# AIC.phmm: Akaike Information Criterion for PHMM In phmm: Proportional Hazards Mixed-Effects Model

## Description

Function calculating the Akaike information criterion for PHMM fitted model objects, according to the formula -2*log-likelihood + k*npar, where npar represents the number of parameters in the fitted model. The function returns a list of AIC calculations corresponding different likelihood estimations: conditional and marginal likelihoods calculated by Laplace approximation, reciprocal importance sampling, and bridge sampling (only implemented for nreff < 3). The default k = 2, is for the usual AIC.

## Usage

 ```1 2``` ```## S3 method for class 'phmm' AIC(object, ..., k = 2) ```

## Arguments

 `object` an object of class `phmm`. `...` optionally more fitted model objects. `k` numeric, the penalty per parameter to be used; the default k = 2 is the classical AIC.

## Value

Returns a list of AIC values corresonding to all available log-likelihood values from the fit. See `phmm` for details of the log-likelihood values.

## References

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-.

`phmm`, `AIC`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48``` ```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