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Using Statistical Models to Understand Functional Disability Among The Elderly

Activities of Daily Living (ADLs) and Instrumental Activities of Daily Living (IADLs) have a long tradition as powerful predictors of future disability and service needs for the elderly. ADLs and IADLs are a set of measures of functional disability that are considered normal and necessary for everyday living. ADLs include basic activities of hygiene and personal care, such as bathing, dressing, getting around inside. IADLs include basic activities necessary to reside in the community, such as managing money, using the telephone, doing grocery shopping. Most of the research on changes in functional status over time has been limited to a discussion of the total number of ADL/IADL difficulties, without regard to the difficulty of the items (ADLs and IADLs). However, further questions, e.g., how to measure individual disability more precisely, or why disability rates experience changes, require a more complex micro-level measure of disability. Latent structure models that allow for statistical inference about subject or item parameters, or both, can be useful in analyzing functional disability data.

A relatively new latent structure model, Grade of Membership (GoM), deals with individual heterogeneity by introducing a set of extreme profiles and a vector of individual membership scores for each extreme profile for each individual. We show that the GoM model can simultaneously be thought of as being a multivariate latent trait model and a constrained latent class model. We treat the membership scores as coming from a known distribution and estimate the extreme profiles by using a Gibbs sampler algorithm.

We illustrate these concepts and methodology using an extract of 6 ADL and 10 IADL measures from the National Long Term Care Survey data, pooled across four survey waves. The findings demonstrate that functional disability among elderly clearly has a multidimensional structure which could potentially be successfully described by the GoM model. Estimation of the parameters of the membership scores distribution and incorporation of the longitudinal data structure may be helpful to understand recent controversial findings about sharp decline in disability among older Americans.