Relational Models of Disability: What Technique Should be Used to Estimate Parameters?

This paper evaluates three different procedures for the estimation of parameters in a Brass relational model of disability. These are ordinary least squares regression (OLS), weighted least squares regression (WLS) and maximum likelihood estimation (ML). This contribution is valuable for two reasons. First, the method for estimating relational model parameters is an area of debate with examples in the literature that recommend each of the three approaches above for the estimation of mortality schedules. Second, the use of relational models to estimate disability schedules represents a new application which requires a solid grounding in terms of the best technique for parameter estimation. The relational model of disability fitted here is based on Brass" relational model for mortality. The model combines data from two sources, using a schedule of limiting long term illness rates (2001 census) as the standard and adjusting this using two parameters to represent a disability schedule for a particular disability type (Health Survey for England 2000/01). This is useful because even at national level schedules of disability rates from the Health Survey for England show considerable sampling fluctuations particularly at the oldest ages which are smoothed by the model estimates. Brass relational models are fitted using each of the three procedures for overall disability and locomotor (mobility) disability and for males and females. In addition to a visual comparison of model fit, two tests are used to evaluate the models; ratios between model residual sums of squares and comparison of the model and observed crude rates of disability. The results show that ML consistently overestimates rates of disability at the oldest ages. ML has a significantly higher residual sum of squares than the OLS and WLS models thus explaining less of the variability in observed disability rates. The OLS and WLS model fitting procedures give very similar and good fits to the observed data. The conclusion of this paper is to recommend WLS as the procedure for fitting relational models of disability. WLS gives a better fit to the observed data compared to ML and whilst OLS gives a comparable fit this approach is known to be less robust in a statistical sense.