cAIC.phmm: Conditional Akaike Information Criterion for PHMM

In phmm: Proportional Hazards Mixed-Effects Model

Description

Function calculating the conditional Akaike information criterion (Vaida and Blanchard 2005) for PHMM fitted model objects, according to the formula -2*log-likelihood + k*rho, where rho represents the "effective degrees of freedom" in the sense of Hodges and Sargent (2001). The function uses the log-likelihood conditional on the estimated random effects; and trace of the "hat matrix", using the generalized linear mixed model formulation of PHMM, to estimate rho. The default k = 2, conforms with the usual AIC.

Usage

## S3 method for class 'phmm'
cAIC(object, method = "direct", ..., k = 2)

Arguments

object	A fitted PHMM model object of class phmm.
method	Passed to traceHat. Options include "direct", "pseudoPois", or "HaLee". The methods "direct" and "HaLee" are algebraically equivalent.
...	Optionally more fitted model objects.
k	numeric, the penalty per parameter to be used; the default k = 2 conforms with the classical AIC.

Value

Returns a numeric value of the cAIC corresonding to the PHMM fit.

References

Vaida, F, and Blanchard, S. 2005. Conditional Akaike information for mixed-effects models. Biometrika, 92(2), 351-.

Donohue, MC, Overholser, R, Xu, R, and Vaida, F (January 01, 2011). Conditional Akaike information under generalized linear and proportional hazards mixed models. Biometrika, 98, 3, 685-700.

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.

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-.

Hodges, JS, and Sargent, DJ. 2001. Counting degrees of freedom in hierarchical and other richly-parameterised models. Biometrika, 88(2), 367-.

See Also

phmm, AIC

Examples

n <- 50      # total sample size
nclust <- 5  # number of clusters
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)
phmmd <- data.frame(Z)
phmmd$cluster <- clusters
phmmd$time <- time
phmmd$event <- event

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

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

library(lme4)
fit.lmer <- glmer(m~-1+as.factor(time)+z1+z2+
  (-1+w1+w2|cluster)+offset(log(N)),
  as.data.frame(as(poisphmmd, "matrix")), family=poisson, nAGQ=0)

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)

summary(fit.lmer)

phmm documentation built on March 26, 2020, 5:10 p.m.