The Copula Information Criteria

We derive two types of Akaike information criterion (AIC)‐like model‐selection formulae for the semiparametric pseudo‐maximum likelihood procedure. We first adapt the arguments leading to the original AIC formula, related to empirical estimation of a certain Kullback–Leibler information distance. This gives a significantly different formula compared with the AIC, which we name the copula information criterion. However, we show that such a model‐selection procedure cannot exist for copula models with densities that grow very fast near the edge of the unit cube. This problem affects most popular copula models. We then derive what we call the cross‐validation copula information criterion, which exists under weak conditions and is a first‐order approximation to exact cross validation. This formula is very similar to the standard AIC formula but has slightly different motivation. A brief illustration with real data is given.     

Recognizing and visualizing departures from independence in bivariate data using local Gaussian correlation

It is well known that the traditional Pearson correlation in many cases fails to capture non-linear dependence structures in bivariate data. Other scalar measures capable of capturing non-linear dependence exist. A common disadvantage of such measures, however, is that they cannot distinguish between negative and positive dependence, and typically the alternative hypothesis of the accompanying test of independence is simply “dependence”. This paper discusses how a newly developed local dependence measure, the local Gaussian correlation, can be used to construct local and global tests of independence. A global measure of dependence is constructed by aggregating local Gaussian correlation on subsets of \(\mathbb{R}^{2}\) , and an accompanying test of independence is proposed. Choice of bandwidth is based on likelihood cross-validation. Properties of this measure and asymptotics of the corresponding estimate are discussed. A bootstrap version of the test is implemented and tried out on both real and simulated data. The performance of the proposed test is compared to the Brownian distance covariance test. Finally, when the hypothesis of independence is rejected, local independence tests are used to investigate the cause of the rejection.     

Eliciting Risk and Time Preferences

We design experiments to jointly elicit risk and time preferences for the adult Danish population. Since subjects are generally risk averse, we find that joint elicitation provides estimates of discount rates that are significantly lower than those found in previous studies and more in line with what would be considered as a priori reasonable rates. The statistical specification relies on a theoretical framework that involves a latent trade‐off between long‐run optimization and short‐run temptation. Estimation of this specification is undertaken using structural, maximum likelihood methods. Our main results based on exponential discounting are robust to alternative specifications such as hyperbolic discounting. These results have direct implications for attempts to elicit time preferences, as well as debates over the appropriate domain of the utility function when characterizing risk aversion and time consistency.     

Decision‐making in child welfare services: Professional discretion versus standardized templates

The article explores differences in the assessment and decision‐making processes, in child welfare services where a standardized template is implemented and in services where it is not. Child welfare services in several countries use different approaches to assess children's and families' need for intervention. In Norway, as in other European countries, there is a shortage of knowledge about decision‐making strategies. The article examines how 36 child welfare caseworkers in 6 different teams in Norway investigate, assess, and make decisions at the phase of an incoming referral. The analysed data were collected by focus group interviews. We use decision theory as a theoretical frame of reference. The analysis shows variation in the assessment procedure at different points of the process, depending on which approach was used. Despite such differences, the final decisions made were almost identical. Even though the data has its limitations because of the small number of informants, the results indicate that choice of approach is not decisive for decision‐making in the child welfare services.     

Functional logistic regression: a comparison of three methods

Functional logistic regression is becoming more popular as there are many situations where we are interested in the relation between functional covariates (as input) and a binary response (as output). Several approaches have been advocated, and this paper goes into detail about three of them: dimension reduction via functional principal component analysis, penalized functional regression, and wavelet expansions in combination with Least Absolute Shrinking and Selection Operator penalization. We discuss the performance of the three methods on simulated data and also apply the methods to data regarding lameness detection for horses. Emphasis is on classification performance, but we also discuss estimation of the unknown parameter function.     

A Measure of Dependence Between Two Compositions

We consider the problem of describing the correlation between two compositions. Using a bicompositional Dirichlet distribution, we calculate a joint correlation coefficient, based on the concept of information gain, between two compositions. Numerical values of the joint correlation coefficient are calculated for compositions of two and three components, respectively. We also present an estimator of the joint correlation coefficient for a sample from a bicompositional Dirichlet distribution. Two confidence intervals are presented and we examine their empirical confidence coefficients using a Monte Carlo study. Finally, we apply the estimator to a data set analysing the joint correlation between the 1967 and 1997, and the 1977 and 1997 compositions of the government gross domestic product for the 50 states of the USA and the District of Columbia.     

Q methodology in social work research

This article examines Q methodology as an empirical method for use in social work research. Q methodology applies statistical analysis to the qualitative study of human subjectivity such as attitudes, beliefs, feelings and opinions. Q methodology is effective for obtaining data from small samples, and it offers respondents a concise and valid way of expressing their viewpoints with minimal researcher interference. The article provides an overview of Q methodology and presents an actual example of a small‐scale Q study to facilitate a better understanding of the method. We conclude that Q methodology is especially suitable in social work research with respondents who may have difficulties in expressing themselves when more conventional research methods are used. Q methodology is an efficient tool in research involving the exploration and comparison of different points of view.     

Role of National Divorce Rates in Moderating the Association Between Marriage Duration and Body Mass Index

The aim of this study was to investigate the moderating effects of the national divorce rate on the association between body weight and marriage duration. Previous studies argued that a high divorce rate at country level reduces the body weight of married people because of an increased risk of a return to the marriage market. To examine the association in question, this study used retrospective data from 14,083 middle-aged individuals in Europe. For women the divorce rate, the percentage change, and the trend of change did not moderate the positive association between body mass index and marriage duration. In contrast, for men a high divorce rate and a steady decline over time positively moderated the relation between body mass index and marriage duration.