dimensionality of the latent structure and item selection via latent class multidimensional irt...
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Dimensionality of the latent structure and item selection via
latent class multidimensional IRT models
FRANCESCO BARTOLUCCI
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Outline
• Introduction• Data set• Statistic Methodology• Strategy of Analysis• Application to the Dataset• Conclusion
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Introduction
• Dimensionality issue of health conditions: Subjects show a degenerative health status to a specific pathology, but have overall good health status.
• Assume the population is divided into a certain number of latent classes.
• Address the issue of item selection.
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The ULISSE Dataset
• A network on health care services for older people
• Longitudinal survey• Filled out by the nursing assistant• Since 2004 through the repeated
administration every 6months• 79 items– 1: presence of a specific health problem– 0: its absence
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Model
• Latent class
• Multidimensional 2PL
– Constraint:
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Latent class model
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Model
• log-likelihood
• number of free parameter– LC:
– 2PL:
– Difference between them:
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Estimate
• Expectation-Maximization (EM)• E-step: conditional expected value
• M-step: maximizing the log-likelihood where is replaced.
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Strategy of Analysis
• Selection of the number of latent class• Validation of the multidimensional 2PL model• Assessment of the number of dimensions• Reduction of the number of items
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Step 1. Selection of the number of latent classes
• BIC: – LC or 2PL
• #par: penalization term– Number of classes increasing, #par rising
•
• AIC tends to overestimate the number of classes
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Step 2. Validation of the Multidimensional 2PL model
• Compare the LC and 2PL model by BIC.• For validate the structure of the
questionnaire.• LC, which is completely unconstrained, allows
each item to measure a separate dimension.• If 2PL proves preferable in BIC, the evidence
of item structure is found.
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Step 3. Assessment of the Number of Dimensions
• Chi-square, df=k-2
– is the probability under the s dimensions– is the probability under the s-1 dimensions
• When sample size is large, the criterion is too severe, it may lead to overestimating the number of dimensions.
• Adopt BIC
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Step 4. Reduction of the Number of Items
• Discrimination index between 0 and 1 (constraint)
• Minimum number of items is 5 retained for each dimension.
• However, indices are not comparable across dimensions, so latent trait standardized for each dimension is required.
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Step 4. Reduction of the Number of Items
•
• Standardized ability: • Transform the items parameter:
• normalized Garma:
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Step 4. Reduction of the Number of Items
•
• Item reduction changes the classification of the subjects.
• – Posterior on the full set items, and then on the
subset.– Use the same parameter obtained with the initial
set.
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Application to the ULISSE Dataset
• Selection of the Number of Latent Classes
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Application to the ULISSE Dataset
• Validation of the 2PL Model– 2PL: BIC=68,653.32 <– LC: BIC=69845.39
• 2PL proves preferable• The structure is also validated, and the
assumption (each section measures each dimension) is supported.
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Application to the ULISSE Dataset
• Assessment of the Number of Dimensions
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Application to the ULISSE Dataset
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Application to the ULISSE Dataset• The initial number of dimension (8) may be
excessive.
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Application to the ULISSE Dataset
• The latent classes can be interpretation of different degrees of impairment of health status.
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Application to the ULISSE Dataset
• investigate the stability of 5 dimension, compare between s=5 and s=4 model.– Cross –validated log-liklihood.
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Cross-validated log-liklihood
• 2 Randomly chosen partitions of equal size– Training data– Test data
• Training: s=4 Test: s=4Training: s=5 Test: s=5
• BIC: s=5 is a proper solution
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Reduction of the Number of Items
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Reduction of the Number of Items
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Reduction of the Number of Items
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Conclusion
• More general structure• Missing responses• Polytomous items
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Question
• why not studying the number of latent classes and dimensionality simultaneously?
• MNSQ item-fit statistic used to reducing items could be tried in this process.
• Simulation studies should be conducted to confirm its efficiency and accuracy of the proposed approach.