Comparison of conditional main effects analysis to the analysis of follow‐up experiments for separating confounded two‐factor interaction effects in 2IVk−p fractional factorial experiments

2020 ◽  
Vol 36 (4) ◽  
pp. 1454-1472
Author(s):  
John Lawson
Keyword(s):  
Interaction Effects ◽  
Fractional Factorial ◽  
Factorial Experiments ◽  
Main Effects ◽  
Factor Interaction

Exploring the Role of Interaction Effects in Visual Conjoint Analysis

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Brian Sylcott ◽  
Jeremy J. Michalek ◽  
Jonathan Cagan
Keyword(s):  
Conjoint Analysis ◽  
Consumer Preferences ◽  
Consumer Preference ◽  
Interaction Effects ◽  
Fractional Factorial ◽  
Main Effects ◽  
Full Factorial ◽  
Biased Estimates ◽  
Data Requirements

In conjoint analysis, interaction effects characterize how preference for the level of one product attribute is dependent on the level of another attribute. When interaction effects are negligible, a main effects fractional factorial experimental design can be used to reduce data requirements and survey cost. This is particularly important when the presence of many parameters or levels makes full factorial designs intractable. However, if interaction effects are relevant, main effects design can create biased estimates and lead to erroneous conclusions. This work investigates consumer preference interactions in the nontraditional context of visual choice-based conjoint analysis, where the conjoint attributes are parameters that define a product's shape. Although many conjoint studies assume interaction effects to be negligible, they may play a larger role for shape parameters. The role of interaction effects is explored in two visual conjoint case studies. The results suggest that interactions can be either negligible or dominant in visual conjoint, depending on consumer preferences. Generally, we suggest using randomized designs to avoid any bias resulting from the presence of interaction effects.

The Mechanisms by Which Adaptive One-factor-at-a-time Experimentation Leads to Improvement

2005 ◽  
Vol 128 (5) ◽  
pp. 1050-1060 ◽  
Author(s):  
Daniel D. Frey ◽  
Rajesh Jugulum
Keyword(s):  
Case Studies ◽  
Random Error ◽  
High Probability ◽  
Fractional Factorial ◽  
Engineering Systems ◽  
Factorial Experiments ◽  
Physical Experiments ◽  
Simulation Results ◽  
Main Effects ◽  
Full Factorial

This paper examines mechanisms underlying the phenomenon that, under some conditions, adaptive one-factor-at-a-time experiments outperform fractional factorial experiments in improving the performance of mechanical engineering systems. Five case studies are presented, each based on data from previously published full factorial physical experiments at two levels. Computer simulations of adaptive one-factor-at-a-time and fractional factorial experiments were carried out with varying degrees of pseudo-random error. For each of the five case studies, the average outcomes are plotted for both approaches as a function of the strength of the pseudo-random error. The main effects and interactions of the experimental factors in each system are presented and analyzed to illustrate how the observed simulation results arise. The case studies show that, for certain arrangements of main effects and interactions, adaptive one-factor-at-a-time experiments exploit interactions with high probability despite the fact that these designs lack the resolution to estimate interactions. Generalizing from the case studies, four mechanisms are described and the conditions are stipulated under which these mechanisms act.

Characteristic of Competitive Adsorption of Dimethoate with a Variety of Pollutants on Surficial Sediments through Fractional Factorial Design

2012 ◽  
Vol 599 ◽  
pp. 467-471
Author(s):  
Meng Wang ◽  
Xiao Li Li ◽  
Yu Li
Keyword(s):  
Factorial Design ◽  
Fractional Factorial Design ◽  
Design Method ◽  
Interaction Effects ◽  
Second Order ◽  
Fractional Factorial ◽  
Surficial Sediments ◽  
Order Interaction ◽  
Compound Pollution ◽  
Main Effects

In order to reveal the combined pollution characteristic of dimethoate adsorption onto the surficial sediments in pesticide (dimethoate, metalaxyl, atrazine, malathion, prometryn)/heavy metals (copper, zinc, lead, cadmium, nickel) composite contamination system, a completely foldover design and confounding design assisted resolution Ⅲ of 210-6 fractional factorial design method is used to identify the main effects and interactions of these ten pollution factors. The study found that the main effects of zinc, cadmium, malathion, prometryn have significant effect (α=0.05) to dimethoate adsorption on the sediment, in which zinc and cadmium will significantly antagonism to adsorption of dimethoate, while metalaxyl and prometryn will significantly collaborative to adsorption of dimethoate, and these main effects’ contribution rates are 64.4% and the second-order interaction effects’ contributions are 35.6%. According to the effect estimates of main effects and second-order interaction effects, zinc*prometryn and cadmium*atrazine have significantly antagonism to adsorption of dimethoate. Moreover, we also can estimate the compound pollution levels about the target pollutant on these main effects and second-order interaction effects of pollutant factors.

Étude des conditions de la réaction de condensation de Claisen–Schmidt de la furylméthylcétone sur le 2,5-furanedicarboxaldehyde

1992 ◽  
Vol 70 (8) ◽  
pp. 2306-2309 ◽  
Author(s):  
Carmen Dominguez ◽  
Joaquín Plumet ◽  
Antoine Gaset ◽  
Luc Rigal
Keyword(s):  
Factorial Design ◽  
Fractional Factorial Design ◽  
Interaction Effects ◽  
Fractional Factorial ◽  
Reaction Conditions ◽  
Schmidt Reaction ◽  
Five Factors ◽  
Main Effects

The Claisen–Schmidt reaction of 2,5-furandicarboxaldehyde (FDC) with 2-acetylfuran allows for the synthesis of three products as a function of the reaction conditions. The main effects of five factors and their interaction effects on seven responses have been quantified by means of a fractional factorial design.

Towards Understanding the Role of Interaction Effects in Visual Conjoint Analysis

2013 ◽  
Author(s):  
Brian Sylcott ◽  
Jeremy J. Michalek ◽  
Jonathan Cagan
Keyword(s):  
Conjoint Analysis ◽  
Consumer Preferences ◽  
Consumer Preference ◽  
Interaction Effects ◽  
Fractional Factorial ◽  
Factorial Designs ◽  
Shape Parameterization ◽  
New Space ◽  
Main Effects

We investigate consumer preference interactions in visual choice-based conjoint analysis, where the conjoint attributes are parameters that define shapes shown to the respondent as images. Interaction effects are present when preference for the level of one attribute is dependent on the level of another attribute. When interaction effects are negligible, a main-effects fractional factorial experimental design can be used to reduce data requirements and survey cost. This is particularly important when the presence of many parameters or levels makes full factorial designs intractable. However, if interaction effects are relevant, a main-effects design creates biased estimates and potentially misleading conclusions. Most conjoint studies assume interaction effects are negligible; however, interactions may play a larger role for shape parameters than for other types of attributes. We conduct preliminary tests on this assumption in three visual conjoint studies. The results suggest that interactions can be either negligible or dominant in visual conjoint, depending on both consumer preferences and shape parameterization. When interactions are anticipated, it is possible in some cases to re-parameterize the shape such that interactions in the new space are negligible. Generally, we suggest that randomized designs are better than fractional factorial designs at avoiding bias due to the presence of interactions and/or the organization of profiles into choice sets.

scholarly journals Updating the evidence on the effectiveness of the alcohol reduction app, Drink Less: using Bayes factors to analyse trial datasets supplemented with extended recruitment

F1000Research ◽  
2019 ◽  
Vol 8 ◽  
pp. 114
Author(s):  
Claire Garnett ◽  
Susan Michie ◽  
Robert West ◽  
Jamie Brown
Keyword(s):  
Interaction Effects ◽  
Outcome Data ◽  
Bayes Factors ◽  
Factorial Experiment ◽  
Weak Evidence ◽  
Audit Score ◽  
The Uk ◽  
Main Effects ◽  
Alcohol Reduction

Background: A factorial experiment evaluating the Drink Less app found no clear evidence for main effects of enhanced versus minimal versions of five components but some evidence for an interaction effect. Bayes factors (BFs) showed the data to be insensitive. This study examined the use of BFs to update the evidence with further recruitment. Methods: A between-subject factorial experiment evaluated the main and two-way interaction effects of enhanced versus minimal version of five components of Drink Less. Participants were excessive drinkers, aged 18+, and living in the UK. After the required sample size was reached (n=672), additional data were collected for five months. Outcome measures were change in past week alcohol consumption and Alcohol Use Disorders Identification Test (AUDIT) score at one-month follow-up, amongst responders only. BFs (with a half-normal distribution) were calculated for those for which we had outcome data (BF<0.33 indicate evidence for null hypothesis; 0.33<BF<3 indicate data are insensitive). Results: Of the sample of 2586, 342 (13.2%) responded to follow-up. Data were mainly insensitive but tended to support there being no large main effects of the enhanced version of individual components on consumption (0.22<BF<0.83) or AUDIT score (0.14<BF<0.98). Data no longer supported there being two-way interaction effects. In an unplanned comparison, participants receiving the four most promising components averaged a numerically greater reduction in consumption than those not receiving any (21.6 versus 12.1 units), but the data were insensitive (BF=1.42). Conclusions: Data from extended recruitment in a factorial experiment evaluating components of the Drink Less app remained insensitive but tended towards individual and pairs of components not having a large effect. There was weak evidence for a synergistic effect of four components. In the event of uncertain results, calculating BFs can be used to update the strength of evidence of a dataset supplemented with extended recruitment.

Optimal Design Procedure for Two-Level Fractional Factorial Experiments Given Partial Prior Information about Parameters

1978 ◽  
Vol 22 (1) ◽  
pp. 598-598
Author(s):  
Steven M. Sidik ◽  
Arthur G. Holms
Keyword(s):  
Optimal Design ◽  
Prior Knowledge ◽  
Prior Information ◽  
Design Procedure ◽  
Fractional Factorial ◽  
Factorial Experiment ◽  
Factorial Experiments ◽  
Full Factorial Experiment ◽  
Main Effects ◽  
Full Factorial

In many cases in practice an experimenter has some prior knowledge of indefinite validity concerning the main effects and interactions which would be estimable from a two-level full factorial experiment. Such information should be incorporated into the design of the experiment.

scholarly journals Updating the evidence on the effectiveness of the alcohol reduction app, Drink Less: using Bayes factors to analyse trial datasets supplemented with extended recruitment

F1000Research ◽  
2019 ◽  
Vol 8 ◽  
pp. 114 ◽  
Author(s):  
Claire Garnett ◽  
Susan Michie ◽  
Robert West ◽  
Jamie Brown
Keyword(s):  
Additional Data ◽  
Interaction Effects ◽  
Exploratory Analysis ◽  
Bayes Factors ◽  
Factorial Experiment ◽  
Audit Score ◽  
The Uk ◽  
Main Effects ◽  
Alcohol Reduction

Background: A factorial experiment evaluating the Drink Less app found no clear evidence for main effects of enhanced versus minimal versions of five components but some evidence for an interaction effect. Bayes factors (BFs) showed the data to be insensitive. This study examined the use of BFs to update the evidence with further recruitment. Methods: A between-subject factorial experiment evaluated the main and two-way interaction effects of enhanced versus minimal version of five components of Drink Less. Participants were excessive drinkers, aged 18+, and living in the UK. After the required sample size was reached (n=672), additional data were collected for five months. Outcome measures were change in past week alcohol consumption and Alcohol Use Disorders Identification Test (AUDIT) score at one-month follow-up, amongst responders only (those who completed the questionnaire). BFs (with a half-normal distribution) were calculated (BF<0.33 indicate evidence for null hypothesis; 0.33<BF<3 indicate data are insensitive). Results: Of the sample of 2586, 342 (13.2%) responded to follow-up. Data were mainly insensitive but tended to support there being no large main effects of the enhanced version of individual components on consumption (0.22<BF<0.83) or AUDIT score (0.14<BF<0.98). Data no longer supported there being two-way interaction effects (0.31<BF<1.99). In an additional exploratory analysis, participants receiving four of the components averaged a numerically greater reduction in consumption than those not receiving any (21.6 versus 12.1 units), but the data were insensitive (BF=1.42). Conclusions: Data from extended recruitment in a factorial experiment evaluating components of Drink Less remained insensitive but tended towards individual and pairs of components not having a large effect. In an exploratory analysis, there was weak, anecdotal evidence for a synergistic effect of four components. In the event of uncertain results, calculating BFs can be used to update the strength of evidence of a dataset supplemented with extended recruitment.

Are More Profiles Better Than Fewer?: Searching for Parsimony and Relevance in Stated Choice Experiments

2000 ◽  
Vol 1719 (1) ◽  
pp. 165-174 ◽  
Author(s):  
Peter R. Stopher ◽  
David A. Hensher
Keyword(s):  
New Zealand ◽  
Degrees Of Freedom ◽  
Choice Model ◽  
Fractional Factorial ◽  
Sources Of Information ◽  
Stated Choice ◽  
Complex Design ◽  
Data Collection Instrument ◽  
Main Effects ◽  
Better Than

Transportation planners increasingly include a stated choice (SC) experiment as part of the armory of empirical sources of information on how individuals respond to current and potential travel contexts. The accumulated experience with SC data has been heavily conditioned on analyst prejudices about the acceptable complexity of the data collection instrument, especially the number of profiles (or treatments) given to each sampled individual (and the number of attributes and alternatives to be processed). It is not uncommon for transport demand modelers to impose stringent limitations on the complexity of an SC experiment. A review of the marketing and transport literature suggests that little is known about the basis for rejecting complex designs or accepting simple designs. Although more complex designs provide the analyst with increasing degrees of freedom in the estimation of models, facilitating nonlinearity in main effects and independent two-way interactions, it is not clear what the overall behavioral gains are in increasing the number of treatments. A complex design is developed as the basis for a stated choice study, producing a fractional factorial of 32 rows. The fraction is then truncated by administering 4, 8, 16, 24, and 32 profiles to a sample of 166 individuals (producing 1, 016 treatments) in Australia and New Zealand faced with the decision to fly (or not to fly) between Australia and New Zealand by either Qantas or Ansett under alternative fare regimes. Statistical comparisons of elasticities (an appropriate behavioral basis for comparisons) suggest that the empirical gains within the context of a linear specification of the utility expression associated with each alternative in a discrete choice model may be quite marginal.

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