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

<b>Purpose: </b>We present functional logistic mixed-effects models (FLMEMs) for estimating population and individual-level learning curves in longitudinal experiments.<b>Method: </b>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.<b>Results: </b>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.<b>Conclusion: </b>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.<br>Included is an <b>R package</b> implementing the authors' method, including an instruction manual and demos. <br>The paper here includes posterior computation, convergence diagnostics, and additional comments on implementation issues. <br> Included are the following supplemental figures:<br><b><br></b><b> Supplemental Material S1.</b> Traceplots of the sampled values of three individual curves <i>μ_i</i>(<i>t₀</i>), (denoted by the different colors) at the same time point <i>t</i>₀ = 1.<b> </b><b><br></b><b> Supplemental Material S2. </b>Plot of 8 quadratic (<i>q</i> = 2) B-splines on [<i>a</i>, <i>b</i>] defined using 11 knot points that divide [<i>a</i>, <i>b</i>] into <i>K</i> = 6 equal subintervals.<br><b><br></b><b> Supplemental Material S3.</b> 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 <i>β</i>. The weighted splines are shown in other varied colors.<br><b><br></b><b> Supplemental Material S4. </b>Distribution of the mean integrated squared errors (MISEs) between the true and the estimated population function <i>π</i>(<i>t</i>) estimated by the three models under different simulation scenarios.<br><br>Paulon, G., Reetzke, R., Chandrasekaran, B., &amp; Sarkar, A. (2019). Functional logistic mixed-effects models for learning curves from longitudinal binary data. <i>Journal of Speech, Language, and Hearing Research, 62,</i> 543–553. https://doi.org/10.1044/2018_JSLHR-S-ASTM-18-0283<br><br><b>Publisher Note: </b>This article is part of the Research Forum: Advancing Statistical Methods in Speech, Language, and Hearing Sciences.