In this series, I previously gave an overview of the main types of study design and the techniques used to minimise biased results. Here, I describe cross-sectional studies, their uses, advantages and limitations.

The aim was to develop and test a brief revised version of the family affluence scale. A total of 7120 students from Denmark, Greenland, Italy, Norway, Poland, Romania, Scotland and Slovakia reported on a list of 16 potential indicators of affluence. Responses were subject to item screening and test of dimensionality. Bifactor analysis revealed a strong general factor of affluence in all countries, but with additional specific factors in all countries. The specific factors mainly reflected overlapping item content. Item screening was conducted to eliminate items with low discrimination and local dependence, reducing the number of items from sixteen to six: Number of computers, number of cars, own bedroom, holidays abroad, dishwasher, and bathroom. The six-item version was estimated with Samejima's graded response model, and tested for differential item functioning by country. Three of the six items were invariant across countries, thus anchoring the scale to a common metric across countries. The six-item Child Ind Res (2016) 9:771-784

We build upon the existing literature to formulate a class of models for multivariate mixtures of Gaussian, ordered or unordered categorical responses and continuous distributions that are not Gaussian, each of which can be defined at any level of a multilevel data hierarchy. We describe a Markov chain Monte Carlo algorithm for fitting such models. We show how this unifies a number of disparate problems, including partially observed data and missing data in generalized linear modelling. The two-level model is considered in detail with worked examples of applications to a prediction problem and to multiple imputation for missing data. We conclude with a discussion outlining possible extensions and connections in the literature. Software for estimating the models is freely available.

There are a number of measures of life satisfaction for use with adolescent samples. The adapted Cantril Ladder is one such measure. This has been collected by the Health Behaviour in School-aged Children (HBSC) study in HBSC member countries across Europe and North America for several survey cycles, dating back to 2002. Although this measure has been piloted in the HBSC member countries, and analysed and reported in several international scientific journals and reports, it has never been formally validated. This study aims to be a first step in validating the adapted Cantril Ladder to establish if it is fit for purpose in the measurement of global life satisfaction among adolescents in Scotland. The study found that across samples of 11-15 year old pupils, the Cantril Ladder showed good reliability, and among 11 year olds, better than that of the Students' Life Satisfaction Scale, an often used measure in adolescent samples. The Cantril Ladder also showed good convergent validity with other emotional well-being measures, perceived health and subjective health. Gender differences were noted in the convergent analysis suggesting gender differences in factors influencing or influenced by life satisfaction measured using this instrument.