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