Likelihood Factorizations for Mixed Discrete and Continuous Variables

Some general remarks are made about likelihood factorizations, distinguishing parameter-based factorizations and concentration-graph factorizations. Two parametric families of distributions for mixed discrete and continuous variables are discussed. Conditions on graphs are given for the circumstances under which their joint analysis can be split into separate analyses, each involving a reduced set of component variables and parameters. The result shows marked differences between the two families although both involve the same necessary condition on prime graphs. This condition is both necessary and sufficient for simplified estimation in Gaussian and for discrete log linear models.     

A general condition for avoiding effect reversal after marginalization

Summary.  The paper examines the effect of marginalizing over a possibly unobserved background variable on the conditional relation between a response and an explanatory variable. In particular it is shown that some conclusions derived from least squares regression theory apply in general to testing independence for arbitrary distributions. It is also shown that the general condition of independence of the explanatory variable and the background ensures that mono- tonicity of dependence is preserved after marginalization. Relations with effect reversal and with collapsibility are sketched.     

Methamphetamine use: hazards and social influences

Use of methamphetamine, a potent central nervous system stimulant, increased in the early- to mid-1990s in the United States, concentrated in the west, midwest, and south. The use and trade of methamphetamine was facilitated by a fairly simple production process and the involvement of numerous small entrepreneurs as well as drug-trafficking syndicates. National data from the 1994 Drug Abuse Warning network revealed that for the period from 1991 to 1994 methamphetamine use among short-stay hospital patients more than tripled, and methamphetamine-related deaths reported by medical examiner offices nearly tripled. In addition, the Treatment Episode Data Set revealed a 43 percent increase in treatment-program admissions in which clients identified methamphetamine as the primary drug of abuse. Nonetheless, methamphetamine use did not become widespread in the U.S. population. Low-income and unemployed young white men continue to be the group most likely to use methamphetamine, but by the mid-1990s the drug had increased in popularity in more diverse populations and regions. Economic and social pressures experienced by a broad array of Americans may partially explain expanded methamphetamine use; for example, depressed economic conditions in rural and semi-rural areas have contributed to methamphetamine's appeal as a source of income. A "war against drugs" approach has characterized the policy response, with increased criminal justice penalties. A public health approach is recommended, including prevention campaigns, harm-reduction outreach and treatment approaches, and pharmacologic and abstinence-based drug treatment approaches.     

Joint response graphs and separation induced by triangular systems

Summary.  We consider joint probability distributions generated recursively in terms of univariate conditional distributions satisfying conditional independence restrictions. The independences are captured by missing edges in a directed graph. A matrix form of such a graph, called the generating edge matrix, is triangular so the distributions that are generated over such graphs are called triangular systems. We study consequences of triangular systems after grouping or reordering of the variables for analyses as chain graph models, i.e. for alternative recursive factorizations of the given density using joint conditional distributions. For this we introduce families of linear triangular equations which do not require assumptions of distributional form. The strength of the associations that are implied by such linear families for chain graph models is derived. The edge matrices of chain graphs that are implied by any triangular system are obtained by appropriately transforming the generating edge matrix. It is shown how induced independences and dependences can be studied by graphs, by edge matrix calculations and via the properties of densities. Some ways of using the results are illustrated.     

Some determinants of the migration of professional manpower

Determinants of migration of professional manpower are investigated using data from a 1970 survey of immigrants to the United States. From a respondent's stated "intent to stay" in the United States and five other characteristics a six-dimensional contingency table is formed. We find a well-fitting log-linear model for this table. Thus, we establish the importance of selected determinants of migration and present a table of predicted rates of intent to stay in the United States.