Decomposing primary and secondary effects: A new decomposition method

One strand of educational inequality research aims at decomposing the effect of social class origin on educational choices into primary and secondary effects. We formalize this distinction and present a new and simple method that allows empirical assessment of the relative magnitudes of primary and secondary effects. Contrary to other decomposition methods, this new method is unbiased, is more intuitive, and decomposes effects of both discrete and continuous measures of social origin. The method also provides analytically derived statistical tests and is easily calculated with standard statistical software. We give examples using the Danish Longitudinal Survey of Youth.     

Latent Class Models in action: Bridging social capital & Internet usage

This paper explores how Latent Class Models (LCM) can be applied in social research, when the basic assumptions of regression models cannot be validated. We examine the usefulness of this method with data collected from a study on the relationship between bridging social capital and the Internet. Social capital is defined here as the resources that are potentially available in one’s social ties. Bridging is a dimension of social capital, usually related to weak ties (acquaintances), and a source of instrumental resources such as information. The study surveyed a stratified random sample of 417 inhabitants of Lisbon, Portugal. We used LCM to create the variable bridging social capital, but also to estimate the relationship between bridging social capital and Internet usage when we encountered convergence problems with the logistic regression analysis. We conclude by showing a positive relationship between bridging and Internet usage, and by discussing the potential of LCM for social science research.     

Reversible jump Markov chain Monte Carlo algorithms for Bayesian variable selection in logistic mixed models

In this article, to reduce computational load in performing Bayesian variable selection, we used a variant of reversible jump Markov chain Monte Carlo methods, and the Holmes and Held (HH) algorithm, to sample model index variables in logistic mixed models involving a large number of explanatory variables. Furthermore, we proposed a simple proposal distribution for model index variables, and used a simulation study and real example to compare the performance of the HH algorithm with our proposed and existing proposal distributions. The results show that the HH algorithm with our proposed proposal distribution is a computationally efficient and reliable selection method.     

Robust Designs in Generalized Linear Models: A Quantile Dispersion Graphs Approach

This article studies design selection for generalized linear models (GLMs) using the quantile dispersion graphs (QDGs) approach in the presence of misspecification in the link and/or linear predictor. The uncertainty in the linear predictor is represented by a unknown function and estimated using kriging. For addressing misspecified link functions, a generalized family of link functions is used. Numerical examples are shown to illustrate the proposed methodology.     

Robust models in probability sampling

In the estimation of a population mean or total from a random sample, certain methods based on linear models are known to be automatically design consistent, regardless of how well the underlying model describes the population. A sufficient condition is identified for this type of robustness to model failure; the condition, which we call 'internal bias calibration', relates to the combination of a model and the method used to fit it. Included among the internally bias-calibrated models, in addition to the aforementioned linear models, are certain canonical link generalized linear models and nonparametric regressions constructed from them by a particular style of local likelihood fitting. Other models can often be made robust by using a suboptimal fitting method. Thus the class of model-based, but design consistent, analyses is enlarged to include more realistic models for certain types of survey variable such as binary indicators and counts. Particular applications discussed are the estimation of the size of a population subdomain, as arises in tax auditing for example, and the estimation of a bootstrap tail probability.     

Local logisitic regression an application to army penetration data

There have been a number of procedures used to analyze non-monotonic binary data to predict the probability of response. Some classical procedures are the Up and Down strategy, the Robbins–Monro procedure, and other sequential optimization designs. Recently, nonparametric procedures such as kernel regression and local linear regression (llogr) have been applied to this type of data. It is a well known fact that kernel regression has problems fitting the data near the boundaries and a drawback with local linear regression is that it may be “too linear” when fitting data from a curvilinear function. The procedure introduced in this paper is called local logistic regression, which fits a logistic regression function at each of the data points. An example is given using United States Army projectile data that supports the use of local logistic regression when analyzing non-monotonic binary data for certain response curves. Properties of local logistic regression will be presented along with simulation results that indicate some of the strengths of the procedure.     

Calculating the power or sample size for the logistic and proportional hazards models

An algorithm is presented for calculating the power for the logistic and proportional hazards models in which some of the covariates are discrete and the remainders are multivariate normal. The mean and covariance matrix of the multivariate normal covariates may depend on the discrete covariates.

The algorithm, which finds the power of the Wald test, uses the result that the information matrix can be calculated using univariate numerical integration even when there are several continuous covariates. The algorithm is checked using simulation and in certain situations gives more accurate results than current methods which are based on simple formulae. The algorithm is used to explore properties of these models, in particular, the power gain from a prognostic covariate in the analysis of a clinical trial or observational study. The methods can be extended to determine power for other generalized linear models.     

Assessing the performance of variational methods for mixed logistic regression models

We present a variational estimation method for the mixed logistic regression model. The method is based on a lower bound approximation of the logistic function [Jaakkola, J.S. and Jordan, M.I., 2000, Bayesian parameter estimation via variational methods. Statistics & Computing, 10, 25–37.]. Based on the approximation, an EM algorithm can be derived that results in a considerable simplification of the maximization problem in that it does not require the numerical evaluation of integrals over the random effects. We assess the performance of the variational method for the mixed logistic regression model in a simulation study and an empirical data example, and compare it to Laplace's method. The results indicate that the variational method is a viable choice for estimating the fixed effects of the mixed logistic regression model under the condition that the number of outcomes within each cluster is sufficiently high.     

The social class of Catholics in Scotland

The social status of people brought up as Catholics in Scotland, as measured by their occupational class, is analysed by using cross-sectional survey data gathered in 1997. The main finding is that Catholics have probably risen in social status to a greater extent than non-Catholics. The experience of Scottish Catholics seems to be distinctive, because no such patterns are found for England, and indeed in this respect Scottish Catholics more closely resemble members of non-Christian religions in England than they do English Catholics. The most likely explanation is the particular role which state-funded Catholic schools have played in Scotland, especially the system of comprehensive secondary schools that was set up after 1965. However, the analysis is suggestive rather than definitive and needs to be replicated on cohort data with larger sample sizes.     

A new mixture model for capture heterogeneity

Summary.  We propose a mixture of binomial and beta–binomial distributions for estimating the size of closed populations. The new mixture model is applied to several real capture–recapture data sets and is shown to provide a convenient, objective framework for model selection. The new model is compared with three alternative models in a simulation study, and the results shed light on the general performance of models in this area. The new model provides a robust flexible analysis, which automatically deals with small capture probabilities.