<p>Linear regression is one of the most studied model, it assumes a clear hypothesis of linearity. Spurious correlations from a whole sample lead to hidden nonlinearities which are prone to induce a biased model and a mistaken interpretation. The model for explaining the outcome cannot be kept the same for the whole sample if it changes with the dependent variable. It is proposed a stratification of the outcome which leads to a new family of mixture models of regressions. After splitting the sample into two parts it is explained how the three resulting correlations are related to lead to spurious values. A break along the outcome changes the linear regression into two components instead of just one. Thereby, the partitioning is defined by a threshold on the outcome. A double check of the change is obtained via an additional ordinal model and a discretization of the outcome. The new method is implemented in a Python library with multiple regressions across two or more groups. With a threshold equal to the median for two groups, the approach is validated on several real datasets in the presented experiments. It is applied to a medical dataset from the Covid-19 lockdown in 2020.</p>

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Family of linear regression mixture models stratified along the outcome

  • Rodolphe Priam

摘要

Linear regression is one of the most studied model, it assumes a clear hypothesis of linearity. Spurious correlations from a whole sample lead to hidden nonlinearities which are prone to induce a biased model and a mistaken interpretation. The model for explaining the outcome cannot be kept the same for the whole sample if it changes with the dependent variable. It is proposed a stratification of the outcome which leads to a new family of mixture models of regressions. After splitting the sample into two parts it is explained how the three resulting correlations are related to lead to spurious values. A break along the outcome changes the linear regression into two components instead of just one. Thereby, the partitioning is defined by a threshold on the outcome. A double check of the change is obtained via an additional ordinal model and a discretization of the outcome. The new method is implemented in a Python library with multiple regressions across two or more groups. With a threshold equal to the median for two groups, the approach is validated on several real datasets in the presented experiments. It is applied to a medical dataset from the Covid-19 lockdown in 2020.