A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

Vera, José Ramón Navarro; Rooij, Mark de

doi:10.1080/00273171.2019.1634995

Cited by 4 publications

(6 citation statements)

References 35 publications

(51 reference statements)

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“…We also illustrate the performance of the model in a person‐oriented approach to data analysis, focusing on the personal profiles of the categorical variables (Bergman & Magnusson, 1997). To do so, we considered a personality data set (Spinhoven, de Rooij, Heiser, Penninx, & Smit, 2009) that was previously analysed, taking a person‐oriented approach, by Vera and de Rooij (2020) for sparse tables. In this paper, we analyse a non‐sparse data set in which the row profiles are based on the personality variables of Agreeableness and Conscientiousness, while the column profiles are cross‐classifications of the four mental disorders Major Depressive Disorder, Generalized Anxiety Disorder, Social Phobia, and Panic Disorder.…”

Section: Resultsmentioning

confidence: 99%

“…However, in this case the association plot may be difficult to interpret due to the presence of a large number of points (profiles). In this framework, a practical alternative is to combine latent class models (Vera, de Rooij, & Heiser, 2014) and latent block models (Vera & de Rooij, 2020), in conjunction with DA models. This approach makes it possible to represent associations in relation to the estimated clusters.…”

Section: Introductionmentioning

confidence: 99%

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Distance‐based logistic model for cross‐classified categorical data

Vera

2022

Brit J Math & Statis

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Logistic regression models are a powerful research tool for the analysis of cross-classified data in which a categorical response variable is involved. In a logistic model, the effect of a covariate refers to odds, and the simple relationship between the coefficients and the odds ratio often makes these the parameters of interest due to their easy interpretation. In this article we present a distance-based logistic model that allows a simple graphical interpretation of the association coefficients using the odds ratio in a contingency table. Two configurations are estimated, one for the rows and one for the columns, as the categories of a polytomous predictor and a nominal response variable respectively, such that the local odds ratio and the distances between the predictor and response categories are inversely related. The associations in terms of the odds ratios, or the ratios of the odds to their geometric means, are interpreted through distances for the most common coding schemes of the predictor variable, and the relationship between the distances related to different codings is investigated in its full dimension. The performance of the estimation procedure is analysed with a Monte Carlo experiment. The interpretation of the model and its performance, as well as its comparison with a two-step procedure involving first a logistic regression and then unfolding, is illustrated using real data sets.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distance‐based logistic model for cross‐classified categorical data

Vera

2022

Brit J Math & Statis

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“…For example, an interesting case is when several categorical explanatory variables are combined to conform a large number of profiles. [40][41][42] In this situation, the combination of categories forming the profiles causes a large number of auxiliary variables to emerge after recoding using dummy variables, and a problem of over-calibration may arise in this qualitative information framework. Other methods for selecting the optimal set of variables are also being investigated, in particular, related to combined MDS and cluster methods that allow reducing dimensionality.…”

Section: Discussionmentioning

confidence: 99%

A unified approach based on multidimensional scaling for calibration estimation in survey sampling with qualitative auxiliary information

Vera

Zuleta

Rueda

2023

Stat Methods Med Res

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Survey calibration is a widely used method to estimate the population mean or total score of a target variable, particularly in medical research. In this procedure, auxiliary information related to the variable of interest is used to recalibrate the estimation weights. However, when the auxiliary information includes qualitative variables, traditional calibration techniques may be not feasible or the optimisation procedure may fail. In this article, we propose the use of linear calibration in conjunction with a multidimensional scaling-based set of continuous, uncorrelated auxiliary variables along with a suitable metric in a distance-based regression framework. The calibration weights are estimated using a projection of the auxiliary information on a low-dimensional Euclidean space. The approach becomes one of the linear calibration with quantitative variables avoiding the usual computational problems in the presence of qualitative auxiliary information. The new variables preserve the underlying assumption in linear calibration of a linear relationship between the auxiliary and target variables, and therefore the optimal properties of the linear calibration method remain true. The behaviour of this approach is examined using a Monte Carlo procedure and its value is illustrated by analysing real data sets and by comparing its performance with that of traditional calibration procedures.

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“…Distance association (DA) models enable the representation of associations for a saturated log‐linear model in terms of squared Euclidean distances 2‐4 . It has been shown that the DA model produces the same expected frequencies than the RC(M) model, 5 although the graphical interpretation of the associations is easier in the DA model in terms of points in a Euclidean space 2 .…”

Section: Introductionmentioning

confidence: 99%

“…In low dimensions, the distance association model is an approximation to the traditional log‐linear model and, in general, it is more efficient than a two‐step procedure that first performs traditional log‐linear analysis and then represents the associations in terms of Euclidean distances. In a combined procedure of clustering and distance association model to deal with sparse data sets, the superiority of a simultaneous strategy compared to a two‐step procedure has been explicitly shown by Vera, de Rooij and Heiser 3 for the latent class distance association model and by Vera and de Rooij 4 for the latent block distance association model.…”

Section: Introductionmentioning

confidence: 99%

A two‐step log‐linear procedure for graphical representation and inference of associations in cross‐classified data for disease diagnosis

Vera,

Roldán‐Nofuentes

2023

Statistics in Medicine

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Biometrical sciences and disease diagnosis in particular, are often concerned with the analysis of associations for cross‐classified data, for which distance association models give us a graphical interpretation for non‐sparse matrices with a low number of categories. In this framework, usually binary exploratory and response variables are present, with analysis based on individual profiles being of great interest. For saturated models, we show the usual linear relationship for log‐linear models is preserved in full dimension for the distance association parameterization. This enables a two‐step procedure to facilitate the analysis and the interpretation of associations in terms of unfolding after the overall and main effects are removed. The proposed procedure can deal with cross‐classified data for profiles by binary variables, and it is easy to implement using traditional statistical software. For disease diagnosis, the problems of a degenerate solution in the unfolding representation, and that of determining significant differences between the profile locations are addressed. A hypothesis test of independence based on odds ratio is considered. Furthermore, a procedure is proposed to determine the causes of the significance of the test, avoiding the problem of error propagation. The equivalence between a test for equality of odds ratio pairs and the test for equality of location for two profiles in the unfolding representation in the disease diagnosis is shown. The results have been applied to a real example on the diagnosis of coronary disease, relating the odds ratios with performance parameters of the diagnostic test.

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A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

Cited by 4 publications

References 35 publications

Distance‐based logistic model for cross‐classified categorical data

Distance‐based logistic model for cross‐classified categorical data

A unified approach based on multidimensional scaling for calibration estimation in survey sampling with qualitative auxiliary information

A two‐step log‐linear procedure for graphical representation and inference of associations in cross‐classified data for disease diagnosis

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