Piecewise Random-Effects Modeling Software Programs

In this software review, we provide a brief overview of four different functions to fit a piecewise random-effects model with unknown changepoints (knots). Specifically, the four functions are: FitPMM from the R routine developed by (Zopluoglu, Harring, & Kohli, 2014), PROC NLMIXED from SAS, BayesPGM from the BayesianPGMM package in R developed by (Lock, Kohli, and Bose, 2018), and stancode_randomchangecorr function developed by (Brilleman, Howe, Wolfe, & Tilling, 2017) implemented to interface with Stan from R using the rstan package. We illustrate the estimation of the piecewise random-effects model using each of these functions by using a sample dataset. We provide appropriate commented code for the four functions, and briefly discuss the strengths and weaknesses of each function.     

Non-negativity test of multidimensional Hermitian matrices

Arguments are advanced to point out that simplification analogous to that in the computational test for positive definiteness of multidimensional Hermitian matrices is not possible when the Hermitian matrix is to be tested for non-negative definiteness.