We propose to develop a costing system for nursing homes, based on the initial health evaluation of elderly people at the time of their admission. The data set reflects the complexity items of the interRAI Long Term Care Facilities (LTCF) assessment form, and comprises N = 387 individuals institutionalized in a non-profit nursing home in Portugal. We begin by decomposing the data in fuzzy clusters using the grade of membership model. The model based on a fuzzy 3-partition fits the data better than any other competitor. We notice the hierarchical nature of this partition, i.e. Low, Medium and High complexity, and also that almost all individuals share at most two fuzzy clusters in increasing order of complexity. This particular distribution of individuals subsequently leads them to be indexed by a real number such that the higher the number the higher the complexity of the individual. In the next step, we solve the inverse problem by means of a linear regression model, which allows us to estimate the position (i.e. the complexity) of a given individual in the fuzzy 3-partition on the basis of his/her initial health assessment. In the final step, we establish a relation between the current cost and the estimated complexity of individuals using another regression model. Noting that the cost is not a linear function of the complexity, we add a second order term to account for the nonlinear effects, and obtain a model with good fit, as measured by the adjusted coefficient of determination, R2adj = 0.83. We validate our model by considering 10 additional cases and find a good association between the estimated cost and the cost currently practiced in the nursing home, ? = 0.90. We hope our approach can provide an alternative way to predict the referred cost through LTCF form for health assessment purposes.

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Nursing Homes,Fuzzy Clustering

• Economia e Gestão - Ciências Sociais