Direction dependence in a regression line

Dodge, Yadolah; Rousson, Valentin

doi:10.1080/03610920008832589

Cited by 67 publications

(69 citation statements)

References 8 publications

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“…Consideration of the skewness and kurtosis of two metric variables can lead to situations in which variables are no longer exchangeable in their status as predictor and outcome without causing systematic violations of model assumptions. In the bivariate case, an outcome variable will always be closer to the normal distribution than the predictor, that is, the (absolute value of the) skewness and the kurtosis of an outcome will always be smaller than the (absolute value of the) skewness and kurtosis of the predictor (Dodge & Rousson, 2000Dodge & Yadegari, 2010). Similar asymmetric properties exist for the error terms of competing models (Wiedermann, 2015;Wiedermann, Hagmann, & von Eye, 2015;Wiedermann & von Eye, 2015a, 2015b.…”

Section: Introductionmentioning

confidence: 70%

Direction of dependence in measurement error models

Wiedermann

Merkle

Eye

2017

Brit J Math & Statis

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Methods to determine the direction of a regression line, that is, to determine the direction of dependence in reversible linear regression models (e.g., x?y vs. y?x), have experienced rapid development within the last decade. However, previous research largely rested on the assumption that the true predictor is measured without measurement error. The present paper extends the direction dependence principle to measurement error models. First, we discuss asymmetric representations of the reliability coefficient in terms of higher moments of variables and the attenuation of skewness and excess kurtosis due to measurement error. Second, we identify conditions where direction dependence decisions are biased due to measurement error and suggest method of moments (MOM) estimation as a remedy. Third, we address data situations in which the true outcome exhibits both regression and measurement error, and propose a sensitivity analysis approach to determining the robustness of direction dependence decisions against unreliably measured outcomes. Monte Carlo simulations were performed to assess the performance of MOM-based direction dependence measures and their robustness to violated measurement error assumptions (i.e., non-independence and non-normality). An empirical example from subjective wellbeing research is presented. The plausibility of model assumptions and links to modern causal inference methods for observational data are discussed.

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Section: Introductionmentioning

confidence: 70%

Direction of dependence in measurement error models

Wiedermann

Merkle

Eye

2017

Brit J Math & Statis

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“…If the residuals are normally distributed, k e = 0, this expression simplifies to k F Y = r 4 k F X and we obtain, for component score variables, r 4 = k F Y =k F X : In applications in which researchers aim to determine whether F X or F Y is the explanatory variable, both kurtosis measures must be unequal to zero. In a similar way, we can derive the relationship between r and skewness that was originally derived, for manifest variables, by Dodge and Rousson (2000). Specifically, we now raise the expression in (30) to the third power and obtain…”

Section: Component Scores and Directional Dependencementioning

confidence: 95%

On Direction of Dependence in Latent Variable Contexts

Eye

Wiedermann

2013

Educational and Psychological Measurement

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Approaches to determining direction of dependence in nonexperimental data are based on the relation between higher-than second-order moments on one side and correlation and regression models on the other. These approaches have experienced rapid development and are being applied in contexts such as research on partner violence, attention deficit hyperactivity disorder, and currency exchange rates. In this article, we propose using these methods in the context of latent variables analysis. Specifically, we propose creating component or factor scores and relating the component score or factor score variables to each other by using methods for the determination of direction of dependence. Empirical examples use data from the development of aggression in adolescence. In the discussion, issues concerning the establishment of causal relation in empirical research are addressed. Keywords direction of effects, latent variables, PCA, SEMIn nonexperimental research, the direction of dependence, also called the direction of effects, is not always obvious. For example, Dodge and Rousson (2001) asked which of the world currencies affects others to increase or decrease in value. Nigg et al. (2008) asked whether an increased blood lead content is the cause for attention deficit hyperactivity disorder or whether attention deficit hyperactivity disorder has the effect that children expose themselves more often to lead-tainted objects. von Eye and DeShon (2012) asked whether intimate partner violence has the effect that the

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“…has derived an additional face of correlation coefficient and claims that it is more genralized result of Dodge and Rousson (2000) and Muddapur (2003). His result is given in the following theorem.…”

mentioning

confidence: 90%

A Remark on the Paper “A Note on Directional Dependence in Regression Setting” By Engin A. Sungur

Muddapur¹

2008

Communications in Statistics - Theory and Methods

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Direction dependence in a regression line

Cited by 67 publications

References 8 publications

Direction of dependence in measurement error models

Direction of dependence in measurement error models

On Direction of Dependence in Latent Variable Contexts

A Remark on the Paper “A Note on Directional Dependence in Regression Setting” By Engin A. Sungur

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