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Rational Karmiloff-Smith (1998) argued that development is the key to understanding developmental disorders such as SLI PowerPoint Presentation
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Acknowledgement This study was supported by contract NIH-DC-19-90 from the National Institute on Deafness and Other Communication Disorders and clinical research center grant P0-DC-02748, also from the National Institute on Deafness and Other Communication Disorders. Abstract

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Acknowledgement

This study was supported by contract NIH-DC-19-90 from the National Institute on Deafness and Other Communication Disorders and clinical research center grant P0-DC-02748, also from the National Institute on Deafness and Other Communication Disorders.

Abstract

519 children were followed from kindergarten to eighth grade. Language performance represented on a Rasch scale were obtained at kindergarten, second grade, fourth grade and eighth grade. Nonlinear Mixed growth analysis showed that there were individual differences in growth in the three parameters (starting level, overall change, and rate of growth toward asymptote); however, the variation in starting point dominated individual differences. Differences in growth between LI and normals was primarily due to starting point, but the children with LI also approached asymptote more quickly. Thus, children with LI started lower, reached asymptote more quickly than normals. Their overall amount of growth was the same as the normals.

Linear Model

Quadratic Model

Exponential Function

y = b x + a

y = -a x2 + b x + c

y = -e-x

Lack of Individual Difference in the Language Growth Rate from Kindergarten to Eighth Grade

Xuyang Zhang and J. Bruce Tomblin

The University of Iowa, Iowa City

Measures

The Item Response Theory (IRT) was used to calibrate the item difficulty and discriminating power and persons’ ability. Only those items with adequate difficulty level were entered into the analysis. (See Table 1 for specific items used)

An effort was also made to balance the number of items measuring each of the four language areas: receptive vocabulary (R-V), expressive vocabulary (E-V), receptive grammar (R-G), and expressive grammar (E-G). Prior analyses demonstrated that these items represent one latent trait (Tomblin & Zhang, 2001)

Scores at each observation interval (kindergarten, 2nd, 4th, 8th grades) were represented as Rasch scores.

Results

Unconditional Model :

This analysis revealed that there were significant individual differences for each parameter.

Growth Functions

Growth consists of change over time. The manner in which the variable of interest (e.g. language ability) changes with time can range from simple to complex. The growth characteristics are described by equations . The terms in the functions pertain to aspects of the growth.

Conditional Model:

The groups were significantly different in:

starting level (a)

rate to reach the asymptote (1-e-ct)

Groups were not significantly different in the increment (b)

(see Table 2 and figures).

Table 2. Growth curve difference between groups.

Asymptote

  • Statistical Analysis:
  • Item analysis generated Rasch score of language level for each child at each grade level. This score is appropriate for individual growth curve analysis.
  • Nonlinear Mixed Modeling from SAS permited the use of exponential models for growth curve analysis. Specifically the model employed is:
    • E(yt)=a+b(1-e-ct)
    • a=starting level; b=(asymptote-starting level); 1-e-ct= rate of growth toward asymptote
  • Unconditioinal Model: exponential growth curve with three random parameters was fitted to the data to determine if there were significant individual differences among these parameters.
  • Conditional Model: The diagnostic categories of LI and Normal were added to the model to determine whether the groups differed according to the 3 parameters.

Rational

Karmiloff-Smith (1998) argued that development is the key to understanding developmental disorders such as SLI.

Recent approaches to growth curve analysis provide an important tool for describing the basic nature of language growth.

  • Leonard (1998) hypothesized that language growth in children with SLI could differ from normal language learners with respect to one or more of the following parameters
  • initial levels of development (intercept)
  • rate of growth (slope)
  • presence and timing of asymptote

Linear growth has an intercept and slope but does not capture the nonlinear decline in rate. Thus, growth has no limiting property.

Quadratic growth provides for the nonlinear deceleration in growth, but assumes that growth then reverses.

Exponential growth captures the nonlinear aspects of growth without the reversal in growth found in the quadratic. Unlike the other functions, an exponential function has an asymptotic component that represents the limit to growth. Exponential growth appears to characterize the data from Rice et al. and Tomblin and Zhang studies.

Leonard noted that it was not clear whether the model with or without asymptote was the most appropriate for SLI

Issue

The data from Rice et al. and Tomblin and Zhang studies were fit with linear and quadratic growth models. Inspection of the data from these studies shows that the pattern of development appears to be an inverse negative exponential or logarithmic function. Thus, it would seem useful to study language growth using an inverse exponential function.

Table 1. Language items used for computation of language scores

Rice, Wexler, & Hershberger (1998) modeled growth in tense usage of children with SLI.

  • Growth of tense was found to be nonlinear for children with and without SLI.
  • Significant heterogeneity was found among children however, the two groups differed only in their intercept, but no differences were found in the linear or quadratic terms that reflect rate of growth.
  • Questions
  • Does an exponential growth model fit longitudinal language data?
  • In what ways does the exponential growth of language in children with Language Impairment (LI) differ from typically developing children?
  • Do children with language impairment eventually catch up? That is, will children with language impairment eventually reach the same asymptote as other children or will their language development asymptote be lower?
  • Discussion
  • After having entered kindergarten, most children follow the same developmental trajectory. Individual differences in growth during the school years is mostly accounted for by the starting level. This is the principal way children with LI differ from normals.
  • The only other way children with LI differ from normals is in the rate of growth toward asymptote. LI children approach asymptote more quickly. Thus, asymptote occurs earlier in LI children than normals. Thus, LI children do not catch up with normals.
  • Children with LI show the same amount of growth during the school years as do normal children. Thus, they actually have somewhat faster growth during the early school years than normals, but loose these gains by achieving asymptote earlier.
  • However, the group difference is not a clear cut. Due to measurement error, there is a great overlap between the two groups. Individual identity is much more important than group identity.
  • Overall, the growth characteristics of most children during the school years is largely the same, differing only in overall level. This suggests considerable constraint in growth characteristics despite substantial environmental differences.
  • Tomblin and Zhang (2001) examined the growth of language in children with and without SLI from kindergarten through fourth grade.
  • Group differences were found for intercept and linear and quadratic terms for growth.
  • Methods
  • Participants
  • 519 children assessed at four time points: Kindergarten, second grade, fourth grade, and eighth grade.
  • At kindergarten, diagnosis was based on language measures that were independent of those used for measurement of growth.
  • 181 language impairment (LI): Language composite score below -1.14.
  • 338 typically developing (TD): Language composite score above -1.14.