On Estimating Causal Effects based on Supplemental Variables

Takahiro Hayashi, Manabu Kuroki
Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, PMLR 33:312-319, 2014.

Abstract

This paper considers the problem of estimating causal effects of a treatment on a response using supplementary variables. Under the assumption that a treatment is associated with a response through a univariate supplementary variable in the framework of linear regression models, Cox (1960) showed that the estimation accuracy of the regression coefficient of the treatment on the response in the single linear regression model can be improved by using the recursive linear regression model based on the supplementary variable from the viewpoint of the asymptotic variance. However, such assumptions may not hold in many practical situations. In this paper, we consider the situation where a treatment is associated with a response through a set of supplementary variables in both linear and discrete models. Then, we show that the estimation accuracy of the causal effect can be improved by using the supplementary variables. Different from Cox (1960), the results of this paper are derived without the assumption of Gaussian error terms in linear models or dichotomous variables in discrete models. The results of this paper help us to obtain the reliable evaluation of causal effects from observed data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v33-hayashi14, title = {{On Estimating Causal Effects based on Supplemental Variables}}, author = {Hayashi, Takahiro and Kuroki, Manabu}, booktitle = {Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics}, pages = {312--319}, year = {2014}, editor = {Kaski, Samuel and Corander, Jukka}, volume = {33}, series = {Proceedings of Machine Learning Research}, address = {Reykjavik, Iceland}, month = {22--25 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v33/hayashi14.pdf}, url = {https://proceedings.mlr.press/v33/hayashi14.html}, abstract = {This paper considers the problem of estimating causal effects of a treatment on a response using supplementary variables. Under the assumption that a treatment is associated with a response through a univariate supplementary variable in the framework of linear regression models, Cox (1960) showed that the estimation accuracy of the regression coefficient of the treatment on the response in the single linear regression model can be improved by using the recursive linear regression model based on the supplementary variable from the viewpoint of the asymptotic variance. However, such assumptions may not hold in many practical situations. In this paper, we consider the situation where a treatment is associated with a response through a set of supplementary variables in both linear and discrete models. Then, we show that the estimation accuracy of the causal effect can be improved by using the supplementary variables. Different from Cox (1960), the results of this paper are derived without the assumption of Gaussian error terms in linear models or dichotomous variables in discrete models. The results of this paper help us to obtain the reliable evaluation of causal effects from observed data.} }
Endnote
%0 Conference Paper %T On Estimating Causal Effects based on Supplemental Variables %A Takahiro Hayashi %A Manabu Kuroki %B Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2014 %E Samuel Kaski %E Jukka Corander %F pmlr-v33-hayashi14 %I PMLR %P 312--319 %U https://proceedings.mlr.press/v33/hayashi14.html %V 33 %X This paper considers the problem of estimating causal effects of a treatment on a response using supplementary variables. Under the assumption that a treatment is associated with a response through a univariate supplementary variable in the framework of linear regression models, Cox (1960) showed that the estimation accuracy of the regression coefficient of the treatment on the response in the single linear regression model can be improved by using the recursive linear regression model based on the supplementary variable from the viewpoint of the asymptotic variance. However, such assumptions may not hold in many practical situations. In this paper, we consider the situation where a treatment is associated with a response through a set of supplementary variables in both linear and discrete models. Then, we show that the estimation accuracy of the causal effect can be improved by using the supplementary variables. Different from Cox (1960), the results of this paper are derived without the assumption of Gaussian error terms in linear models or dichotomous variables in discrete models. The results of this paper help us to obtain the reliable evaluation of causal effects from observed data.
RIS
TY - CPAPER TI - On Estimating Causal Effects based on Supplemental Variables AU - Takahiro Hayashi AU - Manabu Kuroki BT - Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics DA - 2014/04/02 ED - Samuel Kaski ED - Jukka Corander ID - pmlr-v33-hayashi14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 33 SP - 312 EP - 319 L1 - http://proceedings.mlr.press/v33/hayashi14.pdf UR - https://proceedings.mlr.press/v33/hayashi14.html AB - This paper considers the problem of estimating causal effects of a treatment on a response using supplementary variables. Under the assumption that a treatment is associated with a response through a univariate supplementary variable in the framework of linear regression models, Cox (1960) showed that the estimation accuracy of the regression coefficient of the treatment on the response in the single linear regression model can be improved by using the recursive linear regression model based on the supplementary variable from the viewpoint of the asymptotic variance. However, such assumptions may not hold in many practical situations. In this paper, we consider the situation where a treatment is associated with a response through a set of supplementary variables in both linear and discrete models. Then, we show that the estimation accuracy of the causal effect can be improved by using the supplementary variables. Different from Cox (1960), the results of this paper are derived without the assumption of Gaussian error terms in linear models or dichotomous variables in discrete models. The results of this paper help us to obtain the reliable evaluation of causal effects from observed data. ER -
APA
Hayashi, T. & Kuroki, M.. (2014). On Estimating Causal Effects based on Supplemental Variables. Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 33:312-319 Available from https://proceedings.mlr.press/v33/hayashi14.html.

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