Longitudinal Data Analysis with Linear Mixed Effects Models
Jessica Murphy, Nicholas Weaver, and Audrey Hendricks
University of Colorado Denver
EasyLME is a web application developed to facilitate the analysis of longitudinal data using linear mixed effects models in R. The app performs the following functions according to the tabs above:
- Data Summary: univariate summaries of each variable selected by the user
- Exploratory Plots: interactive plots of the response variable vs time for the random effect and grouping variables
- Model Results: table of coefficient estimates for each model, log likelihoods of each model, and p-values from likelihood ratio tests of nested models
- Diagnostic Plots: interactive residual profile plots for each model
- Fitted lines: interactive plots of the fitted lines for a particular model selected by the user
Note: The app automatically treats the response and time variables as continuous and the grouping and random effect variables as categorical. However, categorical covariates (e.g. sex) should be coded as characters (e.g. male/female); otherwise, numerically coded covariates will be treated as continuous.
To begin, use the menu on the left-hand side to choose to upload your own data or to explore the features of the app with the demo data. If uploading your own data, be sure it is a CSV in long format, where each row is a single time point. More information about the demo data can be found here.
Figure 1. Scatterplot of the response variable vs time.
This plot can be used to verify the linearity assumption between the response
variable and time before proceeding with a linear mixed effects model.
Figure 3. Trendlines faceted by the higher-level random effect variable.
These plots can help determine if a random slope and/or random intercept would be
appropriate for the higher-level random effect variable.
Figure 4. Coefficient plot of the fixed effect estimates with 95% confidence intervals.
This plot is helpful to visualize the information presented in the Model Results table above.
The optimizers are listed below preceded by a dollar sign.
Each optimizer is followed by its warning message(s) or none (no warnings).
The default optimizer is NLOPT_LN_BOBYQA.
Figure 5. Residual profile plots in increasing order of model complexity,
where each line represents a single profile of the random effect variable.
These plots are useful to visually compare the different model fits. Models with a
large, nonconstant variability in the residuals over time indicate a worse model fit, whereas
models with a small, constant variability in the residuals over time indicate a better model fit.