TY - JOUR
T1 - A proportional likelihood ratio model
AU - Luo, Xiaodong
AU - Tsai, Wei Yann
N1 - Funding Information:
The authors thank the associate editor and the reviewers for their helpful comments and suggestions, which greatly improved this paper, and Dr Mary Sano for providing the neuropsychological data. Luo was partly support by a grant from the US National Institute for Aging. Tsai is also affiliated with the Department of Statistics, National Cheng Kung University, Taiwan.
PY - 2012/3
Y1 - 2012/3
N2 - We propose a semiparametric proportional likelihood ratio model which is particularly suitable for modelling a nonlinear monotonic relationship between the outcome variable and a covariate. This model extends the generalized linear model by leaving the distribution unspecified, and has a strong connection with semiparametric models such as the selection bias model (Gilbert et al., 1999), the density ratio model (Qin, 1998; Fokianos & Kaimi, 2006), the single-index model (Ichimura, 1993) and the exponential tilt regression model (Rathouz & Gao, 2009). A maximum likelihood estimator is obtained for the new model and its asymptotic properties are derived. An example and simulation study illustrate the use of the model.
AB - We propose a semiparametric proportional likelihood ratio model which is particularly suitable for modelling a nonlinear monotonic relationship between the outcome variable and a covariate. This model extends the generalized linear model by leaving the distribution unspecified, and has a strong connection with semiparametric models such as the selection bias model (Gilbert et al., 1999), the density ratio model (Qin, 1998; Fokianos & Kaimi, 2006), the single-index model (Ichimura, 1993) and the exponential tilt regression model (Rathouz & Gao, 2009). A maximum likelihood estimator is obtained for the new model and its asymptotic properties are derived. An example and simulation study illustrate the use of the model.
KW - Biased sampling
KW - Nonlinear monotonicity
KW - Semiparametric generalized linear model
UR - http://www.scopus.com/inward/record.url?scp=84857514465&partnerID=8YFLogxK
U2 - 10.1093/biomet/asr060
DO - 10.1093/biomet/asr060
M3 - Article
AN - SCOPUS:84857514465
SN - 0006-3444
VL - 99
SP - 211
EP - 222
JO - Biometrika
JF - Biometrika
IS - 1
ER -