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Impact of Linear Regression Predictor Omission on Estimation and Inference (303622)

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Keywords: model mis-specification, predictor omission, interaction, correlation

When modeling “big data” sets there is often discussion about the impact of sample size on estimation and inference. Less consideration has been given to the impact of an incorrect assumed model, especially omitted predictors from the model, even though the data set may be large. In this study, the impact of omitting predictors in models on estimation and inference is considered to assist data analysts and statisticians collaborating on big data modeling. Particular attention is paid to an omitted predictor that is correlated and/or interacting with a predictor already included in the model. The impact on estimation bias and the Type I error rate is considered, theoretically and via simulation, on the included predictor. The changes in the impacts of the omitted predictor due to increasing sample size will be considered. Results suggest that for a given sample size, the Type I error rate for a hypothesis test of the included predictor is inflated when a correlated predictor is omitted; and the Type I error rate is not as impacted when an interacting predictor is omitted.