# Introduction to ModLR

# Overview

ModLR provides an information-theoretic framework for moderation analysis using multi-model inference based on Akaike’s Information Criterion (AIC and AICc). Traditional approaches to moderation analysis typically rely on a single model with an interaction term. However, such approaches may lead to spurious moderation effects when nonlinear relationships are present but not properly modeled. The ModLR package addresses this limitation by comparing multiple candidate models and identifying the most appropriate specification based on information criteria.

# Basic Example

    set.seed(123)

    n <- 400

    z <- sample(c(0, 1), n, replace = TRUE)
    x <- ifelse(z == 0, runif(n, 0.5, 6.5), runif(n, 3.5, 9.5))
    y <- (0.8 * x^2) + (30 * z) + rnorm(n, 0, 5)

    ddat <- data.frame(x = x, y = y, z = z)

    result <- moderated_regression(dat, iv = "x", moderator = "z", dv = "y")
    print(result)
    compare_models(result)

The output shows competing models ranked according to AIC or AICc. Lower values indicate better model fit, allowing the researcher to identify whether the interaction model is truly supported by the data.

# Interpreting Model Comparison

The ModLR framework evaluates alternative model specifications rather than relying on a single model. This approach helps determine:

- whether the interaction model improves fit
- whether nonlinear models provide a better explanation
- the relative strength of evidence for each model

By focusing on model comparison, researchers can avoid incorrectly concluding that moderation is present when it is actually due to model misspecification.

# Additional Analyses

## Simple Slopes

Simple slopes estimate the effect of the independent variable at specific levels of the moderator, helping clarify how the relationship changes across conditions.

    simple_slopes(result)

## Johnson–Neyman Analysis

The Johnson–Neyman procedure identifies the range of moderator values for which the effect of the independent variable is statistically significant.

    johnson_neyman(result)

## Visualization

Visualization helps communicate moderation effects clearly by showing how the relationship between variables changes across levels of the moderator.

    plot_moderation(result)

# Methodological Background

The framework implemented in ModLR is based on Daryanto (2019), which proposes an information-theoretic approach to moderation analysis. By comparing alternative models using AIC/AICc, this approach reduces the risk of identifying spurious moderation effects arising from nonlinear relationships.

# Conclusion

ModLR provides a principled approach to moderation analysis by integrating multi-model inference with interpretation tools. The package allows researchers to go beyond traditional single-model approaches and to conduct more robust and reliable analyses.

# References

Daryanto, A. (2019). Avoiding spurious moderation effects: An information-theoretic approach to moderation analysis. Journal of Business Research, 103, 110–118.