Lack of Individual Difference in the Language Growth Rate from Kindergarten to Eighth Grade Acknowledgement
This study was supported by contract NIH-DC-19-90 from the
Xuyang Zhang and J. Bruce Tomblin National Institute on Deafness and Other Communication
Disorders and clinical research center grant P0-DC-02748,
The University of Iowa, Iowa City also from the National Institute on Deafness and Other
Communication Disorders.
Measures
Results
Growth Functions
Abstract The Item Response Theory (IRT) was used to calibrate the item difficulty and discriminating Unconditional Model :
power and persons’ ability. Only those items with adequate difficulty level were entered into the 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
519 children were followed from kindergarten to eighth grade. Language performance represented on a Rasch analysis. (See Table 1 for specific items used)
ability) changes with time can range from simple to complex. The growth characteristics are described
scale were obtained at kindergarten, second grade, fourth grade and eighth grade. Nonlinear Mixed growth by equations . The terms in the functions pertain to aspects of the growth.
analysis showed that there were individual differences in growth in the three parameters (starting level, An effort was also made to balance the number of items measuring each of the four language
overall change, and rate of growth toward asymptote); however, the variation in starting point dominated areas: receptive vocabulary (R-V), expressive vocabulary (E-V), receptive grammar (R-G), and
individual differences. Differences in growth between LI and normals was primarily due to starting point, but expressive grammar (E-G). Prior analyses demonstrated that these items represent one latent
the children with LI also approached asymptote more quickly. Thus, children with LI started lower, reached Linear Model Quadratic Model Exponential Function trait (Tomblin & Zhang, 2001)
asymptote more quickly than normals. Their overall amount of growth was the same as the normals. Scores at each observation interval (kindergarten, 2nd, 4th, 8th grades) were represented as
Rasch scores. Conditional Model: Table 2. Growth curve difference between groups.
Asymptote The groups were significantly different in:
starting level (a)
Statistical Analysis: rate to reach the asymptote (1-e-ct) Parameter Normal LI p
Rational 1. Item analysis generated Rasch score of language level for each child at each grade Groups were not significantly different in the
level. This score is appropriate for individual growth curve analysis. increment (b)
Karmiloff-Smith (1998) argued that development is the key to understanding developmental disorders such as SLI. Start level 2.3 1.1 <.0001
2. Nonlinear Mixed Modeling from SAS permited the use of exponential models for (see Table 2 and figures).
Recent approaches to growth curve analysis provide an important tool for describing the basic nature of language y= bx+a
y = -a x2 + b x + c growth curve analysis. Specifically the model employed is:
growth. y= -e-x Increment 5.1 5.2 ns
E(yt)=a+b(1-e-ct)
Leonard (1998) hypothesized that language growth in children a=starting level; b=(asymptote-starting level); 1-e-ct= rate of growth
Rate 0.22 0.27 <.0001
with SLI could differ from normal language learners with respect to toward asymptote
one or more of the following parameters 3. Unconditioinal Model: exponential growth curve with three random parameters was
Linear growth has an intercept and slope but does not capture the nonlinear decline in rate. Thus, fitted to the data to determine if there were significant individual differences among
initial levels of development (intercept) growth has no limiting property. these parameters.
rate of growth (slope)
presence and timing of asymptote Quadratic growth provides for the nonlinear deceleration in growth, but assumes that growth then
reverses. 4. 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.
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 Examples of Individual Language Growth Curves
Scatter Plot and Group Average Growth Curves
et al. and Tomblin and Zhang studies. from Kindergarten to Eighth Grade
10 8
Language Level above Kindergarten Minimum
Language Level above Kindergarten Minimum
Leonard noted that it was not clear whether the model with or
without asymptote was the most appropriate for SLI 8
Issue 6
Table 1. Language items used for computation of language scores
6
The data from Rice et al. and Tomblin and Zhang studies were fit with linear and quadratic growth
Rice, Wexler, & Hershberger (1998) modeled growth in tense models. Inspection of the data from these studies shows that the pattern of development appears to 4
usage of children with SLI. be an inverse negative exponential or logarithmic function. Thus, it would seem useful to study 4
Growth of tense was found to be nonlinear for children language growth using an inverse exponential function.
Items K 2nd 4th 8th # of items area 2
with and without SLI. Picture vocabulary Item 8 to 23 X 16 R-V 2
Significant heterogeneity was found among children Oral vocabulary Item 1 to 16 X 16 E-V Normal
however, the two groups differed only in their intercept, but Questions Grammatic Understanding X 16 R-G LI Normal Group
Normal 0
Item 10 to 25 0 LI Group
no differences were found in the linear or quadratic terms LI
Sentence Imitation Item 4 to 11 X 8 E-G
that reflect rate of growth. • Does an exponential growth model fit longitudinal language data? TOLD Grammatic Completion X 8 E-G
Item 5 to 12 0 2 4 6 8 10 12
• In what ways does the exponential growth of language in children with Language Impairment (LI) item 48 to 55 (group 2 and 3) X 2 R-V 0 2 4 6 8 10
differ from typically developing children? item 56 to 95 (group 4 to 13) X X 10 R-V Age above Kindergarten Minimum Age Age above Kindergarten Minimum Age
item 96 to 111 (Group 14 to 17) X X X 4 R-V
• Do children with language impairment eventually catch up? That is, will children with language Item 112 to 119 (group 18 to 19) X X 2 R-V Discussion
impairment eventually reach the same asymptote as other children or will their language PPVT-R item 120 to 151 (group 20 to 27) X 8 R-V 1. After having entered kindergarten, most children follow the same developmental trajectory. Individual
Tomblin and Zhang (2001) examined the growth of language in 540
development asymptote be lower? item 1 X 1 E-V differences in growth during the school years is mostly accounted for by the starting level. This is the
children with and without SLI from kindergarten through item 2 to 10 X X 9 E-V
fourth grade. principal way children with LI differ from normals.
520
CREVT item 11 to 16 X X X 6 E-V
item 17 X X 1 E-V 2. The only other way children with LI differ from normals is in the rate of growth toward asymptote. LI
Group differences were found for intercept and linear and
Language W-Score
500
item 18 to 24 X 7 E-V children approach asymptote more quickly. Thus, asymptote occurs earlier in LI children than normals.
quadratic terms for growth. Methods Word structure Item 25 to 32 X 8 E-G Thus, LI children do not catch up with normals.
480 Sent Structure Item 13 to 20 X 8 R-G 3. Children with LI show the same amount of growth during the school years as do normal children. Thus,
Normal Obtained Participants Recall Sent Item 5 to 7 X 3 E-G they actually have somewhat faster growth during the early school years than normals, but loose these
Normal Group Average
460
SLI Obtained Recall Sent Item 8 X X 1 E-G gains by achieving asymptote earlier.
SLI Group Average
NLI Obtained
519 children assessed at four time points: Kindergarten, second grade, fourth grade, and eighth grade. Recall Sent Item 9 to 12 X X X 4 E-G
440 NLI Group Average At kindergarten, diagnosis was based on language measures that were independent of those used for CELF Recall Sent Item 13 to 15 X X 3 E-G 4. However, the group difference is not a clear cut. Due to measurement error, there is a great overlap
Low Cognitive Obtained
LC Group Average measurement of growth. Recall Sent Item 16 to 22 X 7 E-G between the two groups. Individual identity is much more important than group identity.
420 Concept & Direction X 2 R-G 5. Overall, the growth characteristics of most children during the school years is largely the same, differing
4 5 6 7 8 9 10 11 12 181 language impairment (LI): Language composite score below -1.14. Item 15 to 16
only in overall level. This suggests considerable constraint in growth characteristics despite substantial
Age Concept & Direction X X 6 R-G
environmental differences.
338 typically developing (TD): Language composite score above -1.14. Item 17 to 22
Concept & Direction X X X 8 R-G
Item 23 to 30
Formulated Sentences X 8 E-G
Item 5 to 12