Maximum Likelihood Estimation for the Proportional Odds Model With Random Effects

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Most Likely Transformations (2015, methodology): “A mixed transformation model for cluster data (Cai et al. 2002; Huber-Carol and Vonta 2004; Zeng et al. 2005; Choi and Huang 2012) is often based on the transformation function h(y | x, i) = hY (y)+δi+hx(x) with random intercept (or “frailty” term) δi for the ith observational unit.”
Maximum likelihood estimation in semiparametric regression models with censored data (2007, background): “Zeng et al. (2005) studied the NPMLE for the proportional odds model with normal random effects and found the estimators of Cai et al. (2002) to be considerably less efficient.”
Conditional transformation models (2012, background): “…first variable x1; Lu and Zhang 2010), the varying coefficient model hx(x) = x >(0, 0,α)> + hsmooth(x1)x2 (Chen and Tong 2010), random effects models (Zeng, Lin, and Yin 2005), and various approaches to additive transformation and accelerated failure time models, such as the boosting approaches by…”