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Modeling the covariance structure of random coefficients to characterize quality variation in health plans

Laura Hatfield, Harvard 
*Alan Zaslavsky, Department of Health Care Policy, Harvard Medical School 

Keywords: quality surveys, Medicare, CAHPS, covariance structure, casemix adjustment

Medicare beneficiaries enrolled in Medicare Advantage managed care plans report on health care quality through the Consumer Assessments of Healthcare Providers and Systems (CAHPS) survey, which includes items concerning experiences with the plan, individual physicians, prescriptions, and access to care. Age, general health status, and education are important predictors of quality ratings, and public reports are adjusted for predictable effects of these variables. Hierarchical modeling shows that coefficients of these variables vary significantly across plans. This variation reflects subgroup-specific dimensions of quality that may complicate comparisons among plans for specific beneficiaries. Interpretation of the large Level 2 covariance matrix of these coefficients (11 outcome models X 4 coefficients + 3 compositional coefficients, or 47 variables) is challenging. We present a parsimonious summary of their associations using a Kronecker structure that may be a useful adjunct to standard factor analysis in covariance analysis of cross-classified sets of variables.