The polychoric instrumental variable (PIV) approach is a recently proposed method to fit a confirmatory factor analysis model with ordinal data. In this paper, we first examine the small-sample properties of the specification tests for testing the validity of instrumental variables (IVs). Second, we investigate the effects of using different numbers of IVs. Our results show that specification tests derived for continuous data are extremely oversized at all sample sizes when applied to ordinal variables. Possible modifications for ordinal data are proposed in the present study. Simulation results show that the modified specification tests with all available IVs are able to detect model misspecification. In terms of estimation accuracy, the PIV approach where the IVs outnumber the endogenous variables by one produces a lower bias but a higher variation than the PIV approach with more IVs for correctly specified factor loadings at small samples.

Accelerometer devices are becoming efficient tools in clinical studies for automatically measuring the activities of daily living. Such data provides a time series describing activity level at every second and displays a subject’s activity pattern throughout a day. However, the analysis of such data is very challenging due to the large number of observations produced each second and the variability among subjects. The purpose of this study is to develop efficient statistical analysis techniques for predicting the recovery level of the upper limb function after stroke based on the free-living accelerometer data. We propose to use a Gaussian Mixture Model (GMM)-based method for clustering and extracting new features to capture the information contained in the raw data. A nonlinear mixed effects model with Gaussian Process prior for the random effects is developed as the predictive model for evaluating the recovery level of the upper limb function. Results of applying to the accelerometer data for patients after stroke are presented.

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We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student t-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting conditional means as well interpolation and extrapolation for the subject-specific inferences. We develop bootstrap prediction intervals for conditional mean curves. Numerical studies show that the proposed model provides robust analysis against data contamination or distribution misspecification, and the proposed prediction intervals maintain the nominal confidence levels. A real data application is presented as an illustrative example.