New Measure Of Association Research Articles

Association Between Nominal Categorical Variables: New Measure Formulation Based on Metric Distances and Value Validity

When dealing with nominal categorical data, it is often desirable to know the degree of association or dependence between the categorical variables. While there is literally no limit to the number of alternative association measures that have been proposed over the years, they all yield greatly varying, contradictory, and unreliable results due to their lack of an important property: value validity. After discussing the value-validity property, this paper introduces a new measure of association (dependence) based on the mean Euclidean distance between probability distributions, one being a distribution under independence. Both the asymmetric form, when one variable can be considered as the explanatory (independent) variable and one as the response (dependent) variable, and the symmetric form of the measure are introduced. Particular emphasis is given to the important 2 × 2 case when each variable has two categories, but the general case of any number of categories is also covered. Besides having the value-validity property, the new measure has all the prerequisites of a good association measure. Comparisons are made with the well-known Goodman–Kruskal lambda and tau measures. Statistical inference procedure for the new measure is also derived and numerical examples are provided.

Bell correlations outside physics

Correlations are ubiquitous in nature and their principled study is of paramount importance in scientific development. The seminal contributions from John Bell offer a framework for analyzing the correlations between the components of quantum mechanical systems and have instigated an experimental tradition which has recently culminated with the Nobel Prize in Physics (2022). In physics, Bell’s framework allows the demonstration of the non-classical nature of quantum systems just from the analysis of the observed correlation patterns. Bell’s ideas need not be restricted to physics. Our contribution is to show an example of a Bell approach, based on the insight that correlations can be broken down into a part due to common, ostensibly significant causes, and a part due to noise. We employ data from finance (price changes of securities) as an example to demonstrate our approach, highlighting several general applications: first, we demonstrate a new measure of association, informed by the assumed causal relationship between variables. Second, our framework can lead to streamlined Bell-type tests of widely employed models of association, which are in principle applicable to any discipline. In the area of finance, such models of association are Factor Models and the bivariate Gaussian model. Overall, we show that Bell’s approach and the models we consider are applicable as general statistical techniques, without any domain specificity. We hope that our work will pave the way for extending our general understanding for how the structure of associations can be analyzed.

Functional Correlations in the Pursuit of Performance Assessment of Classifiers

In statistical classification and machine learning, as well as in social and other sciences, a number of measures of association have been proposed for assessing and comparing individual classifiers, raters, as well as their groups. In this paper, we introduce, justify, and explore several new measures of association, which we call CO-, ANTI-, and COANTI-correlation coefficients, that we demonstrate to be powerful tools for classifying confusion matrices. We illustrate the performance of these new coefficients using a number of examples, from which we also conclude that the coefficients are new objects in the sense that they differ from those already in the literature.

Causal criteria: time has come for a revision.

Epidemiologists study associations but they are usually interested in causation that could lead to disease prevention. Experience show, however, that many of the associations we identify are not the causes we take an interest in (correlation is not causation). In order to proper translate association into causes, a set of causal criteria was developed 50-60years ago and they became important tools guiding this translational process (sometimes correlation is causation). Best known of these are the Bradford Hill 'criteria'. In these last 50years, epidemiologic theory and infrastructure have advanced rapidly without changes in these causal criteria. We think time has come to revisit the 'old' criteria to see which ones we should keep and which ones should be taken out or be replaced by new measures of association. Robustness of these criteria in attempts to make the association go away should have high priority. A group of renowned internationally recognized researchers should have this task. Since classifying associations as causes is often done in order to reduce or eliminate the exposures of concern results from conditional outcome research should also be used. We therefore suggest to add a 'consequence' criterion. We argue that a consequence criterion that provides a framework for assessing or prescribing action worthy or right in social contexts is needed. A consequence criterion will also influence how strict our causal criteria need to be before leading to action and will help in separating the 'causal discussion' and the discussion on what to do about it. A consequence criterion will be a tool in handling dilemmas over values (as social solidarity, fairness, autonomy). It will have implications for the interpretation and use of the procedural criteria of causality. Establishing interconnected procedural and consequence criteria should be a task for institutions representing and being recognized by experts, civil society and the state.

A new measure of association between random variables

We propose a new measure of association between two continuous random variables X and Y based on the covariance between X and the log-odds rate associated to Y. The proposed index of correlation lies in the range [\(-1\), 1]. We show that the extremes of the range, i.e., \(-1\) and 1, are attainable by the Fr\(\acute{\mathrm{e}}\)chet bivariate minimal and maximal distributions, respectively. It is also shown that if X and Y have bivariate normal distribution, the resulting measure of correlation equals the Pearson correlation coefficient \(\rho \). Some interpretations and relationships to other variability measures are presented. Among others, it is shown that for non-negative random variables the proposed association measure can be represented in terms of the mean residual and mean inactivity functions. Some illustrative examples are also provided.

Collapsibility of some association measures and survival models

Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables Y and X equals the marginal measure of association. In this paper, we discuss the average collapsibility of certain well-known measures of association, and also with respect to a new measure of association. The concept of average collapsibility is more general than collapsibility, and requires that the conditional average of an association measure equals the corresponding marginal measure. Sufficient conditions for the average collapsibility of the association measures are obtained. Some interesting counterexamples are constructed and applications to linear, Poisson, logistic and negative binomial regression models are discussed. An extension to the case of multivariate covariate W is also analyzed. Finally, we discuss the collapsibility conditions of some dependence measures for survival models and illustrate them for the case of linear transformation models.

Matrix spectral norm Wielandt inequalities with statistical applications

In this article, we construct a new matrix spectral norm Wielandt inequality. Then we apply it to give the upper bound of a new measure of association. Finally, a new alterative based on the spectral norm for the relative gain of the covariance adjusted estimator of parameters vector is given.

A reformulation of the aggregate association index using the odds ratio

Since its inception in the 1950s the odds ratio has become one of the most simple and popular measures available for analysing the association between two dichotomous variables. Since the direction and magnitude of the association can be captured in such a simple measure, its impact has been felt throughout much of scientific research, in particular in epidemiology and clinical trials. Despite this, its applicability for analysing aggregate data has rarely been considered. In this paper we shall express a new measure of association (the aggregate association index, or AAI), in terms of the classic odds ratio. The advantage of doing so is that we are able to explore the use of the odds ratio in a context for which it was not originally intended, and that is for the analysis of a 2×2 table where only the aggregate data is known.

On measures of association among genetic variables

SummarySystems involving many variables are important in population and quantitative genetics, for example, in multi-trait prediction of breeding values and in exploration of multi-locus associations. We studied departures of the joint distribution of sets of genetic variables from independence. New measures of association based on notions of statistical distance between distributions are presented. These are more general than correlations, which are pairwise measures, and lack a clear interpretation beyond the bivariate normal distribution. Our measures are based on logarithmic (Kullback-Leibler) and on relative ‘distances’ between distributions. Indexes of association are developed and illustrated for quantitative genetics settings in which the joint distribution of the variables is either multivariate normal or multivariate-t, and we show how the indexes can be used to study linkage disequilibrium in a two-locus system with multiple alleles and present applications to systems of correlated beta distributions. Two multivariate beta and multivariate beta-binomial processes are examined, and new distributions are introduced: the GMS-Sarmanov multivariate beta and its beta-binomial counterpart.

Measures of association for identifying microRNA-mRNA pairs of biological interest.

MicroRNAs are a class of small non-protein coding RNAs that play an important role in the regulation of gene expression. Most studies on the identification of microRNA-mRNA pairs utilize the correlation coefficient as a measure of association. The use of correlation coefficient is appropriate if the expression data are available for several conditions and, for a given condition, both microRNA and mRNA expression profiles are obtained from the same set of individuals. However, there are many instances where one of the requirements is not satisfied. Therefore, there is a need for new measures of association to identify the microRNA-mRNA pairs of interest and we present two such measures. The first measure requires expression data for multiple conditions but, for a given condition, the microRNA and mRNA expression may be obtained from different individuals. The new measure, unlike the correlation coefficient, is suitable for analyzing large data sets which are obtained by combining several independent studies on microRNAs and mRNAs. Our second measure is able to handle expression data that correspond to just two conditions but, for a given condition, the microRNA and mRNA expression must be obtained from the same set of individuals. This measure, unlike the correlation coefficient, is appropriate for analyzing data sets with a small number of conditions. We apply our new measures of association to multiple myeloma data sets, which cannot be analyzed using the correlation coefficient, and identify several microRNA-mRNA pairs involved in apoptosis and cell proliferation.

Matrix Euclidean norm Wielandt inequalities and their applications to statistics

In this paper we shall establish a new matrix inequality which will fill the gap that there has not been any matrix Euclidean norm version of the Wielandt inequality in the literature yet. This inequality can be used to present an upper bound of a new measure of association which plays a very important role in statistics, especially in multivariate analysis. A new alternative based on Euclidean norm for relative gain of the covariance adjusted estimator of parameters is provided.

A new measure of association for bivariate survival data

Time dependent association measures between variables are of interest in bivariate survival data. Several such measures have been proposed in literature for the modelling and analysis of survival data. In this paper, we introduce a new measure of association for bivariate survival data using product moment residual life function and mean residual life function. Various properties of the proposed measure and its relationship with existing measures are discussed. We also develop a non-parametric estimator of the measure and study its asymptotic properties. The application of the result is illustrated using a real life data. Finally, a stimulation study is carried out to assess the performance of the estimator.

Statistical identification of gene association by CID in application of constructing ER regulatory network

BackgroundA variety of high-throughput techniques are now available for constructing comprehensive gene regulatory networks in systems biology. In this study, we report a new statistical approach for facilitating in silico inference of regulatory network structure. The new measure of association, coefficient of intrinsic dependence (CID), is model-free and can be applied to both continuous and categorical distributions. When given two variables X and Y, CID answers whether Y is dependent on X by examining the conditional distribution of Y given X. In this paper, we apply CID to analyze the regulatory relationships between transcription factors (TFs) (X) and their downstream genes (Y) based on clinical data. More specifically, we use estrogen receptor α (ERα) as the variable X, and the analyses are based on 48 clinical breast cancer gene expression arrays (48A).ResultsThe analytical utility of CID was evaluated in comparison with four commonly used statistical methods, Galton-Pearson's correlation coefficient (GPCC), Student's t-test (STT), coefficient of determination (CoD), and mutual information (MI). When being compared to GPCC, CoD, and MI, CID reveals its preferential ability to discover the regulatory association where distribution of the mRNA expression levels on X and Y does not fit linear models. On the other hand, when CID is used to measure the association of a continuous variable (Y) against a discrete variable (X), it shows similar performance as compared to STT, and appears to outperform CoD and MI. In addition, this study established a two-layer transcriptional regulatory network to exemplify the usage of CID, in combination with GPCC, in deciphering gene networks based on gene expression profiles from patient arrays.ConclusionCID is shown to provide useful information for identifying associations between genes and transcription factors of interest in patient arrays. When coupled with the relationships detected by GPCC, the association predicted by CID are applicable to the construction of transcriptional regulatory networks. This study shows how information from different data sources and learning algorithms can be integrated to investigate whether relevant regulatory mechanisms identified in cell models can also be partially re-identified in clinical samples of breast cancers.Availabilitythe implementation of CID in R codes can be freely downloaded from .

Matrix trace Wielandt inequalities with statistical applications

The vector correlation coefficient and other measures of association play a very important role in statistics and especially in multivariate analysis. In this paper a new measure of association is proposed and its upper bound is presented by using a matrix trace Wielandt inequality. Also given are relevant results involving Wishart matrices widely used in multivariate analysis, and especially a new alternative for the relative gain of the covariance adjusted estimator of a vector of parameters.

Identification of Base-triples in RNA using Comparative Sequence Analysis

Comparative sequence analysis has proven to be a very efficient tool for the determination of RNA secondary structure and certain tertiary interactions. However, base-triples, an important RNA structural element, cannot be predicted accurately from sequence data. We show here that the poor base correlations observed at base-triple positions are the result of two factors. (1) Base covariation is not as strictly required in triples as it is in Watson-Crick pairs. (2) Base-triple structures are less conserved among homologous molecules. A particularity of known triple-helical regions is the presence of multiple base correlations that do not reflect direct pairing. We suggest that natural mutations in base-triples create structural changes that require compensatory mutations in adjacent base-pairs and triples to maintain the triple-helix conformation. On the basis of these observations, we devised two new measures of association that significantly enhance the base-triple signal in correlation studies. We evaluated correlations between base-pairs and single stranded bases, and correlations between adjacent base-pairs. Positions that score well in both analyses are the best triple candidates. This procedure correctly identifies triples, or interactions very close to the proposed triples, in type I and type II tRNAs and in the group I intron.

Ein neues Zusammenhangsmaß für ordinalskalierte Merkmale / A New Measure of Association for Ordinal Variables

Zusammenfassung In dieser Arbeit wird das Zusammenhangsmaß T) vorgeschlagen, das die Stärke und die Richtung monotoner Beziehungen zwischen ordinalskalierten Merkmalen mißt. Dieser Zusammenhang wird unter der Bedingung gegebener Randverteilungen dieser Merkmale gemessen, weil diese Randverteilungen die Zusammenhangsstruktur der betrachteten Merkmale entscheidend determinieren. Die Konstruktion des Maßes beruht daher auf geeignet modifizierten Abständen bzw. der Position der gegebenen zweidimensionalen Häufigkeitsverteilung zu den aus ihren Randverteilungen ableitbaren zweidimensionalen Häufigkeitsverteilungen, die durch einen vollständigen monoton positiven bzw. negativen Zusammenhang gekennzeichnet sind. Ein Nachteil von T) ist sicherlich seine komplizierte Konstruktion und Berechnung, aber mit Hilfe eines Computerprogramms kann r) in Bruchteilen von Sekunden berechnet werden. Demgegenüber steht der Vorteil seiner anschaulichen Interpretierbarkeit auf der Grundlage der Position der gegebenen zweidimensionalen Häufigkeitsverteilung zwischen den beiden aus ihren Randverteilungen ableitbaren Extremen.

A Family of Multivariate Measures of Association for Nominal Independent Variables

A new measure of association is introduced which measures the degree of association between a nominal independent variable and nominal, ordinal, or interval dependent variables. An extension to multivariate problems provides analyses of multiple dependent variables, including mixtures of interval, ordinal, and/or nominal dependent variables. A commensuration technique is given for standardizing dependent variables. A permutation test of significance is provided for the new measures.

A new measure of association

This paper presents a new measure of association. It is applicable to polytomies of either categorical or numerical type. It has the desirable property of being 0 if and only if the polytomies are independent. Its properties are studied and compared to those of existing measures. An interpretation of it is given. One situation where it is particularly useful is in measuring the ability to predict one polytomy given knowledge of the other. An example is given where the proposed measure is more relevant in describing the degree of association between two polytomies than are any of the existing measures. The corresponding sample quantity is presented and its asymptotic properties are studied. A discussion of its use in inference is given. The test for independence based on this measure is contrasted with the chi-square test.

New measures of association for numerical variables

Hypothesis-testing in the social sciences has been constrained by the inability of conventional measures of association for numerical variables to model only a restricted class of one-to-one predictive statements. In order to test ‘if-then’ or other one-to-many predictions, we require a suitable paradigm for constructing new measures of bivariate association. This paper combines concepts from fuzzy set theory and the proportional reduction of error logic (PRE) which has been used for measures of association in contingency table problems, thereby providing a general framework for custom-designing measures of association. This framework incorporates probabilistic, fuzzy, and distance models for measuring deviation away from a prediction. This paper explores criteria for choosing among several competing measures, the issue of relative predictive stringency, estimation bias and stability, and optimization procedures for fitting a priori predictions to data. Examples are provided from real data sets.

Medida de asociación propia entre variables aleatorias discretas

In this work we study the association between two (non-cardinal) discrete random variables defining a new measure of association which is based on the speed of convergence of the vector of probability corresponding to the Markov chain associated to the joint probability distribution of the studied variables. We pay particular attention to the sampling study and to the properties of the corresponding estimators. Their asymptotic distributions under multinomial sampling and independent multinomial sampling in the rows are computed.