Reduced rank models for contingency tables

Leeuw, Jan de; Heijden, P.G.M. van der

doi:10.1093/biomet/78.1.229

Cited by 17 publications

(2 citation statements)

References 16 publications

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“…The joint contingency table of (Z 1 , Z 2 ) can then be expressed as a two-way table of size d K × d K , where each entry in the table corresponds to the probability of a response pattern of the original vector y and all these probabilities sum up to one. This setting can be considered as a reduced rank model for two-way contingency table (matrix) (De Leeuw and Van der Heijden, 1991), where the rank of the matrix is |{0, 1} K | = 2 K , equal to the number of states the latent vector α can take. It is well-known that such a matrix factorization generally can not be unique.…”

Section: Theoretical Results Of Generic Identifiability and Their Ill...mentioning

confidence: 99%

Blessing of Dependence: Identifiability and Geometry of Discrete Models with Multiple Binary Latent Variables

Gu¹

2022

Preprint

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Identifiability of discrete statistical models with latent variables is known to be challenging to study, yet crucial to a model's interpretability and reliability. This work presents a general algebraic technique to investigate identifiability of complicated discrete models with latent and graphical components. Specifically, motivated by diagnostic tests collecting multivariate categorical data, we focus on discrete models with multiple binary latent variables. In the considered model, the latent variables can have arbitrary dependencies among themselves while the latent-to-observed measurement graph takes a "star-forest" shape. We establish necessary and sufficient graphical criteria for identifiability, and reveal an interesting and perhaps surprising phenomenon of blessing-of-dependence geometry: under the minimal conditions for generic identifiability, the parameters are identifiable if and only if the latent variables are not statistically independent. Thanks to this theory, we can perform formal hypothesis tests of identifiability in the boundary case by testing certain marginal independence of the observed variables. Our results give new understanding of statistical properties of graphical models with latent variables. They also entail useful implications for designing diagnostic tests or surveys that measure binary latent traits.

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Section: Theoretical Results Of Generic Identifiability and Their Ill...mentioning

confidence: 99%

Blessing of Dependence: Identifiability and Geometry of Discrete Models with Multiple Binary Latent Variables

Gu¹

2022

Preprint

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“…In this paper, we show how to estimate the JCA model by means of maximum likelihood (ML). For standard CA of two-way tables, ML estimation methods have been developed, yielding what is known as a row-column correlation model (Goodman, 1985(Goodman, , 1987 or canonical analysis of two-way tables (Gilula & Haberman, 1986;De Leeuw & Van der Heijden, 1991). To be able to estimate the JCA model by ML, it has to be defined as a model for the full K-way distribution rather than as a model for the bivariate marginal distributions.…”

Section: Introductionmentioning

confidence: 99%

Joint Correspondence Analysis (JCA) by Maximum Likelihood

Vermunt

Anderson

2005

Methodology

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Parameter estimation in joint correspondence analysis (JCA) is typically performed by weighted least squares using the Burt matrix as the data matrix.In this paper, we show how to estimate the JCA model by means of maximum likelihood. For that purpose, JCA is defined as a model for the full K-way distribution by generalizing the correspondence analysis model for three-way tables proposed by Choulakian (1988aChoulakian ( , 1988b. The advantage of placing JCA in a more formal statistical framework is that standard chisquared tests can be applied to assess the goodness-of-fit of unrestricted and restricted models.

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Quantification of fluorescence properties of lymphocytes in peripheral blood mononuclear cell suspensions using a latent class model

et al. 1993

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Lymphocytes, monocytes, granulocytes, and other blood cells can be distinguished on the basis of their forward (FSC) and sideward (SSC) light scatter properties and their expression of CD45 and CD14. A FSC,SSC gate can be set to include >95% of the lymphocytes using a "back gating" procedure on the CD45 + , CD14-cells. However, nonlymphoid cells such as monocytes have light scattering properties similar to lymphocytes. This problem occurs particularly in patient populations where the light scattering properties of lymphocyte subsets have changed (e.g., due to activation) and are similar to those of the monocytes. Thus, immunophenotyping using antibodies specific for other markers than CD45 and CD14 does not allow a direct assessment of the percentage of all lymphocytes positive for those markers. In order to optimize immunophenotyping we have developed an analytic model in which the FSC,SSC dot plot is partitioned into six nonoverlapping light scatter regions. Each light scatter region containsThe identification and quantitative analysis of lymphocyte subsets are an important application of flow cytometry. Lymphocytes can be distinguished from other types of blood cells on the basis of their forward (FSC) and sideward (SSC) light scattering properties (8,lO). Recently, the technique of setting a light scatter gate around the lymphocytes has been optimized by including the expression of CD45 and CD14 in the definition of lymphocytes (5). With this technique, termed a mixture population of different cell types, i.e., lymphocytes, monocytes, granulocytes, and other cells. The proportions of each cell type are known from the CD45,CD14 expression within each light scatter region. Under the assumption of independence of fluorescence and scatter properties conditional on cell type, the expression of markers other than CD45 or CD14 are derived from the cell type composition and the fluorescence properties on the other markers of each light scatter region. The underlying statistical model is a latent class model, and maximum likelihood estimates are computed using the expectation-maximization (EM) algorithm. The application of the model for immunophenotyping of lymphocytes of healthy individuals and cancer patients receiving immunotherapy is shown.

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Reduced rank models for contingency tables

Cited by 17 publications

References 16 publications

Blessing of Dependence: Identifiability and Geometry of Discrete Models with Multiple Binary Latent Variables

Blessing of Dependence: Identifiability and Geometry of Discrete Models with Multiple Binary Latent Variables

Joint Correspondence Analysis (JCA) by Maximum Likelihood

Quantification of fluorescence properties of lymphocytes in peripheral blood mononuclear cell suspensions using a latent class model

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