This function fits the semi-parametric negative binomial mixed-effect independent model to repeated count responses (Zhao et al. 2013). The conditional distribution of response count given random effect is modelled by Negative Binomial as described in description of lmeNB. The conditional dependence among the response counts of a subject is assumed independent. The semiparametric procedure is employed for random effects. See descriptions of lmeNB.
Let m[i] be the number of pre-measurements and n[i] be the total number of repeated measures. Then the repeated measure of a subject can be divided into a pre-measurement set and a new measurement set as Y[i]=(Y[i,pre],Y[i,new]) , where Y[i,pre]=(y[i,1],cdots,Y[i,m[i]]) and Y[i,new]=(Y[i,m[i]+1],...,Y[i,n[i]]) . Given an output of fitParaIND, fitParaAR1, fitSemiIND, fitSemiAR1 or lmeNB, this function computes the probability of observing the response counts as large as those new observations of subject i, y[i,new] conditional on the subject's previous observations y[i,pre] for subject i. That is, this function returns a point estimate and its asymptotic 95% confidence interval (for a parametric model) of the conditional probability for each subject:
This function simulates a dataset based on the negative binomial mixed-effect independent/AR(1) model with two treatment groups described in Zhao et al (2013). The group mean can be different at each time point, but no other covariates are allowed. See fitParaIND, fitParaAR1 for details of the model explanations.
This function fits a negative binomial mixed-effect AR(1) model in the formulation described Zhao et al. (2013). The conditional distribution of response counts given random effect is modelled by Negative Binomial as described in description of lmeNB. The conditional dependence among the response counts of a subject is modeled with AR(1) structure. The random effects are modelled with either gamma or log-normal distributions. See descriptions of lmeNB.
This function fits the parametric negative binomial mixed-effect independent model in the formulation described Zhao et al (2013). The conditional distribution of response count given random effect is modelled by Negative Binomial as described in description of lmeNB. The conditional dependence among the response counts of a subject is assumed independent. The random effects are modelled with either gamma or log-normal distributions. See descriptions of lmeNB.
This function fits the semi-parametric negative binomial mixed-effect AR(1) model in the formulation described Zhao et al (2013). The conditional distribution of response counts given random effect is modelled by Negative Binomial as described in description of lmeNB. The conditional dependence among the response counts of a subject is modeled with AR(1) structure. The semiparametric procedure is employed for random effects. See descriptions of lmeNB.
Given the parameter estimates of α,θ, δ, β[0], β[1],... of the negative binomial mixed effect AR(1) model, these functions compute the following conditional probability:
Given the parameter estimates of α,θ, β[0], β[1],... of the negative binomial mixed effect AR(1) model, these functions compute the following conditional probability:
Let Y[ij] be the response count at jth repeated measure from ith subject. The negative binomial mixed-effect independent model assumes that given the random effect G[i]=g[i], the count response Y[ij] follows the negative binomial distribution:
providing 
.