%0 DATA
%A Giorgio, Paulon
%A Rachel, Reetzke
%A Bharath, Chandrasekaran
%A Abhra, Sarkar
%D 2019
%T Functional logistic mixed effects models (Paulon et al., 2019)
%U https://asha.figshare.com/articles/Functional_logistic_mixed_effects_models_Paulon_et_al_2019_/7822568
%R 10.23641/asha.7822568.v1
%2 https://asha.figshare.com/ndownloader/files/14574707
%2 https://asha.figshare.com/ndownloader/files/14574767
%2 https://asha.figshare.com/ndownloader/files/14574770
%2 https://asha.figshare.com/ndownloader/files/14574773
%2 https://asha.figshare.com/ndownloader/files/14574776
%2 https://asha.figshare.com/ndownloader/files/14574779
%K speech
%K Advancing Statistical Methods in Speech, Language, and Hearing Sciences
%K functional
%K logistic
%K mixed-effects
%K model
%K learning curve
%K longitudinal
%K binary
%K data
%K population
%K estimate
%K individual
%K experiment
%K analysis
%K Bayesian
%K hierarchy
%K framework
%K nonlinear
%K uncertainty
%K aspects
%K layers
%K R package
%K simulation
%K study
%K utility
%K linear
%K language
%K hearing
%K scientist
%K research
%K investigation
%K statistics
%X **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}(*t*_{0}), (denoted by the different colors) at the same time point *t*_{0} = 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.