Assessing the goodness of fit of linear regression via higher-order least squares

by   Christoph Schultheiss, et al.

We introduce a simple diagnostic test for assessing the goodness of fit of linear regression, and in particular for detecting hidden confounding. We propose to evaluate the sensitivity of the regression coefficient with respect to changes of the marginal distribution of covariates by comparing the so-called higher-order least squares with the usual least squares estimates. In spite of its simplicity, this strategy is extremely general and powerful. Specifically, we show that it allows to distinguish between confounded and unconfounded predictor variables as well as determining ancestor variables in structural equation models.



page 1

page 2

page 3

page 4


Correlation Estimation System Minimization Compared to Least Squares Minimization in Simple Linear Regression

A general method of minimization using correlation coefficients and orde...

Average group effect of strongly correlated predictor variables is estimable

It is well known that individual parameters of strongly correlated predi...

Model-free Study of Ordinary Least Squares Linear Regression

Ordinary least squares (OLS) linear regression is one of the most basic ...

A Model-free Approach to Linear Least Squares Regression with Exact Probabilities and Applications to Covariate Selection

The classical model for linear regression is Y= xβ +σε with i.i.d. stan...

Higher-Order Partial Least Squares (HOPLS): A Generalized Multi-Linear Regression Method

A new generalized multilinear regression model, termed the Higher-Order ...

An Intrinsic Treatment of Stochastic Linear Regression

Linear regression is perhaps one of the most popular statistical concept...

Distribution free testing for linear regression. Extension to general parametric regression

Recently a distribution free approach for testing parametric hypotheses ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.