Reading difficulties are one of the most pervasive learning impairments found among school-aged children, with 5–10% of students experiencing problems with reading (Compton et al., 2014). Far and beyond all other theories, the prevailing explanation for reading difficulties is a deficit in phonological processing, but recent work has shown that insufficiencies in the EF system may also be underlying deficient reading development (Gombert, 2003; Altemeier et al., 2008; Booth et al., 2010). For example, when accounting for deficiencies in the phonological system, children with RD still have shown diminished performance on tasks assessing EF, such as inhibition and working memory (Swanson et al., 2006; Altemeier et al., 2008; Booth et al., 2010). Indeed, evidence shows that EF deficits are a fundamental feature of RD (Gioia et al., 2002).

The important link between reading and EF lies in the transition from learning to read to reading to learn. At first, the linguistic knowledge necessary for reading is acquired implicitly through regular exposure to patterns in orthography, phonology, and morphology (Gombert, 1992, 2003). This unconscious exposure leads to the creation of a subconsciously-organized and instance-bound linguistic lexicon that includes rudimentary awareness of grapheme to phoneme correspondence (GPC; Gombert, 2003). Then, formal reading instruction begins, ramping up print exposure, while students are taught the explicit rules of GPC. As reading instruction advances, students must be able to take conscious control and monitor their linguistic lexicons in order to respond to unexpected external demands, like reading an unknown word (Gombert, 2003) or properly resolving a conflict between phonology and orthography based on the current context (Bitan et al., 2009). This movement from subconscious to conscious and implicit to explicit is accompanied by a developmental increase in executive control (Gombert, 2003; Bitan et al., 2009). The executive control conferred by EF modulates both top-down and bottom-up processing according to reading task demands (Bitan et al., 2009), which enables readers to discriminate between task-relevant and task-irrelevant information quickly (Bitan et al., 2009) so that reading may become automatic (Gombert, 2003). Without the level of mastery and quick adaptability that EF makes possible, reading difficulties may emerge.

There are many inconsistencies found in the literature exploring the exact role of EF in relation to reading difficulties. According to meta-analytic work, these incongruities can be boiled down to two main moderators: RD definitions and EF task modalities (Stuebing et al., 2002; Booth et al., 2010). Despite the poor 1-year stability of IQ-achievement discrepancy definitions (Schatschneider et al., 2016), they have continued to be one of the most common RD definitions utilized in practice (Spencer et al., 2014), including their use in studies linking EF and RD (e.g., Altemeier et al., 2008). Based on the results from two meta-analyses (Stuebing et al., 2002; Booth et al., 2010), the association of EF to IQ-achievement discrepancy definitions of RD shows lower mean effect sizes than the association of EF to non-discrepancy definitions of RD (Booth et al., 2010). One possible explanation for this difference is that IQ-discrepant readers are no different than IQ-consistent readers, and that the RD definition used only appears to matter because of differences in EF and IQ task modality (Booth et al., 2010). For example, verbal versus non-verbal IQ may yield different results when included with EF in an IQ-discrepant RD framework, especially depending on whether a verbal or non-verbal EF task is used. Since a majority of EF tasks incorporate a verbal component (e.g., Altemeier et al., 2008), it is difficult to parse out whether the driving force behind the task performance is truly EF or the phonological or verbal processing needed to complete the task.

In response to the confusion presented in the literature examining the role of EF in reading achievement due to EF task modality and RD definitions, we implemented two main techniques in the present study to assist in drawing clearer conclusions about the association between EF and RD. First, we measured EF with the Behavior Rating Inventory of Executive Function (BRIEF), which is a non-verbal instrument that captures EF as it is manifested behaviorally. By employing a non-verbal EF measure, we are able to avoid the uncertainty about the contributing role of verbal processing to EF performance. In addition, most of the work on EF and RD thus far has used cognitive indices of EF ability (e.g., Altemeier et al., 2008), which have been shown to correlate poorly with behavioral EF measures (e.g., McCauley et al., 2010), so our use of the BRIEF subscales in predicting RD may yield interesting new results. Second, in order to avoid the potential pitfalls embedded in the use of IQ-discrepant RD definitions, we employed a hybrid model approach to RD classification, the benefits of which we discuss in more detail in the following section.

A promising solution to the low reliability of IQ discrepancy-based and other single-criterion RD models, and their inconsistent association with EF, is the implementation of hybrid models for RD classification (Wagner, 2008; Waesche et al., 2011; Fletcher et al., 2013; Spencer et al., 2014). Historically, RD models have relied on a single benchmark, which is most commonly based on either IQ-achievement discrepancy (Bateman, 1965), cognitive discrepancy (Stuebing et al., 2012), or response-to-intervention (RTI) or instruction (Fuchs and Fuchs, 2006) definitions. Hybrid models take a multi-component approach to RD measurement, which makes them comparatively more stable than other RD classification techniques (Spencer et al., 2014; Schatschneider et al., 2016). Fundamentally, the hybrid model approach to RD classification is based on the idea that a construct is more precisely captured by measuring it in many ways. As such, the hybrid model employed in the present study defined RD as a latent construct made up of four measured symptoms that are described in more detail below.

A recent publication by Spencer et al. (2014) examined the 1- and 2-year stability of a hybrid model approach to RD classification utilizing four indicators of RD that were all chosen based on traditional RD definitions. The RD indicators included low achievement in word reading, unexpected low achievement in word reading, poorer reading comprehension compared to listening comprehension, and a dual-discrepancy RTI model that necessitated both low achievement and low growth in word reading. In this version of the hybrid model, RD was characterized using a symptom approach, similar to the method employed in the Diagnostic and Statistical Manual of Mental Disorders (5th ed.; DSM-V; American Psychiatric Association, 2013). The symptoms were calculated utilizing cutoff points ranging in severity from the 3rd to the 25th percentile, and regardless of which symptom was examined, results revealed that severity and stability were inversely related, with the highest cutoff points (i.e., the 25th percentile), yielding the most stable results for RD classification. In the same vein, Schatschneider et al. (2016) conducted a simulation study that found that hybrid models that incorporated many symptoms of RD, instead of any one RD benchmark, provided the most stable classification scheme for RD, and that the 25th percentile was also the most stable cutoff point for each symptom in a constellation (i.e., multi-symptom) model. The findings of these two investigations, as well as the results yielded by a similar study conducted by Waesche et al. (2011), provide clear evidence for the advantages of using a hybrid model that classifies RD as a latent construct made up of many measured symptoms of RD as the most reliable and state of the science approach to RD classification. Additionally, the methods and findings outlined by these papers (Waesche et al., 2011; Spencer et al., 2014; Schatschneider et al., 2016) clearly point to the 25th percentile as the best cutoff point for achieving the highest reliability in RD symptom identification within a hybrid model. Accordingly, a 25th percentile cut was utilized for the calculation of each RD symptom in the hybrid model utilized in the present study. Next, we will take a closer look at the each of the four hybrid model symptoms. The first symptom, low achievement in word reading, represents the simplest conceptualization of RD, and is based on the fact that students who fail to reach a certain level of word reading performance at the end of the school year are likely to be reading disabled and require some form of additional intervention. Unexpected low achievement, an IQ-achievement discrepancy definition for RD, was operationalized as unexpectedly low word reading achievement based on verbal aptitude. This symptom was modeled after the idea that a student who demonstrates a certain capacity in his/her general intelligence should be able to translate that same capacity into all domains, including reading achievement. Our reason for focusing on word reading in these initial two symptoms was that phonological awareness, which underlies word reading ability, serves as a precursor to more advanced reading skills (e.g., Holloway et al., 2015), so it provides a useful early indicator of reading difficulties before reading demands become more advanced (Fletcher et al., 2007; Spencer et al., 2014).

In an effort to differentiate between reading-specific deficits and general insufficiencies in overall cognitive processing the hybrid model also included a symptom based on a cognitive discrepancy definition of RD (Torgesen, 2002; Spencer et al., 2014). Cognitive discrepancy refers to a situation in which a student’s achievement in one cognitive domain outperforms his/her achievement in another cognitive domain. More specifically, the symptom was defined as poorer reading comprehension compared to listening comprehension performance. The advantage of this symptom is that it picks up on students that may not be performing poorly in general, but are failing to achieve at the same level in reading as they are in other domains.

Finally, the dual-discrepancy RTI RD symptom requires two elements for qualification: low word reading growth over the school year in conjunction with low end-of-the-year word reading performance (Schatschneider et al., 2016). This symptom is based on the fact that when a student receives direct reading instruction in a classroom and fails to grow or reach a certain level of reading achievement it is an indication that the child has failed to respond to intervention or instruction (Fuchs et al., 2002; Spencer et al., 2014; Schatschneider et al., 2016).

Past research reveals mixed findings on the differential role of specific EF components associated with RD (e.g., Swanson, 2003; Swanson et al., 2006; Booth et al., 2010; Sáez et al., 2012). There is a general consensus that inhibition is a fundamental element of executive processing, which both allows for the development, and also constrains the performance, of all other executive functioning components (Miyake et al., 2000; Foy and Mann, 2013). On its own, inhibitory ability may be especially important for early reading skills, like processing or making judgments about phonemes (Foy and Mann, 2013). In the case of working memory, poor inhibitory skills are likely to lead to intrusion errors (DeBeni et al., 1998; Foy and Mann, 2013) and the expression of inappropriate responses or guesses (Stevens et al., 2009; Foy and Mann, 2013), and for shifting, poor inhibition will likely result in representational inflexibility, such as an over-reliance on sight word reading (Diamond, 2002). All of these scenarios may create circumstances in which reading difficulties and errors are more likely (Reiter et al., 2005; Altemeier et al., 2008). For example, performance on the Stroop task, a test of inhibitory ability, is diminished in children with reading difficulties (Everatt et al., 1997; Booth et al., 2010). However, as a task that requires reading, the Stroop task may be revealing reading difficulties unrelated to EF. Even though some work has failed to find a significant difference between typically-developing and RD readers on tests of inhibitory control (Bexkens et al., 2015), Reiter et al. (2005) found that children with RD were impaired on inhibitory tasks in their processing time and error correction abilities and were more likely to commit more errors overall. These results provide support for similar findings of specific inhibitory decrements in children with reading difficulties (DeBeni et al., 1998; Altemeier et al., 2008), even when controlling for age, short-term memory, and vocabulary (Foy and Mann, 2013). Further research into the specific relation between inhibition and RD would contribute to resolving these inconsistent findings.

Working memory is the most extensively explored of the EFs (e.g., Swanson, 2003; Pickering and Gathercole, 2004; Reiter et al., 2005; Gathercole et al., 2006; Cutting et al., 2009; Kieffer et al., 2013), but its relation with RD is still not fully understood. While the original conceptualization of EF by Baddeley and Hitch (1974) was divided into a three-part system comprised of the phonological loop, the visuospatial sketchpad, and the central executive, the results yielded by modern factor analytic work (e.g., Miyake et al., 2000) have transformed the contemporary operationalization of EF by creating a working memory component (along with inhibition and shifting components; Miyake et al., 2000). Most commonly, the phonological loop and visuospatial sketchpad are either collapsed into a singular working memory construct (e.g., Cutting et al., 2009), or re-conceptualized as verbal working memory and non-verbal working memory, respectively (e.g., Gathercole et al., 2006). Importantly, studies have found a vital link between working memory and literacy skills, whether working memory was operationalized singularly (Cutting et al., 2009) or divided into its verbal and non-verbal parts (Gathercole et al., 2006). There is evidence that verbal working memory may be especially important for reading-related skills (St Clair-Thompson and Gathercole, 2006; Foy and Mann, 2013), along with evidence that working memory, as a singular measure, also supports reading comprehension and reading fluency growth in school-aged children (Swanson and Jerman, 2007). Given the evidence for a significant relation between reading outcomes and working memory, regardless of which conceptualization was employed, we chose to utilize a single-component definition for working memory in the present study.

Looking specifically at reading difficulties, the relations found with working memory and RD are also mixed. In a study of 6- to 49-year-olds that examined the relation of working memory and reading difficulties, working memory deficits were present in individuals with reading difficulties across all ages (Chiappe et al., 2000). Even when accounting for potentially confounding variables by including a battery of tasks for related cognitive skills, RD readers have still demonstrated working memory impairments (Reiter et al., 2005). In some cases, the association of working memory and (word-level) reading difficulties has lacked a significant relation because EF deficits can be fully accounted for by shortcomings in decoding (Sesma et al., 2009) or phonological processing (Locascio et al., 2011), while other studies have shown that poor reading performance cannot be fully attributed to insufficiencies in the phonological system (Swanson, 2003; Swanson et al., 2006). In fact, reading success is most likely the product of both phonological processing skills and the supportive role played by updating working memory (Iglesias-Sarmiento et al., 2015). Beyond phonological processing, studies that account for additional cognitive abilities, like intelligence, still find suppressed working memory task performance in children with reading difficulties (e.g., Gathercole et al., 2006; Swanson et al., 2006). These findings may be explained by the fact that working memory capacity constrains an individual’s ultimate level of proficiency in any academic realm, including reading, by serving as a limiting factor on the amount of knowledge and skill an individual can ultimately acquire (Gathercole et al., 2006). It stands to reason that individuals who demonstrate difficulties in reading may simply have a low working memory capacity that limits their capability for reading skill acquisition. By including Updating Working Memory in our model of EF we hope to further elucidate its role in reading disabilities.

Shifting, the third component of the EF model proposed by Miyake et al. (2000), is the most under-explored of the EFs, and findings about its role in reading performance are still conflicting (Stoet et al., 2007). There is some evidence that shifting may be a weaker predictor of reading skills deficits (Bierman et al., 2008) and early literacy skills (e.g., Foy and Mann, 2013) than inhibition and working memory. In fact, some investigators posit that shifting is simply an expansion of inhibitory control and its interaction with attention, and not a separable skill (Diamond, 2002; Diamond et al., 2005). Although others have found a specific role for shifting in processing linguistic information (Wolf et al., 1986), recent neurological work utilizing EEG technology has found that children with RD do not show impaired performance on shifting tasks when compared with typically developing controls (Horowitz-Kraus, 2014). On the contrary, Poljac et al. (2010) found a shifting-specific delay in RD children but not in autistic children. When considering these conflicting results, there is an obvious need for further exploration of the role played by shifting for children with reading difficulties.

Taken together, these findings suggest that there is a relation between executive functioning and RD. Overall, EF and its component skills contribute to reading by helping students organize, recall, and integrate new and existing information, but the details of the specific relation between EF and RD are still mixed. Furthermore, work examining the association of EF with RD has not previously used a hybrid model approach for defining RD, which is a more comprehensive and modern definition of RD than single-criterion models. In this paper, we will examine the relation of the three-component model of EF, which includes Inhibition, Updating Working Memory, and Shifting (Miyake et al., 2000; Booth et al., 2010; Nouwens et al., 2016), with the hybrid model of RD (Spencer et al., 2014; Schatschneider et al., 2016). Moreover, we will explore the predictive strength of each EF component skill in order to determine whether one EF is more important for RD identification or not. Our first research question was “How does EF predict RD classification in a hybrid model of RD?” Our second research question was “Is one EF component more important than the others for RD classification?”

The participants in this study were 420 children (51.20% female) who participated in Project KIDS. Project KIDS had two components. The first component involved combining data, using integrative data analysis (IDA), from eight completed literacy and math randomized-control trial intervention projects that occurred in north Florida schools at some point during the 2005–2006 to the 2012–2013 school years (Connor et al., 2007, 2011a,b, 2013; Al Otaiba et al., 2011a,b, 2014a,b). This data integration resulted in a dataset of literacy, math, and related achievement tests of 3868 children, which then served as the population to draw from for the second component of Project KIDS. This second component involved an extensive parental questionnaire, including a parental report of EF. During the spring and summer of 2014, questionnaires were mailed to the last known addresses of the original intervention participants’ families. The final sample size for the second component of Project KIDS was n = 445, however only n = 420 had EF data available, so those 420 participants were moved forward into all analyses.

Given the low response rate for the questionnaire portion of Project KIDS, comparisons of the differences between the original population (n = 3868) and the sample of this current report (n = 420) were done for the achievement measures used in this report, as well as on demographic information. There were significant differences between the groups for word reading [t(3315) = 3.46, p < 0.01; original population M = 35.52, SD = 11.88, n = 2946; report sample M = 37.77, SD = 11.21, n = 371], reading comprehension [t(3320) = 3.45, p < 0.01; original population M = 17.94, SD = 7.47, n = 2942; report sample M = 19.34, SD = 7.17, n = 380], and vocabulary [t(3348) = 4.11, p < 0.0001; original population M = 20.10, SD = 3.49, n = 2977; report sample M = 20.89, SD = 3.53, n = 373]. There were no significant differences noted between the original population and the current report sample for age [t(3864) = -1.36, p = 0.18], sex [χ²(1) = 1.42, p = 0.23], and race-ethnicity [χ²(1) = 0.89, p = 0.35], although there was a significant difference for free and reduced lunch status, with the questionnaire sample showing fewer students qualified for free or reduced lunch [χ²(1) = 4.67, p = 0.03].

The original intervention projects occurred when the children were in kindergarten, first, second, or third grade (age M = 6.63 years, SD = 1.04 years, range = 4.79–10.40 years), although at the time of questionnaire completion, the participants had a mean age of 13.21 years (SD = 1.54 years; range = 10.47–16.63 years). The demographic distribution of the current sample included 56.56% White, 35.08% Black/African American, 5.73% Other or Mixed children. Parental informed consent in writing was obtained for all participants in Project KIDS. The Florida State University Institutional Review Board approved all aspects of Project KIDS.

One caregiver of the original intervention project children (88% biological mother responded) was asked to complete a questionnaire either by mail or online, using Qualtrics. This questionnaire asked about the parents’ basic demographic information, such as age, education level, occupation, household income, ethnicity, and race and about the siblings of the child involved in the study, including their age, gender, and relationship to the participant. The questionnaire also included a section on family medical history that asked about learning difficulties and learning disability diagnoses, and a series of questionnaires concerning the home environment, child’s behaviors (including the BRIEF), nutrition, and sleep habits. All children completed a large battery of cognitive ability and achievement measures during the original intervention projects’ protocols, usually administered three times during the original intervention year, early fall, winter (early spring semester), and late spring semester.

Prior to analyses specific to this paper, IDA (Curran et al., 2008, 2014) was used to combine all eight intervention projects’ early fall (pre-intervention) and late spring (post-intervention) LWID data. At the heart of IDA lies measurement invariance modeling. Measurement invariance modeling in IDA is a disciplined approach to combining datasets from multiple projects. IDA involves using a moderated non-linear factor analysis (MNLFA), which allows for raw item-level data to be combined across projects, modeling potential sources of heterogeneity (e.g., sampling, age/grade) using differential item functioning (DIF). In this case, the MNLFA was the equivalent of a 2-PL model with project, and age (both linear and quadratic terms) DIF modeled. As recommended by Curran et al. (2014), we randomly selected one time point per student for a calibration sample, and also pruned any item that did not have at least 5% coverage of responses (resulting in LWID items 11–75 being included). Using the calibration sample, we first tested for DIF on the factor mean and variance. Second, we tested for DIF on each item intercept and loadings, accounting for factor DIF. Any non-significant DIF for a parameter was constrained to equality. After the final model was settled, the full data was run using code where the final beta weights were fixed, and the factor score was saved out as the new LWID score for both time points for each child. All analyses were conducted in Mplus 7.3 (Muthén and Muthén, 1998–2012). After conducting IDA on LWID, we found that the new IDA LWID factor scores and the previous simply combined LWID raw total scores were correlated at r = 0.97 (early fall) and r = 0.99 (late spring). We believe these high correlations are the result of the WJ tests being developed using Item Response Theory models for their scoring and having standardized administration. The original project staff for all projects were very experienced, and the children were relatively close in age and geographic region, meaning that chances for DIF were minimized. Given the computational time for doing the IDA was very large (weeks of run time on a dedicated server) and the correlations between raw score and ability score were so high, we decided to use the raw total scores for all the WJ measures.

Since the hybrid model was based on the WJ LWID, PV, and PC assessments administered in the original project, and some assessment data were missing, we first conducted multiple imputation (Rubin, 1987) to avoid case-wise deletion and enable all analyses to be conducted on a full data set with no missing values. Multiple imputation requires that all variables be normally distributed, and inspection of descriptive statistics confirmed that this assumption was met (see Table 1; skewness and kurtosis between ±2; Tannenbaum et al., 2009). Prior to performing the imputation, students missing all data for the assessments needed for symptom calculation were dropped from the sample (n = 168, 4% of overall sample), since they had no achievement data on which to estimate replacement values, resulting in a drop in the sample size from 4036 to 3868. As a next step, we assessed the missingness of each of our variables of interest and found that no variable was missing more than 14.19% of data (see Table 1). Additionally, a Shifting score was missing for one of the Project KIDS questionnaire participants, so Shifting was also included in the imputation model in order to replace the missing value. Finally, Proc MI (multiple imputation) in SAS 9.4 was used to impute 20 datasets based on the covariance matrix of all available data. The resulting 20 data sets were combined, and a mean score of all 20 data points was calculated for each missing value to replace previously missing data points. Pre-imputation descriptive statistics are presented in Table 1, and post-imputation descriptives are presented in Table 2. The tables show that the means and standard deviations before and after imputation are comparable, and that the data moving forward after multiple imputation are complete, with no missing values for the EF subscales or the WJ assessments used to calculate the hybrid model symptoms.

The hybrid model of RD was operationalized following Spencer et al. (2014) and Schatschneider et al. (2016), where students were categorized as having any one, two, three, or four symptoms of RD (modeling the “ANYn” categorization in Spencer et al., 2014). The four symptoms of RD included low word reading achievement, unexpected low word reading achievement, poorer reading comprehension compared to listening comprehension, and a dual-discrepancy RTI model that required both low growth and low achievement in word reading. All symptoms were calculated using the full sample of achievement data (n = 3868) in SAS 9.4. Low achievement was operationalized as any score below the 25th percentile on spring word reading scores. Unexpected low achievement, an IQ-achievement discrepancy definition for RD, was operationalized as unexpectedly low word reading achievement based on verbal aptitude. It was calculated by residualizing spring word reading scores on spring vocabulary scores (a proxy for verbal aptitude) and implementing a 25th percentile cut. Poorer reading comprehension compared to listening comprehension captured the cognitive discrepancy definition of RD, and was calculated by residualizing spring PC scores on spring PV scores (a proxy for listening comprehension; Senechal et al., 2006; Spencer et al., 2014). The dual-discrepancy RTI symptom, as its name suggests, required two parts and was calculated with a 25th percentile cut on the slopes (i.e., growth) and intercepts (i.e., end-of-the-year score) of each child’s residualized gains in word reading. After the calculation of these four symptoms, children were assigned a value of 0 (i.e., not showing any symptom), 1 (showing any one symptom), 2 (showing any two symptoms), 3 (showing any three symptoms), or 4 (showing all four symptoms).

Descriptive statistics for all EF components and WJ assessments used in subsequent analyses are displayed in Table 2. These values reflect unstandardized values and the BRIEF scores before reverse-scoring, so that high scores on any BRIEF subscale represented weaker executive functioning. Table 3 shows the Pearson and Spearman correlation coefficients for the three components of EF, the WJ assessments, and the hybrid model symptoms and RD groups. Prior to calculating the correlations, all scores were standardized, and, for ease of interpretation, BRIEF scores were reversed so that high scores reflected high executive functioning. The correlations of the EF components indicated that they are separable indices (r = 0.59–0.65, p < 0.0001). Inhibition and Shifting were significantly correlated with all four hybrid model symptoms separately, but Updating Working Memory was only significantly associated with two of the four hybrid model symptoms, namely low word reading achievement and dual-discrepancy RTI in word reading. All three EF components were significantly negatively correlated with the hybrid model of RD variable, indicating that higher EF was associated with having fewer symptoms of RD. Table 4 displays the frequency of students identified in the one-, two-, three, and four-symptom RD groups of the hybrid model as well as the frequency of students exhibiting each specific symptom.