Rational

1
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.
Table 2. Growth curve difference between groups.
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).
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)ab(1-e-ct)
• astarting 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.