A New Method for Testing Interaction in Unreplicated Two-Way Analysis of Variance

Kharrati-Kopaei, Mahmood; Sadooghi-Alvandi, S. M.

doi:10.1080/03610920701386851

Cited by 14 publications

(30 citation statements)

References 17 publications

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“…This package contributes to available computational resources by (a) providing statistical and graphical diagnostic tools within the context of hidden additivity that enable the user to go beyond overall tests of additivity towards the inferential goal of characterizing and quantifying the magnitude of interaction, and (b) providing p-value computations for five methods to detect non-additivity. Supported tests include those proposed in Tukey (1949), Mandel (1961), Kharrati-Kopaei and Sadooghi-Alvandi (2007), Franck et al (2013), and Malik et al (2014). The latter three are newly available in an open-source repository via the hiddenf package, which is available from the Comprehensive R Archive Network (CRAN).…”

Section: The Hiddenf Packagementioning

confidence: 99%

“…The "Liming" data arises from an experiment that explores the utility of seven types of blast furnace slags as liming material in agriculture on three types of soil (Carter et al, 1951). The data were analyzed in the context of non-additivity in Johnson and Graybill (1972) and Kharrati-Kopaei and Sadooghi-Alvandi (2007). The outcome variable is yields of corn in bushels per acre.…”

Section: Data Examplesmentioning

confidence: 99%

“…This is problematic because inferences conducted under (1) will be incorrect if (1) fails to describe the true nature of the variables under investigation. Fortunately, many methods have been devised to assess non-additivity in these designs, including those in Tukey (1949), Anscombe and Tukey (1963), Mandel (1961), Mandel (1971), Johnson and Graybill (1972), Hirotsu (1982), Kharrati-Kopaei and Sadooghi-Alvandi (2007), Tusell (1990), Boik (1993a), Franck et al (2013), and Malik et al (2014). Alin and Kurt (2006) provide a review of methods available up to 2006.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exploring Interaction Effects in Two-Factor Studies using the hiddenf Package in R.

Franck¹,

Osborne²

2016

The R Journal

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In crossed, two-factor studies with one observation per factor-level combination, interaction effects between factors can be hard to detect and can make the choice of a suitable statistical model difficult. This article describes hiddenf, an R package that enables users to quantify and characterize a certain form of interaction in two-factor layouts. When effects of one factor (a) fall into two groups depending on the level of another factor, and (b) are constant within these groups, the interaction pattern is deemed "hidden additivity" because within groups, the effects of the two factors are additive, while between groups the factors are allowed to interact. The hiddenf software can be used to estimate, test, and report an appropriate factorial effects model corresponding to hidden additivity, which is intermediate between the unavailable full factorial model and the overly-simplistic additive model. Further, the software also conducts five statistical tests for interaction proposed between 1949 and 2014. A collection of 17 datasets is used for illustration.

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Section: The Hiddenf Packagementioning

confidence: 99%

Section: Data Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exploring Interaction Effects in Two-Factor Studies using the hiddenf Package in R.

Franck¹,

Osborne²

2016

The R Journal

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“…Violations of these assumptions can have a wide variety of negative consequences on inference; see Rencher and Schaalje (2008), Deschamps (1991) and Scheffé (1959). Model misspecification can lead to notion of latent group-based effects from the two-way layout to linear models; see Kharrati-Kopaei and Sadooghi-Alvandi (2007); Franck et al (2013); Franck and Osborne (2016), and Franck (2018).…”

Section: Introductionmentioning

confidence: 99%

“…Many methods exist to detect heteroscedasticity or conduct inference in its presence. To our knowledge, ours is the first proposal of latent group-based heteroscedasticity alongside possibly unique regression effects and/or hidden interactions.While an extension to more than two groups is natural, our choice of two groups is still a reasonable approach in many problems; Kharrati-Kopaei and Sadooghi-Alvandi (2007) and Franck (2018) study factor level groupings based on two groups in unreplicated two-way layouts, while Goldfeld and Quandt (1965) model heteroscedasticity as a function of two groups, where groups are created by partitioning observations ordinally.The main contribution of this work is to propose a method of probabilistically detecting the presence of hidden categorical level groupings, and to describe the model specifications that capture the effect of such groupings, through the use of Bayesian model selection. This work generalizes the…”

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confidence: 99%

Detection of latent heteroscedasticity and group-based regression effects in linear models via Bayesian model selection

Metzger

Franck

2020

Technometrics

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Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way unreplicated layout has shown that hidden groupings among the levels of one categorical predictor frequently interact with the ungrouped factor. We extend the notion of a "latent grouping factor" to linear models in general. The proposed work allows researchers to determine whether an apparent grouping of the levels of a categorical predictor reveals a plausible hidden structure given the observed data. Specifically, we offer Bayesian model selection-based approaches to reveal latent groupbased heteroscedasticity, regression effects, and/or interactions. Failure to account for such structures can produce misleading conclusions. Since the presence of latent group structures is frequently unknown a priori to the researcher, we use fractional Bayes factor methods and mixture g-priors to overcome lack of prior information. additional problems; see Rencher and Schaalje (2008), Rao (1971), and Deegan (1976.Regarding the detection of heteroscedasticity, many analyses follow a two-stage approach. These include the methods proposed by Bartlett (1937), Levene (1960), Brown andForsythe (1974), andHartley (1950). When heteroscedasticity is believed to be a function of a continuous predictor, many methods are available, including Breusch and Pagan (and Cribari-Neto and Zarkos (1999). Many methods exist to detect heteroscedasticity or conduct inference in its presence. To our knowledge, ours is the first proposal of latent group-based heteroscedasticity alongside possibly unique regression effects and/or hidden interactions.While an extension to more than two groups is natural, our choice of two groups is still a reasonable approach in many problems; Kharrati-Kopaei and Sadooghi-Alvandi (2007) and Franck (2018) study factor level groupings based on two groups in unreplicated two-way layouts, while Goldfeld and Quandt (1965) model heteroscedasticity as a function of two groups, where groups are created by partitioning observations ordinally.The main contribution of this work is to propose a method of probabilistically detecting the presence of hidden categorical level groupings, and to describe the model specifications that capture the effect of such groupings, through the use of Bayesian model selection. This work generalizes the

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Comparing means of several treatments with a control when one observation exists per treatment

Kharrati-Kopaei

2008

Metrika

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A New Method for Testing Interaction in Unreplicated Two-Way Analysis of Variance

Cited by 14 publications

References 17 publications

Exploring Interaction Effects in Two-Factor Studies using the hiddenf Package in R.

Exploring Interaction Effects in Two-Factor Studies using the hiddenf Package in R.

Detection of latent heteroscedasticity and group-based regression effects in linear models via Bayesian model selection

Comparing means of several treatments with a control when one observation exists per treatment

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