Multiple LMER Models? No Problem! Adjusting P-Values for Multiple Testing Made Easy

Are you a researcher or data analyst dealing with multiple lmer models and wondering how to adjust the p-values for multiple testing? Well, you’re in the right place! In this article, we’ll dive into the world of multiple testing corrections and provide you with a step-by-step guide on how to adjust those pesky p-values. So, let’s get started!

What’s the Problem with Multiple Testing?

When working with multiple models, you’re essentially performing multiple tests, which can lead to an increased chance of obtaining false positives. This phenomenon is known as the multiple testing problem. To put it simply, the more tests you perform, the higher the likelihood of obtaining a statistically significant result by chance alone.

For example, let’s say you’re analyzing the effect of different factors on a response variable using multiple lmer models. You might get a few significant results, but are they really significant, or did you just get lucky? That’s where multiple testing corrections come in.

Common Multiple Testing Corrections

There are several methods to correct for multiple testing, each with its own strengths and weaknesses. Here are some of the most popular ones:

• Bonferroni Correction: This method is based on the idea of adjusting the significance level (α) by dividing it by the number of tests performed. The Bonferroni correction is a conservative approach, but it can be overly stringent, leading to a loss of power.
• Holm-Bonferroni Method: This method is a step-down procedure that adjusts the significance level based on the number of tests performed and the desired family-wise error rate (FWER). It’s more powerful than the Bonferroni correction but still conservative.
• Benjamini-Hochberg (BH) Procedure: This method controls the false discovery rate (FDR) by adjusting the p-values based on the number of tests performed and the desired FDR level. It’s a more liberal approach than the Bonferroni correction and Holm-Bonferroni method.
• Hochberg’s GT2 Method: This method is a variant of the Holm-Bonferroni method that’s more powerful and less conservative. It’s particularly useful when the number of tests is small.

Adjusting P-Values in R

Now that you know the different multiple testing corrections, let’s see how to implement them in R using the p.adjust function. We’ll use the following example:

# Load the lme4 package
library(lme4)

# Fit multiple lmer models
model1 <- lmer(response ~ factor1 + (1|group), data = df)
model2 <- lmer(response ~ factor2 + (1|group), data = df)
model3 <- lmer(response ~ factor3 + (1|group), data = df)

# Extract p-values from each model
p_values <- c(summary(model1)$coefficients[2,4], 
               summary(model2)$coefficients[2,4], 
               summary(model3)$coefficients[2,4])

Now, let’s adjust the p-values using different multiple testing corrections:

# Bonferroni correction
p_adjusted_bonferroni <- p.adjust(p_values, method = "bonferroni")

# Holm-Bonferroni method
p_adjusted_holm <- p.adjust(p_values, method = "holm")

# Benjamini-Hochberg procedure
p_adjusted_bh <- p.adjust(p_values, method = "BH")

# Hochberg's GT2 method
p_adjusted_gt2 <- p.adjust(p_values, method = "hochberg")

You can then use the adjusted p-values to determine the significance of your results.

Multiple Testing Corrections in Practice

Let’s say you’ve fitted three lmer models to analyze the effect of different factors on a response variable:

Factor	P-Value
Factor 1	0.01
Factor 2	0.03
Factor 3	0.05

If you use a significance level of 0.05, you’d normally reject the null hypothesis for all three factors. However, let’s adjust the p-values using the Benjamini-Hochberg procedure:

p_values <- c(0.01, 0.03, 0.05)
p_adjusted_bh <- p.adjust(p_values, method = "BH")

The adjusted p-values would be:

Factor	Adjusted P-Value
Factor 1	0.017
Factor 2	0.043
Factor 3	0.075

Now, if you use a significance level of 0.05, you’d only reject the null hypothesis for Factor 1 and Factor 2.

Conclusion

Adjusting p-values for multiple testing is a crucial step in ensuring the validity of your results. By using multiple testing corrections, you can reduce the likelihood of false positives and increase the confidence in your findings. Remember to choose the correction method that best suits your research question and data.

In this article, we’ve covered the basics of multiple testing corrections, including the Bonferroni correction, Holm-Bonferroni method, Benjamini-Hochberg procedure, and Hochberg’s GT2 method. We’ve also demonstrated how to adjust p-values in R using the p.adjust function.

By following these guidelines, you’ll be well on your way to tackling the multiple testing problem and producing more reliable results. Happy modeling!

Additional Resources

• Multiple Comparisons Problem on Wikipedia
• Benjamini and Hochberg (1995) – Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing
• lme4 Package on CRAN

Frequently Asked Question

Are you struggling with adjusting p-values for multiple testing in your lmer models?