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New Statistical Methods for the Study of Change Over Time: Implications for Research in Child Language Disorders |
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David Kaplan - University of Wisconsin-Madison
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| SRCLD Year: |
2009 |
| Presentation Type: |
Invited Speaker |
| Presentation Time: |
(na) |
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This tutorial lecture presents an overview of quantitative methodologies
for the study of stage-sequential development based on extensions of
Markov chain modeling. Four methods are presented that exemplify the
flexibility of this approach. The first method is the manifest Markov
model which provides estimates of transitions over time in categorical
responses that are assumed to be measured with perfect reliability. The
second method is the latent Markov model which directly accounts for
measurement error and provides transition probabilities at the latent
level. The third method is latent transition analysis, which addresses
the use of multiple indicators of a latent categorical variable and is
arguably better suited for the study of stage-sequential developmental
processes than the manifest or latent Markov model. The final method is
the mixed Markov model. This latter model addresses unobserved
heterogeneity in the Markov chains. A special case of the mixture latent
Markov model, the so-called “mover-stayer" model, is presented in this
lecture. Issues of model specification, estimation, and testing are
briefly discussed. These four methods are applied to an example of
stage sequential development in reading competency in the early school
years utilizing data from the Early Childhood Longitudinal Study –
Kindergarten Cohort. The tutorial closes with a brief discussion of
Bayesian approaches when sample sizes are small.
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