Comparison of imputation techniques to deal with censored responses in a bivariate experimental design

Cecilia Abigail Zuñiga Maldonado, Manuel Darío Hernández Ripalda, José Alfredo Jiménez García


Introduction: The analysis of designs of experiments with bivariate answers can be a challenge for the researcher, especially when some data of the answers are censored. Chowdhury and Aggarwala (2007) presented a set of techniques to impute values to the censored data, in this work those techniques are compared. A method proposed by Chiao and Hamada (2001) is used to identify the optimal setting of parameters. The case with the data here is the one reported by Harper, Kosbe and Peyton (1987) about the imbalance of a plastic wheel cover component.                       

Method: The data of the experiment are not censored originally, these are analyzed in order to have a base of comparison. Criteria are then implemented to censor 16 and 21 percent of the responses, generating two new data sets, to which the imputation techniques are applied: 1) conditional expectation after regression of the responses, 2) order statistics and 3) simulated observations. For each generated data set, the optimal setting of parameters (Xopt) is determined and the sum of squares of the error (SCE) is calculated.                       

Results: With the censored data at 16%, the imputation techniques: conditional expectation starting with Y1, order statistics for Y1 and simulated observations for Y2, generate values with which a Xopt is obtained that agrees with the original data. With the censored data at 21%, none of the techniques obtains a Xopt that matches the original data. The sum of squares of the error of the response 1 (SCE1) of simulated observations for Y2 is significantly smaller compared to that of the other methods. The difference between the SCE2 resulting in all the techniques is not considerable.                    

Conclusion: After comparing the Xopt and the SCE resulting from the data sets imputed with the mentioned techniques it can be said that the simulated observations method with Y2 works better to deal with censored responses of the bivariate experiment design that is being worked on here.                    


design of bivariate experiments; censored data; imputation method; optimal setting of parameters


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