On the Use of a Log-Rate Model for Survey-Weighted Categorical Data

For the analysis of survey-weighted categorical data, one recommended method of analysis is a log-rate model. For each cell in a contingency table, the survey weights are averaged across subjects and incorporated into an offset for a loglinear model. Supposedly, one can then proceed with the analysis of unweighted observed cell counts. We provide theoretical and simulation-based evidence to show that the log-rate analysis is not an effective statistical analysis method and should not be used in general. The root of the problem is in its failure to properly account for variability in the individual weights within cells of a contingency table. This results in goodness-of-fit tests that have higher-than-nominal error rates and confidence intervals for odds ratios that have lower-than-nominal coverage.     

The firm and managerial misdirection of worker effort

This article models how a level of management between workers and the owner of a firm can affect the owner's decision either to internally integrate a function to make inputs or to contract out to buy inputs from an independent supplier. In the model, a self-serving manager can direct her workers to perform activities that serve her interests rather than those of the firm. This reduces the effectiveness of worker performance incentives intended to promote efforts that benefit the owner. Incentives may have to be increased to a level such that the owner prefers to buy inputs rather than make them internally.     

Market stability: backward-bending supply in a laboratory experimental market. 1999 Presidential address Western Economic Association

This article investigates the stability properties of markets with backward-bending supply curves. Parameters are chosen so that the two classic models of price dynamics, the Walrasian model and the Marshallian model, give opposite predictions. The results are (1) market instability can be observed, and (2) in the backward-bending case stability is captured by the Walrasian model and the Marshallian model of dynamics is rejected. Previous experiments have demonstrated that the Marshallian model works in the forward-falling case. Thus, which theory of dynamics is appropriate for a market depends on the underlying reasons for demand and supply shapes.     

Modeling Association Between Two or More Categorical Variables that Allow for Multiple Category Choices

Multiple-response (or pick any/c) categorical variables summarize responses to survey questions that ask “pick any” from a set of item responses. Extensions to loglinear model methodology are proposed to model associations between these variables across all their items simultaneously. Because individual item responses to a multiple-response categorical variable are likely to be correlated, the usual chi-square distributional approximations for model-comparison statistics are not appropriate. Adjusted statistics and a new bootstrap procedure are developed to facilitate distributional approximations. Odds ratio and standardized Pearson residual measures are also developed to estimate specific associations and examine deviations from a specified model.     

The relationship between organizational factors and resident satisfaction with nursing home care and life

We examined the relationships between nursing home (NH) resident satisfaction and NH organizational characteristics, while controlling for the effect of resident characteristics within facilities. We used a stratified, random sample of NHs (N = 72) from two states and a prescreened and randomized sample of 1496 residents. Data sources included resident interviews, an administrator survey, the Minimum Data Set (MDS), and the Online Survey, Certification and Reporting System (OSCAR). Using Hierarchical Linear Modeling (HLM) techniques, we found that non-chain affiliation, certified nursing assistant staffing, and provision of a family council had significant positive effects on total resident satisfaction. The presence of a special care unit was associated with lower levels of satisfaction.     

Modeling multiple‐response categorical data from complex surveys

Although “choose all that apply” questions are common in modern surveys, methods for analyzing associations among responses to such questions have only recently been developed. These methods are generally valid only for simple random sampling, but these types of questions often appear in surveys conducted under more complex sampling plans. The purpose of this article is to provide statistical analysis methods that can be applied to “choose all that apply” questions in complex survey sampling situations. Loglinear models are developed to incorporate the multiple responses inherent in these types of questions. Statistics to compare models and to measure association are proposed and their asymptotic distributions are derived. Monte Carlo simulations show that tests based on adjusted Pearson statistics generally hold their correct size when comparing models. These simulations also show that confidence intervals for odds ratios estimated from loglinear models have good coverage properties, while being shorter than those constructed using empirical estimates. Furthermore, the methods are shown to be applicable to more general problems of modeling associations between elements of two or more binary vectors. The proposed analysis methods are applied to data from the National Health and Nutrition Examination Survey. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

Informative Retesting

In situations where individuals are screened for an infectious disease or other binary characteristic and where resources for testing are limited, group testing can offer substantial benefits. Group testing, where subjects are tested in groups (pools) initially, has been successfully applied to problems in blood bank screening, public health, drug discovery, genetics, and many other areas. In these applications, often the goal is to identify each individual as positive or negative using initial group tests and subsequent retests of individuals within positive groups. Many group testing identification procedures have been proposed; however, the vast majority of them fail to incorporate heterogeneity among the individuals being screened. In this paper, we present a new approach to identify positive individuals when covariate information is available on each. This covariate information is used to structure how retesting is implemented within positive groups; therefore, we call this new approach "informative retesting." We derive closed-form expressions and implementation algorithms for the probability mass functions for the number of tests needed to decode positive groups. These informative retesting procedures are illustrated through a number of examples and are applied to chlamydia and gonorrhea testing in Nebraska for the Infertility Prevention Project. Overall, our work shows compelling evidence that informative retesting can dramatically decrease the number of tests while providing accuracy similar to established non-informative retesting procedures.     

Multiple Marginal Independence Testing for Pick Any/C Variables

Many survey questions allow respondents to pick any number out of c possible categorical responses or “items”. These kinds of survey questions often use the terminology “choose all that apply” or “pick any”. Often of interest is determining if the marginal response distributions of each item differ among r different groups of respondents. Agresti and Liu (1998, 1999) call this a test for multiple marginal independence (MMI). If respondents are allowed to pick only 1 out of c responses, the hypothesis test may be performed using the Pearson chi-square test of independence. However, since respondents may pick more or less than 1 response, the test's assumptions that responses are made independently of each other is violated. Recently, a few MMI testing methods have been proposed. Loughin and Scherer (1998) propose using a bootstrap method based on a modified version of the Pearson chi-square test statistic. Agresti and Liu (1998, 1999) propose using marginal logit models, quasisymmetric loglinear models, and a few methods based on Pearson chi-square test statistics. Decady and Thomas (1999) propose using a Rao-Scott adjusted chi-squared test statistic. There has not been a full investigation of these MMI testing methods. The purpose here is to evaluate the proposed methods and propose a few new methods. Recommendations are given to guide the practitioner in choosing which MMI testing methods to use.     

Balance of care—a user's view of a new approach to joint strategic planning

Planning for care of the Elderly has to face the problems of an increasing elderly population; a wide range of alternative ways of caring for them (at widely differing costs); the fact that services are provided by several different organisations all facing difficult financial constraints; a range of professional opinion about the desirability or otherwise of alternative patterns of care and use of resources; a lack of data on how care is at present distributed; the lack of a structure for organising such data as are available; and the lack of an appropriate computer-based model for manipulating the large number of data elements necessary to describe and help to evaluate alternative plans for the future. The Balance of Care approach to the Joint Strategic Planning of Health and Social Services provision for the Elderly, is being used in pilot applications in two Areas in the UK. Its contribution to the solution of the problems outlined above is described by authors from the two Areas. The approach and the underlying model can be extended to strategic planning for other client groups requiring non-acute care.