The Warwick-Edinburgh Mental Well-Being Scale

Background There is increasing international interest in the concept of mental well-being and its contribution to all aspects of human life. Demand for instruments to monitor mental well-being at a population level and evaluate mental health promotion initiatives is growing. This article describes the development and validation of a new scale, comprised only of positively worded items relating to different aspects of positive mental health: the Warwick-Edinburgh Mental Well-Being Scale (WEMWBS). Methods WEMWBS was developed by an expert panel drawing on current academic literature, qualitative research with focus groups, and psychometric testing of an existing scale. It was validated on a student and representative population sample. Content validity was assessed by reviewing the frequency of complete responses and the distribution of responses to each item. Confirmatory factor analysis was used to test the hypothesis that the scale measured a single construct. Internal consistency was assessed using Cronbach’s alpha. Criterion validity was explored in terms of correlations between WEMWBS and other scales and by testing whether the scale discriminated between population groups in line with pre-specified hypotheses. Test-retest reliability was assessed at one week using intra-class correlation coefficients. Susceptibility to bias was measured using the Balanced Inventory of Desired Responding. Results WEMWBS showed good content validity. Confirmatory factor analysis supported the single factor hypothesis. A Cronbach’s alpha score of 0.89 (student sample) and 0.91 (population sample) suggests some item redundancy in the scale. WEMWBS showed high correlations with other mental health and well-being scales and lower correlations with scales measuring overall health. Its distribution was near normal and the scale did not show ceiling effects in a population sample. It discriminated between population groups in a way that is largely consistent with the results of other population surveys. Test–retest reliability at one week was high (0.83). Social desirability bias was lower or similar to that of other comparable scales. Conclusions WEMWBS is a measure of mental well-being focusing entirely on positive aspects of mental health. As a short and psychometrically robust scale, with no ceiling effects in a population sample, it offers promise as a tool for monitoring mental well-being at a population level. Whilst WEMWBS should appeal to those evaluating mental health promotion initiatives, it is important that the scale’s sensitivity to change is established before it is recommended in this context.

Towards the systematic simplification of mechanistic models

Mechanistic models used for prediction should be parsimonious, as models which are over-parameterised may have poor predictive performance. Determining whether a model is parsimonious requires comparisons with alternative model formulations with differing levels of complexity. However, creating alternative formulations for large mechanistic models is often problematic, and usually time-consuming. Consequently, few are ever investigated. In this paper, we present an approach which rapidly generates reduced model formulations by replacing a model’s variables with constants. These reduced alternatives can be compared to the original model, using data based model selection criteria, to assist in the identification of potentially unnecessary model complexity, and thereby inform reformulation of the model. To illustrate the approach, we present its application to a published radiocaesium plant-uptake model, which predicts uptake on the basis of soil characteristics (e.g. pH, organic matter content, clay content). A total of 1024 reduced model formulations were generated, and ranked according to five model selection criteria: Residual Sum of Squares (RSS), AICc, BIC, MDL and ICOMP. The lowest scores for RSS and AICc occurred for the same reduced model in which pH dependent model components were replaced. The lowest scores for BIC, MDL and ICOMP occurred for a further reduced model in which model components related to the distinction between adsorption on clay and organic surfaces were replaced. Both these reduced models had a lower RSS for the parameterisation dataset than the original model. As a test of their predictive performance, the original model and the two reduced models outlined above were used to predict an independent dataset. The reduced models have lower prediction sums of squares than the original model, suggesting that the latter may be overfitted. The approach presented has the potential to inform model development by rapidly creating a class of alternative model formulations, which can be compared.