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When focusing on changes in political party support, it is crucial to determine whether or not there has been a change in the aggregate. From this perspective, various types of marginal homogeneity models have been proposed. We propose local marginal homogeneity models, which indicate that there are symmetric structures of probabilities for only one pair of symmetric marginal probabilities or cumulative probabilities. In addition, we propose two measures, one for nominal categories and one for ordered categories, to express the degree of departure from local marginal homogeneity models. We also apply the measures to data and confirm that the measures help compare the degree of departure from the model in several tables.

The analysis of contingency tables focuses on a statistical model instead of independence when the independence between row and column variables does not hold. Many association models have been proposed to indicate the structure of odds ratios. Additionally, symmetry and asymmetry models have been proposed to analyze the cell probabilities of square contingency tables with symmetric or asymmetric structures. This paper proposes an asymmetry plus association model for square contingency tables with ordinal categories and partitioning of the test statistic for goodness-of-fit using our proposed model.

Developmental responses to nutritional variation represent one of the ecologically most important classes of adaptive plasticity. However, knowledge of genome-wide patterns of nutrition-responsive gene expression is limited. Here, we studied genome-wide transcriptional responses to nutritional variation and their dependency on trait and sex in the beetle Onthophagus taurus. We find that averaged across the transcriptome, nutrition contributes less to overall variation in gene expression than do sex or body region, but that for a modest subset of genes nutrition is by far the most important determinant of expression variation. Furthermore, our results reject the hypothesis that a common machinery may underlie nutrition-sensitive development across body regions. Instead, we find that magnitude (measured by number of differentially expressed contigs), composition (measured by functional enrichment) and evolutionary consequences (measured by patterns of sequence variation) are heavily dependent on exactly which body region is considered and the degree of sexual dimorphism observed on a morphological level. More generally, our findings illustrate that studies into the developmental mechanisms and evolutionary consequences of nutrition-biased gene expression must take into account the dynamics and complexities imposed by other sources of variation in gene expression such as sexual dimorphism and trait type.

For square contingency tables with ordered categories, Iki, Tahata and Tomizawa (2012) considered a measure to represent the degree of departure from marginal homogeneity. However, the maximum value of this measure cannot distinguish two kinds of marginal inhomogeneity. The present paper proposes a measure which can distinguish two kinds of marginal inhomogeneity. In particular, the proposed measure is useful for representing the degree of departure from marginal homogeneity when the marginal cumulative logistic model holds.

The quasisymmetry (QS) model for square contingency tables is revisited, highlighting properties and features on the basis of its alternative definitions. More parsimonious QS-type models, such as the ordinal QS model for ordinal classification variables and models based on association models (AMs) with homogeneous row and column scores, are discussed. All these models are linked to the local odds ratios (LOR). QS-type models and AMs were extended in the literature for generalized odds ratios other than LOR. Furthermore, in an information-theoretic context, they are expressed as distance models from a parsimonious reference model (the complete symmetry for QS and the independence for AMs), while they satisfy closeness properties with respect to Kullback–Leibler (KL) divergence. Replacing the KL by ϕ divergence, flexible classes of QS-type models for LOR, AMs for LOR, and AMs for generalized odds ratios were generated. However, special QS-type models that are based on homogeneous AMs for LOR have not been extended to ϕ-divergence-based classes so far, or the QS-type models for generalized odds ratios. In this work, we develop these missing extensions, and discuss QS-type models and their generalizations in depth. These flexible families enrich the modeling options, leading to models of better fit and sound interpretation, as illustrated by representative examples.

In contingency table analysis, statistical models have been used to study the linkage between variables. The independent model is used to analyze whether or not there is an association between variables. In particular, a contingency table in which the rows and columns consist of the same classification is called a square contingency table, and in square contingency table analysis, the variables are strongly related to each other and independence is not established. In this case, alternative statistical models are considered instead of the independence model. For instance, symmetric or asymmetric models have been proposed, which show symmetric or asymmetric structure for cell probabilities. A number of association models have also been considered to analyze complex data. In this paper, we propose models that include both asymmetry and association structures. We provide some theorems on the necessary and sufficient conditions of a certain model based on the proposed model. Additionally, we prove that the likelihood ratio statistic for our models are separable into two statistics. These theorems help interpret results.

For square contingency tables with ordered categories, Tomizawa, Biometrica J. 28 (1986), 387–393, considered the conditional point symmetry model. Kurakami et al ., J. Stat. Adv. Theory Appl. 17 (2017), 33–42, considered the another point symmetry and the reverse global symmetry model. The present paper proposes Kullback—Leibler information type measures to represent the degree of departure from each of the models. Also this paper shows a theorem that the measure for the another point symmetry model is equal to the sum of the measures for the reverse global symmetry model and for the conditional point symmetry model.

Background Lysine succinylation is a type of protein post-translational modification which is widely involved in cell differentiation, cell metabolism and other important physiological activities. To study the molecular mechanism of succinylation in depth, succinylation sites need to be accurately identified, and because experimental approaches are costly and time-consuming, there is a great demand for reliable computational methods. Feature extraction is a key step in building succinylation site prediction models, and the development of effective new features improves predictive accuracy. Because the number of false succinylation sites far exceeds that of true sites, traditional classifiers perform poorly, and designing a classifier to effectively handle highly imbalanced datasets has always been a challenge. Results A new computational method, iSuc-ChiDT, is proposed to identify succinylation sites in proteins. In iSuc-ChiDT, chi-square statistical difference table encoding is developed to extract positional features, and has a higher predictive accuracy and fewer features compared to common position-based encoding schemes such as binary encoding and physicochemical property encoding. Single amino acid and undirected pair-coupled amino acid composition features are supplemented to improve the fault tolerance for residue insertions and deletions. After feature selection by Chi-MIC-share algorithm, the chi-square decision table (ChiDT) classifier is constructed for imbalanced classification. With a training set of 4748:50,551(true: false sites), ChiDT clearly outperforms traditional classifiers in predictive accuracy, and runs fast. Using an independent testing set of experimentally identified succinylation sites, iSuc-ChiDT achieves a sensitivity of 70.47%, a specificity of 66.27%, a Matthews correlation coefficient of 0.205, and a global accuracy index Q 9 of 0.683, showing a significant improvement in sensitivity and overall accuracy compared to PSuccE, Success, SuccinSite, and other existing succinylation site predictors. Conclusions iSuc-ChiDT shows great promise in predicting succinylation sites and is expected to facilitate further experimental investigation of protein succinylation.

Correspondence analysis (CA) is a powerful technique, commonly used by sociologists to summarize the structure of the association observed in a contingency table (also known as cross-table). In contrast, approaches derived from CA, or similar in their use, but offering superior properties, are only known by a restricted audience in France: the CA of incomplete contingency table and log-multiplicative association models. This first article uses classic CA and CA of incomplete contingency table to analyze a socioeconomic homogeny table (based on the two-digit categories socioprofessionnelles of the spouses) from the INSEE Labour Force Surveys conducted between 2003 and 2010. It shows the interest of giving a special status to endogamous couples (in which the spouses belong exactly to the same group), in order to represent better the social space. Adapted from the source document.

While it is not possible to identify exact sources for the square tables that Johannes Trithemius and, after him, Blaise de Vigenère presented in their cryptographic publications, there is good evidence that Trithemius may have been influenced by a variety of materials: He knew the figural poetry of Rabanus Maurus (780-856) that frequently used squares with a grid of 36 letters; he was fully aware of the medieval ars combinatoria and the works of the Mallorcan philosopher and theologian Raymundus Lullus (1233-1316), where he would have also found combinatorial circular disks; and he may have discerned a pattern for his square table in the medieval Easter or Lenten tables used for the calculation of the forty days of Lent and the days of Easter over a period of years.