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We propose a novel molecular computing scheme for statistical inference. We focus on the much-studied statistical inference problem of computing maximum likelihood estimators for log-linear models. Our scheme takes log-linear models to reaction systems, and the observed data to initial conditions, so that the corresponding equilibrium of each reaction system encodes the corresponding maximum likelihood estimator. The main idea is to exploit the coincidence between thermodynamic entropy and statistical entropy. We map a Maximum Entropy characterization of the maximum likelihood estimator onto a Maximum Entropy characterization of the equilibrium concentrations for the reaction system. This allows for an efficient encoding of the problem, and reveals that reaction networks are superbly suited to statistical inference tasks. Such a scheme may also provide a template to understanding how in vivo biochemical signaling pathways integrate extensive information about their environment and history.

A proficiency model that provides information on individuals' mastery status on specific skills is illustrated. The model describes the construction and scoring of mastery tests as well as the organization and reporting of individual and group testing results. With the model, an individual's mastery status with respect to various skills can be represented by a victor with n elements, where n equals the number of skills tested. This multivariate quantitative data is analyzed by the log-linear model, incorporating both a sampling factor and a response structure. Thus, the model provides test statistics to assess the differences in capability of the sampled groups as well as the structure represented by the response factors. Two examples are presented which illustrate the applicability of the model in the analysis of proficiency assessment results. The log-linear model permitted a concise analysis of data arising from the use of mastery measurements. (Author/GK)

This paper describes the submission of the AMU (Adam Mickiewicz University) team to the Automatic Post-Editing (APE) task of WMT 2016. We explore the application of neural translation models to the APE problem and achieve good results by treating different models as components in a log-linear model, allowing for multiple inputs (the MT-output and the source) that are decoded to the same target language (post-edited translations). A simple string-matching penalty integrated within the log-linear model is used to control for higher faithfulness with regard to the raw machine translation output. To overcome the problem of too little training data, we generate large amounts of artificial data. Our submission improves over the uncorrected baseline on the unseen test set by -3.2\% TER and +5.5\% BLEU and outperforms any other system submitted to the shared-task by a large margin.

This paper describes the submission of the AMU (Adam Mickiewicz University) team to the Automatic Post-Editing (APE) task of WMT 2016. We explore the application of neural translation models to the APE problem and achieve good results by treating different models as components in a log-linear model, allowing for multiple inputs (the MT-output and the source) that are decoded to the same target language (post-edited translations). A simple string-matching penalty integrated within the log-linear model is used to control for higher faithfulness with regard to the raw machine translation output. To overcome the problem of too little training data, we generate large amounts of artificial data. Our submission improves over the uncorrected baseline on the unseen test set by -3.2\% TER and +5.5\% BLEU and outperforms any other system submitted to the shared-task by a large margin.

This article is from BMC Medical Research Methodology , volume 11 . Abstract Background: Log-linear association models have been extensively used to investigate the pattern of agreement between ordinal ratings. In 2007, log-linear non-uniform association models were introduced to estimate, from a cross-classification of two independent raters using an ordinal scale, varying degrees of distinguishability between distant and adjacent categories of the scale. Methods: In this paper, a simple method based on simulations was proposed to estimate the power of non-uniform association models to detect heterogeneities across distinguishabilities between adjacent categories of an ordinal scale, illustrating some possible scale defects. Results: Different scenarios of distinguishability patterns were investigated, as well as different scenarios of marginal heterogeneity within rater. For sample size of N = 50, the probabilities of detecting heterogeneities within the tables are lower than .80, whatever the number of categories. In additition, even for large samples, marginal heterogeneities within raters led to a decrease in power estimates. Conclusion: This paper provided some issues about how many objects had to be classified by two independent observers (or by the same observer at two different times) to be able to detect a given scale structure defect. Our results also highlighted the importance of marginal homogeneity within raters, to ensure optimal power when using non-uniform association models.

Traditionally, the Dirichlet-multinomial distribution has been recognized as a key model for contingency tables generated by cluster sampling schemes. There are, however, other possible distributions appropriate for these contingency tables. This paper introduces new test-statistics capable to test log-linear modeling hypotheses with no distributional specification, when the individuals of the clusters are possibly homogeneously correlated. The estimator for the intracluster correlation coefficient proposed in Alonso-Revenga et al. (2016), valid for different cluster sizes, plays a crucial role in the construction of the goodness-of-fit test-statistic.

This paper introduces a novel class of models for binary data, which we call log-mean linear models. The characterizing feature of these models is that they are specified by linear constraints on the log-mean linear parameter, defined as a log-linear expansion of the mean parameter of the multivariate Bernoulli distribution. We show that marginal independence relationships between variables can be specified by setting certain log-mean linear interactions to zero and, more specifically, that graphical models of marginal independence are log-mean linear models. Our approach overcomes some drawbacks of the existing parameterizations of graphical models of marginal independence.

We propose a new class of models for random permutations, which we call log-linear models, by the analogy with log-linear models used in the analysis of contingency tables. As a special case, we study the family of all Luce-decomposable distributions, and the family of those random permutations, for which the distribution of both the permutation and its inverse is Luce-decomposable. We show that these latter models can be described by conditional independence relations. We calculate the number of free parameters in these models, and describe an iterative algorithm for maximum likelihood estimation, which enables us to test if a set of data satisfies the conditional independence relations or not.

We provide a polyhedral description of the conditions for the existence of the maximum likelihood estimate (MLE) for a hierarchical log-linear model. The MLE exists if and only if the observed margins lie in the relative interior of the marginal cone. Using this description, we give an algorithm for determining if the MLE exists. If the tree width is bounded, the algorithm runs in polynomial time. We also perform a computational study of the case of three random variables under the no three-factor effect model.

Log-linear modeling was employed to explore the conceptual relationships among community college student persistence and nine variables, including student demographics, purpose for enrolling, intentions to return, frequency of informal interaction with faculty, and satisfaction with the institution in general. The study sample was 369 new and continuing students enrolled at a surburban community college during fall 1984. Four hierarchical models that are posited indicate significant interactions between persistence and intentions to return and persistence and sex (i.e., full-time female students had greater persistence than their male counterparts). Measures of academic integration, such as grade-point average, number of hours spent studying each week, and frequency of interaction with faculty, had independent effects. Review of conceptual models of persistence focusing on four-year colleges and universities suggests that academic integration may be of less importance in explaining persistence at community colleges than at four-year institutions. The application of log-linear modeling to higher education research, and specifically persistence studies, is discussed. (SW)

In Bayesian analysis of multi-way contingency tables, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of conjugate priors for the wide class of discrete hierarchical log-linear models, which includes the class of graphical models. These priors are defined as the Diaconis--Ylvisaker conjugate priors on the log-linear parameters subject to "baseline constraints" under multinomial sampling. We also derive the induced prior on the cell probabilities and show that the induced prior is a generalization of the hyper Dirichlet prior. We show that this prior has several desirable properties and illustrate its usefulness by identifying the most probable decomposable, graphical and hierarchical log-linear models for a six-way contingency table.

Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical and applied machine learning literature. In this paper, we analyze a recently proposed technique known as "self-normalization", which introduces a regularization term in training to penalize log normalizers for deviating from zero. This makes it possible to use unnormalized model scores as approximate probabilities. Empirical evidence suggests that self-normalization is extremely effective, but a theoretical understanding of why it should work, and how generally it can be applied, is largely lacking. We prove generalization bounds on the estimated variance of normalizers and upper bounds on the loss in accuracy due to self-normalization, describe classes of input distributions that self-normalize easily, and construct explicit examples of high-variance input distributions. Our theoretical results make predictions about the difficulty of fitting self-normalized models to several classes of distributions, and we conclude with empirical validation of these predictions.

We present a comprehensive study of graphical log-linear models for contingency tables. High dimensional contingency tables arise in many areas such as computational biology, collection of survey and census data and others. 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. First, we explore connections between the conditional independence in probability and graphs; thereafter we provide a few illustrations to describe how graphical log-linear model are useful to interpret the conditional independences between factors. We also discuss the problem of estimation and model selection in decomposable models.

We extend the log-mean linear parameterization introduced by Roverato et al. (2013) for binary data to discrete variables with arbitrary number of levels, and show that also in this case it can be used to parameterize bi-directed graph models. Furthermore, we show that the log-mean linear parameterization allows one to simultaneously represent marginal independencies among variables and marginal independencies that only appear when certain levels are collapsed into a single one. We illustrate the application of this property by means of an example based on genetic association studies involving single-nucleotide polymorphisms. More generally, this feature provides a natural way to reduce the parameter count, while preserving the independence structure, by means of substantive constraints that give additional insight into the association structure of the variables.

Model selection and learning the structure of graphical models from the data sample constitutes an important field of probabilistic graphical model research, as in most of the situations the structure is unknown and has to be learnt from the given dataset. In this paper, we present a new forward model selection algorithm for graphical log-linear models. We use mutual conditional independence check to reduce the search space which also takes care of the evaluation of the joint effects and chances of missing important interactions are eliminated. We illustrate our algorithm with a real dataset example.

Log linear models are proposed for the analysis of structural relations among multidimensional developmental contingency tables. Model of quasi-independence are suggested for testing specific hypothesized patterns of development. Transitions in developmental categorizations are described by Markov models applied to successive contingency tables. A discussion of the role of Pearson chi square and log likelihood significance tests in model selection is followed by two illustrative data sets. (Author)

Includes bibliographical references (p. 17)

Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific independence. However, parameter estimation is often simpler under a direct parameterization, provided that the model enjoys certain decomposability properties. Here we introduce a cyclical projection algorithm for obtaining maximum likelihood estimates of log-linear parameters under an arbitrary context-specific graphical log-linear model, which needs not satisfy criteria of decomposability. We illustrate that lifting the restriction of decomposability makes the models more expressive, such that additional context-specific independencies embedded in real data can be identified. It is also shown how a context-specific graphical model can correspond to a non-hierarchical log-linear parameterization with a concise interpretation. This observation can pave way to further development of non-hierarchical log-linear models, which have been largely neglected due to their believed lack of interpretability.

Log-linear models are arguably the most successful class of graphical models for large-scale applications because of their simplicity and tractability. Learning and inference with these models require calculating the partition function, which is a major bottleneck and intractable for large state spaces. Importance Sampling (IS) and MCMC-based approaches are lucrative. However, the condition of having a "good" proposal distribution is often not satisfied in practice. In this paper, we add a new dimension to efficient estimation via sampling. We propose a new sampling scheme and an unbiased estimator that estimates the partition function accurately in sub-linear time. Our samples are generated in near-constant time using locality sensitive hashing (LSH), and so are correlated and unnormalized. We demonstrate the effectiveness of our proposed approach by comparing the accuracy and speed of estimating the partition function against other state-of-the-art estimation techniques including IS and the efficient variant of Gumbel-Max sampling. With our efficient sampling scheme, we accurately train real-world language models using only 1-2% of computations.

The last decade has witnessed the success of the traditional feature-based method on exploiting the discrete structures such as words or lexical patterns to extract relations from text. Recently, convolutional and recurrent neural networks has provided very effective mechanisms to capture the hidden structures within sentences via continuous representations, thereby significantly advancing the performance of relation extraction. The advantage of convolutional neural networks is their capacity to generalize the consecutive k-grams in the sentences while recurrent neural networks are effective to encode long ranges of sentence context. This paper proposes to combine the traditional feature-based method, the convolutional and recurrent neural networks to simultaneously benefit from their advantages. Our systematic evaluation of different network architectures and combination methods demonstrates the effectiveness of this approach and results in the state-of-the-art performance on the ACE 2005 and SemEval dataset.

The last decade has witnessed the success of the traditional feature-based method on exploiting the discrete structures such as words or lexical patterns to extract relations from text. Recently, convolutional and recurrent neural networks has provided very effective mechanisms to capture the hidden structures within sentences via continuous representations, thereby significantly advancing the performance of relation extraction. The advantage of convolutional neural networks is their capacity to generalize the consecutive k-grams in the sentences while recurrent neural networks are effective to encode long ranges of sentence context. This paper proposes to combine the traditional feature-based method, the convolutional and recurrent neural networks to simultaneously benefit from their advantages. Our systematic evaluation of different network architectures and combination methods demonstrates the effectiveness of this approach and results in the state-of-the-art performance on the ACE 2005 and SemEval dataset.

In regression models for categorical data a linear model is typically related to the response variables via a transformation of probabilities called the link function. We introduce an approach based on two link functions for binary data named log-mean (LM) and log-mean linear (LML), respectively. The choice of the link function plays a key role for the interpretation of the model, and our approach is especially appealing in terms of interpretation of the effects of covariates on the association of responses. Similarly to Poisson regression, the LM and LML regression coefficients of single outcomes are log-relative risks, and we show that the relative risk interpretation is maintained also in the regressions of the association of responses. Furthermore, certain collections of zero LML regression coefficients imply that the relative risks for joint responses factorize with respect to the corresponding relative risks for marginal responses. This work is motivated by the analysis of a dataset obtained from a case-control study aimed to investigate the effect of HIV-infection on multimorbidity, that is simultaneous presence of two or more noninfectious commorbidities in one patient.

Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a sub-class of MLL models which correspond to Acyclic Directed Mixed Graphs (ADMGs) under the usual global Markov property. We characterize for precisely which graphs the resulting parametrization is variation independent. The MLL approach provides the first description of ADMG models in terms of a minimal list of constraints. The parametrization is also easily adapted to sparse modelling techniques, which we illustrate using several examples of real data.

Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a sub-class of MLL models which correspond to Acyclic Directed Mixed Graphs (ADMGs) under the usual global Markov property. We characterize for precisely which graphs the resulting parametrization is variation independent. The MLL approach provides the first description of ADMG models in terms of a minimal list of constraints. The parametrization is also easily adapted to sparse modelling techniques, which we illustrate using several examples of real data.

When some treatments are ordered according to the categories of an ordinal categorical variable (e.g., extent of side effects) in a monotone order, one might be interested in knowing wether the treatments are equally effective or not. One way to do that is to test if the likelihood ratio order is strictly verified. A method based on log-linear models is derived to make statistical inference and phi-divergence test-statistics are proposed for the test of interest. Focussed on loglinear modeling, the theory associated with the asymptotic distribution of the phi-divergence test-statistics is developed. An illustrative example motivates the procedure and a simulation study for small and moderate sample sizes shows that it is possible to find phi-divergence test-statistic with an exact size closer to nominal size and higher power in comparison with the classical likelihood ratio.

In the Bayesian analysis of contingency table data, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameter is a major challenge. Though the conjugate prior on cell probabilities has been defined by Dawid and Lauritzen (1993) for decomposable graphical models, it has not been identified for the larger class of graphical models Markov with respect to an arbitrary undirected graph or for the even wider class of hierarchical log-linear models. In this paper, working with the log-linear parameters used by GLIM, we first define the conjugate prior for these parameters and then derive the induced prior for the cell probabilities: this is done for the general class of hierarchical log-linear models. We show that the conjugate prior has all the properties that one expects from a prior: notational simplicity, ability to reflect either no prior knowledge or a priori expert knowledge, a moderate number of hyperparameters and mathematical convenience. It also has the strong hyper Markov property which allows for local updates within prime components for graphical models.

In the Bayesian analysis of contingency table data, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameter is a major challenge. Though the conjugate prior on cell probabilities has been defined by Dawid and Lauritzen (1993) for decomposable graphical models, it has not been identified for the larger class of graphical models Markov with respect to an arbitrary undirected graph or for the even wider class of hierarchical log-linear models. In this paper, working with the log-linear parameters used by GLIM, we first define the conjugate prior for these parameters and then derive the induced prior for the cell probabilities: this is done for the general class of hierarchical log-linear models. We show that the conjugate prior has all the properties that one expects from a prior: notational simplicity, ability to reflect either no prior knowledge or a priori expert knowledge, a moderate number of hyperparameters and mathematical convenience. It also has the strong hyper Markov property which allows for local updates within prime components for graphical models.

In this paper we have fitted the double binomial and multiplicative binomial distributions as log-linear models using sufficient statistics. This approach is not new as several authors have employed this approach, most especially in the analysis of the Human sex ratio in [1]. However, obtaining the estimated parameters of the distributions may be problematic, especially for the double binomial where the parameter estimate of π may not be readily available from the Log-Linear (LL) parameter estimates. Other issues associated with the LL approach is its implementation in the generalized linear model with covariates. The LL uses far more parameters than the procedure that employs conditional log-likelihoods functions where the marginal likelihood functions are minimized over the parameter space. This is the procedure employed in SAS PROC NLMIXED. The two procedures are essentially equivalent for frequency data. For models with covariates, the LL uses far more parameters and the marginal likelihood functions approach are employed here on three data set having covariates. Keywords

Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for multivariate categorical data, while log linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to the nonnegative rank of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate advantages of the new decompositions in simulations and an application to functional disability data.

Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for multivariate categorical data, while log linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. We derive several results relating the support of a log-linear model to the nonnegative rank of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate advantages of the new decompositions in simulations and an application to functional disability data.

This paper deals with the issue of testing hypothesis in symmetric and log-symmetric linear regression models in small and moderate-sized samples. We focus on four tests, namely the Wald, likelihood ratio, score, and gradient tests. These tests rely on asymptotic results and are unreliable when the sample size is not large enough to guarantee a good agreement between the exact distribution of the test statistic and the corresponding chi-squared asymptotic distribution. Bartlett and Bartlett-type corrections typically attenuate the size distortion of the tests. These corrections are available in the literature for the likelihood ratio and score tests in symmetric linear regression models. Here, we derive a Bartlett-type correction for the gradient test. We show that the corrections are also valid for the log-symmetric linear regression models. We numerically compare the various tests, and bootstrapped tests, through simulations. Our results suggest that the corrected and bootstrapped tests exhibit type I probability error closer to the chosen nominal level with virtually no power loss. The analytically corrected tests, including the Bartlett-corrected gradient test derived in this paper, perform as well as the bootstrapped tests with the advantage of not requiring computationally-intensive calculations. We present two real data applications to illustrate the usefulness of the modified tests. Keywords: Symmetric regression models; Bartlett correction; Bartlett-type correction; Bootstrap; Log-symmetric regression models; gradient statistic; score statistic; likelihood ratio statistic; Wald statistic.

Log-linear modeling is a popular method for the analysis of contingency table data. When the table is sparse, and the data falls on a proper face $F$ of the convex support, there are consequences on model inference and model selection. Knowledge of the cells determining $F$ is crucial to mitigating these effects. We introduce the R package (R Core Team (2016)) eMLEloglin for determining $F$ and passing that information on to the glm package to fit the model properly.

We consider partly linear transformation models applied to current status data. The unknown quantities are the transformation function, a linear regression parameter and a nonparametric regression effect. It is shown that the penalized MLE for the regression parameter is asymptotically normal and efficient and converges at the parametric rate, although the penalized MLE for the transformation function and nonparametric regression effect are only $n^{1/3}$ consistent. Inference for the regression parameter based on a block jackknife is investigated. We also study computational issues and demonstrate the proposed methodology with a simulation study. The transformation models and partly linear regression terms, coupled with new estimation and inference techniques, provide flexible alternatives to the Cox model for current status data analysis.

We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and investigate estimability of the natural and mean-value parameters under a nonexistent MLE. Our conditions focus on the role of sampling zeros in the observed table. We situate our results within the framework of extended exponential families, and we exploit the geometric properties of log-linear models. We propose algorithms for extended maximum likelihood estimation that improve and correct the existing algorithms for log-linear model analysis.

Log-linear models are a well-established method for describing statistical dependencies among a set of n random variables. The observed frequencies of the n-tuples are explained by a joint probability such that its logarithm is a sum of functions, where each function depends on as few variables as possible. We obtain for this class a new model selection criterion using nonasymptotic concepts of statistical learning theory. We calculate the VC dimension for the class of k-factor log-linear models. In this way we are not only able to select the model with the appropriate complexity, but obtain also statements on the reliability of the estimated probability distribution. Furthermore we show that the selection of the best model among a set of models with the same complexity can be written as a convex optimization problem.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis-Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. Here we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis-Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Social networks and other large sparse data sets pose significant challenges for statistical inference, as many standard statistical methods for testing model fit are not applicable in such settings. Algebraic statistics offers a theoretically justified approach to goodness-of-fit testing that relies on the theory of Markov bases and is intimately connected with the geometry of the model as described by its fibers. Most current practices require the computation of the entire basis, which is infeasible in many practical settings. We present a dynamic approach to explore the fiber of a model, which bypasses this issue, and is based on the combinatorics of hypergraphs arising from the toric algebra structure of log-linear models. We demonstrate the approach on the Holland-Leinhardt $p_1$ model for random directed graphs that allows for reciprocated edges.

This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on the interaction parameters calculated within marginal distributions. We undertake a comprehensive Bayesian analysis of these models, involving suitable choices of prior distributions, estimation, model determination, as well as the allied computational issues. The methodology is illustrated with reference to two real data sets.

The use of log-linear models for investigating differential item functioning (DIF) associated with examinee/respondent background characteristics was examined. The Likert-type items used in this study were drawn from a 36-item self-report measure--the Suicide Probability Scale. Specifically, log-linear models were used to investigate whether contingency tables for ethnicity (55 African Americans, 186 Anglo Americans, and 189 Hispanic Americans) or gender (332 males and 627 females) by item response by mental health status suggested evidence of an interaction between the background variable and item response. The investigation focused on a set of 35 Likert-type items that measure subjective well- being and coping behavior. Several log-linear models were fit to the data, and rationale for the composition of the various models is discussed. Among tables where a statistically significant ethnicity by item response interaction or a gender by item response interaction was found, the technique of proportional standardization to unity was used to plot response rates according to ethnic and gender subgroups. Plots show that most of the interaction comes from respondents whose mental health status is diminished. In general, log-linear models were found useful for investigating DIF. Two tables and 24 graphs present study data. (Author/SLD)

The use of log-linear models for investigating differential item functioning (DIF) associated with examinee/respondent background characteristics was examined. The Likert-type items used in this study were drawn from a 36-item self-report measure--the Suicide Probability Scale. Specifically, log-linear models were used to investigate whether contingency tables for ethnicity (55 African Americans, 186 Anglo Americans, and 189 Hispanic Americans) or gender (332 males and 627 females) by item response by mental health status suggested evidence of an interaction between the background variable and item response. The investigation focused on a set of 35 Likert-type items that measure subjective well- being and coping behavior. Several log-linear models were fit to the data, and rationale for the composition of the various models is discussed. Among tables where a statistically significant ethnicity by item response interaction or a gender by item response interaction was found, the technique of proportional standardization to unity was used to plot response rates according to ethnic and gender subgroups. Plots show that most of the interaction comes from respondents whose mental health status is diminished. In general, log-linear models were found useful for investigating DIF. Two tables and 24 graphs present study data. (Author/SLD)

The general diagnostic model (GDM) utilizes located latent classes for modeling a multidimensional proficiency variable. In this paper, the GDM is extended by employing a log-linear model for multiple populations that assumes constraints on parameters across multiple groups. This constrained model is compared to log-linear models that assume separate sets of parameters to fit the distribution of latent variables in each group of a multiple-group model. Estimation of these constrained log-linear models using iterative weighted least squares (IWLS) methods is outlined and an application to NAEP data exemplifies the differences between constrained and unconstrained models in the presence of larger numbers of group-specific proficiency distributions. The use of log-linear models for the latent skill space distributions using constraints across populations allows for efficient computations in models that include many proficiency distributions.

In this paper we consider use of some special log-linear models and minimum delta estimation in the multivariate classification problem posed by Martin and Bradley (1972). We first define these models, called log-difference models, and show that the minimum risk classification rule depends only on a certain subset of the new parameters. We then review minimum delta estimation, in particular the minimum delta estimator, the approximate minimum delta estimator, and their existence properties. Two examples are worked. The first involves detergent preference and illustrates how extensions to the case in which not all variables are dichotomous may be obtained through the use of orthogonal polynomials. The second example involves infant hypoxic trauma, and many cells are empty. The existence conditions are used to find a model for which estimates a cell frequencies exist and are in good agreement with the observed data. (Author)

Two new methods for estimation of parameters in log-linear models are proposed and their properties considered in this article. Conditions for the existence of the new estimators are derived, and the new estimators are shown to possess appropriate asymptotic properties.