Mixture modelling for cluster analysis

Cluster analysis via a finite mixture model approach is considered. With this approach to clustering, the data can be partitioned into a specified number of clusters g by first fitting a mixture model with g components. An outright clustering of the data is then obtained by assigning an observation to the component to which it has the highest estimated posterior probability of belonging; that is, the ith cluster consists of those observations assigned to the ith component (i = 1,..., g). The focus is on the use of mixtures of normal components for the cluster analysis of data that can be regarded as being continuous. But attention is also given to the case of mixed data, where the observations consist of both continuous and discrete variables.

Investigation of the benefits of HIV/AIDS caregiving and relations among caregiving adjustment, benefit finding, and stress and coping variables

The present study explored the nature of benefit finding in HIV/AIDS caregiving, and examined relations among caregiver adjustment, benefit finding, and stress and coping variables. A total of 64 HIV/AIDS caregivers and 46 care recipients completed interviews and questionnaires. First, the study aimed to explore the types of benefits associated with HIV/AIDS caregiving. Content analyses of caregiver responses to an interview question inquiring about gains from caregiving revealed eight benefit themes. Second, the study aimed to examine relations between caregiver adjustment and both benefit finding and stress and coping variables. We hypothesized that number of caregiver reported benefits, social support, challenge and control appraisals, and problem focused coping would be inversely related to poorer adjustment, whereas care recipient reported global distress and illness, caregiver threat appraisal and passive-avoidant emotion-focused coping would be positively associated with poorer adjustment. Correlations indicated that poorer adjustment (measured by global distress, depression, caregiving impact, social adjustment and health status) was positively correlated with care-recipient distress, threat appraisals and passive avoidant coping and inversely correlated with social support, and number of reported benefits. Unexpectedly, problem-focused coping, controllability and challenge appraisals, and care recipient illness were unrelated to adjustment. Third, the study aimed to examine relations between benefit finding and stress and coping variables. Correlations indicated that benefit finding was related to social support use, seeking social support coping and problem-solving coping. Findings indicate that the benefit finding and stress/coping frameworks have utility in guiding research into adaptation to HIV/AIDS caregiving. Results also indicate targets for intervention in the provision of services for HIV/AIDS caregivers.

Warranty and discrete preventive maintenance

Preventive maintenance actions over the warranty period have an impact on the warranty servicing cost to the manufacturer and the cost to the buyer of fixing failures over the life of the product after the warranty expires. However, preventive maintenance costs money and is worthwhile only when these costs exceed the reduction in other costs. The paper deals with a model to determine when preventive maintenance actions (which rejuvenate the unit) carried out at discrete time instants over the warranty period are worthwhile. The cost of preventive maintenance is borne by the buyer. (C) 2003 Elsevier Ltd. All rights reserved.

Dimensions of quality of life and psychosocial variables most salient to colorectal cancer patients

Colorectal cancer is one of the most common invasive cancers, and is responsible for considerable physical and psychosocial morbidity. Understanding the quality of life experienced by colorectal cancer patients is essential for evaluating the full impact of the disease on individuals, their families and their communities. Patient perspective is essential in establishing a proper understanding of the quality of life of colorectal cancer patients. Despite this, few studies have employed a qualitative methodology to explore quality of life issues for colorectal cancer patients. A review of the literature identified only seven qualitative studies pertaining to quality of life issues for colorectal cancer patients, a surprising finding given the prevalence of this cancer. Accordingly, this study sought to build on the findings of previous qualitative research by providing descriptive data on the quality of life and psychosocial variables most salient to colorectal cancer patients. Six core themes emerged from interview and focus group data: Satisfaction with diagnosis and treatment; support (including information provision); quality of life; benefits of diagnosis; making sense of the cancer experience; and coping strategies. The information derived from this study will help inform the development of supportive care services to address the needs of the increasing number of people diagnosed with colorectal cancer. Copyright (c) 2005 John Wiley & Sons, Ltd.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Toward a better understanding of the influences on physical activity: The role of determinants, correlates, causal variables, mediators, moderators, and confounders

Background: For research on physical activity interventions to progress systematically, the mechanisms of action must be studied. In doing so, the research methods and their associated concepts and terminology become more complex. It is particularly important to clearly distinguish among determinants, correlates, mediators, moderators, and confounder variables used in physical activity research. This article examines the factors that are correlated with and that may have a causal relationship to physical activity. Methods and Results: We propose that the term correlate be used, instead of determinant, to describe statistical associations or correlations between measured variables and physical activity. Studies of the correlates of physical activity are reviewed. The findings of these studies can help to critique existing theories of health behavior change and can provide hypotheses to be tested in intervention studies from which it is possible to draw causal inferences. Mediator, moderator, and confounder variables can act to influence measured changes in physical activity. Intervening causal variables that are necessary to complete a cause-effect pathway between an intervention and physical activity are termed mediators. The relationship between an intervention and physical activity behaviors may vary for different groups; the strata by which they vary are levels of moderators of the relationship. Other factors may distort or affect the observed relationships between program exposure and physical activity, and are known as confounders. Conclusions: Consistent use of terms and additional research on mediators and moderators of intervention effects will improve our ability to understand and influence physical activity.