Univariate Modeling

TL;DR

Models the relationship between a single predictor variable and an outcome.
Common methods include linear regression (for continuous outcomes) and logistic regression (for binary outcomes).
Useful for simple association analysis but cannot account for the effects of multiple predictors.

Definition

Univariate modeling is a statistical technique that involves analyzing and modeling a single variable or feature. This type of modeling is often used when the goal is to understand the relationships between a particular variable and a response or outcome.

Explanation

Univariate modeling focuses on one predictor at a time to characterize its relationship with a response variable. For continuous outcomes, linear regression fits a straight line that minimizes the sum of the squared differences between observed and predicted values; the slope indicates the strength of the relationship and the intercept predicts the response when the predictor is zero. For binary outcomes, logistic regression estimates the probability of the outcome given the predictor and is typically fit using maximum likelihood estimation; it assumes the log-odds of the response are a linear function of the predictor and that the errors follow a binomial distribution.

Appropriate application of univariate models requires meeting method-specific assumptions (for example, linearity and normally distributed, homoscedastic errors for linear regression). If these assumptions are violated, model results may be biased or inaccurate. Because univariate modeling considers only a single predictor, it cannot account for the influence of additional predictors; when multiple predictors may affect the outcome, multivariate modeling is often more appropriate.

Examples

Linear regression

A linear regression model relates a continuous predictor variable (such as age or income) to a continuous response variable (such as weight or blood pressure). The model fits a straight line that minimizes the sum of the squared differences between observed and predicted values. The slope represents the strength of the relationship between predictor and response, and the intercept represents the predicted value of the response when the predictor is zero.

Logistic regression

A logistic regression model relates a predictor variable (such as education level or income) to a binary response variable (such as whether or not an individual has a disease). The model estimates the probability that an individual will have the binary outcome given their value on the predictor variable. The model is typically fit using maximum likelihood estimation, which finds the parameters that maximize the likelihood of the observed data given the model.

Use cases

Using linear regression to understand the relationship between age and weight in a group of individuals.
Using logistic regression to understand the relationship between education level and the likelihood of having a certain disease.

Notes or pitfalls

Linear regression assumes a linear relationship between predictor and response and that errors are normally distributed with constant variance.
Logistic regression assumes the log-odds of the response are a linear function of the predictor and that errors follow a binomial distribution.
If method-specific assumptions are not met, model results may be biased or inaccurate.
Univariate modeling only considers a single predictor variable; it cannot account for the effects of multiple predictor variables and may be inappropriate when multiple predictors influence the response.

Linear regression
Logistic regression
Multivariate modeling