phmm (version 0.6.3)

traceHat: Trace of the "hat" matrix from PHMM-MCEM fit

Description

Compute trace of the ``hat'' matrix from PHMM-MCEM fit using a direct approximation method (Donohue, et al, submitted), an approximation via hierarchical likelihoods (Ha et al, 2007), or an approximation via a generalized linear mixed-effects model (GLMM) (Donohue, et al, submitted).

Usage

traceHat(x, method="direct")
 traceHat.default(z, w, cluster, Sigma, fitted)

Arguments

x

an object of class phmm,

method

acceptable values are "direct", "pseudoPois", "HaLee" or coxph (no random effects),

z

matrix of fixed effects covariates,

w

matrix of random effects covariates,

cluster

integer valued cluster indices,

Sigma

variance-covariance matrix of fit,

fitted

linear predictors (fixed and random).

Value

• The trace of the "hat" matrix which can be used as a measure of complexity of the model.

References

Breslow, NE, Clayton, DG. (1993). Approximate Inference in Generalized Linear Mixed Models. Journal of the American Statistical Association, Vol. 88, No. 421, pp. 9-25.

Donohue, M, Xu, R, Vaida, F, Haut R. Model Selection for Clustered Data: Conditional Akaike Information under GLMM and PHMM. Submitted.

Ha, ID, Lee, Y, MacKenzie, G. (2007). Model Selection for multi-component frailty models. Statistics in Medicine, Vol. 26, pp. 4790-4807.

Whitehead, J. (1980). Fitting Cox's Regression Model to Survival Data using GLIM. Journal of the Royal Statistical Society. Series C, Applied statistics, 29(3), 268-.

See Also

phmm, AIC.phmm

Examples

N <- 100
B <- 100
n <- 50
nclust <- 5
clusters <- rep(1:nclust,each=n/nclust)
beta0 <- c(1,2)
set.seed(13)
#generate phmm data set
Z <- cbind(Z1=sample(0:1,n,replace=TRUE),
           Z2=sample(0:1,n,replace=TRUE),
           Z3=sample(0:1,n,replace=TRUE))
b <- cbind(rep(rnorm(nclust),each=n/nclust),rep(rnorm(nclust),each=n/nclust))
Wb <- matrix(0,n,2)
for( j in 1:2) Wb[,j] <- Z[,j]*b[,j]
Wb <- apply(Wb,1,sum)
T <- -log(runif(n,0,1))*exp(-Z[,c('Z1','Z2')]%*%beta0-Wb)
C <- runif(n,0,1)
time <- ifelse(T<C,T,C)
event <- ifelse(T<=C,1,0)
mean(event)
phmmdata <- data.frame(Z)
phmmdata$cluster <- clusters
phmmdata$time <- time
phmmdata$event <- event

fit.phmm <- phmm(Surv(time, event)~Z1+Z2+cluster(cluster),
   ~-1+Z1+Z2, phmmdata, Gbs = 100, Gbsvar = 1000, VARSTART = 1,
   NINIT = 10, MAXSTEP = 100, CONVERG=90)

# Same data can be fit with lmer,
# though the correlation structures are different.
poisphmmdata <- pseudoPoisPHMM(fit.phmm)

library(lme4)
fit.lmer <- lmer(m~-1+as.factor(time)+z1+z2+
  (-1+w1+w2|cluster)+offset(log(N)), 
  poisphmmdata, family=poisson)

fixef(fit.lmer)[c("z1","z2")]
fit.phmm$coef

VarCorr(fit.lmer)$cluster
fit.phmm$Sigma

logLik(fit.lmer)
fit.phmm$loglik

traceHat(fit.phmm)