Log-linear Models For Contingency Tables Research Articles

Extension of generalized Poisson log-linear regression models for analysing three-way contingency table: Application to malaria data

This study presents the extension of generalized Poisson (GP-1 and GP-2) models for three-way contingency table. We assume a mixed systematic component of the log-linear models for contingency tables to produce a linear transformation for the link function of Generalized Linear Models (GLMs). Maximum likelihood estimation method was derived for the parameters estimates of the models. An over-dispersed malaria data of 2019 was considered for the study. The GP-1 and GP-2 models for three-way contingency table was used to model the data. Based on Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) goodness-of-fits measures, the GP-2 model outperformed the GP-1 model for three-way contingency table on malaria data. We found that some parameters of the full model were statistically significant as; malaria cases was sensitive to all ages considered in the study, and people were more infected with malaria in the month of April, June, and July 2019.

Education and Social Fluidity: A Reweighting Approach

Although sociologists have devoted considerable attention to studying the role of education in intergenerational social class mobility using log-linear models for contingency tables, indings in this literature are not free from rescaling or non-collapsibility bias caused by adjusting for education in these models. Drawing on the methodological literature on inverse probability reweighting, I present a straightforward standardization approach free from this bias. The approach reweighs in an initial step the mobility table cell frequencies to create a pseudo-population in which social class origins and education are independent of each other, after which one can apply any loglinear model to the reweighted mobility table. In contrast to the Karlson-Holm-Breen method, the approach yields coefficients that are comparable across different studies because they are unaffected by education's predictive power of class destinations. Moreover, the approach is easily applied to models for various types of mobility patterns such as those in the core model of fluidity; it yields a single summary measure of overall mediation; and it can incorporate several mediating variables, allowing researchers to control for additional merit proxies such as cognitive skills or potential confounders such as age. I illustrate the utility of the approach in four empirical examples.

Asymptotic cumulants of the minimum phi-divergence estimator for categorical data under possible model misspecification

The asymptotic cumulants of the minimum phi-divergence estimators of the parameters in a model for categorical data are obtained up to the fourth order with the higher-order asymptotic variance under possible model misspecification. The corresponding asymptotic cumulants up to the third order for the studentized minimum phi-divergence estimator are also derived. These asymptotic cumulants, when a model is misspecified, depend on the form of the phi-divergence. Numerical illustrations with simulations are given for typical cases of the phi-divergence, where the maximum likelihood estimator does not necessarily give best results. Real data examples are shown using log-linear models for contingency tables.

Lasso Regularization for Selection of Log-linear Models: An Application to Educational Assortative Mating

Log-linear models for contingency tables are a key tool for the study of categorical inequalities in sociology. However, the conventional approach to model selection and specification suffers from at least two limitations: reliance on oftentimes equivocal diagnostics yielded by fit statistics, and the inability to identify patterns of association not covered by model candidates. In this article, we propose an application of Lasso regularization that addresses the aforementioned limitations. We evaluate our method through a Monte Carlo experiment and an empirical study of educational assortative mating in Chile, 1990–2015. Results demonstrate that our approach has the virtue, relative to ad hoc specification searches, of offering a principled statistical criterion to inductively select a model. Importantly, we show that in situations where conventional fit statistics provide conflicting diagnostics, our Lasso-based approach is consistent in its model choice, yielding solutions that are both predictive and parsimonious.

Bias-corrected estimation of the Rudas-Clogg-Lindsay mixture index of fit.

Rudas, Clogg, and Lindsay (1994, J. R Stat Soc. Ser. B, 56, 623) introduced the so-called mixture index of fit, also known as pi-star (π*), for quantifying the goodness of fit of a model. It is the lowest proportion of 'contamination' which, if removed from the population or from the sample, makes the fit of the model perfect. The mixture index of fit has been widely used in psychometric studies. We show that the asymptotic confidence limits proposed by Rudas etal. (1994, J. R Stat Soc. Ser. B, 56, 623) as well as the jackknife confidence interval by Dayton (, Br. J. Math. Stat. Psychol., 56, 1) perform poorly, and propose a new bias-corrected point estimate, a bootstrap test and confidence limits for pi-star. The proposed confidence limits have coverage probability much closer to the nominal level than the other methods do. We illustrate the usefulness of the proposed method in practice by presenting some practical applications to log-linear models for contingency tables.

Graphical log-linear models: fundamental concepts and applications

A comprehensive study of graphical log-linear models for contingency tables is presented. High-dimensional contingency tables arise in many areas. Analysis of contingency tables involving several factors or categorical variables is very hard. To determine interactions among various factors, graphical and decomposable log-linear models are preferred. Connections between the conditional independence in probability and graphs are explored, followed with illustrations to describe how graphical log-linear model are useful to interpret the conditional independences between factors. The problem of estimation and model selection in decomposable models is discussed.

Remittances in Albania in the Frame Work of South-Eastern European Countries and Crises Gripped European Union Members

Our study aims at defining the reasons of a downward trend of remittances in Albania lately. We mainly adopted the method of the questionnaire to study such a topic. Our questionnaire covers Albanian migrants in Greece and Italy. The analyses of the data provided by our questionnaire defines such factors influencing the level of the remittances: - The economic crises i.e. the economic situation in the host country; - Job insecurity and wage lowering; - Living cost increase as well as rising costs of children’s education; - Family reunion; - Weaker links of the migrants and his family members in Albania. Our study attempts that using rather simple methods to rank the factors influencing the money flow of the remittances based on their importance. There is quite a host of methods to analyze the main factors yet we adopted one of the simplest methods that of the contingences tables and Log-Linear Models for Contingency Tables as the data offered by the questionnaire are subjective ones and not so massive, too. The data on the money flow of the remittances are rather few and unstable ones thus all the predictions based on all other methods offer similar results. We stress the fact that it is beyond any doubt that the remittances follow a downward trend every year. Judging by the models there is a very law probability to this series that it changes its trend (i.e.it increases). The main factors influencing the flow of the remittances to Albania are the economic crises and the family reunion. DOI: 10.5901/ajis.2015.v4n2s1p193

Split variable selection for tree modeling on rank data

A variable selection method for constructing decision trees with rank data is proposed. It utilizes conditional independence tests based on loglinear models for contingency tables. Compared with other selection methods, our method is computationally more efficient. Moreover, our method is relatively unbiased and powerful in selecting the correct split variables. Simulation results and a real data study are given to demonstrate the strength of our method.

An Introduction to Categorical Data Analysis (second edition) Alan Agresti (2007) ISBN: 9780471226185; 372 pages; £50.30, $94.9, €66.40 Wiley; http://www.wiley.com/

This second edition is pitched at a level suitable for those taking an introductory course in categorical data analysis. The presentation has a low technical level and does not require familiarity with advanced mathematics. However, the author comments that as well as students it is also written for applied statisticians and practising scientists involved in data analysis. The high quality of the book can be judged from the fact that all of these are likely to find the book irreplaceable as a standard text on the subject. The author expresses a preference for logistic regression over log linear models because most applications have a single binomial or multinomial response variable. Therefore, this new edition places greater emphasis on logistic regression and less on log linear models compared with the first edition. From a pharmaceutical perspective this looks to be a good change in emphasis. The other main change from the first edition is the addition of two chapters. The new Chapter 9 covers the analysis of clustered correlated categorical data introducing marginal models and generalized estimating equations. Chapter 10 focuses on random effects and generalized linear mixed models. The content is arranged in 11 chapters as follows: Introduction; Contingency Tables; Generalized Linear Models; Logistic Regression; Building and Applying Logistic Regression Models; Multicategory Logit Models; Loglinear Models for Contingency Tables; Models for Matched Pairs; Modelling Correlated, Clustered Responses; Random Effects: Generalized Linear Mixed Models; A Historical Tour of Categorical Data Analysis. Each chapter ends with a problem section that will enable the reader to work on further examples and idiosyncratically some of the odd-numbered examples have solutions at the back of the book. An Appendix giving the SAS code for some of the examples is also included as well as a link to other software packages if SAS is not your software of choice. There are so many excellent features of this book that it is hard to know where to start. First of all the range of techniques covered is impressive. The practising statistician or scientist is likely to find all he or she needs to know day to day about categorical data analysis in this one book. Next the clarity of the exposition is superb; particularly so because the book avoids heavy mathematical development in favour of well-written English. The slow transition from basic concepts in the early chapters to the later more complex methods is handled very well and it encourages the reader to explore less familiar analysis techniques. The author also takes care to point out when methods may not be optimum due to small sample sizes or sparse cells. It is good to see the consistent focus on estimation, interpretation and understanding alongside statistical inference. Some useful guidance is given on the use of statistical software to implement the methods. The range of examples is very broad, covering data sets such as collisions involving British trains, width of female crab shells, AZT and Aids, teratology in rats and many, many more. An index of examples is provided, which covers more than three pages – showing how strongly the text is based on real data sets. All are well chosen and interesting and do an excellent job illustrating the range of analysis techniques discussed. This book has to be an essential reference for any practising pharmaceutical statistician. Is it needed alongside Alan Agresti's other superb book Categorical Data Analysis (Second Edition 2002)? I think so. The latter is more complete in terms of technical development and covers a broader range of topics. However, for me An Introduction to Categorical Data Analysis is the first volume to refer to when guidance is needed. It will also be a useful source of ideas to explain the essence of categorical data analyses to non-statisticians. Non-statisticians may well find the whole book too challenging but they will learn much from the early chapters, which are easy to follow and cover many of the important ideas in categorical data analysis.

Categorical data analysis with SAS and SPSS applications

Contents: Preface. Introduction. Probability Models. One-Way Classification. Models for 2 x 2 Contingency Tables. The General I x J Contingency Table. Log-Linear Models for Contingency Tables. Strategies for Log-Linear Model Selection. Models for Binary Responses. Logit and Multinomial Response Models. Models in Ordinary Contingency Tables. Analysis of Doubly Classified Data. Analysis of Repeated Measures Data. Appendices.

Stepping and kicking behaviour during milking in relation to response in human–animal interaction test and clinical health in loose housed dairy cows

Associations between kicking and stepping behaviour during milking and response to humans, getting up behaviour as well as clinical health status in loose housed dairy cows were investigated. During a 12-month period behavioural and clinical data from 10 commercial Danish dairy herds were collected including in total 1196 individual cows. Hierarchical log-linear models for contingency tables were applied for an analysis of conditional associations among the included parameters. Results showed a general herd effect on occurrence of stepping and kicking behaviour during milking ( P<0.001). In general, stepping during milking was associated positively to daily milk yield ( P<0.05). However, low yielding cows showing avoidance behaviour at the clinical examination were also more likely to step during milking. Furthermore, stepping during milking was positively associated to avoidance in a human approach test ( P<0.001) as well as occurrence of ticks ( P<0.05), and cows with tick lesions that further avoided human approach were most likely to step during milking. Cows with teat lesions were more likely to kick during milking ( P<0.001), especially if they did not avoid human approach. The analysis showed no relation between lameness and kicking or stepping behaviour during milking.

Associations between lying-down behaviour problems and body condition, limb disorders and skin lesions of lactating sows housed in farrowing crates in commercial sow herds

Health problems, difficulties in lying down and skin lesions are relevant indicators of poor welfare in sows confined in farrowing crates. This study investigated limb disorders, injuries, body condition and lying-down behaviour in 10 commercial sow herds. Five hundred seventy lactating sows were examined clinically, and 555 sows were further observed when lying down. Forty-one percent of the sows showed some difficulties in lying down and 15% were lame. Skin lesions were most frequently observed on lateral hind feet or shoulders, each in approximately 20% of the sows. The data were analysed for conditional associations among the parameters applying hierarchical log-linear models for contingency tables. Slipping and interruptions while lying down were associated ( P<0.05), but other difficulties in lying down were conditionally independent within the herd. Shoulder wounds were more common in thin or lame sows (odds ratio 5.5 and 2.5, respectively), and lameness was further related to hock lesions (OR 11.9, severely lame sows), hind feet lesions (OR 2.5–4.3 depending on the severity of lameness) and uncontrolled lying-down behaviour (OR 1.8–5.8). Fat sows were more likely to show stepping behaviour when lying down (OR 2.7), slipping was associated with hind feet lesions (OR 2.2) and overgrown hooves were associated with abnormal lying-down behaviour (OR 11.5). The specific difficulties in lying down may provide relevant support for the clinical findings.

Analysis of discrete data: Rerandomization methods and complexity

Analysis of discrete data, and especially contingency table data, plays a central role in biostatistics. Traditional methods rely on approximations based on asymptotic results which are very powerful but not always appropriate. In this article we show that efficient rerandomization methods may be developed for many commonly used models and tests: multinomial testing, specifically goodness-of-fit and max tests; and goodness-of-fit of log-linear models for contingency tables. The feasibility (complexity) of these algorithms is a function of the sufficient statistics for the models. By contrast, algorithms which require the explicit enumeration of all outcomes in the sample space are exponential in the degrees of freedom, and are usually not feasible except when sample sizes are unrealistically small. The algorithms we present are different from recently proposed methods since we show how to calculate permutation distributions of commonly used statistics rather than calculating p-values for exact tests, and we emphasize underlying probability formulas rather than implementation details.

Log-Linear Models

This book examines log-linear models for contingency tables. It uses previous knowledge of analysis of variance and regression to motivate and explicate the use of log-linear models. It is a textbook primarily directed at advanced Masters degree students in statistics but can be used at both higher and lower levels. Outlines for introductory, intermediate and advanced courses are given in the preface. All the fundamental statistics for analyzing data using log-linear models are given.

A modified iterative proportional scaling algorithm for estimation in regular exponential families

An algorithm for maximum likehood estimation in regular exponential families is proposed. The algorithm is a modification of the well-known iterative proportional scaling algorithm used for estimating loglinear models for contingency tables. As illustration, the algorithm is applied to an example from the class of graphical association models (Lauritzen and Wermuth, 1989).

A criterion for selecting log-linear models for contingency tables

A new discrepancy, the Gauss discrepancy of the logarithms of frequencies, is introduced for the selection of log-linear models for contingency tables. Under the assumption of Poisson sampling the loglinear model becomes orthogonal for this discrepancy: the model selection criterion is the sum of the contributions (to the criterion) of the effects in the model. It is, therefore, sufficient for model selection to compute the contributions of the effects in the saturated model. The selected model contains then all effects with negative contributions. It is not necessary to recompute the value of the criterion for all possible models. Two examples are given.

PRU Measures of Association for Contingency Table Analysis

This paper introduces new predictive measures of association that may be used for contingency table analysis much as the simple, partial, and multiple correlation coefficients are used for regression analysis. The new measures are based on the combination of (1) the logic of the PRE (proportional reduction in error) measures of association, (2) the use of uncertainty (or maximum-likelihood-ϰ2) as indirect measures of errors in prediction, and (3) analysis strategy of log-linear models for contingency tables.

Discrete Statistical Models With Social Science Applications.

According to the preface, this is the first book of a series of two. The second book will deal with continuous statistical models. The main subjects of the present book are based on three developments: (1) the theory of exponential families, (2) the theory of log-linear models, and (3) the theory of logistic models in psychometrics. More specifically, some of the models dealt with are loglinear models for contingency tables, latent trait models, Markov chains, and the Bradley-Terry model for paired comparisons. Each chapter contains a large number of examples and exercises. Solutions to the exercises are, however, not given. Before presenting general conclusion about the book, each chapter will be reviewed separately. Overview The first chapter (Statistical Models; 8 pages) gives an introduction to the use of statistical models in the social sciences. Examples from a variety of social disciplines, including medicine, are given. The intention of chapter 2 (Preliminary Theory; 44 pages) is to refresh the reader’s knowledge of probability theory and statistics, which are applied in the rest of the book. The given survey of subjects serves this goal well, except for the treatment of statistical optimality theory. Optimality concepts are introduced; but they are hardly, if ever, used in the rest of the book. A more serious drawback of the

Multicenter survey of the etiology of pancreatic diseases. Relationship between the relative risk of developing chronic pancreaitis and alcohol, protein and lipid consumption.

The relationship between the average daily intake of alcohol and the risk of developing chronic pancreatitis was studied in two surveys, one in Marseille (France), the other in 9 centers, in Caucasian-populated countries. In the latter survey, the interactions between alcohol, protein and fat consumption and the risk of chronic pancreatitis have also been statistically analyzed. These studies were performed with hierarchical log-linear models for contingency tables, the relative odds being taken as an approximation of the relative risk. It has been shown that there is no apparent threshold of toxicity of alcohol on the human pancreas. The logarithm of the relative risk of chronic pancreatitis increases linearly as a function of the quantity of alcohol and protein consumed, and varies quadratically as a function of average daily lipid intake (a low- or high-lipid diet increases the risk of developing chronic pancreatitis in comparison to an average-fat diet (85--110 g fat per day). The effects on log-relative risk of alcohol, fat and protein daily consumption are additive. In Marseille, the average duration of alcohol consumption before the appearance of symptoms is 18 +/- 11 years for males and 11 +/- 8 years for females, which is much shorter than the duration of alcohol consumption before onset of symptoms in cirrhotic patients.