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When is Plasmode simulation superior to parametric simulation when estimating the MSE of the least squares estimator in linear regression?

7 December 2023
Marieke Stolte
Nicholas Schreck
Alla Slynko
Maral Saadati
Axel Benner
Jörg Rahnenführer
Andrea Bommert
ArXiv (abs)PDFHTML
Abstract

Simulation is a crucial tool for the evaluation and comparison of statistical methods. How to design fair and neutral simulation studies is therefore of great interest for both researchers developing new methods and practitioners confronted with the choice of the most suitable method. The term simulation usually refers to parametric simulation, that is, computer experiments using artificial data made up of pseudo-random numbers. Plasmode simulation, that is, computer experiments using the combination of resampling feature data from a real-life dataset and generating the target variable with a user-selected outcome-generating model (OGM), is an alternative that is often claimed to produce more realistic data. We compare parametric and Plasmode simulation for the example of estimating the mean squared error of the least squares estimator in linear regression. If the true underlying data-generating process (DGP) and the OGM were known, parametric simulation would be the best choice in terms of estimating the MSE well. However, in reality, both are usually unknown, so researchers have to make assumptions: in Plasmode simulation studies for the OGM, in parametric simulation for both DGP and OGM. Most likely, these assumptions do not reflect the truth. Here, we aim to find out how assumptions deviating from the true DGP and the true OGM affect the performance of parametric simulation and Plasmode simulations in the context of MSE estimation for the least squares estimator and in which situations which simulation type is preferable. Our results suggest that the preferable simulation method depends on many factors, including the number of features, and how the assumptions of a parametric simulation differ from the true DGP. Also, the resampling strategy used for Plasmode influences the results. In particular, subsampling with a small sampling proportion can be recommended.

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