Fast stable direct fitting and smoothness selection for Generalized Additive Models

Existing computationally efficient methods for penalized likelihood GAM fitting employ iterative smoothness selection on working linear models (or working mixed models). Such schemes fail to converge for a non-negligible proportion of models, with failure being particularly frequent in the presence of concurvity. If smoothness selection is performed by optimizing `whole model' criteria these problems disappear, but until now attempts to do this have employed finite difference based optimization schemes which are computationally inefficient, and can suffer from false convergence. This paper develops the first computationally efficient method for direct GAM smoothness selection. It is highly stable, but by careful structuring achieves a computational efficiency that leads, in simulations, to lower mean computation times than the schemes based on working-model smoothness selection. The method also offers a reliable way of fitting generalized additive mixed models

Bayesian comparison of latent variable models: Conditional vs marginal likelihoods

Typical Bayesian methods for models with latent variables (or random effects) involve directly sampling the latent variables along with the model parameters. In high-level software code for model definitions (using, e.g., BUGS, JAGS, Stan), the likelihood is therefore specified as conditional on the latent variables. This can lead researchers to perform model comparisons via conditional likelihoods, where the latent variables are considered model parameters. In other settings, however, typical model comparisons involve marginal likelihoods where the latent variables are integrated out. This distinction is often overlooked despite the fact that it can have a large impact on the comparisons of interest. In this paper, we clarify and illustrate these issues, focusing on the comparison of conditional and marginal Deviance Information Criteria (DICs) and Watanabe-Akaike Information Criteria (WAICs) in psychometric modeling. The conditional/marginal distinction corresponds to whether the model should be predictive for the clusters that are in the data or for new clusters (where "clusters" typically correspond to higher-level units like people or schools). Correspondingly, we show that marginal WAIC corresponds to leave-one-cluster out (LOcO) cross-validation, whereas conditional WAIC corresponds to leave-one-unit out (LOuO). These results lead to recommendations on the general application of the criteria to models with latent variables.Comment: Manuscript in press at Psychometrika; 31 pages, 8 figure

Predicting Progression in Parkinson's Disease Using Baseline and 1-Year Change Measures.

BackgroundImproved prediction of Parkinson's disease (PD) progression is needed to support clinical decision-making and to accelerate research trials.ObjectivesTo examine whether baseline measures and their 1-year change predict longer-term progression in early PD.MethodsParkinson's Progression Markers Initiative study data were used. Participants had disease duration ≤2 years, abnormal dopamine transporter (DAT) imaging, and were untreated with PD medications. Baseline and 1-year change in clinical, cerebrospinal fluid (CSF), and imaging measures were evaluated as candidate predictors of longer-term (up to 5 years) change in Movement Disorders Society-Unified Parkinson's Disease Rating Scale (MDS-UPDRS) score and DAT specific binding ratios (SBR) using linear mixed-effects models.ResultsAmong 413 PD participants, median follow-up was 5 years. Change in MDS-UPDRS from year-2 to last follow-up was associated with disease duration (β= 0.351; 95% CI = 0.146, 0.555), male gender (β= 3.090; 95% CI = 0.310, 5.869), and baseline (β= -0.199; 95% CI = -0.315, -0.082) and 1-year change (β= 0.540; 95% CI = 0.423, 0.658) in MDS-UPDRS; predictors in the model accounted for 17.6% of the variance in outcome. Predictors of percent change in mean SBR from year-2 to last follow-up included baseline rapid eye movement sleep behavior disorder score (β= -0.6229; 95% CI = -1.2910, 0.0452), baseline (β= 7.232; 95% CI = 2.268, 12.195) and 1-year change (β= 45.918; 95% CI = 35.994,55.843) in mean striatum SBR, and 1-year change in autonomic symptom score (β= -0.325;95% CI = -0.695, 0.045); predictors in the model accounted for 44.1% of the variance.ConclusionsBaseline clinical, CSF, and imaging measures in early PD predicted change in MDS-UPDRS and dopamine-transporter binding, but the predictive value of the models was low. Adding the short-term change of possible predictors improved the predictive value, especially for modeling change in dopamine-transporter binding