mlmhelper: An R helper package for estimating multilevel models
Author: Louis Rocconi, Ph.D.
In this blog post, I want to introduce you to the R package mlmhelpr, which my colleague and ESM alumni, Dr. Anthony Schmidt, and I created. mlmhelpr is a collection of helper functions designed to streamline the process of running multilevel or linear mixed models in R. The package assists users with common tasks such as computing the intraclass correlation and design effect, centering variables, and estimating the proportion of variance explained at each level.
Multilevel modeling, also known as linear mixed modeling or hierarchical linear modeling, is a statistical technique used to analyze nested data (e.g., students in schools) or longitudinal data. Both nested and longitudinal data often result in correlated observations, violating the assumption of independent observations. This issue is common in educational, social, health, and behavioral research. Multilevel modeling addresses this by modeling and accounting for the variability at each level, leading to more accurate estimates and inferences.
The inspiration for developing mlmhelpr came from my experience teaching a multilevel modeling course. Throughout the semester, I found myself repeatedly writing custom functions to help students perform various tasks mentioned in our readings. Additionally, students often expressed frustration that lme4, the primary R package for estimating multilevel models, did not provide all the necessary information required by our textbooks and readings. After the semester ended, Anthony and I discussed the need to consolidate these functions into a single R package, making them accessible to everyone. mlmhelpr offers tests and statistics from many popular multilevel modeling textbooks such as Raudenbush and Bryk (2002), Hox et al. (2018), and Snijders and Bosker (2012), and like every other R package, it is free to use!
The following is a list of package functions and descriptions.
boot_se
This function computes bootstrap standard errors and confidence intervals for fixed effects. This function is mainly a wrapper for lme4::bootMer function with the addition of confidence intervals and z-tests for fixed effects. This function can be useful in instances where robust_se does not work, such as with nonlinear models (e.g., glmer models).
center
This function refits a model using grand-mean centering, group-mean/within cluster centering (if a grouping variable is specified), or centering at a user-specified value. For additional information on centering variables in multilevel models, see Enders and Tofighi (2007).
design_effect
This function calculates the design effect, which quantifies the degree to which a sample deviates from a simple random sample. In the multilevel modeling context, this can be used to determine whether clustering will bias standard errors and whether the assumption of independence is held.
hausman
This function performs a Hausman test to test for differences between random- and fixed-effects models. This test determines whether there are significant differences between fixed-effect and random-effect models with similar specifications. If the test statistic is not statistically significant, a random effects model (i.e. a multilevel model) may be more suitable (i.e., efficient). The Hausman test is based on Fox (2016, p. 732, footnote 46). I consider this function experimental and would interpret the results with caution.
icc
This function calculates the intraclass correlation. The ICC represents the proportion of group-level variance to total variance. The ICC can be calculated for two or more levels in random-intercept models. For models with random slopes, it is advised to interpret results with caution. According to Kreft and De Leeuw (1998, p. 63), “The concept of intra-class correlation is based on a model with a random intercept only. No unique intra-class correlation can be calculated when a random slope is present in the model.” However, Snijders and Bosker (2012) offer a calculation to derive this value (equation 7.9), and their approach is implemented. For logistic models, the estimation method follows Hox et al. (2018, p. 107). For a discussion of different methods for estimating the intraclass correlation for binary responses, see Wu et al. (2012).
ncv_tests
This function computes three different non-constant variance tests: (1) the H test as discussed in Raudenbush and Bryk (2002, pp. 263-265) and Snijders and Bosker (2012, p. 159-160), (2) an approximate Levene’s test discussed by Hox et al. (2018, p. 238), and (3) a variation of the Breusch-Pagan test. The H test computes a standardized measure of dispersion for each level-2 group and detects heteroscedasticity in the form of between-group differences in the level-one residual variances. Levene’s test computes a one-way analysis of variance of the level-2 grouping variable on the squared residuals of the model. This test examines whether the variance of the residuals is the same in all groups. The Breusch-Pagan test regresses the squared residuals on the fitted model. A likelihood ratio test is used to compare this model with a null model that regresses the squared residuals on an empty model with the same random effects. This test examines whether the variance of the residuals depends on the predictor variables.
plausible_values
This function computes the plausible value range for random effects. The plausible values range is useful for gauging the magnitude of variation around fixed effects. For more information, see Raudenbush and Bryk (2002, p. 71) and Hoffman (2015, p. 166).
r2_cor
This function calculates the squared correlation between the observed and predicted values. This pseudo R-squared is similar to the R-squared used in OLS regression. It indicates the amount of variation in the outcome that is explained by the model (Peugh, 2010; Singer & Willett, 2003, p. 36). For additional pseudo-R2 measures, see the r2glmm and performance packages.
r2_pve
This function computes the proportion of variance explained for each random effect level in the model (i.e., level-1, level-2) as discussed by Raudenbush & Bryk (2002, p. 79). For additional pseudo-R2 measures, see the r2glmm and performance packages.
reliability
This function computes reliability coefficients for random effects according to Raudenbush and Bryk (2002) and Snijders and Bosker (2012). The reliability coefficient indicates how much of the variance in the random effect is due to true differences between clusters rather than random noise. The empirical Bayes estimator for the random effect combines the cluster mean and the grand mean, with the weight determined by the reliability coefficient. A reliability close to 1 puts more weight on the cluster mean while a reliability close to 0 puts more weight on the grand mean.
robust_se
This function computes robust standard errors for linear models. It is a wrapper function for the cluster-robust standard errors from the clubSandwich package that includes confidence intervals. See the clubSandwich package for additional information and mlmhelpr::boot_se for an alternative.
taucov
This function calculates the covariance between random intercepts and slopes. It is used to quickly get the covariance and correlation between intercepts and slopes. By default, lme4 only displays the correlation.
As of August 26, 2024, the package has been downloaded 5,062 times! If you use R to estimate multilevel models, give mlmhelpr a try, and let me know if you find any errors or mistakes. I hope you find it helpful. If you are interested in creating your own R package, check out the excellent R Package development book by Wickham and Bryan: https://r-pkgs.org/.
Happy modeling!
Resources and References
Enders, C. K., & Tofighi, D. (2007). Centering predictor variables in cross-sectional multilevel models: A new look at an old issue. Psychological Methods, 12(2), 121-138.
Fox, J. (2016). Applied regression analysis and generalized linear models (3rd ed.). SAGE Publications.
Hoffman, L. (2015). Longitudinal analysis: Modeling within-person fluctuation and change. Routledge.
Hox, J. J., Moerbeek, M., & van de Schoot, R. (2018). Multilevel analysis: Techniques and applications (3rd ed.). Routledge.
Kreft, I. G. G., & De Leeuw, J. (1998). Introducing multilevel modeling. SAGE Publications.
Peugh, J. L. (2010). A practical guide to multilevel modeling. Journal of School Psychology, 48(1), 85-112.
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). SAGE Publications.
Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. Oxford University Press.
Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel analysis: An introduction to basic and advanced multilevel modeling (2nd ed.). SAGE Publications.
Wu, S., Crespi, C. M., & Wong, W. K. (2012). Comparison of methods for estimating the intraclass correlation coefficient for binary responses in cancer prevention cluster randomized trials. Contemporary Clinical Trials, 33(5), 869.