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21
Binary models for marginal independence
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B
, 2005
"... A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a versi ..."
Abstract

Cited by 16 (2 self)
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A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. The approach is illustrated on a simple example. Relations to multivariate logistic and dependence ratio models are discussed.
Analyzing Incomplete Discrete Longitudinal Clinical Trial Data
, 2006
"... Abstract. Commonly used methods to analyze incomplete longitudinal clinical trial data include complete case analysis (CC) and last observation carried forward (LOCF). However, such methods rest on strong assumptions, including missing completely at random (MCAR) for CC and unchanging profile after ..."
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Cited by 1 (1 self)
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Abstract. Commonly used methods to analyze incomplete longitudinal clinical trial data include complete case analysis (CC) and last observation carried forward (LOCF). However, such methods rest on strong assumptions, including missing completely at random (MCAR) for CC and unchanging profile after dropout for LOCF. Such assumptions are too strong to generally hold. Over the last decades, a number of full longitudinal data analysis methods have become available, such as the linear mixed model for Gaussian outcomes, that are valid under the much weaker missing at random (MAR) assumption. Such a method is useful, even if the scientific question is in terms of a single time point, for example, the last planned measurement occasion, and it is generally consistent with the intentiontotreat principle. The validity of such a method rests on the use of maximum likelihood, under which the missing data mechanism is ignorable as soon as it is MAR. In this paper, we will focus on nonGaussian outcomes, such as
Algebraic Descriptions of Nominal Multivariate Discrete Data
 J. Multivariate Anal
, 1995
"... Traditionally, multivariate discrete data are analyzed by means of loglinear models. In this paper we show how an algebraic approach leads naturally to alternative models, parametrized in terms of the moments of the distribution. Moreover we derive a complete characterization of all meaningful tran ..."
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Cited by 1 (0 self)
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Traditionally, multivariate discrete data are analyzed by means of loglinear models. In this paper we show how an algebraic approach leads naturally to alternative models, parametrized in terms of the moments of the distribution. Moreover we derive a complete characterization of all meaningful transformations of the components and show how transformations affect the moments of a distribution. It turns out that our models provide the necessary formal description of longitudinal data; moreover in the classical case, they can be considered as an analysis tool, complementary to loglinear models. 1 Introduction We start with a given multivariate discrete nominal variable X. Questions of interest about X can be roughly divided into two groups. One group is related to conditional characteristics such as conditional independencies or questions concerning the sign and/or magnitude of logodds ratios. The other group focuses on marginal characteristics such as marginal independencies or multiv...
DOI: 10.1007/S113360079034Z MOKKEN SCALE ANALYSIS FOR DICHOTOMOUS ITEMS USING MARGINAL MODELS
, 2008
"... Scalability coefficients play an important role in Mokken scale analysis. For a set of items, scalability coefficients have been defined for each pair of items, for each individual item, and for the entire scale. Hypothesis testing with respect to these scalability coefficients has not been fully de ..."
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Scalability coefficients play an important role in Mokken scale analysis. For a set of items, scalability coefficients have been defined for each pair of items, for each individual item, and for the entire scale. Hypothesis testing with respect to these scalability coefficients has not been fully developed. This study introduces marginal modelling as a framework to derive the standard errors for the scaling coefficients and test hypotheses about these coefficients. Several examples demonstrate the possibilities of marginal modelling in Mokken scale analysis. These possibilities include testing whether Mokken’s criteria for a scale are satisfied, testing whether scalability coefficients of different items are equal, and testing whether scalability coefficients are equal across different groups. Key words: marginal models, Mokken scale analysis, scalability coefficients, test construction. 1.
ℓEM: A general program for the analysis of categorical data 1
, 1997
"... When you report results obtained with ℓEM, you should refer to this manual as “Vermunt, J.K. ..."
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When you report results obtained with ℓEM, you should refer to this manual as “Vermunt, J.K.
DECOMPOSITIONS OF MARGINAL HOMOGENE ITY MODEL USING CUMULATIVE LOGISTIC MODELS FOR MULTIWAY CONTINGENCY TABLES Authors:
, 2006
"... the marginal cumulative logistic (ML) model, which is an extension of the marginal homogeneity (MH) model. Miyamoto, Niibe and Tomizawa (2005) proposed the conditional marginal cumulative logistic (CML) model which is defined off the main diagonal cells, and gave the decompositions of the MH model u ..."
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the marginal cumulative logistic (ML) model, which is an extension of the marginal homogeneity (MH) model. Miyamoto, Niibe and Tomizawa (2005) proposed the conditional marginal cumulative logistic (CML) model which is defined off the main diagonal cells, and gave the decompositions of the MH model using the ML (CML) model. This paper (1) considers the ML and CML models for multiway tables, and (2) gives the decompositions of the MH model into the ML (CML) model and the model of the equality of marginal means for multiway tables. An example is given. KeyWords: decomposition; marginal cumulative logistic model; marginal homogeneity; marginal mean; multiway contingency table. AMS Subject Classification: • 62H17. 164 K. Tahata, S. Katakura and S. TomizawaDecompositions of Marginal Homogeneity Model 165
Biometrics DOI: 10.1111/j.15410420.2006.00525.x Multivariate Extensions of McNemar’s Test
"... Summary. This article considers global tests of differences between paired vectors of binomial probabilities, based on data from two dependent multivariate binary samples. Difference is defined as either an inhomogeneity in the marginal distributions or asymmetry in the joint distribution. For detec ..."
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Summary. This article considers global tests of differences between paired vectors of binomial probabilities, based on data from two dependent multivariate binary samples. Difference is defined as either an inhomogeneity in the marginal distributions or asymmetry in the joint distribution. For detecting the first type of difference, we propose a multivariate extension of McNemar’s test and show that it is a generalized score test under a GEE approach. Univariate features such as the relationship between the Wald and score test and the dropout of pairs with the same response carry over to the multivariate case and the test does not depend on the working correlation assumption among the components of the multivariate response. For sparse or imbalanced data, such as occurs when the number of variables is large or the proportions are close to zero, the test is best implemented using a bootstrap, and if this is computationally too complex, a permutation distribution. We apply the test to safety data for a drug, in which two doses are evaluated by comparing multiple responses by the same subjects to each one of them.
with application to safety studies for drugs
, 2003
"... Multivariate tests comparing binomial probabilities, ..."
Alternative parametrizations and reference priors for decomposable discrete graphical models
, 2007
"... ..."
Incomplete hierarchical data
, 2007
"... The researcher collecting hierarchical data is frequently confronted with incompleteness. Since the processes governing missingness are often outside the investigator’s control, no matter how well the experiment has been designed, careful attention is needed when analyzing such data. We sketch a sta ..."
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The researcher collecting hierarchical data is frequently confronted with incompleteness. Since the processes governing missingness are often outside the investigator’s control, no matter how well the experiment has been designed, careful attention is needed when analyzing such data. We sketch a standard framework and taxonomy largely based on Rubin’s work. After briefly touching upon (overly) simple methods, we turn to a number of viable candidates for a standard analysis, including direct likelihood, multiple imputation and versions of generalized estimating equations. Many of these require socalled ignorability. With the latter condition not necessarily satisfied, we also review flexible models for the outcome and missingness processes at the same time. Finally, we illustrate how such methods can be very sensitive to modeling assumptions and then conclude with a number of routes for sensitivity analysis. Attention will be given to the feasibility of the proposed modes of analysis within a regulatory environment. 1