Limits...
A new visualization and conceptualization of categorical longitudinal development: measurement invariance and change.

Boom J - Front Psychol (2015)

Bottom Line: These (orthogonal) dimensions make it possible to adequately conceptualize measurement invariance in this complex context.As the result is difficult to conceptualize without extensive visualization, special 3-D figures will be used to illustrate and a dynamic (rotatable and scalable) version will be made available as Computable Document Format object (Mathematica).The model was successfully applied in several microgenetic studies.

View Article: PubMed Central - PubMed

Affiliation: Developmental Psychology, Utrecht University Utrecht, Netherlands.

ABSTRACT
The Overlapping Waves Model (OWM) is a metaphor introduced by Siegler (1996) to illustrate a typical sequence of increasing and decreasing use of strategies during development. Going beyond metaphor, a new model synthesized from Latent Growth Modeling (LGM) and Item Response Theory (IRT) will be presented to analyze such categorical longitudinal data. Use of strategies can be scored as a variable with only a few ordinal categories. IRT provides the means to relate the usage of strategies to position on an underlying developmental dimension. LGM allows to model movement of individuals along this dimension, acknowledging individual differences both in starting point and in speed of progress. Measuring and modeling such strategy development requires that at each time point the same categories are used, in the sense that item difficulties must remain invariant over time. Whether, discrimination can be relaxed is still an issue. The problem that had to be solved was disentangling the between-person-individual differences from real intra-individual developmental differences. Figures with polytomous or multi-category Item Characteristic Curves (ICC's) resemble the OWM in many respects. However, such figures are usually taken to represent inter-individual differences, whereas the OWM usually represents development (so intra-individual differences), and we cannot have both at the same time. The solution came from creating a framework with ability differences on one axis and the effect of time on another axis, resulting in a 3-D model. These (orthogonal) dimensions make it possible to adequately conceptualize measurement invariance in this complex context. As the result is difficult to conceptualize without extensive visualization, special 3-D figures will be used to illustrate and a dynamic (rotatable and scalable) version will be made available as Computable Document Format object (Mathematica). The model was successfully applied in several microgenetic studies.

No MeSH data available.


Related in: MedlinePlus

Item characteristic curves for a five-category polytomous item.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4375919&req=5

Figure 3: Item characteristic curves for a five-category polytomous item.

Mentions: Suppose responses of participants are scored as representing the use of one of a few strategies, suppose furthermore -following IRT modeling- that the likelihood of using one of the strategies depends on a single latent variable by a mathematical function known as the item response function. The Partial Credit Model is particularly useful to model responses that are ordered as a series of steps that must be mastered in sequence (Millsap, 2010). The latent variable normally represents inter-individual differences in ability, which in this case translates to being more or less advanced in terms of strategy use as is illustrated in Figure 3. Figures are based on a micro-genetic study (Van der Ven et al., 2012) and just used to illustrate here. The multiplication strategies examples given earlier are from this study.


A new visualization and conceptualization of categorical longitudinal development: measurement invariance and change.

Boom J - Front Psychol (2015)

Item characteristic curves for a five-category polytomous item.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4375919&req=5

Figure 3: Item characteristic curves for a five-category polytomous item.
Mentions: Suppose responses of participants are scored as representing the use of one of a few strategies, suppose furthermore -following IRT modeling- that the likelihood of using one of the strategies depends on a single latent variable by a mathematical function known as the item response function. The Partial Credit Model is particularly useful to model responses that are ordered as a series of steps that must be mastered in sequence (Millsap, 2010). The latent variable normally represents inter-individual differences in ability, which in this case translates to being more or less advanced in terms of strategy use as is illustrated in Figure 3. Figures are based on a micro-genetic study (Van der Ven et al., 2012) and just used to illustrate here. The multiplication strategies examples given earlier are from this study.

Bottom Line: These (orthogonal) dimensions make it possible to adequately conceptualize measurement invariance in this complex context.As the result is difficult to conceptualize without extensive visualization, special 3-D figures will be used to illustrate and a dynamic (rotatable and scalable) version will be made available as Computable Document Format object (Mathematica).The model was successfully applied in several microgenetic studies.

View Article: PubMed Central - PubMed

Affiliation: Developmental Psychology, Utrecht University Utrecht, Netherlands.

ABSTRACT
The Overlapping Waves Model (OWM) is a metaphor introduced by Siegler (1996) to illustrate a typical sequence of increasing and decreasing use of strategies during development. Going beyond metaphor, a new model synthesized from Latent Growth Modeling (LGM) and Item Response Theory (IRT) will be presented to analyze such categorical longitudinal data. Use of strategies can be scored as a variable with only a few ordinal categories. IRT provides the means to relate the usage of strategies to position on an underlying developmental dimension. LGM allows to model movement of individuals along this dimension, acknowledging individual differences both in starting point and in speed of progress. Measuring and modeling such strategy development requires that at each time point the same categories are used, in the sense that item difficulties must remain invariant over time. Whether, discrimination can be relaxed is still an issue. The problem that had to be solved was disentangling the between-person-individual differences from real intra-individual developmental differences. Figures with polytomous or multi-category Item Characteristic Curves (ICC's) resemble the OWM in many respects. However, such figures are usually taken to represent inter-individual differences, whereas the OWM usually represents development (so intra-individual differences), and we cannot have both at the same time. The solution came from creating a framework with ability differences on one axis and the effect of time on another axis, resulting in a 3-D model. These (orthogonal) dimensions make it possible to adequately conceptualize measurement invariance in this complex context. As the result is difficult to conceptualize without extensive visualization, special 3-D figures will be used to illustrate and a dynamic (rotatable and scalable) version will be made available as Computable Document Format object (Mathematica). The model was successfully applied in several microgenetic studies.

No MeSH data available.


Related in: MedlinePlus