Random Effects Misspecification Can Have Severe Consequences for Random Effects Inference in Linear Mixed Models

There has been considerable and controversial research over the past two decades into how successfully random effects misspecification in mixed models (i.e. assuming normality for the random effects when the true distribution is non‐normal) can be diagnosed and what its impacts are on estimation and inference. However, much of this research has focused on fixed effects inference in generalised linear mixed models. In this article, motivated by the increasing number of applications of mixed models where interest is on the variance components, we study the effects of random effects misspecification on random effects inference in linear mixed models, for which there is considerably less literature. Our findings are surprising and contrary to general belief: for point estimation, maximum likelihood estimation of the variance components under misspecification is consistent, although in finite samples, both the bias and mean squared error can be substantial. For inference, we show through theory and simulation that under misspecification, standard likelihood ratio tests of truly non‐zero variance components can suffer from severely inflated type I errors, and confidence intervals for the variance components can exhibit considerable under coverage. Furthermore, neither of these problems vanish asymptotically with increasing the number of clusters or cluster size. These results have major implications for random effects inference, especially if the true random effects distribution is heavier tailed than the normal. Fortunately, simple graphical and goodness‐of‐fit measures of the random effects predictions appear to have reasonable power at detecting misspecification. We apply linear mixed models to a survey of more than 4 000 high school students within 100 schools and analyse how mathematics achievement scores vary with student attributes and across different schools. The application demonstrates the sensitivity of mixed model inference to the true but unknown random effects distribution.     

A coming ‘Magnesian’ age? Small states,the global system,and the international community

Since Plato, we have considered that the ideal polis, or political community, is the small state, akin to the idyllic ‘Magnesia’ of the Laws. The Platonic ideal, however, generally has been considered unrealistic. Even in the ancient world, the Alexandrine model ‐ an expanding, pluralistic network of large trading cities under a single aegis ‐ came to contradict it. Subsequent history, especially the imperialism of the nineteenth century which swallowed up many small polities around the world, seemed to prove that only large and powerful entities were ‘fit’ to survive. Why, then, are there still so many small‐sized countries in the world today? Why is their number actually increasing? Decolonisation, the end of bipolarity, democratisation, trade liberalisation and the digital revolution are five factors that have given small states more freedom. Yet many are vulnerable, and the economics of their situations are precarious. The workings of the global system, particularly the globalisation of business, may harm them even while promoting their freedom. The international community, a large part of which is now in fact made up of small states, should be prepared to act, for the global public good as well as out of sheer political and also environmental self‐interest, to help safeguard the livelihood of the world's many and varied small states, whose ‘Magnesian’ venues and values can be of both functional and normative importance for mankind as a whole.     

Prostitution services: an exploratory empirical analysis

This study provides an empirical analysis of the market for some male prostitution services in the UK. Flexible working hours, part-time working, and multiple job holding are considered as important labour market characteristics in this service sector. Statistical models helping explain the provision of a deviant and a more mainstream sexual service is reported, utilizing cross-section data drawn from individual prostitute advertisements. The significance of various declared intrinsic endowments of the prostitutes are examined in relation to the offer of these services, including age, ethnicity, physique, and masculine demeanour.     

Parental preferences and choice of school

This paper provides a UK high resolution microeconometric study of parental preferences and the choice process for secondary schools. Given the particular geographical features of the region, first preference almost entirely related to one of two state schools, which is a situation that perhaps better reflects the real nature of the options faced by most parents in the UK. In contrast to earlier work, distance and access considerations were explicitly incorporated in the preference and choice models estimated and found to be a significant influence on parental decisions. Further significant factors were found, dependent upon the parents' actual choice of school.     

Consumption, Housing Rents and Housing Price: A Test Of A Real Estate Pricing Model Using Hong Kong Data

The present study investigates whether Hong Kong's volatile real estate market is consistent with a non–linear consumption–based–asset–pricing model. It finds that the asset–pricing model is not rejected for some types of properties. However, the differentials between the returns to residential properties and risk–free rate are too large to be explained by the model.     

Trading-up on unmet expectations? Evaluating consumers’ expectations in online premium grocery shopping logistics

Geography and retail store locations are inherently bound together; this study links food retail changes to systemic logistics changes in an emerging market. The later include raising income and education, access to a wide range of technologies, traffic and transport difficulties, lagging retail provision, changing family structure and roles, as well as changing food culture and taste. The study incorporates demand for premium products defined by Kapferer and Bastien [2009b. The Luxury Strategy. London: Kogan Page] as comprising a broad variety of higher quality and unique or distinctive products and brands including in grocery organic ranges, healthy options, allergy free selections, and international and gourmet/specialty products through an online grocery model (n?=?356) that integrates a novel view of home delivery in Istanbul. More importantly from a logistic perspective our model incorporates any products from any online vendors broadening the range beyond listed items found in any traditional online supermarkets. Data collected via phone survey and analysed via structural equation modelling suggest that the offer of online premium products significantly affects consumers’ delivery logistics expectations. We discuss logistics operations and business management implications, identifying the emerging geography of logistic models which respond to consumers’ unmet expectations using multiple sourcing and consolidation points.     

Formation of inflation expectations in the U.K.: Pitfalls in the use of the error-learning model

This paper examines the formation of explicitly-reported price expectations in the UK. Expectations are formed over a long period, and a general distributed lag provides a superior explanation to that provided by a second-order error-learning form. The error-learning mechanism is shown to be biased when lagged expectations incorporate a random shock, and when expectations are reported more frequently than the length of the forecast horizon.     

On the quantitative significance of imperfect information

Economic models of markets with imperfect information have increasingly involved high degrees of theoretical sophistication. So far there has been no movement beyond qualitative prediction. This paper attempts to make quantitative assessments of the new features arising from imperfect information following on recent work by Braverman (1980) and Braverman and Dixit (1981). The information structure of these models is based on non-sequential search, where consumers enter the market only once. It is of interest to question under what circumstances single price equilibria will exist under different assumptions about the distribution of search costs. Therefore for particular families of demand, cost and information conditions, the possibilities of competitive, monopolistic and two price equilibria are examined and their relative likelihoods assessed.     

Unpredictable times: the extent,characteristics and correlates of insecure hours of work in Britain

This article presents new British evidence that suggests that cutting working hours at short notice is twice as prevalent as zero-hours contracts and triple the number of employees are very anxious about unexpected changes to their hours of work. The pay of these employees tends to be lower, work intensity higher, line management support weaker and the threat of dismissal and job loss greater. In addition, the well-being of these employees is lower and they are less committed to the organisations that employ them. However, the prevalence of insecure working hours is reduced by workplace level employee involvement exercised individually or through collective representation.