A direct derivation of the REML likelihood function

The original derivation of the widely cited form of the REML likelihood function for mixed linear models is difficult and indirect. This paper derives it directly using familiar operations with matrices and determinants.     

A multivariate version of Gini's rank association coefficient

In this paper, we introduce a multivariate generalization of the population version of Gini's rank association coefficient, giving a response to this open question posed in [4]. We also study some properties of this version, present the corresponding results for the sample statistic, and provide several examples.     

Out-of-Pocket Health Care Expenditures by Russian Consumers with Different Health Status

The paper uses the Russia Longitudinal Monitoring Survey 2003 database to study the types of official and shadow out-of-pocket health care expenditures by consumers with high and low health status. The analysis shows that the inability of less healthy people to pay unofficially for more effective outpatient care results in their higher demand for official inpatient and outpatient treatment. This pattern creates the need to sustain excessive inpatient facilities and slows down health care restructuring. Yet, since the state is incapable of fulfilling its obligations for providing free health care and meet the current demand, in inpatient institutions all consumers, and less healthy ones in particular, spend considerable sums on drugs, even though the latter are guaranteed to be free. Consequently, the current Russian health system itself leads to replacing outpatient with inpatient care, which is more costly both for the patients and for the state.      

Axiomatic foundations for fairness-motivated preferences

Much work in social choice theory takes individual preferences as uninvestigated inputs into aggregation functions designed to reflect considerations of fairness. Advances in experimental and behavioural economics show that fairness can also be an important motivation in the preferences of individuals themselves. A proper characterisation of how fairness concerns enter such preferences can enrich the informational basis of many social choice exercises. This paper proposes axiomatic foundations for individual fairness-motivated preferences that cover most of the models developed to rationalise observed behaviour in experiments. These models fall into two classes: Outcome-based models, which see preferences as defined only over distributive outcomes, and context-dependent models, which allow rankings over distributive outcomes to change systematically with non-outcome factors. I accommodate outcome-based and context-sensitive fairness concerns by modelling fairness-motivated preferences as a reference-dependent preference structure. I first present a set of axioms and two theorems that generate commonly used outcome-based models as special cases. I then generalise the axiomatic basis to allow for reference-dependence, and derive a simple functional form in which the weight on each person’s payoff depends on a reference vector of how much each person deserves.     

Gamson’s law and hedonic games

This note adds one celebrated coalition formation game due to Gamson (Am Soc Rev 26:373–382 1961a, Am Soc Rev 26:565–573, 1961b) in the list of applications of the theory of hedonic games explored by Banerjee et al. (Soc Choice Welf 18:135–153, 2001) and Bogomolnaia and Jackson (Games Econ Behav 38: 204–230, 2002). We apply their results to study the original Gamson game and offer extensions both to a multi-dimensional characteristics space and to an infinite number of players.     

A note on the paradox of smaller coalitions

We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy’s (Int J Game Theory 8:133–164, 1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (Social Choice Welfare 18:135–153, 2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy’s paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy’s paradox is not present for at least one minimal winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.     

Analysis of breeding bird communities along an urban-rural gradient in Berlin,Germany, by Hasse Diagram Technique

Breeding bird communities in Berlin were investigated at five study sites, which represent an structural urban-rural gradient, from densely built-up areas with sealed ground to green areas such as large parks. In this paper, we tested the Hasse Diagram Technique (HDT), an approach belonging to partial order theory, for its appropriateness to extract information about changes in species composition from our data set. As expected, the overall number of bird species was positively correlated with the urban-rural gradient, increasing from 12 found in the city center to 28 in an urban park. By HDT analysis, four different sub-groups of birds could be identified, contributing differentially to the increase in species number: (1) ubiquists, i.e., species found at each study site, (2) a sub-group, the species’ number of which was positively correlated with the urban-rural gradient, increasing with increasingly green areas, (3) a sub-group, the species’ number of which was negatively correlated with the urban-rural gradient, decreasing with a declining density of buildings, and (4) species, the distribution of which did not show any correlation with the urban-rural gradient. The results show that HDT is a suitable tool for formalized analysis of the pattern of species’ communities along an environmental gradient.     

Civil Society Opposition to Nonferrous Metals Mining in Montana

This paper discusses the opposition of civil society to nonferrous metals mining in Montana. The mineral resources and mining history of Montana are discussed, as is the vibrant civil society of that state. Montana’s civil society has opposed mining due to its environmental effects, particularly upon areas of high conservation value. This opposition has involved litigation and the implementation of a ban on the use of cyanide by the mining industry. The paper concludes with a discussion of whether this opposition to mining has damaged the economy of the state and Montana’s future as an example of the “New West,” wherein amenities based growth act as the principal agent of economic activity.     

Simulated classical tests in multinomial probit models

This paper compares the application of different versions of the simulated counterparts of the Wald test, the score test, and the likelihood ratio test in one- and multiperiod multinomial probit models. Monte Carlo experiments show that the use of the simple form of the simulated likelihood ratio test delivers relatively robust results regarding the testing of several multinomial probit model specifications. In contrast, the inclusion of the Hessian matrix of the simulated loglikelihood function into the simulated score test and (in the multiperiod multinomial probit model) particularly the inclusion of the quasi-maximum likelihood theory into the simulated likelihood ratio test leads to substantial computational problems. The combined application of the quasi-maximum likelihood theory with the simulated Wald test or the simulated score test is not systematically superior to the application of the other versions of these two simulated classical tests either. Neither an increase in the number of observations nor in the number of random draws in the incorporated Geweke-Hajivassiliou-Keane simulator systematically lead to more precise conformities between the frequencies of type I errors and the basic significance levels. An increase in the number of observations only decreases the frequencies of type II errors, particularly regarding the simulated classical testing of multiperiod multinomial probit model specifications.