Efficiency of reduced logistic regression models

One feature of the usual polychotomous logistic regression model for categorical outcomes is that a covariate must be included in all the regression equations. If a covariate is not important in all of them, the procedure will estimate unnecessary parameters. More flexible approaches allow different subsets of covariates in different regressions. One alternative uses individualized regressions which express the polychotomous model as a series of dichotomous models. Another uses a model in which a reduced set of parameters is simultaneously estimated for all the regressions. Large-sample efficiencies of these procedures were compared in a variety of circumstances in which there was a common baseline category for the outcome and the covariates were normally distributed. For a correctly specified model, the reduced estimates were over 100% efficient for nonzero slope parameters and up to 500% efficient when the baseline frequency and the effect of interest were small. The individualized estimates could have efficiencies less than 50% when the effect of interest was large, but were also up to 130% efficient when the baseline frequency was large and the effect of interest was small. Efficiency was usually enhanced by correlation among the covariates. For an underspecified reduced model, asymptotic bias in the reduced estimates was approximately proportional to the magnitude of the omitted parameter and to the reciprocal of the baseline frequency.     

Assimilation and Localism: Some Very Small Towns in Mass Society

A major theme in social theory concerns the transformation of social relationships in small communities as a result of modernization. This paper examines changing social relations in some small towns in southeastern Pennsylvania. For several hundred years, the residents of these towns have continuously developed institutions to preserve their local identity and maintain personal relations at the same time that they are incorporated into larger, regional social systems. The same local institutions and relations, however, are replicated in each small town, suggesting that local and particular interests are expressed through regional institutions. Although focused on a few small towns in one region of the United States, this paper examines the local expression of processes which are global.     

A characterization of the efficiency of individualized logistic regressions

The use of individualized regressions, which reduces the polychotomous logistic regression model to several dichotomous models, has been proposed as a solution to some practical difficulties for binary covariates (Begg and Gray 1984, Biometrika, 71, 11–18). Its disadvantages, however, include loss of efficiency and the complexity of making comparisons among regressions. Using expressions for the large-sample distribution of the maximum-likelihood estimates, the efficiency of the individualized procedure relative to the polychotomous procedure is evaluated for the case in which the covariates are assumed to follow a multivariate normal distribution. The relative efficiency when the logistic slope vectors from different regressions are collinear can be substantially lower compared to the efficiency with orthogonal slope vectors. Further evaluations for binary covariates using collinear and orthogonal slope parametrizations lead to a similar characterization.     

Kyne–Donner Model of Authority’s Recommendation and Hurricane Evacuation Decisions: A Study of Hypothetical Hurricane Event in the Rio Grande Valley,Texas

Many previous studies identified factors influencing hurricane evacuation decisions by testing the protective action decision model (PADM). This study further examines factors that affect the trust in authority’s recommendation and evacuation decision-making in a proposed Kyne–Donner Model. The model provides an understanding of the predictive factors influencing evacuation decision-making through the mediating factor of trust in authority’s recommendation. This study takes advantage of the structural equation modeling method to simultaneously test multi-stages of the model. There are factors, namely, age, gender, education, household size, decision maker, risk area, house materials, hurricane evacuation experience, information seeking frequency, information seeking behavior, and information sources which influence trust in authority’s recommendation which, together with hurricane evacuation impediments, influence the hurricane evacuation decision. The study’s findings are consistent with the PADM and demonstrate the importance of trust in authority’s recommendation and hurricane evacuation decision-making.     

The design of a clinical trial when there are two categories of patients

Strategies are investigated for selecting one of two medical treatments when patients may be stratified into two distinct categories on the basis of their expected difference in response to the two treatments. The relative effectiveness of the following three strategies are assessed: (1) separate decisions made independently for the two categories, (2) a single overall decision made on the basis of simple pooling, and (3) the Bayes strategy.     

Misogyny: It’s Still the Law—An Empirical Assessment of the Missouri Juvenile Court System’s Processing of Rape and Robbery Offenders

Patriarchal societies have long used their legal systems as a vehicle of oppression. This article examines the extent to which bias against women can still be discerned in the content of the criminal law by comparing and contrasting Missouri??s forcible rape and robbery in the first degree statutes. The study then analyzes the application of these statutes by examining all of the forcible rape and robbery in the first degree cases processed by Missouri??s juvenile court system between January 1, 2001 and December 31, 2004 (N?=?617). The results of these analyses suggest that Missouri??s robbery statute is more protective of victims than is its rape statute. They also indicate that at least among juveniles, robbery offenders are sanctioned more severely than rape offenders in terms of detention, informal adjustment and adjudication.     

The design of a clinical trial with several patient categories

Various strategies are investigated for selecting one of two medical treatments when patients may be divided into k ≥ 2 categories on the basis of their expected differences in response to the two treatments. The strategies compared are (1) k independent decisions, (2) a single overall decision made on the basis of simple pooling, and (3) the Bayes strategy. The optimal clinical trial size is supplied for each strategy, and conditions delineated under which each of the strategies is to be preferred.     

Some aspects of the design and analysis of cluster randomization trials

Trials which randomize intact social groups, or clusters, to different interventions are becoming increasingly widespread. Although statistically less efficient than trials which randomize individuals, such designs are often preferred from a practical or ethical point of view, particularly in the evaluation of health care or educational strategies. We discuss selected issues that arise in the conduct of such trials, including the choice of design, ethical implications, sample size estimation and approaches to the analysis. The discussion is closely tied to methodological issues that have arisen in a recent evaluation trial of a new antenatal care programme, as sponsored by the Special Programme of Research, Development and Research Training in Human Reproduction of the World Health Organization.