A STRATEGY FOR INTEGRATING QUANTITATIVE TECHNIQUES INTO THE BUSINESS CURRICULUM*

Quantitative methods courses play an increasingly significant role in the programs of Schools of Business. However, maximum utilization of the concepts can occur only when these quantitative techniques have been integrated into the various functional areas via a faculty knowledgeable with such techniques and their applications. Lacking sufficient stimuli, this integrative process is observed to be one of an evolutionary nature. This article presents a strategy for stimulation of this process.     

Estimation of the Force of Infection from Current Status Data Using Generalized Linear Mixed Models

Based on sero-prevalence data of rubella, mumps in the UK and varicella in Belgium, we show how the force of infection, the age-specific rate at which susceptible individuals contract infection, can be estimated using generalized linear mixed models (McCulloch & Searle, 2001). Modelling the dependency of the force of infection on age by penalized splines, which involve fixed and random effects, allows us to use generalized linear mixed models techniques to estimate both the cumulative probability of being infected before a given age and the force of infection. Moreover, these models permit an automatic selection of the smoothing parameter. The smoothness of the estimated force of infection can be influenced by the number of knots and the degree of the penalized spline used. To determine these, a different number of knots and different degrees are used and the results are compared to establish this sensitivity. Simulations with a different number of knots and polynomial spline bases of different degrees suggest - for estimating the force of infection from serological data - the use of a quadratic penalized spline based on about 10 knots.     

Non-parametric Estimation of the Residual Distribution

Consider a heteroscedastic regression model Y = m ( X ) +σ( X )ε, where the functions m and σ are smooth, and ε is independent of X . An estimator of the distribution of ε based on non-parametric regression residuals is proposed and its weak convergence is obtained. Applications to prediction intervals and goodness-of-fit tests are discussed.     

Percentile Related Bounds and Estimator for the Mean of the Negative Binomial Distribution

Upper and lower bounds are obtained for the mean of the negative binomial distribution. These bounds are simple functions of a percentile determined by the shape parameter. The result is then used to obtain a robust estimate of the mean when the shape parameter is known.     

A Bivariate Generalization of Gamma Distribution

In this article, a bivariate generalisation of the gamma distribution is proposed by using an unsymmetrical bivariate characteristic function; an extension to the non central case also receives attention. The probability density functions of the product and ratio of the correlated components of this distribution are also derived. The benefits of introducing this generalized bivariate gamma distribution and the distributions of the product and the ratio of its components will be demonstrated by graphical representations of their density functions. An example of this generalized bivariate gamma distribution to rainfall data for two specific districts in the North West province is also given to illustrate the greater versatility of the new distribution.     

Diagnostic checks for discrete data regression models using posterior predictive simulations

Model checking with discrete data regressions can be difficult because the usual methods such as residual plots have complicated reference distributions that depend on the parameters in the model. Posterior predictive checks have been proposed as a Bayesian way to average the results of goodness-of-fit tests in the presence of uncertainty in estimation of the parameters. We try this approach using a variety of discrepancy variables for generalized linear models fitted to a historical data set on behavioural learning. We then discuss the general applicability of our findings in the context of a recent applied example on which we have worked. We find that the following discrepancy variables work well, in the sense of being easy to interpret and sensitive to important model failures: structured displays of the entire data set, general discrepancy variables based on plots of binned or smoothed residuals versus predictors and specific discrepancy variables created on the basis of the particular concerns arising in an application. Plots of binned residuals are especially easy to use because their predictive distributions under the model are sufficiently simple that model checks can often be made implicitly. The following discrepancy variables did not work well: scatterplots of latent residuals defined from an underlying continuous model and quantile–quantile plots of these residuals.     

Underestimating busyness: Indications of nonresponse bias due to work-family conflict and time pressure

International research shows that both work-family conflict and time pressure are increasing in Western societies. With these increased pressures, precisely those people who are combining work and family obligations may be missing from survey estimates. This study investigates whether the measurement of work-family conflict (WFC) and time pressure is influenced by nonresponse bias. Using the Flemish “Work, Family and Time use in Flanders”-survey and the Basic Question survey for nonrespondents of this survey, we investigate whether nonrespondents score higher on subjective and objective indicators of WFC and time pressure than respondents. Results show that nonrespondents are indeed those sample units who experience significantly more WFC and time pressure, demonstrating that WFC and time pressure related nonresponse biases exist. Implications and suggestions to reduce bias in data collections are discussed.     

Income inequality and participation: A comparison of 24 European countries

Previous research suggests that when there is a high level of inequality, there is a low rate of participation. Two arguments are generally offered: First, inequality depresses participation because people from different status groups have fewer opportunities to share common goals. Second, people may participate more in civic and social life when they have more resources. However, until now, these explanations have not been separated empirically. Using EU-SILC data for 24 European countries, we analyze how income inequality is related to civic and social participation. Our results indicate that the main effects of inequality manifest via resources at the individual and societal level. However, independent of these resources, higher inequality is associated with lower civic participation. Furthermore, inequality magnifies the relationship between income and participation. This finding is in line with the view that inter-individual processes explain why inequality diminishes participation.