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An easily accessible introduction to log-linear modeling for non-statisticians Highlighting advances that have lent to the topic's distinct, coherent methodology over the past decade, Log-Linear Modeling: Concepts, Interpretation, and Application provides an essential, introductory treatment of the subject, featuring many new and advanced log-linear methods, models, and applications. The book begins with basic coverage of categorical data, and goes on to describe the basics of hierarchical log-linear models as well as decomposing effects in cross-classifications and goodness-of-fit tests. Additional topics include: The generalized linear model (GLM) along with popular methods of coding such as effect coding and dummy coding Parameter interpretation and how to ensure that the parameters reflect the hypotheses being studied Symmetry, rater agreement, homogeneity of association, logistic regression, and reduced designs models Throughout the book, real-world data illustrate the application of models and understanding of the related results. In addition, each chapter utilizes R, SYSTAT®, and ¤EM software, providing readers with an understanding of these programs in the context of hierarchical log-linear modeling. Log-Linear Modeling is an excellent book for courses on categorical data analysis at the upper-undergraduate and graduate levels. It also serves as an excellent reference for applied researchers in virtually any area of study, from medicine and statistics to the social sciences, who analyze empirical data in their everyday work.

Patterns in, and the underlying dynamics of, species co‐occurrence is of interest in many ecological applications. Unaccounted for, imperfect detection of the species can lead to misleading inferences about the nature and magnitude of any interaction. A range of different parameterizations have been published that could be used with the same fundamental modeling framework that accounts for imperfect detection, although each parameterization has different advantages and disadvantages. We propose a parameterization based on log‐linear modeling that does not require a species hierarchy to be defined (in terms of dominance) and enables a numerically robust approach for estimating covariate effects. Conceptually, the parameterization is equivalent to using the presence of species in the current, or a previous, time period as predictor variables for the current occurrence of other species. This leads to natural, “symmetric,” interpretations of parameter estimates. The parameterization can be applied to many species, in either a maximum likelihood or Bayesian estimation framework. We illustrate the method using camera‐trapping data collected on three mesocarnivore species in South Texas.

A general methodology is introduced for the construction and effective application of control variates to estimation problems involving data from reversible Markov chain Monte Carlo samplers. We propose the use of a specific class of functions as control variates, and we introduce a new consistent estimator for the values of the coefficients of the optimal linear combination of these functions. For a specific Markov chain Monte Carlo scenario, the form and proposed construction of the control variates is shown to provide an exact solution of the associated Poisson equation. This implies that the estimation variance in this case (in the central limit theorem regime) is exactly zero. The new estimator is derived from a novel, finite dimensional, explicit representation for the optimal coefficients. The resulting variance reduction methodology is primarily (though certainly not exclusively) applicable when the simulated data are generated by a random‐scan Gibbs sampler. Markov chain Monte Carlo examples of Bayesian inference problems demonstrate that the corresponding reduction in the estimation variance is significant, and that in some cases it can be quite dramatic. Extensions of this methodology are discussed and simulation examples are presented illustrating the utility of the methods proposed. All methodological and asymptotic arguments are rigorously justified under essentially minimal conditions.

Financial markets are ultimately seen as a collection of dyadic transactions. We study the temporal evolution of dyadic relationships in the European interbank market, as induced by monetary transactions registered in the electronic market for interbank deposits (e-MID) during a period of 10 years (2006–2015). In particular, we keep track of how reciprocal exchange patterns have varied with macro events and exogenous shocks and with the emergence of the Global Financial Crisis in 2008. The approach adopted extends the model of Holland and Leinhardt to a longitudinal setting where individuals' temporal trajectories for the tendency to connect and reciprocate transactions are explicitly modelled through splines or polynomials, and individual-specific parameters. We estimate the model by an iterative algorithm that maximizes the log-likelihood for every ordered pair of units. The empirical application shows that the methodology proposed may be applied to large networks and represents the process of exchange at a fine-grained level. Further results are available in on-line supplementary material.

Background Surveying regional cancer incidence and mortality provides significant data that can assist in making health policy for local areas; however, the province‐ and region‐based cancer burden in China is seldom reported. In this study, we estimated cancer incidence and mortality in Guangdong Province, China and presented basic information for making policies related to health resource allocation and disease control. Methods A log‐linear model was used to calculate the sex‐, age‐, and registry‐specific ratios of incidence to mortality (I/M) based on cancer registry data from Guangzhou, Zhongshan, and Sihui between 2004 and 2008. The cancer incidences in 2009 were then estimated according to representative I/M ratios and the mortality records from eight death surveillance sites in Guangdong Province. The cancer incidences in each city were estimated by the corresponding sex‐ and age‐specific incidences from cancer registries or death surveillance sites in each area. Finally, the total and region‐based cancer incidences and mortalities for the entire population of Guangdong Province were summarized. Results The estimated I/M ratios in Guangzhou (3.658), Zhongshan (2.153), and Sihui (1.527) were significantly different (P < 0.001), with an average I/M ratio of 2.446. Significant differences in the estimated I/M ratios were observed between distinct age groups and the three cancer registries. The estimated I/M ratio in females was significantly higher than that in males (2.864 vs. 2.027, P < 0.001). It was estimated that there were 163,376 new cancer cases (99,689 males and 63,687 females) in 2009; it was further estimated that 115,049 people (75,054 males and 39,995 females) died from cancer in Guangdong Province in 2009. The estimated crude and age‐standardized rate of incidences (ASRI) in Guangdong Province were 231.34 and 246.87 per 100,000 males, respectively, and 156.98 and 163.57 per 100,000 females, respectively. The estimated crude and age‐standardized rate of mortalities (ASRM) in Guangdong Province were 174.17 and 187.46 per 100,000 males, respectively, and 98.59 and 102.00 per 100,000 females, respectively. In comparison with the western area and the northern mountain area, higher ASRI and ASRM were recorded in the Pearl River Delta area and the eastern area in both males and females. Conclusions Cancer imposes a heavy disease burden, and cancer patterns are unevenly distributed throughout Guangdong Province. More health resources should be allocated to cancer control, especially in the western and northern mountain areas.

It has previously been shown that, across three British birth cohorts, relative rates of intergenerational social class mobility have remained at an essentially constant level among men and also among women who have worked only full time. We establish the pattern of this prevailing level of social fluidity and its sources and determine whether it also persists over time, and we bring out its implications for inequalities in relative mobility chances. We develop a parsimonious model for the log-odds-ratios which express the associations between individuals' class origins and destinations. This model is derived from a topological model that comprises three kinds of readily interprétable binary characteristics and eight effects in all, each of which does, or does not, apply to particular cells of the mobility table, i.e. effects of class hierarchy, class inheritance and status affinity. Results show that the pattern as well as the level of social fluidity are essentially unchanged across the cohorts, that gender differences in this prevailing pattern are limited and that marked differences in the degree of inequality in relative mobility chances arise with long-range transitions where inheritance effects are reinforced by hierarchy effects that are not offset by status affinity effects.

N-mixture models describe count data replicated in time and across sites in terms of abundance N and detectability p. They are popular because they allow inference about N while controlling for factors that influence p without the need for marking animals. Using a capture-recapture perspective, we show that the loss of information that results from not marking animals is critical, making reliable statistical modeling of N and p problematic using just count data. One cannot reliably fit a model in which the detection probabilities are distinct among repeat visits as this model is overspecified. This makes uncontrolled variation in p problematic. By counter example, we show that even if p is constant after adjusting for covariate effects (the \"constant p\" assumption) scientifically plausible alternative models in which N (or its expectation) is non-identifiable or does not even exist as a parameter, lead to data that are practically indistinguishable from data generated under an N-mixture model. This is particularly the case for sparse data as is commonly seen in applications. We conclude that under the constant p assumption reliable inference is only possible for relative abundance in the absence of questionable and/or untestable assumptions or with better quality data than seen in typical applications. Relative abundance models for counts can be readily fitted using Poisson regression in standard software such as R and are sufficiently flexible to allow controlling for p through the use covariates while simultaneously modeling variation in relative abundance. If users require estimates of absolute abundance, they should collect auxiliary data that help with estimation of p.

Statistical analyses of health programme participation seek to address a number of objectives that are compatible with the evaluation of demand for current resources. In this spirit, a spatial hierarchical model is developed for disentangling patterns in participation at the small area level, as a function of population-based demand and additional variation. For the former, a constrained gravity model is proposed to quantify factors associated with spatial choice and to account for competition effects, for programmes delivered by multiple clinics. The implications of gravity model misspecification within a mixed effects framework are also explored. The model proposed is applied to participation data from a no-fee mammography programme in Brisbane, Australia. Attention is paid to the interpretation of various model outputs and their relevance for public health policy.

Injecting drug users (IDUs) have a direct social and economic effect yet can typically be regarded as a hidden population within a community. We estimate the size of the IDU population across the nine different Government Office regions of England in 2005-2006 by using capture—recapture methods with age (ranging from 15 to 64 years) and gender as covariate information. We consider a Bayesian model averaging approach using log-linear models, where we can include explicit prior information within the analysis in relation to the total IDU population (elicited from the number of drug-related deaths and injectors' drug-related death rates). Estimation at the regional level allows for regional heterogeneity with these regional estimates aggregated to obtain a posterior mean estimate for the number of England's IDUs of 195840 with 95% credible interval (181700, 210480). There is significant variation in the estimated regional prevalence of current IDUs per million of population aged 15–64 years, and in injecting drug-related death rates across the gender x age cross-classifications. The propensity of an IDU to be seen by at least one source also exhibits strong regional variability with London having the lowest propensity of being observed (posterior mean probability 0.21) and the South West the highest propensity (posterior mean 0.46).

1. Butterflies are one of the few insect groups that can be monitored effectively and have the potential to develop national and Europe-wide trends in abundance. 2. For 20 widespread butterfly species, we assess the relative efficiency of reduced-effort schemes compared to the existing design and estimate the number of sites required to detect changes of given magnitudes over specified periods of time. 3. A scheme restricted to three counts during July and August requires twice as many monitored sites on average to achieve comparable precision to the existing 26-week scheme in the United Kingdom. Such a scheme requires 430 monitoring sites on average to achieve 80% power (5% significance level) for detecting a 25% decline in abundance over 10 years. 4. Such a reduced-effort scheme may also mean that volunteers are more willing to record in areas where they are likely to see only a few individuals of a few common species (such as on intensively farmed areas). This could potentially help to ensure that butterfly monitoring schemes achieve a more even geographical coverage and less of a bias towards areas rich in butterflies. 5. Synthesis and applications. Schemes with few sampling visits per year are cost-effective for expanding butterfly monitoring across Europe, and can be applied to national monitoring programmes and lead to effective assessment of continent-wide trends in populations.