Threshold Effects in Nonlinear Models With an Application to the Social Capital‐retirement‐health Relationship

Abstract

This paper considers the relationship between social capital and health in the years before, at and after retirement. This adds to the current literature that only investigates this relationship in either the population as a whole or two subpopulations, pre-retirement and post-retirement. We now investigate if there are further additional subpopulations in the years to and from retirement. We take an information criteria approach to select the optimal model of subpopulations from a full range of potential models. This approach is similar to that proposed for linear models. Our contribution is to show how this may also be applied to nonlinear models and without the need for estimating subsequent subpopulations conditional on previous fixed subpopulations. Our main finding is that the association of social capital with health diminishes at retirement, and this decreases further 10 years after retirement. We find a strong positive significant association of social capital with health, although this turns negative after 20 years, indicating potential unobserved heterogeneity. The types of social capital may differ in later years (e.g., less volunteering) and hence overall social capital may have less of an influence on health in later years.

A time-duration measure of continuity of care to optimise utilisation of primary health care: a threshold effects approach among people with diabetes

“…The optimal model was used to suggest the maximum optimal time interval between GP services where the number of diabetes-related potentially preventable hospitalisations was minimal. The threshold effects model evaluates all subpopulations simultaneously rather than sequentially and therefore extends towards a non-linear model [22, 23, 27] that allows more flexibility in examining the relationship between GP service and the risk of diabetes-related potentially preventable hospitalisation. This approach has been applied in previous studies [24, 31].…”

“…All competing models were compared using their BIC and AIC statistics. The preferred model was the one which minimised the appropriate information criteria (AIC and BIC) [23]. Within each diabetes complication cohort, the preferred model indicated the maximum time interval to a GP service which had minimal risk of diabetes-related potentially preventable hospitalisations and suggested the maximum optimal time interval to a GP service corresponding to each diabetes complication cohort that was subsequently used to operationalise the cover index.…”

How many in a crowd? Assessing overcrowding measures in Australian housing

“…A more flexible and preferable approach is to apply techniques developed by Gannon, Harris et al (2014). Consider the model:…”

“…However, how many breakpoints there should be and where they occur in relation to the observed values of C is unknown. Gannon, Harris et al (2014) show how to simultaneously: uncover the optimal number of breakpoints; where they lie; and estimate all parameters of the model. Here we are specifically interested in the threshold at which the relationship becomes negative (ie.…”

“…The interested reader is referred to Gannon, Harris et al (2014) for more technical details, but in essence, in its simplest form, the technique involves consideration -that is, estimation -of 'every' possible 1-break model in the relationship between the particular measure of overcrowding, C, and the outcome variable, y. That is, C is split into two mutually exclusive variables based on all observed realisations of C, and M separate models estimated for all of these candidate models.…”