Associations Between Speech Perception, Vocabulary, and Phonological Awareness Skill in School-Aged Children With Speech Sound Disorders

Abstract

Purpose

Prior studies report conflicting descriptions of the relationships between phonological awareness (PA), vocabulary, and speech perception in preschoolers with speech disorders. This study sought to determine the nature of these relationships in a sample of school-aged children with residual speech sound errors affecting /ɹ/.

Method

Participants included 110 children aged 7;0–17;4 (years;months) with residual errors impacting /ɹ/. Data on perceptual acuity and perceptual bias in an /ɹ/ identification task, receptive vocabulary, and PA were obtained. A theoretically and empirically motivated path model was constructed with vocabulary mediating the relationship between two measures of speech perception and PA. Model parameters were determined through maximum likelihood estimation with standard errors that were robust to nonnormality. Monte Carlo simulation was used to examine achieved power at the current sample size.

Results

The saturated path model explained 19% of the variance in PA. The direct path between age-adjusted perceptual acuity and PA was significant, as was the direct path between vocabulary and PA. Contrary to our hypothesis, there was no evidence in the current sample that vocabulary skill mediated the relationship between speech perception and PA. Each individual path was adequately powered at the current sample size.

Conclusions

The overall model provided evidence for a continued relationship between speech perception, measured by perceptual acuity of the sound in error, and PA in school-aged children with residual speech errors. Thus, measures of speech perception remain relevant to the assessment of school-aged children and adolescents in this population.

Supplemental Material

https://doi.org/10.23641/asha.13641275

Phonological awareness (PA) is a critical linguistic skill that has strong implications for literacy development (Bus & van Ijzendoorn, 1999; National Reading Panel, 2000). The connections between PA and literacy are well established for typically developing children and for children with speech sound disorders (SSD; e.g., Lewis et al., 2006). Importantly, children with SSD may be at risk for deficits in PA (e.g., Preston & Edwards, 2007), as well as deficits in vocabulary development (e.g., Lewis, Avrich, Freebairn, Hansen, et al., 2011) and speech perception for the sounds they misarticulate (Hearnshaw et al., 2019; Hitchcock et al., 2020). Better understanding of how these—possibly related (e.g., Rvachew & Grawburg, 2006)—deficits impact PA could ultimately lead to enhanced outcomes for those with SSD, including those for whom residual speech errors (RSE) may continue into later elementary years, adolescence, or adulthood (Flipsen, 2015). The current study focuses on complex relationships that may relate to PA development, including relationships with speech perception and vocabulary development, among children with RSE.

Speech perception, breadth of receptive vocabulary, and PA appear to be interconnected at many points throughout development. Infants as young as 8 months of age are hypothesized to use phonetic perception and statistical learning to parse a continuous speech stream by detecting low-probability phoneme sequences to infer the presence of word boundaries (Saffran et al., 1996). The parsed speech stream is believed to be refined by the developing child into lexical entries through processes that match phonological sequences to intended referents, generalizing over every instance in which the phonological sequence has been encountered (Smith & Yu, 2008). These lexical entries are thought to contain stored phonological representations indicating the combination of phonemes that an individual has associated with a given word. Phonological representations are hypothesized to be originally parsed as holistic, word-level units. As a learner's total number of lexical entries increases, along with the density of phonologically similar words within neighborhoods of the lexicon, the lexicon is thought to be restructured from holistic phonological representations of words to representations indexed by finer-grained phonological properties, such as syllable, onset-rimes, and individual phonemes (Ferguson & Farwell, 1975; Metsala & Walley, 1998). This theoretical foundation, expanded upon in the sections that follow, suggests a mediated relationship in which speech perception exerts both a direct effect (e.g., McBride-Chang, 1995) and an indirect effect, through vocabulary development, on PA. Previous examinations of preschool-aged children with SSD, however, have provided conflicting evidence for the direct effect of speech perception on PA and the mediation of that relationship by vocabulary. The current exploration examines the extent to which both a direct relationship between speech perception and PA, as well as the mediation of that relationship by receptive vocabulary size, can be supported within a sample of school-aged children with RSE primarily impacting /ɹ/.

Phonological Awareness

PA is the ability to engage with the sounds of a language through recognition and manipulation independent from semantic meaning (Anthony et al., 2011). It is highly correlated with other phonological processing skills, phonological memory, and phonological access to the lexicon (Anthony & Francis, 2005). PA is a strong contributor to literacy ability in early childhood (e.g., Bradley & Bryant, 1983) as well as in adolescence (e.g., Shaywitz et al., 1999), with evidence suggesting that the relationship between PA and literacy is cross-linguistic and causal (Anthony & Francis, 2005). For example, typically developing children with good phoneme awareness, a specific subcomponent of phonological awareness, tend to have stronger word-reading skills (Sénéchal et al., 2004). Multiple meta-analyses have found that, overall, PA skills are essential for children's reading development (Bus & van Ijzendoorn, 1999; National Reading Panel, 2000).

On average, children with SSD perform worse than children with typical speech on tasks that require storage and retrieval of phonological representations (Edwards et al., 1999; Sutherland & Gillon, 2007). Many children with SSD, including school-aged children with RSE (Preston & Edwards, 2007), have difficulty with PA relative to typically developing peers (Lewis, Avrich, Freebairn, Hansen, et al., 2011; Lewis et al., 2002; Rvachew, 2007). Furthermore, among children with SSD and RSE, there remains marked individual variation in PA ability (Lewis, Avrich, Freebairn, Hansen, et al., 2011; Preston & Edwards, 2010; Roepke & Brosseau-Lapré, 2019). This may reflect individual differences in the specificity of phonological representations (Hoffman et al., 1985; Shuster, 1998), as we discuss in more detail below.

Speech Perception

Speech perception refers to the establishment of sound-based representations from speech input, the processing of which enables identification and discrimination of words, syllables, and sounds (Rvachew & Brosseau-Lapré, 2018). The mapping of a dynamic, transient acoustic signal to acoustic–phonetic and phonological representations begins to form during infancy and the body of speech perception research, as a whole, indicates that speech perception skills do not reach adultlike status until at least 12 years of age (Hazan & Barrett, 2000; Rvachew & Brosseau-Lapré, 2018). As speech perception skills develop, the quality of an individual's phonological representations increases through the refinement of the acoustic targets that correspond with each phoneme (Nittrouer, 2002) and the clarity of boundaries between phoneme categories (Hazan & Barrett, 2000). This development can be demonstrated empirically through classification tasks in which participants are asked to identify acoustically ambiguous stimuli (e.g., speech synthesized along a continuum to have intermediate acoustic characteristics between phonemes such as /ɹ/ and /w/) as belonging to a discrete phoneme category. Improvements in the ability to consistently assign repeated presentations of a single ambiguous token to the same phoneme category have been seen through the second decade of life (e.g., Hazan & Barret, 2000), whereas children who have not yet refined the clarity of the boundary between phoneme categories inconsistently categorize repeat presentations of the same ambiguous token to either of the phonemes used to create the continuum.

Additionally, there is evidence that typically developing children with broader perceptual representations of phonemes also have more protracted speech sound development for that phoneme. In an evaluation of the perception and production of the English /ɹ/–/w/ contrast in 40 typically developing children ages 9–14 years, McAllister Byun and Tiede (2017) found an association between production ability and perceptual acuity within one of the two synthetic continua examined, with perceptual characteristics of the stimuli or attentional factors possibly confounding results for the second continuum. Overall, these results provide preliminary evidence that children who demonstrate more narrowly specified acoustic targets for a phoneme show greater accuracy in perception and greater distinctness in production of that phoneme; a phenomenon has also been attested in adults (Ghosh et al., 2010).

Speech Perception in Children With SSD

Although some children with SSD present with speech perception difficulties, this is not true of all children with SSD (Hearnshaw et al., 2019). Children with SSD tend to exhibit perceptual deficits on the same sounds they produce in error (Brosseau-Lapré et al., 2020; Rvachew & Jamieson, 1989). RSEs that persist into late childhood and adolescence often include difficulty with the phoneme /ɹ/. Children with RSE have been shown, as a group, to have less accurate perception of /ɹ/–/w/ than typically developing children (Cialdella et al., 2020). Hoffman et al. (1985) found that, overall, early elementary school children with /ɹ/ misarticulations demonstrated slower, more overlapping categorization of synthetic /ɹ/ and /w/ than typically developing children. Despite some children with misarticulations performing as well as typically developing children, most performed around the level of chance. Ohde and Sharf (1988) further examined the relationship between perception and production by investigating whether elementary-aged children who misarticulate /ɹ/ differ from typically developing children and adults in how they perceive synthetic speech sounds. They found that children who misarticulated /ɹ/ were significantly less consistent when identifying synthetic /ɹ/–/w/ stimuli than children with typical speech and adults, demonstrating a relationship between speech perception and production. Cabbage et al. (2016) extended this line of inquiry to slightly older children with SSD, finding that children with /ɹ/ misarticulations had specific perceptual deficits related to artificially degraded speech stimuli containing the misarticulated sound, with no perceptual deficit seen in response to stimuli containing nonmisarticulated phonemes. However, most studies still report a subset of children with SSD who exhibit intact perception, even when investigating the specific speech sound(s) produced in error (Cialdella et al., 2020; Rvachew & Jamieson, 1989).

Relating Speech Perception and PA in School-Aged Children With SSD

Speech perception skills represent one possible mechanism for the individual variation in observed PA skills among children with RSE. Although there are several studies examining speech perception and PA in preschool-aged children, which we discuss below, there are few studies examining the speech perception abilities of school-aged individuals with RSE relative to PA. Many school-aged investigations of speech perception and PA have examined this relationship within reading-disabled populations (e.g., Boets et al., 2011, 2008; Watson & Miller, 1993). Such studies have found moderate associations between speech perception and PA; specifically, Boets et al. (2011) argued that recurrent influences among elements of speech perception and PA support reciprocal mechanisms that continue to co-develop during the elementary school years. Moderate correlations have also been found between speech perception and PA in typically developing prereaders—for whom there is no confound of literacy experience—and are partially predictive of growth in PA over time (McBride-Chang et al., 1997).

Vocabulary

The theoretical basis for a relationship between speech perception and PA is also related to the size of an individual's vocabulary. Although vocabulary skill is regarded to be a characteristic feature of language competency, receptive vocabulary scores have also been found to differ between groups with moderate SSD and typically developing children or children whose speech errors have resolved (Lewis, Avrich, Freebairn, Taylor, et al., 2011). Furthermore, speech perception skill measured in early infancy has been found to correlate with measures of language development, including vocabulary acquisition, at 13, 16, and 24 months (Tsao et al., 2004).

Several studies have established the importance of vocabulary skill when accounting for variance in PA (Bishop & Adams, 1990; Elbro et al., 1998; Metsala, 1999; Preston & Edwards, 2010; Rvachew, 2007; Rvachew & Grawburg, 2006). Specifically, Metsala (1999) found that children with increased vocabulary development outperformed children with lower vocabulary development across a variety of PA tasks. The strength of the lexical effect was more pronounced for children with relatively low PA skill. These results support a model in which PA arises, in part, from vocabulary development: specifically, a lexical restructuring model (Metsala & Walley, 1998) in which vocabulary growth promotes the change in lexical representations from holistic recognition to segmentally based recognition, which influence aspects of PA (Metsala, 1999). Edwards et al. (2004) provided additional evidence for segmentalized lexical representations in preschool children through the examination of differences in repetition duration between phototactically probable and phototactically improbable sequences within nonwords, an index of PA. The authors found a more adultlike response pattern (smaller differences in repetition duration) was more strongly correlated with a child's vocabulary size than with age.

Previous Modeling of Speech Perception, Vocabulary, and PA

As described above, the development of PA may be simultaneously influenced by a child's vocabulary and speech perception skills. Specifically, speech perception skills are thought to be necessary to build the underlying phonological representations which form the lexicon, which serve as the foundation for PA. The concurrent relationships between these factors have been examined in preschool-aged children with SSD. However, strong conclusions are difficult to draw from this literature, as participants are not necessarily homogenous in presentation of SSD, nor are studies homogenous in their method of representing the latent constructs of speech perception, vocabulary, and PA (see Hearnshaw et al., 2019, for a review of these points related specifically to speech perception).

Nathan et al. (2004) examined factors associated with early literacy development at three time points in 47 preschool-aged children with speech difficulties, through path modeling in which principal components related to speech perception and literacy were mediated by components related to vocabulary and PA. The authors found support for the role of the component including vocabulary skill in the development of phoneme-level tasks of PA, but found no evidence for predictive relationships between the component including speech perception and the components including vocabulary and PA. Overall, the authors found speech perception to be a poor predictor of the language and literacy outcomes that were modeled within the analysis.

Munson et al. (2005) used a regression analysis to assess the relationship between vocabulary size and PA in a sample of 80 children with phonological disorders and controls aged 3–6 years of age. The authors found no significant association between speech perception (in a consonant–vowel–consonant identification task) or speech production and their PA measure. The authors attributed improvements in PA to lexical restructuring facilitated by increased vocabulary size.

Rvachew and Grawburg (2006) examined how PA, vocabulary knowledge, speech perception, speech production, and literacy were related in a sample of 95 preschool children receiving intervention for SSD. The authors used structural equation modeling to show that good speech perception performance (Speech Assessment and Interactive Learning System category goodness task; AVAAZ Innovations, 1997) was the best predictor of a latent PA factor for preschool children whose vocabulary scores were within average range. Speech production was influenced by speech perception but was not related to PA. Additionally, the authors concluded that children with SSD were at risk of delayed PA skills if they had low speech perception abilities and/or low receptive vocabulary skills relative to the SSD group as a whole. The findings of Rvachew and Grawburg (2006) provide support for an incomplete mediation model in which speech perception has a direct effect on PA as well as an indirect effect on PA through receptive vocabulary.

Current Study

We have presented a theoretical mechanism for a mediated relationship between speech perception, vocabulary, and PA, but the available evidence testing these relationships in preschool-aged children with SSD, presented above, cannot be extrapolated to school-aged children. For example, it is possible that perceptual and linguistic abilities are more strongly connected during the preschool years than they are during school-age years, when the phonological system is more stable. It is also possible that the mediation model implied by the theoretical mechanism changes with maturation, as speech perception skills might no longer impact PA directly, raising the possibility of a complete mediation model in which speech perception influences PA only through vocabulary size. Furthermore, these previous studies of preschool-aged children, broadly, provide conflicting evidence related to the presence of a vocabulary-mediated relationship between speech perception and PA. Such conflicting evidence was seen in the two studies of children with SSD (Nathan et al., 2004; Rvachew & Grawburg, 2006) that used an analysis suited to test whether the data supported a vocabulary-mediated relationship between speech perception and PA.

Insight into whether speech perception influences PA directly or is mediated through an increase in vocabulary size is an important consideration during the design of theoretically motivated interventions for this population, as PA difficulties may be related to RSE in school-aged children (Preston & Edwards, 2007). As such, the present exploration utilized path modeling in a sample of school-aged children with residual /ɹ/ difficulty to determine the associations between speech perception of the sound in error, vocabulary, and PA. Our theoretically and empirically driven hypothesis was that the mediation model would still apply to school-aged children, with speech perception exerting both a direct effect as well as an indirect effect, through vocabulary, on PA.

Method

Participants

Records were retrieved for 142 participants recruited to several speech sound assessment and intervention studies at Syracuse University, New York University, Haskins Laboratories, and Montclair State University. The study procedures for original data collection were approved by the respective institutional review boards. One hundred ten of these participants were children and adolescents with SSD under the age of 20 years, for whom speech perception assessment had been successfully completed; the following analysis is concerned with this subset of 110 participants. All measures were obtained at the pretreatment time point. Recruitment for the original studies was carried out through referrals from local SLPs or responses to fliers placed in communities. For inclusion, participants had to pass a hearing screening and a structural oral mechanism screening, and were required to have a primary SSD not associated with any known developmental disabilities such as Down syndrome and/or autism spectrum disorder. Additionally, all participants were required to score below the seventh percentile on the Goldman-Fristoe Test of Articulation–Second Edition (Goldman & Fristoe, 2000) and demonstrate less than 30% perceptually rated accuracy of /ɹ/ during word-level assessment probes. Some children also currently demonstrated sibilant or interdental errors, and, broadly, represented a wide range of speech sound histories with regards to impacted sounds and previous treatment. The 110 children included in the present investigation had a mean age of 10 years, 11 months (SD = 2 years, 3 months), with all children falling between the ages of 7;0 and 17;4 (years;months). Of the participants, 72 were boys and male adolescents and 38 were girls and female adolescents, reflecting the increased prevalence of speech sound disorder observed in males (Wren et al., 2016). The average standard score on the Goldman-Fristoe Test of Articulation–Second Edition for this cohort was 69.9 (SD = 13.2).

Task and Measures

Speech Perceptual Acuity

When using synthetic speech continua to measure the ability to perceive and categorize speech stimuli, there are two traditional outcomes of interest (e.g., Hazan & Barrett, 2000). The first is auditory perceptual acuity: the size of the overlapping region in which tokens are not consistently placed in one phoneme category or the other (or, inversely, the steepness of the boundary function that separates one phonological category from another). The second is auditory perceptual bias: the relative broadness of each perceptual category (or the offset of the phoneme category boundary from a midpoint).

Perceptual acuity and perceptual bias were measured in this study using the female synthetic speech continuum first reported in McAllister Byun and Tiede (2017). Briefly, the task stimuli, available at Open Science Framework (https://osf.io/ensrh/), were derived from a 10-step continuum that increments in equal steps from “rake” to “wake,” two American English words that differ primarily in height of the second and third formants during the word-initial approximant. The endpoints of the continuum were synthesized directly from child productions of the target words, while tokens within the continuum were resynthesized from 13 calculated linear prediction filter coefficients at 20-ms intervals in order to evenly increment the structure of formant frequencies from /ɹ/ to /w/. Pitch and release noise were held constant during morphing of the tokens, and temporal characteristics of the stimuli were adjusted for naturalness. A full discussion of the development and norming of the synthetic speech continuum utilized in this investigation can be found in McAllister Byun and Tiede (2017).

A forced-choice button press task (Ortiz, 2017) was used to record participant responses to each presented stimulus. After completing an eight-trial training block in which only the endpoints “rake” or “wake” were presented, the children completed the main experimental task in which they were asked to identify nonendpoint stimuli as either “rake” or “wake.” During these trials, nine steps (steps 2–10) within each continuum were presented in random order for a total of eight repetitions (n = 72 trials). Participants were provided with multiple breaks during stimulus presentation.

Participant responses (percent of tokens at a given continuum step identified as “rake”) were plotted and fitted to a logistic function. Perceptual acuity was defined as the distance in steps of the continuum between the 25% and 75% probability points on the response function. A smaller boundary width (higher perceptual acuity) indicates a steeper boundary function and a clearer boundary between “rake” and “wake” categories, while a larger boundary width (lower perceptual acuity) indicates a more gradual boundary function with more overlap between “rake” and “wake” categories. McAllister Byun and Tiede (2017) reported that typical child listeners demonstrated a median boundary width of .98 (median absolute deviation: .71). Perceptual bias was defined as the location of the 50% probability point on the logistic function relative to the steps of the rake–wake continuum (0 = rake endpoint, 10 = wake endpoint). A midpoint location below 5 (bias for /w/) indicates a majority of tokens were perceived as “wake,” while a midpoint location above 5 (bias for /ɹ/) indicates that a majority of tokens were perceived as “rake.” McAllister Byun and Tiede (2017) reported that typical child listeners perceived the median boundary location of this continuum to be at step 5.88 (median absolute deviation: .83). Examples of steep and gradual boundary functions are seen in Figure 1 below.

Figure 1.

Sample logistic functions fitted to participant responses of “rake” or “wake.” The function on the left is an example of a small boundary width (higher perceptual acuity) indicating a clearer boundary between “rake” and “wake” categories, while the function on the right is an example of a larger boundary width (lower perceptual acuity) indicating higher overlap between “rake” and “wake” categories. The midpoint of the logistic function on the left is closer to the origin (x = 4.9) than the function on the right (x = 5.9), reflecting differing values for perceptual bias.

Vocabulary

Breadth of receptive vocabulary was measured using the standard score of the Peabody Picture Vocabulary Test–Fourth Edition (PPVT-4; Dunn & Dunn, 2007). Within this norm-referenced test, children are presented with an array of four illustrated images and are asked to point to the one that best represents a stimulus word presented verbally by the clinician. Standard scores of 80 or greater were required as part of the inclusionary criteria for the studies from which the data were retrieved, as a way to screen for children whose responses to the intervention studies might be confounded by their receptive language skill.

Phonological Awareness

PA skills were measured by the age-adjusted PA composite score from the Comprehensive Test of Phonological Processing–Second Edition (CTOPP-2; Wagner et al., 2013). The PA composite is comprised of the scaled scores of the Blending Words, Elision, and Phoneme Isolation subtests. During the Blending Words subtest, children are asked to synthesize words from subcomponents presented via computer audio, within the frame of “what word do these sounds make?” During the Elision subtest, children are asked to state the word that results when a sound is taken away, within the frame of “say (word) without (sound).” During the Phoneme Isolation subtest, children are asked to produce single words within phonemes, within the frame of “what is the n^th sound in (word)?”

Data Analysis: Path Modeling

There are many statistical methods available to quantify the degree of association between variables and the integrity of the resulting models. Path modeling was selected over regression as the most appropriate analytical tool for this research question because standard multiple regression cannot account for potential mediation between variables within a model. Such a mediated relationship is supported within the literature base as well as in previous models exploring these relationships in preschool-aged children (Rvachew & Grawburg, 2006). Path modeling is a special case of structural equation modeling in which all variables in the model are observed variables (rather than unobserved, latent variables). Path modeling was deemed to be more appropriate than structural equation modeling for the current data set as there were a limited number of observed variables (1–3) available for each potential latent variable.

The a priori path model was informed by the current literature in which speech perception is hypothesized to influence both vocabulary development and PA in younger children. The variables included in this model are described below using italics. The structural paths of the model were designed with perceptual bias and perceptual acuity exerting both a direct effect and indirect effect, through vocabulary ability, on PA. Perceptual acuity was reverse coded so better acuity would result in a higher value. Furthermore, because perceptual acuity continues to develop throughout childhood (Hazan & Barrett, 2000), but the raw perceptual acuity measure does not account for age, this variable was age adjusted. A quadratic polynomial regression (Reid & Allum, 2019) was fit predicting raw perceptual acuity from age (measured in months) and age squared, with the residual values from this model used henceforth as the age-adjusted acuity values. Missing data was observed in the variables PA (89.9% complete) and vocabulary (97.1% complete); missing data were judged by Little's MCAR Test (Little, 1988) to be missing completely at random and were imputed using the MICE package in R (Van Buuren & Groothuis-Oudshoorn, 2010).

Univariate normality was checked using Shapiro–Wilk's test and Kolmogorov–Smirnov's test using the MVN package (Version 1.6; Korkmaz et al., 2014) in R (R Core Team, 2013). The vocabulary variable achieved normality following the natural-log transformation of the PPVT-4 standard score. Univariate normality results conflicted between Shapiro–Wilk's test and Kolmogorov–Smirnov's test for age-adjusted acuity and perceptual bias and are shown in Supplemental Material S1. The combined multivariate normality of these variables was checked using Mardia's tests, Henze–Zirkler's test, and Royston's test within the R MVN package, also shown in Supplemental Material S1. The data were found to be multivariate normal according to Henze–Zirkler's statistic (p = .42) and Mardia's statistic (skewness p = .39, kurtosis p = .95), but not Royston's statistic (p < .004). Therefore, maximum likelihood estimation with standard errors that are robust to nonnormality was selected as the parameter estimation method due to the conflicting information provided by the univariate and multivariate normality tests. Modeling was completed using Mplus (Version. 8.4; Muthén & Muthén, 2020).

Nine free model parameters were calculated based on the variance–covariance matrix for the measured variables; this matrix, along with descriptive statistics for model variables, is shown in Table 1. In path modeling and structural equation modeling, a system of equations that represents the relationships in the specified model is solved based on the variance–covariance matrix of the observed data. When there are just enough pieces of unique information in the variance–covariance matrix relative to the number of model parameters to be estimated, the model is “saturated.” Saturated models have valid and interpretable parameter estimates but lack omnibus fit statistics to assess overall model fit, as the model has zero degrees of freedom (Muthén & Muthén, 2017). Model fit, instead, is assessed locally through standardized residuals.

Table 1.

Variance–covariance matrix and descriptive statistics for variables entered in the model.

Variable	Perceptual bias	Age-adjusted perceptual acuity	Phonological awareness	Vocabulary
Perceptual bias	.76
Age-adjusted perceptual acuity	.16	8.61
Phonological awareness	−.56	11.46	159.30
Vocabulary	.01	0.037	0.51	0.02
Mean (SD) a	5.65 (.87)	2.64 (1.65)	98.01 (12.64)	115.54 (15.51)
Range a	2.60−7.70	0.0−7.71	62−128	86−154

^a Descriptive statistics are provided for raw measures rather than the age-adjusted variable (acuity) or variables transformed for normality (vocabulary) in order to maximize interpretability.

Results

Descriptive Results

The descriptive statistics, including variance–covariances, for these variables are shown in Table 1. We report descriptive statistics for raw measures rather than the age-adjusted variable (acuity) or variables transformed for normality (vocabulary) in order to maximize interpretability. From the categorical perception task, the average raw perceptual acuity was 2.64 (indicating that there were, on average, 2.64 steps of the synthetic speech continuum between participants' 25% and 75% probability points on the fitted logistic function; SD = 1.65, range: 0.0–7.71). For raw perceptual acuity, a lower value indicates a more defined boundary with less overlap between categories. The mean raw perceptual acuity of the children with SSD in the present investigation is 1.5 SDs higher than the mean of children with typical speech previously measured by McAllister Byun and Tiede (2017), including outliers in the original data set (M = 1.23, SD = 0.94), indicating that children with SSD in the present investigation performed worse than the typically developing children previously reported. The average perceptual bias of the children with SSD in the present investigation was 5.65 (indicating that, on average, the location of the boundary between /ɹ/ and /w/ categories was between Steps 5 and 6 of the continuum; SD = 0.87, range: 2.60–7.70. For perceptual bias, a lower value indicates a narrower category for /ɹ/ than for /w/, while a higher value is a broader category for /ɹ/ than for /w/. This value is roughly similar to children with typical speech previously measured by McAllister Byun and Tiede (2017; M = 5.90, SD = 0.73). The mean CTOPP-2 PA composite standard score in the present sample was 98.01 (SD = 12.64; range: 62–128); these scores represent a wide range of ability but the group mean falls within the average range of the normative sample. Participants had a mean PPVT-4 standard score of 115.54 (SD = 15.51; range: 86–154), reflecting scores that are considered, clinically, to fall in the average to above-average range.

Path Modeling Results

The model relating perceptual bias, age-adjusted acuity, vocabulary, and PA converged using the default convergence criterion. Standardized parameter estimates for direct paths are included in Figure 2, with indirect effects and total effects expanded upon in Supplemental Material S2. The total effect between age-adjusted acuity ➔ PA (.31, SE = .11, p = .003) was statistically significant, as was the direct effect from age-adjusted acuity ➔ PA (.29, SE = .10, p = .003). The positive sign of the age-adjusted acuity ➔ PA path indicates that children with less overlap between /ɹ/ and /w/ categories also had better PA. The direct path from vocabulary ➔ PA (.30, SE = .08, p < .001) was also statistically significant, indicating that children with higher vocabulary scores also had higher PA scores. These statistically significant standardized paths are shown in bold in Figure 2; this path model explained 19% of the observed variance in PA and 2% of the observed variance in vocabulary. The remaining paths were not statistically significant, including the covariance between perceptual bias and age-adjusted acuity (.06, SE = .08, p = .44); the indirect path from age-adjusted acuity ➔ PA through vocabulary (.03, SE = .03, p = .353); the total (−.10, SE = .08, p = .18), indirect (.03, SE = .03, p = .212), and direct (−.07, SE = .08, p = .382) effects from perceptual bias ➔PA; and the paths between age-adjusted acuity ➔ vocabulary (.09, SE = .09, p = .327) and perceptual bias ➔ vocabulary (.11, SE = .09, p = .192). As discussed previously, examining the model's standardized residual matrix provides insight into the fit of specific parts of the model. No standardized residual covariances were above a critical value of ± 1.96, indicating that the model adequately fit all individual pairwise covariances.

Figure 2.

The path model tested. Rectangles represent observed variables while arrows represent hypothesized relationships. Parameter estimates are shown above each path and significant relationships supported by the current sample are in bold. Values marked with * are significant at α = .05, values marked with ** are significant at α = .01, and values marked with *** are significant at α = .001.

Power analysis in path modeling and structural equation modeling differs from a power analysis conducted using t-statistics or f-statistics. In a path analysis, the replication of parameter estimates in a Monte Carlo simulation study allows for a post hoc estimate of power to be generated at the observed sample size for each parameter of the model taken individually, based on the parameter's value and mean square error. When assessing power in this manner, the statistical bias of parameters, the statistical bias of standard errors, and overlap between the observed parameter and the 95% confidence interval are examined. It is recommended that neither the statistical bias of parameters nor the statistical bias of standard errors exceed 10% for any parameter, that these biases should not exceed 5% for nonsignificant paths scrutinized during power analysis, and that the 95% confidence interval should cover the observed parameter for 91% to 98% of replications (Muthén & Muthén, 2002). The current Monte Carlo simulation study with 10,000 replications indicated that each of these conditions was met for every individual path in the present investigation; therefore, the current sample size of 110 was deemed sufficient to detect the relationships posited by the model. Achieved power and false positive error rates for individual paths are reported in Supplemental Material S2.

Discussion

There are few discussions of the relationship between speech perception, vocabulary, and PA in the specific context of RSE, as most investigations in previous literature have focused on preschool-aged children. Furthermore, previous studies have produced conflicting evidence about the relationship between speech perception, vocabulary, and PA, possibly due to different methods for measuring these latent variables.

Based on existing theories about the development of PA, we hypothesized that speech perception would directly influence PA in the present sample of school-aged children. We also hypothesized that the relationship would be mediated by vocabulary breadth. Findings from the current study do support the direct relationship between auditory perceptual acuity and PA in school-aged children with RSE: After adjusting for age, children who more consistently assigned the same ambiguous tokens between /ɹ/ and /w/ categories to the same phoneme category on the synthetic rake–wake continuum had higher CTOPP-2 PA composite scores. A positive relationship between speech perception and PA skills has empirical support in some previous studies of preschool-aged individuals with SSD (e.g., Rvachew & Grawburg, 2006; cf. Munson et al., 2005; Nathan et al., 2004) as well as in studies of school-aged individuals with reading disorders (e.g., Boets et al., 2008, 2011; Watson & Miller 1993). The total association observed in this study was moderate and significant, and, when combined with the impact of vocabulary, accounted for 19% of the variance in PA in the present sample of school-aged children and adolescents. These results suggest that, for some children with RSE, speech perception continues to be associated with PA skill following the onset of literacy and that this association is captured by the age-adjusted acuity measure derived from the synthetic rake–wake continuum presented in McAllister Byun and Tiede (2017). No such association, however, was seen for perceptual bias, suggesting that the clarity between phonological categories for a child's phoneme in error was more strongly related to PA skill than whether the breadth of those categories favored /ɹ/ or /w/.

Contrary to our hypothesis, however, the current investigation did not provide evidence that vocabulary was a significant mediator between speech perception and PA for the school-aged children in this sample. Post hoc power analysis deemed the sample large enough to detect a significant relationship between these variables. This contrasts with previous research (Rvachew & Grawburg, 2006) that did find evidence of significant mediation in preschool-aged individuals. We present three possible reasons for this discrepancy. First, it is possible that the present findings differ from past research due to a genuine effect of age on the relationships among the variables studied. For instance, it is possible that the mediating role of vocabulary differs between an emerging literacy time point versus a school-aged time point representing a longer history of literacy. On the other hand, it is possible that the current speech perception tasks were less suited than others in the literature to index the aspects of speech perception relevant to vocabulary learning. For example, Rvachew and Grawburg (2006) used a category goodness speech perception task. It may be that category goodness tasks prompt participants to make a lexical evaluation when determining if the presented word was correctly produced or not, which may relate to vocabulary skill. In contrast, the task in this study focused more on perception of the acoustic properties of individual phonemes, which may be less related to vocabulary skill. Lastly, it is also possible that the lack of support for a vocabulary-mediated relationship between speech perception and PA in this study is an artifact of sampling error. In particular, the fact that individuals in the present data set tended to have high vocabulary skill (mean PPVT-4 score of 115.54), which may be driven in part by the inclusionary criteria of the original studies, could have limited our ability to observe associations with vocabulary that might emerge in a more broadly representative sample. This view may be supported by Rvachew and Grawburg's (2006) observation that preschool children with the highest receptive vocabulary scores also had higher speech perception scores. The negligible magnitude of explained variance for vocabulary in the present investigation suggests that important factors related to vocabulary were not included in the model. Relatedly, the current study was unable to fully investigate any impact of literacy on the model, which is a limitation discussed in further detail below.

Although an association between speech perception and PA was supported for the current sample of children with RSE, only a small proportion of variance in PA was explained by the model. Taken together with the previous discussions of younger children with SSD and school-aged children with reading disability, these results raise the possibility that the relationships between speech perception, vocabulary, and PA might vary across different populations. Variation might also be seen based on developmental history of the disorder (e.g., Flipsen, 2015; Shriberg et al., 2010) and the relative contribution of phonological, motoric, and perceptual factors to those histories (Shriberg et al., 2001). For example, children with longstanding histories of SSD characterized by multiple errors, who now present with residual /ɹ/ distortions, may have different PA skills than children who had normal speech acquisition with the exception of /ɹ/ production. The former group of children would align with Flipsen's (2015) designation of residual speech errors, while the latter would align with the designation of persistent speech errors. Furthermore, participants likely varied in their intervention history, such as the frequency and duration of treatment, as well as whether speech perception and/or PA were emphasized as part of treatment. Some of these factors would likely contribute to additional variance in PA skills of children with RSE but could not be quantified by the current investigation. Thus, to fully account for variance in PA, it is important to represent longitudinal factors as well as static measures of skill. With a large enough sample size, subgroup analysis could be the focus of a future study determining the importance of subtypes of RSE in modeling PA ability.

Limitations and Future Directions

The limitations associated with this analysis extend to all techniques in the structural equation family to which path modeling belongs: the analysis indicates how well a specified model fits the data set, but not whether that model is the optimal model among nontested models. The use of retrospective data analysis in this study yielded a relatively large data set, but it also limited our model to use only those measures collected in previous research. This, in combination with the number of participants, precluded the use of other modeling techniques such as factor analysis and full structural equation modeling. As a consequence, all variables were entered into the model as observed variables rather than latent variables defined by measurement models. This more greatly restricts the analysis from the discussion of the latent construct of speech perception to the associations between the tasks themselves. For example, while the a priori model provided evidence that the age-adjusted acuity measure from the synthetic rake–wake continuum presented by McAllister Byun and Tiede (2017) was significantly associated with PA, the speech perceptual measures were limited in that they only probed perception of the phoneme produced in error. Such measures are likely useful as they may index the most within-participant variability compared to other measures targeting nonerror phonemes (Hearnshaw et al., 2019). However, to fully index the construct of speech perception, it is important to examine a range of target sounds. The use of a single task, perceptual identification, is also a limitation; tasks such as discrimination and category goodness judgment are thought to be important for thorough specification of perceptual ability. It would also be valuable to include additional vocabulary measures, such as vocabulary depth (McGregor et al., 2013). A well-powered longitudinal structural equation model with robust measurement models could provide evidence to resolve the conflicts seen in the literature around the relationship between the latent constructs of speech perception, vocabulary, and PA.

In addition to broadening the range of tasks used within the analysis, the model could be further expanded to include measures of literacy. The present data set lacked information on the literacy skills of participants, including literacy achievement and quality of literacy instruction. PA and literacy are thought to develop with a reciprocal relationship during the elementary school years (Boets et al., 2011; Burgess & Lonigan, 1998), and literacy outcomes for children with SSD are related to vocabulary ability in the elementary school years (Skebo et al., 2013). This suggests that including a reciprocal relationship between literacy and PA may result in a more comprehensive model of the relevant constructs.

Summary

While previous literature has examined the relationship between PA, speech perception, and vocabulary in younger children demonstrating a wider range of SSD phenotypes, there is a paucity of literature examining how these relationships continue to develop throughout childhood and adolescence in individuals with RSE. Examining the appropriateness of a theoretically and empirically supported path model through a large-scale, retrospective investigation provides new information specific to this population. The selected model supports the claim that perceptual acuity, a measure of speech perception, continues to predict PA skill in school-aged children, consistent with findings from preschool-aged children. This model accounted for 19% of the observed variance in PA. Vocabulary skill was also a significant predictor of PA, but a hypothesized mediating role between perception and PA was not substantiated by the model. It is unknown if this is an age-related difference, a task effect, or sampling error. Future studies that include a wider range of indicator variables, as well as the related construct of literacy, are needed to fully elucidate the relationship among these constructs in children and adolescents with RSE, with implications for assessment and intervention in that population.

Funding Statement

This study was supported in part by Syracuse University Gerber Auditory Science Grant (J. Preston, PI) and by National Institutes of Health Grants R03DC013152 (J. Preston, PI), R15DC016426 (J. Preston, PI), R01DC013668 (D. Whalen, PI), and R01DC017476 (T. McAllister, PI).