measures.

For Aim 1c, the ADHD symptom dimensions were modeled using parcels, whereby individual items are combined (e.g., taking the mean of multiple items) and the new composites are used as manifest variables. Parceling has a number of advantageous properties when latent variables are created from a large number of manifest indicators (i.e., nine symptoms of inattention or hyperactivity-impulsivity). These include reducing the amount of unreliable (i.e., error) and item-specific variances, decreasing the likelihood of Type II errors, and increasing generalizability by lowering the likelihood of correlated residuals, dual factor loadings, and sources of sampling error more generally (Little, 2013; Little, Rhemtulla, Gibson, & Schoemann, 2013). The use of parcels was also motivated by the considerable literature supporting the factor structure and validity of ADHD symptom dimensions (e.g., Willcutt et al., 2012) and the study’s focus upon structural relationships with ADHD rather than IN and HI’s measurement.

Following the procedures recommended by Little (2013), unstandardized loadings from CFAs of the Inattention and Hyperactivity/Impulsivity domains were used to assign items to a parcel that would maximize the likelihood of homogenous parcels. Specifically, the items with the highest and lowest unstandardized loadings were assigned to parcel 1, following by the next highest and next lowest items to parcel 2, and so on until all items were assigned to a parcel. As such, the IN and HI constructs were each created using three parcels, each of which was the mean of three symptom ratings items. These parcels were created using the WLSMV estimator, and the CFA models were fitted to polychoric correlations among the individual symptom variables. All other analyses utilized the MLR estimator.

After completing the individual EFAs and CFAs of reading, math, and ADHD ratings, a single CFA was created using all the dependent academic and behavioral ratings constructs. A full structural model was then estimated in which latent reading, math, fluency, inattention, and hyperactivity/impulsivity were simultaneously regressed onto latent PS and RN. Aims 2a through 2c were evaluated by investigation of the significance and strength of the regression paths.

Measurement and structural model analyses were conducted using Mplus (Version 8.1.5; Muthén & Muthén, 2017), and the type=complex feature was used to appropriately adjust standard errors due to the inclusion of twin pairs that are not fully independent from one another. Overall model fit was determined with the robust comparative fit index (CFI; study criteria ≥.90, with approximately .95 being ideal), the Tucker-Lewis Index (TLI; study criteria ≥.90), and the robust root-mean-square error of appoximation (RMSEA; study criteria ≤.08). These fit criteria were selected as evidence of an at least “acceptable” model fit (Little, 2013, pp. 109 and 115). To determine the optimal number of factors from EFAs, we applied Finch (2020) and Garrido’s et al. (2016) suggested criteria for continuous and categorical indicators, respectively, using both .95 cut-offs and improvements of at least .01 for CFI and TLI, as well as RMSEA improvements greater than .015 to select a model with more latent factors.

Missing Data

Covariance coverage for these analyses ranged from .93 to 1.00, indicating that few data points were missing. Furthermore, Little’s χ ² test of missing completely at random (MCAR) was non-significant (χ ²(37) = 28.7, p = .83). Analyses with the WLSMV estimator use pairwise deletion, whereas MLR uses a full-information maximum likelihood approach to missing data, both of which provide minimally biased or even unbiased parameter estimates when data are consistent with an MCAR mechanism or missing at random (Baraldi & Enders, 2010).

Results

Tables 1 and 2 summarize the fit indices and loadings from EFA. Consistent with our predictions, a large and significant chi-squared value indicated that a single factor EFA model in which PS and RN measures loaded on a single factor provided a poor fit to the data (χ² = 862.9; p < .001; Table 1). In contrast, fit was excellent and the aforementioned factorization criteria were met for a two factor EFA model in which the three PS measures loaded on a factor separate from the two RN measures (fit indices are summarized in Table 1 and loading for each measure are provided in Table 2).

Table 1.

Fit Indices for EFAs and CFAs of Cognitive, Academic, and ADHD Constructs

Model	df	χ2	p	CFI	TLI	RMSEA [90% CI]
Processing Speed and Rapid Naming EFA
1 Factor	5	862.9	<.001	.610	.220	.430 [.406, .454]
2 Factors	1	.031	.86	1.000	1.004	.000 [.000, .047]
Reading and Mathematics EFA
1 Factor	20	918.6	<.000	.814	.740	.220 [.208, .232]
2 Factors	13	399.4	<.000	.920	.828	.179 [.164, .194]
3 Factors	7	16.7	.021	.998	.992	.038 [.014, .063]
Parcelled IN and HI EFA
1 Factor	9	996.3	<.001	.738	.563	.356 [.337, .375]
2 Factors	4	10.5	.03	.998	.994	.043 [.011, .076]
Processing Speed and Rapid Naming CFA
2 Factors	103	372.9	<.001	.947	.930	.131 [.117, .145]
Reading and Mathematics CFA
3 Factors	88	140.8	<.001	.990	.984	.063 [.043, .081]
Parcelled IN and HI CFA
2 Factors	8	22.7	<.001	.994	.989	.046 [.024, .069]

Note. EFA/CFA=exploratory/confirmatory factor analysis; IN=inattention; HI=hyperactivity/impulsivity; CFI=comparative fit index; TLI=Tucker-Lewis Index; RMSEA=root-mean-square error of approximation; CI=confidence interval.

Table 2.

EFA Loadings of Cognitive, Academic, and ADHD Constructs

Model	Measure	1-Factor	2-Factors		3-Factors
Speeded Cognition		F1	F1	F2	⎯	⎯	⎯
	WISC Coding	.77	.71	.09	⎯	⎯	⎯
	WISC Symbol Search	.80	.89	−.07	⎯	⎯	⎯
	Identical Pictures	.76	.76	.01	⎯	⎯	⎯
	Rapid Digit Naming	.45	.12	.69	⎯	⎯	⎯
	Rapid Letter Naming	.47	.00	1.11	⎯	⎯	⎯
Academics			F1	F2	F1	F2	F3
	WJ Letter Word ID	⎯	.52	.20	.76	.00	.17
	WJ Passage Comp.	⎯	.28	.71	.82	.00	−.02
	Gates-MacGinitie	⎯	.32	.58	.84	.02	−.01
	WJ Sent. Reading Fluency	⎯	.31	.70	.82	.01	.68
	WJ Calculation	⎯	.60	.32	−.11	.94	.00
	WJ Quant. Concepts	⎯	.72	.23	.03	.86	−.07
	WJ Applied Problems	⎯	.79	.16	.02	.89	.02
	WJ Math Fluency	⎯	.69	.19	.00	.73	.61
ADHD Symptoms		F1	F1	F2	⎯	⎯	⎯
	IN Parcel 1	.79	.94	.01	⎯	⎯	⎯
	IN Parcel 2	.79	.95	−.06	⎯	⎯	⎯
	IN Parcel 3	.82	.77	.09	⎯	⎯	⎯
	HI Parcel 1	.55	.05	.78	⎯	⎯	⎯
	HI Parcel 2	.55	−.01	.87	⎯	⎯	⎯
	HI Parcel 3	.56	.00	.87	⎯	⎯	⎯

Note. Loadings in bold indicate primary factor loadings. EFA=exploratory factor analysis; ID=identification; Comp=comprehension; Sent=sentence; Quant=quantitative; IN=inattention; HI=hyperactivity/impulsivity.

Similarly, one factor EFA models did not provide an adequate fit to the data for the ADHD measures or the measures of academic functioning (Table 1). Instead, EFA indicated that ADHD symptoms were best described by a two-factor model with separate inattention and hyperactivity-impulsivity dimensions (Table 1 and Table 2), consistent with the two symptom dimensions of ADHD described in DSM-5.

EFA further indicated that a three-factor model provided the best fit for the measures of reading and math achievement (Table 1 and Table 2). All reading and math measures loaded as expected onto their respective academic domains. In addition, the WJ-III Sentence Reading Fluency and WJ-III Math Fluency measures also loaded on a third fluency factor that was distinguishable from the primary reading and math factors. After determining the ideal number of factors for each set of measures via EFA and χ ² difference tests, separate CFAs were estimated for each set of measures and demonstrated very good to outstanding global fit (all CFI > .98) and acceptable to close local model fit (all RMSEA < .08; see Table 2).

The dependent factors (i.e., latent academic measures and symptom dimensions of ADHD) were then combined into a single measurement model that demonstrated a very good fit to the data (CFI=.99, TLI=.98, RMSEA=.043; see Figure 1), with the one unexpected result being negative correlations between the latent fluency factor and the two academic factors (i.e., reading and math).

Having supported Aims 1a-c, we then estimated a structural model in which the dependent academic and ADHD factors were regressed onto the speeded cognition factors (see Figure 2). This model also demonstrated very good model fit (CFI=.97, TLI=.96, RMSEA=.051). Hypothesis 2a was supported by significant associations between PS and all five measures of reading, math, and ADHD, and hypothesis 2b was supported by the significant regression of latent fluency on the PS factor (β=.32, p<.001). Finally, hypothesis 2c was supported via significant regression of latent reading on RN (β=.18, p<.001), although additional significant regression paths were also revealed between RN and latent fluency (β=.27, p<.001) and latent math (β=.10, p=.03).

Discussion

The current study aimed to understand both the construct of PS and its role in the overlap between difficulties with reading, math, inattention, and hyperactivity/impulsivity in a large, unselected sample of adolescents. The current findings extend the literature by clarifying the relation between the constructs of PS and RN, and by examining the relationship between PS and RN and multiple aspects of academic skills (e.g., basic, complex, and fluency measures) as well as multiple symptom dimensions of ADHD (i.e., inattention vs. hyperactivity/impulsivity).

Measurement models of learning and ADHD symptoms

As expected, initial measurement models indicated that PS and RN are significantly correlated but separate constructs. This suggests that although these constructs share a speeded component, they also involve some distinct cognitive processes. Similarly, our results indicate that inattention and hyperactivity/impulsivity reflect two highly correlated but distinct dimensions, also consistent with our predictions based on well replicated literature (e.g., Willcutt et al., 2012).

While the majority of previous studies examine only certain aspects of academic domains, such as single-word reading, the current study sought to address this gap in the literature by exploring multiple aspects of academic domains as well as symptom dimensions of ADHD. Initial measurement models indicated that the best fitting model of the academic tasks included correlated but distinguishable latent measures of overall reading (comprised of single-word reading, reading comprehension, and sentence reading fluency), and math (comprised of calculation, applied problems, and math fluency). As expected, all measures of reading and math had high loadings on the latent reading and math measures.

Results also supported our prediction that we would find evidence for a separate academic fluency factor that is independent of the overall variance in the other math and reading tasks. However, we did not predict the small but significant negative associations between academic fluency and the latent reading and math measures.

One possible explanation for these unexpected negative associations is that the variance that remains in "fluency" after accounting for the latent reading and math measures may be more aptly described as the urgency to complete the timed academic tasks hastily. This tendency to respond hastily may occur at the expense of accuracy on these timed reading and math tasks. One possible explanation for these unexpected negative associations is that the variance that remains in "fluency" after accounting for the latent reading and math measures may reflect the tendency to respond hastily on the timed academic tasks, even if this resulted in lower accuracy.

Alternatively, the negative relation between the latent fluency measure and the untimed measures of reading and math could result from a cautious or anxious response style that emphasizes accuracy over speed. Because scores on the fluency measures incorporate speed of response in addition to accuracy, individuals who work slowly and carefully to ensure that all responses are correct may score lower than participants who focus on both speed and accuracy. In either case, these unexpected results await replication in other samples, and underscore the additional work that is still needed to further clarify the nuanced aspects of these relationships.

Full Models

In Aims 2a-2c, we used SEM to test the relationships between PS, RN, and individual differences and overlap among reading, math, inattention, and hyperactivity/impulsivity. As expected, there were significant regression paths between PS and the latent reading, math, academic fluency, and inattention measures, indicating that PS accounted for a significant proportion of the shared variance between these academic skills and symptom dimensions. The association between PS and hyperactivity-impulsivity was also significant, but weaker than the association with the other latent measures.

RN was also uniquely associated with reading difficulties and academic fluency even when PS was included in the model, a finding that was consistent with our initial predictions given the linguistic nature of the RN tasks. In addition, results of the full model also showed a marginally significant association between RN and mathematics ability. Although we did not predict this result, this finding is consistent with other studies that showed a small but significant correlation between RN and math, and particularly for measures of math fluency (e.g., Berg et al., 2008; Koponen et al., 2020).

Finally, it is important to note that the final model included significant residual covariance between the measures of reading, math, and ADHD ratings. These results indicate that PS and RN account for a significant proportion of the covariation among these domains, but additional variance also remains to be explained by other cognitive factors (particularly for reading and math). Overall, the current findings add to a growing literature that suggests that both PS and RN may be two important components of a comprehensive neuropsychological model of reading, math, ADHD, and their covariation.

Limitations and Future Directions

This study makes an important contribution to a relatively sparse body of literature on the cognitive underpinnings of the co-occurrence of reading, math, and ADHD. The current results must also be considered in the context of several limitations, many of which may be useful to address in future studies.

An important strength of the SEM approach is that it allows us to extract error-free measures of the variance that is shared across the PS, RN, reading, and math tasks, providing a powerful test of the relations among these constructs. Further, the individual measures have similar loadings on the latent measures of reading, math, inattention, and hyperactivity-impulsivity (e.g., .71 – .85 for reading, .74 – .91 for math), suggesting that the results are not being driven solely by one measure of these constructs.

These results suggest that PS explains a significant amount of the variance that is shared among different aspects of reading and math. On the other hand, the residual associations between reading, math, and inattention remain significant when both PS and RN are both included in the model, indicating that PS does not fully explain the covariance between these domains. Thus, to further understand this overlap and the comorbidity between the neurodevelopmental disorders related to these academic skills and symptom dimensions (i.e., RD, MD, and ADHD), future studies that include a wider range of key cognitive predictors would provide a useful extension of these findings.

Despite some differences in the extent to which the PS measures required fine motor production and attention to visual details, the three different measures of PS had relatively equal loadings on the latent measure of PS. These results provide important support for our hypothesis that these are valid measures of the latent construct of PS. However, it will be important for future studies to test if these results replicate for the broader range of measures that have been used to assess PS in the literature. For example, the measures in the current study involved a paper-and-pencil response that requiring some degree of graphomotor and perceptual skill, even if minimal. Future studies should include a wider range of PS tasks, including tasks that can be completed orally.

The narrow age-band for the current sample is both a strength and limitation of the study. Restricting our analyses to participants at the end of ninth grade allowed us to examine these associations in a key developmental period that has not been included in most previous studies. Further, our adolescent sample allowed us to examine higher-order academic skills, such as reading comprehension and quantitative reasoning, with more confidence that these measures are capturing more complex academic skills (e.g., comprehension or extracting meaning from reading) as opposed to being driven by more basic skills (e.g., word reading) as they might in a younger sample. On the other hand, our focus on a specific age-band of adolescents with a cross-sectional design leaves us unable to draw conclusions about causality or how these relationships might change over time. This will be an interesting question for a longitudinal study to address, ideally by tracking these associations from pre-academic skills in young children through the end of high school. A full understanding of the developmental trajectory of these skills will inform developmental models of PS, academic skills, and their covariance, and may inform early identification and intervention.

Of note, families were allowed to choose whether to complete the testing in the laboratory or at home to maximize the rate of retention of participants. Small but significant differences were observed on the means of two individual measures in the samples tested at home and in the laboratory, but the means on the other 12 measures were not significantly different, and the overall pattern of correlations was nearly identical in both samples. These results suggest that this limitation is unlikely to change the interpretation of the overall results obtained in the full sample.

Our sample was unselected and we examined our model across the full range of academic ability and symptom dimensions rather than focusing on a sample with learning disabilities. This decision maximized variance and sample size. Further, because evidence suggests that these neurodevelopmental disorders represent the low tail of a continuously distributed symptom dimension (e.g., Pennington, 2014) these results are likely to have important implications for understanding the comorbidities among RD, MD, and ADHD. However, it would be useful for future studies to examine this possibility directly by testing if our results replicate in samples selected for learning disabilities.

Finally, future studies should explore the overlap between neurodevelopmental disorders such as RD, MD, and ADHD using other levels of analysis. For example, the use of brain-based measures may be one useful extension that could help us gain a deeper understanding of the meaning of the shared weaknesses in PS across neurodevelopmental disorders (e.g., is lower PS reflective of decreased white-matter integrity?).

Conclusion

In sum, results from the current study provide further evidence that PS is a key shared cognitive weakness across dimensions of reading, math, inattention, and hyperactivity. Further, this association is similar for multiple aspects of academic skills (e.g., basic, complex, and fluency measures). Future extensions of this work should incorporate additional cognitive predictors as part of comprehensive cognitive models of the shared and unique cognitive correlates of these domains, as well as study designs that allow more insight into potential causality and neural correlates.