Bayesian analysis of mixture modelling using the multivariate t distribution

A finite mixture model using the multivariate t distribution has been shown as a robust extension of normal mixtures. In this paper, we present a Bayesian approach for inference about parameters of t-mixture models. The specifications of prior distributions are weakly informative to avoid causing nonintegrable posterior distributions. We present two efficient EM-type algorithms for computing the joint posterior mode with the observed data and an incomplete future vector as the sample. Markov chain Monte Carlo sampling schemes are also developed to obtain the target posterior distribution of parameters. The advantages of Bayesian approach over the maximum likelihood method are demonstrated via a set of real data.     

Multivariate distributions defined in terms of contours

The paper deals with the problem of using contours as the basis for defining probability distributions. First, the most general probability densities with given contours are obtained and the particular cases of circular and elliptical contours are dealt with. It is shown that the so-called elliptically contoured distributions do not include all possible cases. Next, the case of contours defined by polar coordinates is analyzed including its simulation and parameter estimation. Finally, the case of cumulative distribution functions with given contours is discussed. Several examples are used for illustrative purposes.     

Examples of the use of an equivalence theorem in constructing optimum experimental designs for random-effects nonlinear regression models

The problem considered is that of finding an optimum measurement schedule to estimate population parameters in a nonlinear model when the patient effects are random. The paper presents examples of the use of sensitivity functions, derived from the General Equivalence Theorem for D-optimality, in the construction of optimum population designs for such schedules. With independent observations, the theorem applies to the potential inclusion of a single observation. However, in population designs the observations are correlated and the theorem applies to the inclusion of an additional measurement schedule. In one example, three groups of patients of differing size are subject to distinct schedules. Numerical, as opposed to analytical, calculation of the sensitivity function is advocated. The required covariances of the observations are found by simulation.     

The Best and Worst Times of Life: Narratives and Assessments of Subjective Well-Being by Anamnestic Comparative Self Assessment (ACSA) in the Eastern Cape,South Africa

The Anamnestic Comparative Self Assessment (ACSA) measure of subjective well-being (SWB) aims to reduce the problems of cultural bias and relativity to external standards by allowing people to define the endpoints or ‘anchors’ of the measurement scale. In medical terminology anamnestic denotes ‘based on memory’. The ACSA uses subjects’ memories of the best and worst periods in their lives to define the anchors of the scale. They then assess their current quality of life relative to these personal anchors. The South African pilot study tested the match between self-assessment of SWB with ACSA and the conventional single-item measures of life satisfaction and happiness used in the South African Quality of Life Trends Study and analysed the narratives of the best and worst times of life. The quota sample of 46 consisted of 26 residents of Makana district in the Eastern Cape Province, South Africa, and 20 patients undergoing treatment in the local TB hospital. Mean SWB ratings with all three measures of life satisfaction, happiness and ACSA were between 5 and 6 on a 0–10-point scale. Ratings on all three scales were positively correlated. However, on ACSA the TB patients rated their current SWB 1.84 points lower than the community respondents, suggesting a greater sensitivity of this measure. It was observed that the starting points of the life stories produced by respondents to define the anchor periods for ACSA were related to their current assessment of SWB. A typology was developed that combined the starting point of the life stories with current SWB. The majority of community respondents matched the ‘Achiever’ type who scored positively on ACSA (i.e., above the mid-point of the scale) and whose life stories started with the worst period of their lives and proceeded to the best period. The TB patients were the only respondents to represent the ‘Survivor’ type whose morale had recovered after misfortune in life. ‘Survivors’ started their narratives with the best period in their lives, then moved to the worst (often health-related) one, and gave positive ACSA ratings. Based on the qualitative analysis of narratives, it is concluded that ACSA is a sensitive measurement instrument and therefore particularly useful for monitoring the effects of treatments and social interventions in longitudinal studies. However, further research is required to verify its cross-cultural validity.

The Perceptions of Women’s Roles and Progress: A Study of Malay Women

This study examines the general perceptions of women towards their roles, their interpretation of progress, as well as the facilitating factors and barriers to their progress. Questionnaires were distributed to 1,000 Malay women in Malaysia from rural and urban areas, from various age and income groups. Interviews were also carried out on the selected sample. Using both quantitative and qualitative methods of analyses, the results showed that women were perceived to play a strong, influential, and supportive role in their families. The results also showed how women perceive progress. These findings are discussed in relation to culture, socialization, values and norms of the Malay society.     

Does parents’ valuation of children’s health mimic their valuation of own health?

A single latent variable model of health status and therapeutic health care utilization is estimated for parents and own children of 6,557 US households. The equation system that identifies latent health status simultaneously determines a number of indicators of general health, including presence of morbidity symptoms, mobility limitations, medication needs, and utilization of therapeutic health care services. The main goal of the paper was to obtain an unbiased estimate of parents’ marginal substitution rate between own and child health. Results indicate that parents’ valuation of their children’s health exceeds their valuation of own health by almost twofold on average.

Form Perception of Partly Occluded Shapes in 4‐Month‐Old Infants

Two habituation experiments were conducted to investigate how 4‐month‐old infants perceive partly occluded shapes. In the first experiment, we presented a simple, partly occluded shape to the infants until habituation was reached. Then we showed either a probable completion (one that would be predicted on the basis of both local and global cues) or an improbable completion. Longer looking times were found for the improbably completed shape (compared to probable and control conditions), suggesting that the probable shape was perceived during partial occlusion. In the second experiment, infants were habituated to more ambiguous partly occluded shapes, where local and global cues would result in different completions. For adults, the percept of these shapes is usually dominated by global influences. However, after habituation the infants looked longer at the globally completed shapes. These results suggest that by the age of 4 months, infants are able to infer the perceptual completion of partly occluded shapes, but for more ambiguous shapes, this completion seems to be dominated by local influences.     

Framing Latina/o Immigration, Education, and Activism

Although Latinas/os have a long history in the USA and represent a growing percentage of the population, they remain largely invisible or stereotyped in dominant images and discourses. Such representations are often ahistorical, and they camouflage the effects of US power and inequality. However, the spring 2006 immigrant rights demonstrations disturbed dominant conceptions. The demonstrators called attention to the contradictory US practices that disrupt home countries, recruit labor migrants, and deny immigrants full participation. Likewise, the role of students in these demonstrations spurred reflections on why youth would walk out of their schools for immigrant rights. Inspired by these demonstrations, we combine materials from multiple disciplines to emphasize the significance of US imperialism, exploitation, and exclusion on Latina/o migration, education, and activism. Key to this article is a reframing of how the media, K-12 curriculum, and popular discourse often engage in a cultural cover-up that sustains inequality.     

A semi-parametric approach to robust parameter design

Parameter design or robust parameter design (RPD) is an engineering methodology intended as a cost-effective approach for improving the quality of products and processes. The goal of parameter design is to choose the levels of the control variables that optimize a defined quality characteristic. An essential component of RPD involves the assumption of well estimated models for the process mean and variance. Traditionally, the modeling of the mean and variance has been done parametrically. It is often the case, particularly when modeling the variance, that nonparametric techniques are more appropriate due to the nature of the curvature in the underlying function. Most response surface experiments involve sparse data. In sparse data situations with unusual curvature in the underlying function, nonparametric techniques often result in estimates with problematic variation whereas their parametric counterparts may result in estimates with problematic bias. We propose the use of semi-parametric modeling within the robust design setting, combining parametric and nonparametric functions to improve the quality of both mean and variance model estimation. The proposed method will be illustrated with an example and simulations.