Related papers: Interpretation of Linear Regression Coefficients u…
The interpretation of coefficients from multivariate linear regression relies on the assumption that the conditional expectation function is linear in the variables. However, in many cases the underlying data generating process is…
We study a linear statistical model where outcomes depend on regressors with fixed population coefficients and observation-specific latent coefficients, along with measurement errors. A decision-maker estimates population coefficients and…
In this paper, we consider the problem of treating linear regression equation coefficients in the case of correlated predictors. It is shown that in general there are no natural ways of interpreting these coefficients similar to the case of…
We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables $X$, where $X$ can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the "Fixed-$X$"…
Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…
Machine learning models with both good predictability and high interpretability are crucial for decision support systems. Linear regression is one of the most interpretable prediction models. However, the linearity in a simple linear…
The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed…
The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…
The paper proposes to analyze epidemiological data using regression models which enable subject-matter (epidemiological) interpretation of such data whether with uncorrelated or correlated predictors. To this end, response functions should…
Sensitivity analysis is widely used to assess the robustness of causal conclusions in observational studies, yet its interaction with the structure of measured covariates is often overlooked. When latent confounders cannot be directly…
This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not…
The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
Linear regression is arguably the most fundamental statistical model; however, the validity of its use in randomized clinical trials, despite being common practice, has never been crystal clear, particularly when stratified or…
We propose a novel framework of the model specification test in regression using unlabeled test data. In many cases, we have conducted statistical inferences based on the assumption that we can correctly specify a model. However, it is…
Statisticians usually restrict regression to model relationships that are explicitly defined dependent and independent random variables; this paper outlines the newly developed method of non-response analysis and rotational analysis for…
Linear regression is often deemed inherently interpretable; however, challenges arise for high-dimensional data. We focus on further understanding how linear regression approximates nonlinear responses from high-dimensional functional data,…
Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…