Models For Contingency Tables Research Articles

Asymmetry Plus Association Models for Ordinal Square Contingency Tables

Asymmetry Plus Association Models for Ordinal Square Contingency Tables

Generalized Marginal Cumulative Homogeneity Model for Multi-way Contingency Tables

Generalized Marginal Cumulative Homogeneity Model for Multi-way Contingency Tables

Extended Second-Order Moment Symmetry Model and Decomposition of Symmetry Model for Ordinal Square Contingency Tables

This study proposes the extended second-order moment symmetry model in square contingency tables with same row and column ordinal classifications. The proposed model extends the previous second-order moment symmetry model by incorporating an asymmetry parameter to capture complex structures. The proposed and previous second-order moment symmetry models represent the asymmetry and symmetry structure of the covariance matrix, respectively. The previous study showed the decomposition of the symmetry model using the second-order moment symmetry model. This study shows the decomposition of the second-order moment symmetry model using the proposed model and the decomposition of the symmetry model applying its decomposition. The usefulness of proposed model is illustrated with examples of two real world datasets (cross-classified education of parents and cross-classified social group of fathers and their daughters).

Comparison of prediction results of Dendrolimus punctatus larvae peak occurrence based on eight prediction models

AbstractIn order to clarify the prediction accuracy of eight models for predicting the peak occurrence of the first generation larvae of Dendrolimus punctatus and provide basis for the pest control, a catastrophe prediction model was established based on the peak occurrence of the first generation larvae of Dendrolimus punctatus in Qianshan City, Anhui Province from 1983 to 2016, and compared with other seven prediction models. Comparing the forecasting results in 2015 and 2016 with actual value and taking 1 head/plant as the error standard, the errors of multiple regression models with six factors as independent variables, namely, peak occurrence of pupae in overwintering generation, peak occurrence of eggs in the first generation, cumulative population in overwintering generation, peak occurrence of adults in overwintering generation, rainfall in early April and parasitic rate of Trichogrammatid in the first generation eggs of Dendrolimus punctatus, were 0.21 heads/plant and 0.23 heads/plant with accuracy rate of 100%. The errors of stepwise regression model with the same six factors were 0.23 head/plant and 0.29 head/plant. The prediction accuracy of artificial BP neural network model, Markov chain model, contingency table model, stationary time series model, and fuzzy comprehensive evaluation model was 100%, but variance period extrapolation model had an accuracy rate of 88%. The accuracy of catastrophe prediction model was related to the selection of catastrophe threshold. Comprehensive comparison of the above eight models, multiple regression, stepwise regression, artificial BP neural network, Markov chain model, stationary time series model, and catastrophe prediction model were more accurate.

Adjusted Residuals for Evaluating Conditional Independence in IRT Models for Multistage Adaptive Testing.

The key assumption of conditional independence of item responses given latent ability in item response theory (IRT) models is addressed for multistage adaptive testing (MST) designs. Routing decisions in MST designs can cause patterns in the data that are not accounted for by the IRT model. This phenomenon relates to quasi-independence in log-linear models for incomplete contingency tables and impacts certain types of statistical inference based on assumptions on observed and missing data. We demonstrate that generalized residuals for item pair frequencies under IRT models as discussed by Haberman and Sinharay (J Am Stat Assoc 108:1435-1444, 2013. https://doi.org/10.1080/01621459.2013.835660 ) are inappropriate for MST data without adjustments. The adjustments are dependent on the MST design, and can quickly become nontrivial as the complexity of the routing increases. However, the adjusted residuals are found to have satisfactory Type I errors in a simulation and illustrated by an application to real MST data from the Programme for International Student Assessment (PISA). Implications and suggestions for statistical inference with MST designs are discussed.

Tree-Structured Model with Unbiased Variable Selection and Interaction Detection for Ranking Data

In this article, we propose a tree-structured method for either complete or partial rank data that incorporates covariate information into the analysis. We use conditional independence tests based on hierarchical log-linear models for three-way contingency tables to select split variables and cut points, and apply a simple Bonferroni rule to declare whether a node worths splitting or not. Through simulations, we also demonstrate that the proposed method is unbiased and effective in selecting informative split variables. Our proposed method can be applied across various fields to provide a flexible and robust framework for analyzing rank data and understanding how various factors affect individual judgments on ranking. This can help improve the quality of products or services and assist with informed decision making.

Anti-Sum-Asymmetry Models and Orthogonal Decomposition of Anti-Sum-Symmetry Model for Ordinal Square Contingency Tables

For the analysis of C × C square contingency tables, we usually estimate using a statistical model an unknown probability distribution with high confidence from obtained observations. The statistical model that fits the data well and is easy to interpret is preferred. The anti-sum-symmetry (ASS) and anti-conditional sum-symmetry (ACSS) models have a structure that the ratio of the probability with which the sum of row and column levels is t, for t = 2, . . . , C, and the probability with which the sum of row and column levels is 2(C + 1) − t is always one and constant, respectively. This study proposes two kinds of models that the ratio of those changes exponentially depending on the sum of row and column levels. This study also gives the decomposition theorems of the ASS model using the proposed models. Moreover, we show that the value of the likelihood ratio chi-squared statistics for the ASS model is asymptotically equivalent to the sum of those for the decomposed models. We evaluate the advantage of the proposed models by applying they to a single data set of real-world grip strength data.

The Use of Contingency Table Model of Two-way in Studying Sex Effect on the Famous Affection

We study in this paper the using of the log-liner model in analyzing the categorical data in contingency table of two- way (rxc) , to find a better model which represents the data. This paper includes applied in healthy field. It has been studied sex effect on the affection of diarrhea which is caused by two kinds of parasite through nine syndrome.

Orthogonal decomposition of symmetry model using sum-symmetry model for ordinal square contingency tables

Orthogonal decomposition of symmetry model using sum-symmetry model for ordinal square contingency tables

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.

A pooled Bayes test of independence using restricted pooling model for contingency tables from small areas

A pooled Bayes test of independence using restricted pooling model for contingency tables from small areas

Parsimonious Bivariate T-distribution Type Symmetry Models for Square Contingency Tables

For square contingency tables with ordered categories, Iki, Ishihara and Tomizawa (2013) considered the t-distribution type symmetry model and Iki, Okada and Tomizawa (2018) extended this model. These models are appropriate for a square contingency table if it is reasonable to assume an underlying bivariate t-distribution having any degrees of freedom. This study proposes three kinds of parsimonious models for these models. Additionally, this paper provides the decompositions of the parsimonious symmetry model using the proposed model. Some simulation studies based on bivariate t-distribution show the performances of the proposed models.

Relative exponential sum-symmetry model and orthogonal decomposition of the sum-symmetry model for ordinal square contingency tables

Summary This study proposes a new exponential sum-symmetry model for square contingency tables with same row and column ordinal classifications. In the existing exponential sum-symmetry (ESS) model, the probability that the sum of row and column levels is t, where the row level is less than the column level, is ∆ t− 2 times higher than the probability that the sum of row and column levels is t, where the row level is greater than the column level. On the other hand, in the proposed ESS model, the ratio of these two probabilities is ∆ t/ 3. In other words, in the existing ESS model, the ratio of the two probabilities varies exponentially depending on the absolute gap between t and 2, while in the proposed ESS model, the ratio of the two probabilities varies exponentially depending on the relative gap between t and 3, although in both ESS models, the ratio of the two probabilities is ∆ when t is the minimum value (i.e., t = 3). Moreover, this study introduces a new decomposition theorem for the sum-symmetry model using the proposed ESS. The proposed decomposition theorem satisfies asymptotic equivalence for the test statistic.

Quasi Association Models for Square Contingency Tables with Ordinal Categories

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.

Partial Exchangeability for Contingency Tables

A parameter free version of classical models for contingency tables is developed along the lines of de Finetti’s notions of partial exchangeability.

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.

Families of Generalized Quasisymmetry Models: A ϕ-Divergence Approach

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.

Orthogonal decomposition of the sum-symmetry model for square contingency tables with ordinal categories: Use of the exponential sum-symmetry model

Summary In the existing decomposition theorem, the sum-symmetry model holds if and only if both the exponential sum-symmetry and global symmetry models hold. However, this decomposition theorem does not satisfy the asymptotic equivalence for the test statistic. To address the aforementioned gap, this study establishes a decomposition theorem in which the sum-symmetry model holds if and only if both the exponential sum-symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic. We demonstrate the advantages of the proposed decomposition theorem by applying it to datasets comprising real data and artificial data.

Orthogonal decomposition of the sum-symmetry model using the two-parameters sum-symmetry model for ordinal square contingency tables

Summary Studies have been carried out on decomposing a model with symmetric structure using a model with asymmetric structure. In the existing decomposition theorem, the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and concordancediscordance models hold. However, this existing decomposition theorem does not satisfy the asymptotic equivalence for the test statistic, namely that the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the decomposed models. To address this issue, this study introduces a new decomposition theorem in which the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic—the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models.

A Generalized Two-Dimensional Index to Measure the Degree of Deviation from Double Symmetry in Square Contingency Tables

The double symmetry model satisfies both the symmetry and point symmetry models simultaneously. To measure the degree of deviation from the double symmetry model, a two-dimensional index that can concurrently measure the degree of deviation from symmetry and point symmetry is considered. This two-dimensional index is constructed by combining two existing indexes. Although the existing indexes are constructed using power divergence, the existing two-dimensional index that can concurrently measure both symmetries is constructed using only Kullback-Leibler information, which is a special case of power divergence. Previous studies note the importance of using several indexes of divergence to compare the degrees of deviation from a model for several square contingency tables. This study, therefore, proposes a two-dimensional index based on power divergence in order to measure deviation from double symmetry for square contingency tables. Numerical examples show the utility of the proposed two-dimensional index using two datasets.