A Dimensional CLT for Non-Central Wilks' Lambda in Multivariate Analysis

Abstract.  We consider the non-central distribution of the classical Wilks' lambda statistic for testing the general linear hypothesis in MANOVA. We prove that as the dimension of the observation vector goes to infinity, Wilks' lambda obeys a central limit theorem under simple growth conditions on the non-centrality matrix. In one case we also prove a stronger result: the saddlepoint cumulative distribution function (CDF) approximation for the standardized version of Wilks' lambda converges uniformly on compact sets to the standard normal CDF. These theoretical results go some way towards explaining why saddlepoint approximations to the distribution of Wilks' lambda retain excellent accuracy in high-dimensional cases.     

A Matrix-Based Approach to Uncertainty and Sensitivity Analysis for Fault Trees1

System unavailabilities for large complex systems such as nuclear power plants are often evaluated through use of fault tree analysis. The system unavailability is obtained from a Boolean representation of a system fault tree. Even after truncation of higher order terms these expressions can be quite large, involving thousands of terms. A general matrix notation is proposed for the representation of Boolean expressions which facilitates uncertainty and sensitivity analysis calculations.     

Demographic aspects of lactation and postpartum amenorrhea

Interrelations between lactation and post-partum amenorrhea are studied from the reports of about 5,000 married women included in a 1966 Follow-up Survey of Acceptors of an Intrauterine Device (IUD) in Taiwan. The length of post-partum amenorrhea and of breastfeeding are positively associated. On an average, breastfeeding delayed the resumption of menstruation by about 7 months. The association between lactation and amenorrhea is not accounted for by differences in mother’s age, parity, education and her place of residence. A multiple regression analysis suggests that (1) age affects amenorrhea both directly and through lactation, (2) parity has no independent effect on either lactation or amenorrhea, and (3) education and place of residence affect amenorrhea mainly through the cultural variations in the practice of breastfeeding.     

The current practice of bank long-range planning

This paper reports on a recent survey of long-range planning practices in 105 large United States banks. The survey results indicate that long range planning is a relatively new corporate activity with more than half the respondents initiating long range planning the last 5 years. To the extent these banks lead others, this finding suggests greater adoption of long range planning systems in small and medium size banks in the future. Profitability and growth goals are the primary goals quantified in the planning process. These goals are pursued via various strategies. Profit goals are typically pursued by improving pricing policies, adjusting mix and maturity of assets and liabilities to minimize adverse effects of interest rate fluctuations, managing spreads through proper loan pricing and bond portfolio management and tightening cost control with a particular emphasis on non-interest expense. Growth goals are achieved by branch expansion, use of bank holding companies, and increased market penetration through product diversification and sales training programmes designed to develop new business. In addition, information is presented on trends that appear to be developing in the area of long-range planning in the banking industry.     

A Causal Model of Secondary Deviance: the Case of Homosexuality*

The causal structure of a theory of secondary deviance is fitted to data from a sample of 148 male homosexuals. The model suggests that if one perceives others reacting to him on the basis of the homosexual stereotype, his self definition may incorporate the stereotype. These responses, and the accompanied feelings of stigma, are likely to produce stress. As an adaptation, the individual may shift his reference associations to homosexual groups. While providing for a more positive identity, the ultimate outcome of these associations is often the adoption of a role consistent with the stereotype (i.e., secondary deviance). The basic concepts of the theory are operationally defined in terms of Likert-type scales. Dichotomizing the variables on the basis of median scale scores, a log-linear technique of causal inference is used to test the propositions. Offering support for the theory, the analysis suggests that secondary deviance is caused by association in homosexual groups which is caused by perceived societal rejection. Self definition is shown not to be related to secondary deviance, but is affected by perceived rejection and may affect and be affected by homosexual association. Implications for the labeling, anomie, and social and cultural support theories from which the model originated are also discussed.     

The Role of Ethnicity in the Emergency Decision-Making Process*

Although sociologists have studied for decades the process whereby citizens make emergency decisions in response to disaster warnings, very little attention has been given to understanding the role of ethnicity in this process. Data derived from fatality and injury counts following disasters, though sparse, documents that minority group citizens tend to suffer disproportionately high negative consequences in connection with the impact of disasters. On the basis of this information, it is inferred that differences exist between the emergency decision-making processes of minority and majority citizens. This paper lays the theoretical groundwork for beginning to revise existing conceptual models of warning response behavior to more adequately address the variation associated with minority group status. This goal is accomplished through pursuing three general tasks: (1) examining the process through which personal emergency decisions are made, (2) delineating social factors which impinge upon the outcomes of this decision-making process, and (3) integrating into an existing model of warning response behavior, additional variables which are related to minority status.     

A comparison of the reliability of questionnaire versus diary data

The crucial role that communication plays in organizations has led to the development of various methodologies to collect communications data. Two of the more common techniques are one-shot questionnaires and self-recording diaries completed at the time of the interaction. Questionnaires are often viewed as unreliable since they are based on the memory and perceptions of the participants. Diaries, on the other hand, are considered to be more reliable since they are completed immediately following an interaction when the event is still fresh in the individual's mind. This paper compares the cross-recorder reliability of these two data collection instruments. A reliability measure which indicates the degree to which an individual concurs as to the occurrence of interactions across all individuals is introduced. The results, based on studies in three organizations involving 49, 61 and 110 participants respectively, indicate that diary data are significantly more reliable than data obtained from questionnaires.     

An exploration of recent club drug use among rave attendees

Raves are characterized by large numbers of youth dancing for long periods of time and by the use of "club drugs," such as 3, 4-methylenedioxymethamphetamine (MDMA or "ecstasy"). While a small body of research has explored the use of ecstasy and other club drugs (EOCD) among club rave attendees in the United States, we are aware of no studies that have investigated the relationship between EOCD use and high-risk sexual behaviors among members of this population. We explored the association between EOCD use and high-risk sexual behaviors among a sample of 283 club rave attendees interviewed during the spring and summer of 2005. Data were collected at 13 rave events in two different clubs along the Baltimore-Washington corridor between March 17 and September 3, 2005. Potential respondents were conveniently sampled and approached between 12 a.m. and 5 a.m. as they exited the clubs. Only 12% reported using ecstasy within the two days preceding the interview, findings considerably lower than our earlier studies of club rave attendees. Moreover, no significant relationship was discerned between recent MDMA use and high-risk sexual behavior. These findings suggest that the use of EOCD among rave attendees has diminished and that the allocation of significant resources to combat their proliferation, among this and other populations at risk for EOCD use, may be premature.