#5 LOESS vs. Linear Regression: Two Ways to Uncover Patterns in Your Meta-Analysis

Complete Performance
Apr 5
3 min read

LOESS vs. Linear Regression: Enhancing Pattern Detection is now available in MASimplified

If you’re conducting meta-analyses, understanding how study characteristics (like sample size, publication year or in our example, intervention duration) relate to outcomes is critical. While linear regression is a staple for testing hypotheses, what if the relationship in your data isn’t linear? Enter LOESS (Locally Estimated Scatterplot Smoothing), a flexible tool for visualizing complex trends.

In the updated MASimplified, we’ve integrated both linear and LOESS regression to empower researchers. Here’s how these methods differ and how they can strengthen your meta-analytic workflow.

Linear Regression: Clarity for Hypothesis Testing

Linear regression fits a straight line to model relationships between variables, such as how effect sizes vary with selected covariate (e.g., intervention duration) (Figure 1).

Example in Meta-Analysis:

Test whether studies with longer intervention duration show larger effect sizes—a classic application in investigating a training dose-response relationship.

Why It Shines:

· Simplicity: The slope and intercept provide straightforward insights into the relationship’s direction and magnitude.

· Statistical Power: Efficient for testing predefined hypotheses when a linear trend is plausible.

· Inferential Strength: Generates p-values and confidence intervals, ideal for formal meta-regression models.

But beware: If the true relationship curves or shifts, a straight line may mislead your conclusions.

Figure 1. Meta-regression analysis using a linear model to visualize the association between intervention duration and maximal strength improvement following motor imagery training.

LOESS: Flexibility for Exploring Complex Trends

LOESS fits localized regressions to create a smooth curve, revealing patterns that linear models might miss (Figure 2).

Example in Meta-Analysis:

Detect time trends where effect sizes rise, plateau, and decline—patterns invisible to linear assumptions.

Why It Shines:

· Adaptability: Captures curves, peaks, or plateaus without predefined equations.

· Exploratory Power: Visualizes hidden trends, guiding deeper investigation.

· Robustness: Less swayed by outliers, as it prioritizes local data patterns.

Figure 2. Meta-regression analysis using a LOESS function to visualize the association between intervention duration and maximal strength improvement following motor imagery training.

Comparing Tools for Meta-Analytic Applications

Feature	Linear Regression	LOESS
Assumed Relationship	Straight line	Data-driven shape
Interpretability	High (clear coefficients)	Moderate (visual summary)
Statistical Inference	Strong (p-values, confidence intervals)	Primarily visual (less formal testing)
Outlier Sensitivity	Vulnerable to skewing	Resilient due to localized fitting
Best For	Testing predefined hypotheses	Exploring nonlinear relationships

Why This Matters for Meta-Analysis

Meta-analysis synthesizes diverse studies, making it essential to understand how moderators (e.g., study quality, year, sample size or training-related characteristics) influence observed effect sizes.

Use Linear Regression When:

· Testing specific theories (e.g., “Do longer studies report larger effects?”).

· Formal inference (e.g., calculating confidence intervals for training recommendations).

· Building parsimonious meta-regression models.

Use LOESS When:

· Exploring data visually for unexpected trends.

· Suspecting nonlinear dynamics (e.g., threshold effects or diminishing returns).

· Diagnosing linear model assumptions before analysis.

In MASimplified, LOESS helps researchers visualize patterns before committing to linear models. For instance, a curved LOESS trend might prompt a polynomial regression or segmented analysis, preventing oversimplification.

A Strategic Workflow: Combine Both Methods

1. Start with LOESS to visualize relationships without assumptions.

2. If linear, proceed with regression for hypothesis testing.

3. If nonlinear, consider model transformations (e.g., splines) or retain LOESS for visualization.

This approach balances exploration with rigor, ensuring your models reflect the data’s complexity without unnecessary complexity.

Conclusion: Smarter Meta-Analysis with MASimplified

Linear regression offers clarity for hypothesis testing, while LOESS uncovers nuanced trends. Together, they transform how you interrogate meta-analytic data—turning simple scatterplots into stories of curves, shifts, and insights.

With MASimplified, you’re not just running analyses—you’re revealing the hidden narrative in your data.

Next time you analyze effect sizes, ask: Is this relationship linear, or does it hold a twist?

✏️Author: Assist. Prof. Armin Paravlić, PhD