Model selection in High-Dimensions: A Quadratic-risk based approach

In this article we propose a general class of risk measures which can be used for data based evaluation of parametric models. The loss function is defined as generalized quadratic distance between the true density and the proposed model. These distances are characterized by a simple quadratic form structure that is adaptable through the choice of a nonnegative definite kernel and a bandwidth parameter. Using asymptotic results for the quadratic distances we build a quick-to-compute approximation for the risk function. Its derivation is analogous to the Akaike Information Criterion (AIC), but unlike AIC, the quadratic risk is a global comparison tool. The method does not require resampling, a great advantage when point estimators are expensive to compute. The method is illustrated using the problem of selecting the number of components in a mixture model, where it is shown that, by using an appropriate kernel, the method is computationally straightforward in arbitrarily high data dimensions. In this same context it is shown that the method has some clear advantages over AIC and BIC.Comment: Updated with reviewer suggestion

Latent class analysis variable selection

We propose a method for selecting variables in latent class analysis, which is the most common model-based clustering method for discrete data. The method assesses a variable's usefulness for clustering by comparing two models, given the clustering variables already selected. In one model the variable contributes information about cluster allocation beyond that contained in the already selected variables, and in the other model it does not. A headlong search algorithm is used to explore the model space and select clustering variables. In simulated datasets we found that the method selected the correct clustering variables, and also led to improvements in classification performance and in accuracy of the choice of the number of classes. In two real datasets, our method discovered the same group structure with fewer variables. In a dataset from the International HapMap Project consisting of 639 single nucleotide polymorphisms (SNPs) from 210 members of different groups, our method discovered the same group structure with a much smaller number of SNP

Classification of Westminster Parliamentary constituencies using e-petition data

In a representative democracy it is important that politicians have knowledge of the desires, aspirations and concerns of their constituents. Opportunities to gauge these opinions are however limited and, in the era of novel data, thoughts turn to what alternative, secondary, data sources may be available to keep politicians informed about local concerns. One such source of data are signatories to electronic petitions (e-petitions). Such e-petitions have risen greatly in popularity over the past decade and allow members of the public to initiate and sign an e-petition online, with popular e-petitions resulting in media attention, a response from the government or ultimately a debate in parliament. These data are thus novel in their availability and have not yet been widely used for research purposes. In this article we will use the e-petition data to show how semantic classes of Westminster Parliamentary constituencies, fitted as Gaussian finite mixture models via EM algorithm, can be used to typify constituencies. We identify four classes: Domestic Liberals; International Liberals; Nostalgic Brits and Rural Concerns, and illustrate how they map onto electoral results. The findings and the utility of this approach to incorporate new e-petitions and adapt to changes in electoral geography are discussed

Conscientiousness and fruit and vegetable consumption: exploring behavioural intention as a mediator

Clear associations have emerged between conscientiousness and health behaviours, such that higher levels of conscientiousness are predictive of beneficial health behaviours. This study investigated the conscientiousness-fruit and vegetable consumption relationship and whether behavioural intention mediated this relationship. A large sample of adults (N = 2136) completed an online battery of questionnaires measuring conscientiousness, behavioural intentions to consume fruit and vegetables, together with self-reported behaviour. Correlation analysis revealed that conscientiousness and each of its facets were positively associated with behavioural intention and self-reported behaviour. Hierarchical multiple regression analyses revealed that after controlling for age, gender and education, total conscientiousness, and the facets of responsibility, industriousness, order and virtue predicted self-reported behaviour. Further analysis revealed that in line with the Theory of Planned Behaviour, behavioural intention fully mediated the conscientiousness-fruit and vegetable behaviour relationship. In conclusion, low levels of conscientiousness were found to be associated with lower fruit and vegetable intentions, with the latter also associated with fruit and vegetable consumption

The Nature of Attachment Relationships and Grief Responses in Older Adults: An Attachment Path Model of Grief

BACKGROUND: Various researchers have theorized that bereaved adults who report non-secure attachment are at higher risk of pathological grief. Yet past findings on avoidant attachment representations and grief have yielded limited and contradictory outcomes. Little research has been conducted with older adults to identify the psychological processes that mediate between self-reported attachment representations and the patterns of grief. OBJECTIVE: To examine the impacts of avoidant attachment and anxious attachment dimensions on emotion and non-acceptance, in response to the loss of a conjugal partner, and the mediating effect of yearning thoughts. DESIGN: Men (N = 21) and women (N = 68) aged 60 years and above who had lost a partner within the last 12 to 72 months were invited to participate. Participants rated their levels of yearning thoughts about the deceased, emotions and non-acceptance on the Texas Revised Inventory of Grief (TRIG-Present), and their type and level of general romantic attachment on the Experiences In Close Relationship questionnaire (ECR). RESULTS: Structural equation modelling (SEM) indicated that individuals who reported higher levels of avoidant attachment reported less emotional responses and less non-acceptance. SEM also showed that individuals who reported higher levels of anxious attachment reported greater emotional responses and greater non-acceptance. SEM further indicated that these relationships were mediated by yearning thoughts. CONCLUSION: People adopt different grief coping patterns according to their self-reported attachment representations, with the nature of their yearning thoughts influencing the process. Grief therapy may be organized according to individual differences in attachment representations