Functional logistic mixed effects models (Paulon et al., 2019)

Purpose: We present functional logistic mixed-effects models (FLMEMs) for estimating population and individual-level learning curves in longitudinal experiments.

Method: Using functional analysis tools in a Bayesian hierarchical framework, the FLMEM captures nonlinear, smoothly varying learning curves, appropriately accommodating uncertainty in various aspects of the analysis while also borrowing information across different model layers. An R package implementing our method is available as part of the Supplemental Materials.

Results: Application to speech learning data from Reetzke, Xie, Llanos, and Chandrasekaran (2018) and a simulation study demonstrate the utility of FLMEM and its many advantages over linear and logistic mixed-effects models.

Conclusion: The FLMEM is highly flexible and efficient in improving upon the practical limitations of linear models and logistic linear mixed-effects models. We expect the FLMEM to be a useful addition to the speech, language, and hearing scientist’s statistical toolkit.

Included is an R package implementing the authors' method, including an instruction manual and demos.

The paper here includes posterior computation, convergence diagnostics, and additional comments on implementation issues.

Included are the following supplemental figures:

Supplemental Material S1. Traceplots of the sampled values of three individual curves μ_i(t₀), (denoted by the different colors) at the same time point t₀ = 1.

Supplemental Material S2. Plot of 8 quadratic (q = 2) B-splines on [a, b] defined using 11 knot points that divide [a, b] into K = 6 equal subintervals.

Supplemental Material S3. Flexibility of spline mixtures. The red curve is the function produced by the weighted sum of the spline bases of Figure S.2, weighted by coefficients β. The weighted splines are shown in other varied colors.

Supplemental Material S4. Distribution of the mean integrated squared errors (MISEs) between the true and the estimated population function π(t) estimated by the three models under different simulation scenarios.

Paulon, G., Reetzke, R., Chandrasekaran, B., & Sarkar, A. (2019). Functional logistic mixed-effects models for learning curves from longitudinal binary data. Journal of Speech, Language, and Hearing Research, 62, 543–553. https://doi.org/10.1044/2018_JSLHR-S-ASTM-18-0283

Publisher Note: This article is part of the Research Forum: Advancing Statistical Methods in Speech, Language, and Hearing Sciences.