Motivated by investigating the relationship between progesterone and the days in a menstrual cycle in a longitudinal study, we propose a multikink quantile regression model for longitudinal data analysis. It relaxes the linearity condition and assumes different regression forms in different regions of the domain of the threshold covariate. In this paper, we first propose a multikink quantile regression for longitudinal data. Two estimation procedures are proposed to estimate the regression coefficients and the kink points locations: one is a computationally efficient profile estimator under the working independence framework while the other one considers the within-subject correlations by using the unbiased generalized estimation equation approach. The selection consistency of the number of kink points and the asymptotic normality of two proposed estimators are established. Second, we construct a rank score test based on partial subgradients for the existence of the kink effect in longitudinal studies. Both the null distribution and the local alternative distribution of the test statistic have been derived. Simulation studies show that the proposed methods have excellent finite sample performance. In the application to the longitudinal progesterone data, we identify two kink points in the progesterone curves over different quantiles and observe that the progesterone level remains stable before the day of ovulation, then increases quickly in 5 to 6 days after ovulation and then changes to stable again or drops slightly. 相似文献
Continuous cropping (CC) obstacle is a major threat in legume crops production; however, the underlying mechanisms concerning the roles allelochemicals play in CC obstacle are poorly understood. The current 2-year study was conducted to investigate the effects of different kinds and concentrations of allelochemicals, p-hydroxybenzoic acid (H), cinnamic acid (C), phthalic acid (P), and their mixtures (M) on peanut root growth and productivity in response to CC obstacle. Treatment with H, C, P, and M significantly decreased the plant height, dry weight of the leaves and stems, number of branches, and length of the lateral stem compared with control. Exogenous application of H, C, P, and M inhibited the peanut root growth as indicated by the decreased root morphological characters. The allelochemicals also induced the cell membrane oxidation even though the antioxidant enzymes activities were significantly increased in peanut roots. Meanwhile, treatment with H, C, P, and M reduced the contents of total soluble sugar and total soluble protein. Analysis of ATPase activity, nitrate reductase activity, and root system activity revealed that the inhibition effects of allelochemicals on peanut roots might be due to the decrease in activities of ATPase and NR, and the inhibition of root system. Consequently, allelochemicals significantly decreased the pod yield of peanut compared with control. Our results demonstrate that allelochemicals play a dominant role in CC obstacle-induced peanut growth inhibition and yield reduction through damaging the root antioxidant system, unbalancing the osmolytes accumulation, and decreasing the activities of root-related enzymes.
