Transformations of Multivariate Data

Andrews, D. F.; Gnanadesikan, R.; Warner, Jack L.

doi:10.2307/2528821

Cited by 161 publications

(56 citation statements)

References 12 publications

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“…We investigate this relationship econometrically using the Box-Cox model extended for use with multi-variate data (Box and Cox 1964;Andrews et al 1971). In particular, we adopt the following functional form of the Box-Cox model, which has become an accepted standard in econometric studies in cases where specification of the functional relationship between some variables of interest cannot be based on a priori economic rationale (Sakia 1992):…”

Section: Empirical Strategymentioning

confidence: 99%

Is the Income Elasticity of the Willingness to Pay for Pollution Control Constant?

Barbier

Czajkowski

Hanley

2016

Environ Resource Econ

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How willingness to pay for environmental quality changes as incomes rise is a central question in several areas of environmental economics. This paper explores both theoretically and empirically whether or not the willingness to pay (WTP) for pollution control varies with income. Our model indicates that the income elasticity of the marginal WTP for pollution reduction is only constant under very restrictive conditions. Our empirical analysis tests the null hypothesis that the elasticity of the WTP for pollution control with respect to income is constant, employing a multi-country contingent valuation study of eutrophication reduction in the Baltic Sea. Our findings reject this hypothesis, and estimate an income elasticity of the WTP for eutrophication control of 0.1-0.2 for low-income respondents and 0.6-0.7 for high-income respondents. Thus, our empirical results suggest that the elasticity is not constant but is always less than one. This has implications for how benefits transfer exercises, and for theoretical explanations of the environmental Kuznets curve.

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Section: Empirical Strategymentioning

confidence: 99%

Is the Income Elasticity of the Willingness to Pay for Pollution Control Constant?

Barbier

Czajkowski

Hanley

2016

Environ Resource Econ

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“…A common transformation is the Box-Cox (Box and Cox 28 ) power family of transformation. See also Andrews et al 29 . Furthermore, if the error distribution is considered heavy-tailed, modeling with the multivariate t distribution may be a suitable approach.…”

Section: Summary and Discussionmentioning

confidence: 96%

Compromise ascent directions for multiple‐response applications

Edwards

Fuerte

2011

Quality & Reliability Eng

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A process or system under study often requires the measurement of multiple responses. The optimization of multiple response variables has received considerable attention in the literature with the majority focusing on locating optimal operating conditions within the current experimental region and thus often occurs in the later stages of experimentation. This article focuses instead on the initial experiment and the location of additional experimental runs if the region of interest shifts. Considerable trade-off is often required in the multiple response context. In order to account for uncertainty in the model parameters and correlations among the responses, we propose the computation of Bayesian reliabilities to determine optimal factor settings for future experimental runs. The approach will be described in detail for two common design follow-up strategies: steepest ascent (descent) and shifting factor levels. Illustrative examples are provided for each application.

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“…Since multivariate normality plays a central role in all these approaches, one must, however, remain alert to the impact on the results of possible departures from multivariate normality [Hopper, 19861. Fortunately, if actual data are highly non-normal, it is possible to enhance normality by means of suitable (marginal) data transformations [eg, Andrews et al, 1971Andrews et al, , 1973Rao et al, 1984b;McGue et al, 19871. This may be accomplished by assuming that a certain transformation of X, and not X itself, is multivariate normally distributed [eg, MacLean et al, 1976;George and Elston, 19871.…”

Section: Discussionmentioning

confidence: 99%

Nonrandom sampling in genetic epidemiology: Maximum likelihood methods for multifactorial analysis of quantitative data ascertained through truncation

Rao

Wette

1987

Genetic Epidemiology

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Three types of nonrandom sampling of family data are described, and appropriate maximum likelihood methods are proposed for each. The three types arise depending on whether the selection of probands, based on truncation, is applied directly to the phenotypic distribution, to the distribution of a correlated trait, or to the liability distribution of an associated disease. Family data ascertained through random and nonrandom sampling can be analyzed together in a unified approach. Results of a Monte Carlo study are presented that demonstrate the utility of the proposed methods. In particular, likelihood ratio tests of null hypotheses are shown to be distributed as chi-square, even in samples as small as 50 families (with variable sibship size).

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Transformations of Multivariate Data

Cited by 161 publications

References 12 publications

Is the Income Elasticity of the Willingness to Pay for Pollution Control Constant?

Is the Income Elasticity of the Willingness to Pay for Pollution Control Constant?

Compromise ascent directions for multiple‐response applications

Nonrandom sampling in genetic epidemiology: Maximum likelihood methods for multifactorial analysis of quantitative data ascertained through truncation

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