더블링 기법을 활용한 대응분석에 대한 민감도분석

Preface Contributors List of Tables List of Figures ---------------------- Part I. History and Fundamentals Karl Pearson and the Chi-Squared Test / D.R. Cox Karl Pearson Chi-Square Test-The Dawn of Statistical Inference / C.R. Rao Approximate Models / P.J. Huber -------------------- Part II. Chi-Squared Test Partitioning the Pearson-Fisher Chi-Squared Goodness-of-Fit Statistic / G.D. Rayner Statistical Tests for Normal Family in Presence of Outlying Observations / A. Zerbet Chi-Squared Test for the Law of Annual Death Rates: Case with Censure for Life Insurance Files / L. Gerville-Reache ------------------------ Part III. Goodness-of-Fit Tests for Parametric Distributions Shapiro-Wilk Type Goodness-of-Fit Tests for Normality: Asymptotics Revisited / P. Kumar A Test for Exponentiality Based on Spacings for Progressively Type II Censored Data / N. Balakrishnan, H.K.T. Ng, and N. Kannan Goodness-of- Fit Statistics for the Exponential Distribution When the Data are Grouped / S. Gulati and J. Neus Characterization Theorems and Goodness-of-Fit Tests / C.E. Marchetti and G.S. Mudholkar Goodness-of-Fit Tests Based on Record Data and Generalized Ranked Set Data / B.C. Arnold, R.J. Beaver, E. Castillo, and J.M. Sarabia ------------------------------- Part IV. Regression and Goodness-of-Fit Tests Gibbs Regression and a Test of Goodness-of-Fit / L. Seymour A CLT for the L_2 Norm of the Regression Estimators Under alpha-Mixing: Application to G-O-F Tests / C.A.T. Diack Testing theGoodness-of-Fit of a Linear Model in Nonparametric Regression / Z. Mohdeb and A. Mokkadem A New Test of Linear Hypothesis in Regression / Y. Baraud, S. Huet, and B. Laurent ------------------------------------- Part V. Goodness-of-Fit Tests in Survival Analysis and Reliability Inference in Extensions of the Cox Model for Heterogeneous Populations / O. Pons Assumptions of a Latent Survival Model / M.-L. Ting Lee and G.A. Whitmore Goodness-of-Fit Testing of the Cox Proportional Hazards Model / K. Devarajan and N. Ebrahimi A New Family of Multivariate Distributions for Survival Data / S.T. Gross and C. Huber-Carol Discrimination Index, the Area Under to ROC Curve / B.-H. Nam and R. B. D'Agostino Goodness-of-Fit Tests for Accelerated Life Models / V. Bagdonavicius and M.S. Nikulin ------------------------------ Part VI. Graphic Methods and General Goodness-of-Fit Tests Two Nonstandard Examples of the Classical Stratification Approach to Graphically Assessing Proportionality of Hazards / N. Keiding Association in Contingency Tables, Correspondence Analysis, and (Modified) Andrews Plots / R. Khattree and D.N. Naik Orthogonal Expansions and Distinction Between Logistic and Normal / C.M. Cuadras and D. Cuadras Functional Tests of Fit / D. Bosq Quasi Most Powerful Invariant Tests of Goodness-of-Fit --------------------------------- Part VII. Model Validity in Quality of Life Test of Monotonicity for the Rasch Model J. Bretagnolle Validation of Model Assumptions in Quality of Life Measurements / A. Hamon, J.F. Dupuy, and M. Mesbah &nbsp

We consider the problem of counting the number of contingency tables with given row and column sums. This problem is known to be #P-complete, even when there are only two rows [7]. In this paper we present the first fully-polynomial randomized approximation scheme for counting contingency tables when the number of rows is constant. A novel feature of our algorithm is that it is a hybrid of an exact counting technique with an approximation algorithm, giving two distinct phases. In the first, the columns are partitioned into "small" and "large". We show that the number of contingency tables can be expressed as the weighted sum of a polynomial number of new instances of the problem, where each instance consists of some new row sums and the original large column sums. In the second phase, we show how to approximately count contingency tables when all the column sums are large. In this case, we show that the solution lies in approximating the volume of a single convex body, a problem which is known to be solvable in polynomial time [5].

The importance of breakfast in maintaining a healthy lifestyle is well-documented, yet breakfast omission remains prevalent among children and teenagers, leading to negative health and academic outcomes. The purpose of this study is to identify the association between various levels of breakfast consumption and other related factors. A secondary cross-sectional dataset was used in this study to detect the habits of breakfast consumption and its association between other related factors. As chi-square test shows the association between the two attributes, corresponding analysis was applied in this study to see the level-wise association between the attributes. The dataset contains a total of 509 individuals that were enrolled in high school education in northeastern region of Bangladesh. The results of the study indicated that around fifty percent of the children are skipping breakfast and most of them are from Habiganj and Sunamganj districts. It is found that urban students are higher tendency to miss breakfast compare to rural area. It is also observed that lower levels of parental education are highly associated with not taking and/or irregular taking breakfast. In correspondence analysis, the results revealed that students whose mothers are engaged in government or private sector jobs tend to have a consistent breakfast routine, however, in a chi-square test it was found that mother’s occupation and breakfast consumption is not significantly associated. It indicates correspondence analysis is more suitable to discover the level-wise association. Taken together, it is concluded that parental education and occupation may increase the taking breakfast of school children. This study highlights the need to advocate for breakfast intake among adolescents. The study concludes that correspondence analysis is essential to know the level-wise association between the attributes. Asian J. Med. Biol. Res. 2024, 10(3), 99-109

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.

Correspondence analysis can be described as a technique which decomposes the departure from independence in a two-way contingency table. In this paper a form of correspondence analysis is proposed which decomposes the departure from the quasi-independence model. This form seems to be a good alternative to ordinary correspondence analysis in cases where the use of the latter is either impossible or not recommended, for example, in case of missing data or structural zeros. It is shown that Nora's reconstitution of order zero, a procedure well-known in the French literature, is formally identical to our correspondence analysis of incomplete tables. Therefore, reconstitution of order zero can also be interpreted as providing a decomposition of the residuals from the quasi-independence model. Furthermore, correspondence analysis of incomplete tables can be performed using existing programs for ordinary correspondence analysis.

The use of categorical data in health sciences requires meticulous analytical methodology, such as correspondence analysis for exploring relationships and associations between variables. The objective of this study was to apply and evaluate categorical data analysis techniques, specifically Contingency Tables and Correspondence Analysis, to the Electronic Medical Record (EMR) data from Pringgarata Public Health Center during the First Quarter. This study is expected to provide insights into the distribution patterns of disease in the region. The method employed is a retrospective study of disease types using a Categorical Data Analysis approach. Cross-tabulation was performed for Disease Type with Month and Disease Type with Village (location). The Chi-square test was applied to assess the significance of the relationships, followed by Correspondence Analysis for visualizing patterns in a low-dimensional space. The results indicated that Fever (50.1%) was the most frequent case, with 54% of total cases originating from Pringgarata and Murbaya Villages. A significant association was found between Disease Type and Month (p-value=0.006), and between Disease Type and Village (p-value=0.017). The correspondence plot visualized strong associations: ISPA with March (indicating a seasonal trend), Gastritis with February (potentially linked to lifestyle patterns), ISPA strongly associated with Arjangka Village, and Gastritis strongly associated with Murbaya Village. The application of Correspondence Analysis successfully visualized specific relationship patterns, which can serve as a basis for planning resource allocation and targeting public health programs.

Dual scaling is a set of related techniques for the analysis of a wide assortment of categorical data types including contingency tables and multiple-choice, rank order, and paired comparison data. When applied to a contingency table, dual scaling also goes by the name "correspondence analysis," and when applied to multiple-choice data in which there are more than 2 items, "optimal scaling" and "multiple correspondence analysis. " Our aim of this article was to explain in nontechnical terms what dual scaling offers to an analysis of contingency table and multiple-choice data.

Biomtlrika (1991), 78, 1, pp. 229-32 Printed in Great Britain Reduced rank models for contingency tables BY JAN DE LEEUW Departments of Psychology and Mathematics, University of California, Los Angeles, California 90024-1563, U.S.A. AND PETER G. M. VAN DER HEIJDEN Department of Empirical and Theoretical Sociology, University of Utrecht, 3508 TC Utrecht, The Netherlands SUMMARY Some key words: Canonical analysis; Correspondence analysis; Latent class analysis; Reduced rank models. 1. INTRODUCTION In recent years much attention has been given to models for two-way contingency tables that can be formulated in terms of reduced rank of a matrix with probabilities. A well-known reduced rank model is the independence model, where the rank is one. For rank higher than one distinct classes of reduced rank models are possible. Each has the independence model as the special case for rank one. A first class of such models is closely related to what is known under names as canonical analysis or correspondence analysis. Recently much attention has been given to the maximum likelihood estimation of versions of these models by Goodman (1985, 1986, 1987) and Gilula & Haberman (1986, 1988). A second class of models that can be formulated in terms of reduced rank is latent class analysis, LCA, for two-way tables. Latent class analysis was proposed by Lazersfeld (1950a, b). See Clogg (1981) for a more recent review. In this paper we relate these classes of models to each other. The relation has been discussed earlier by Gilula (1979, 1983, 1984), Gilula & Haberman (1986), Goodman (1987), and van der Heijden, Mooijaart & de Leeuw (1989). We summarize existing results in a simple way using new proofs. Gilula (1979) provided conditions that had to hold for rank-2 correspondence analysis to imply rank-2 latent class analysis. We show here that rank-2 correspondence analysis always implies rank-2 latent class analysis. This implies that the theorem and the example given by Gilula (1979) are incorrect. 2. GENERAL REDUCED RANK MODELS The basic model studied in this paper assumes that a n n x m probability matrix II has rank p, where p = min (n,m). We call this model R p . The probability matrix II has all elements nonnegative, while the sum of the ny is equal to one. We suppose, unless indicated otherwise, that II is full, in the sense that its row sums ir l+ and its column sums v +J are all positive. Thus no row or column is equal to zero. We compare this model with the canonical model C p , in which at most p - 1 of the canonical correlations between the row and the column variables of the table are nonzero. These canonical correlations are the stationary values of the product moment correlation coefficient, seen as a function of scores for rows and scores for columns. Downloaded from biomet.oxfordjournals.org at University of California, Los Angeles on May 18, 2011 Reduced rank models for the analysis of two-way contingency tables are introduced. Two classes of reduced rank models are discerned, with well-known exponents canonical analysis and latent class analysis. The relation between these two classes is discussed. Results on the subject mentioned earlier in the literature are shown to be either redundant or inaccurate.

Statistical Analysis of Square Contingency Tables - Social-professional Homogamy in France II. The Contribution of Association Models: Contrary to correspondence analysis (CA), log-multiplicative association models are only known by a restricted audience in France. This second article uses the latter technique to analyze a socioeconomic homogamy table (based on the two-digit catégories socioprofessionnelles of the spouses) from the INSEE Labour Force Surveys conducted between 2003 and 2010. It illustrates the strong resemblance between the two approaches, and highlights the advantages brought by the greater flexibility of association models. They provide a view of the social space both more accurate and easier to interpret than CA, in particular by giving special status to endogamous couples (in which the spouses belong exactly to the same group). They also allow us to analyze specifically men-women asymmetries which emerge from the choice of a spouse (hypergamy), an essential issue poorly apprehended by classical methods.

Preface. Acknowledgments. 1 Introduction. 1.1 The nature of paleontological data. 1.2 Advantages and pitfalls of paleontological data analysis. 1.3 Software. 2 Basic statistical methods. 2.1 Introduction. 2.2 Statistical distributions. 2.3 Shapiro-Wilk test for normal distribution. 2.4 F test for equality of variances. 2.5 Student's t test and Welch test for equality of means. 2.6 Mann-Whitney U test for equality of medians. 2.7 Kolmogorov-Smirnov test for equality of distributions. 2.8 Permutation and resampling. 2.9 One-way ANOVA. 2.10 Kruskal-Wallis test. 2.11 Linear correlation. 2.12 Non-parametric tests for correlation. 2.13 Linear regression. 2.14 Reduced major axis regression. 2.15 Nonlinear curve fitting. 2.16 Chi-square test. 3 Introduction to multivariate data analysis. 3.1 Approaches to multivariate data analysis. 3.2 Multivariate distributions. 3.3 Parametric multivariate tests. 3.4 Non-parametric multivariate tests. 3.5 Hierarchical cluster analysis. 3.5 K-means cluster analysis. 4 Morphometrics. 4.1 Introduction. 4.2 The allometric equation. 4.3 Principal components analysis (PCA). 4.4 Multivariate allometry. 4.5 Discriminant analysis for two groups. 4.6 Canonical variate analysis (CVA). 4.7 MANOVA. 4.8 Fourier shape analysis. 4.9 Elliptic Fourier analysis. 4.10 Eigenshape analysis. 4.11 Landmarks and size measures. 4.12 Procrustean fitting. 4.13 PCA of landmark data. 4.14 Thin-plate spline deformations. 4.15 Principal and partial warps. 4.16 Relative warps. 4.17 Regression of partial warp scores. 4.18 Disparity measures. 4.19 Point distribution statistics. 4.20 Directional statistics. Case study: The ontogeny of a Silurian trilobite. 5 Phylogenetic analysis. 5.1 Introduction. 5.2 Characters. 5.3 Parsimony analysis. 5.4 Character state reconstruction. 5.5 Evaluation of characters and tree topologies. 5.6 Consensus trees. 5.7 Consistency index. 5.8 Retention index. 5.9 Bootstrapping. 5.10 Bremer support. 5.11 Stratigraphical congruency indices. 5.12 Phylogenetic analysis with Maximum Likelihood. Case study: The systematics of heterosporous ferns. 6 Paleobiogeography and paleoecology. 6.1 Introduction. 6.2 Diversity indices. 6.3 Taxonomic distinctness. 6.4 Comparison of diversity indices. 6.5 Abundance models. 6.6 Rarefaction. 6.7 Diversity curves. 6.8 Size-frequency and survivorship curves. 6.9 Association similarity indices for presence/absence data. 6.10 Association similarity indices for abundance data. 6.11 ANOSIM and NPMANOVA. 6.12 Correspondence analysis. 6.13 Principal Coordinates analysis (PCO). 6.14 Non-metric Multidimensional Scaling (NMDS). 6.15 Seriation. Case study: Ashgill brachiopod paleocommunities from East China. 7 Time series analysis. 7.1 Introduction. 7.2 Spectral analysis. 7.3 Autocorrelation. 7.4 Cross-correlation. 7.5 Wavelet analysis. 7.6 Smoothing and filtering. 7.7 Runs test. Case study: Sepkoski's generic diversity curve for the Phanerozoic. 8 Quantitative biostratigraphy. 8.1 Introduction. 8.2 Parametric confidence intervals on stratigraphic ranges. 8.3 Non-parametric confidence intervals on stratigraphic ranges. 8.4 Graphic correlation. 8.5 Constrained optimisation. 8.6 Ranking and scaling. 8.7 Unitary Associations. 8.8 Biostratigraphy by ordination. 8.9 What is the best method for quantitative biostratigraphy?. Appendix A: Plotting techniques. Appendix B: Mathematical concepts and notation. References. Index

In the past correspondence analysis has been generally applied to two-way and multi-way contingency tables. However, data is sometimes presented m the form of rankings, and the analysis of treatments and their rankings often needs to be made. To apply correspondence analysis to ranked data, Anderson's chi-square statistic is considered instead of the classical Pearson statistic. The alternative approach to correspondence analysis discussed by Beh (1997) is also applicable to rank data if the researcher is interested in how the ranks and treatments compare in terms of location, dispersion and higher order components A brief discussion on the interpretation of the transition formulae of Beh (1997) is also made by considering the 3x3 bean example of Anderson (1959).

Correspondence analysis (CA) is a method of data visualization that is applicable to cross‐tabular data such as counts, compositions, or any ratio‐scale data where relative values are of interest. All the data should be on the same scale and the row and column margins of the table must make sense as weighting factors because the analysis gives varying importance to the respective rows and columns according to these margins. This method is one of a large class of methods based on the singular value decomposition and can be considered as the equivalent of principal component analysis for categorical and ratio‐scale data or as a pair of classical scalings of the rows and columns based on their interpoint χ2 distances, using the margins as weights. For categorical data, this method generalizes to multiple CA, a popular method for analyzing questionnaire data. A linearly constrained form of CA, canonical CA, is extensively used in ecological research where species abundance data at various sampling points are visualized subject to being linearly related to environmental variables measured at the same locations. When certain parameters are introduced into its definition, CA has been shown to have limiting cases of unweighted and weighted log‐ratio analysis (the latter also known as the spectral map), as well as classical multidimensional scaling. Copyright © 2010 John Wiley & Sons, Inc.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

One obvious, minimal pre-requisite in order to use Likert scores as cardinal numbers in data analysis is that they be perceived as more or less equidistant along the dimension of interest. Already 50 years ago, Johann Galtung among others raised serious doubts about the possibility that respondents actually do consider “agree” and “disagree” as equidistant from “uncertain”, given the well-known frequency of acquiescent response sets. In 1973, Benzecri maintained that the technique he had just launched on the academic market (correspondence analysis) supplied an excellent means to also control the assumption of equidistance of one of Likert’s short answers from the two adjoining ones. In the nineties, three young Italian students applied Benzecri’s technique to three different samples of respondents, and found converging results, all widely apart from the assumed equidistance. This essay replicates their survey on a larger sample of Likert scales coming from a dozen different surveys. Unlike the previous controls, the results diverge largely from one another. Yet, only a few offer a mild support to the assumption of perceived equidistance, while in their majority the results raise all sorts of further doubts about it.

Stratification by stepwise regression, correspondence analysis and recursive partition: a comparison of three methods of analysis for survival data with covariates

Putting Things in Order: The Ups and Downs of Detrended Correspondence Analysis