Type: Package
Title: Mixtures of Proportional Hazard Models
Version: 0.7-2
Date: 2015-07-23
Description: Fits multiple variable mixtures of various parametric proportional hazard models using the EM-Algorithm. Proportionality restrictions can be imposed on the latent groups and/or on the variables. Several survival distributions can be specified. Missing values and censored values are allowed. Independence is assumed over the single variables.
License: GPL-2
Imports: graphics, stats, survival, lattice
Depends: R (≥ 3.0.0)
Encoding: UTF-8
LazyData: yes
LazyLoad: yes
ByteCompile: yes
NeedsCompilation: no
Packaged: 2015-07-23 12:11:41 UTC; patrick
Author: Patrick Mair [cre, aut], Marcus Hudec [aut]
Maintainer: Patrick Mair <mair@fas.harvard.edu>
Repository: CRAN
Date/Publication: 2015-07-23 15:14:01

Mixtures of proportional hazard models

Description

This package fits multiple variable mixtures of various parametric proportional hazard models using the EM-Algorithm. Proportionality restrictions can be imposed on the latent groups and/or on the variables. Several survival distributions can be specified. Missing and censored values are allowed. Independence is assumed over the single variables.

Details

Package: mixPHM
Type: Package
Version: 0.7-2
Date: 2015-07-23
License: GPL-2

Author(s)

Patrick Mair, Marcus Hudec

Maintainer: Patrick Mair <mair@fas.harvard.edu>

References

Mair, P., and Hudec, M. (2009). Multivariate Weibull mixtures with proportional hazard restrictions for dwell time based session clustering with incomplete data. Journal of the Royal Statistical Society, Series C (Applied Statistics), 58(5), 619-639.

Kalbfleisch, J.D., and Prentice, R.L. (1980). The statistical analysis of failure time data. New York: Wiley.

Celaux, G., and Govaert, G. (1992). A classification EM algorithm for clustering and two stochastic versions. Computational Statistics and Data Analysis, 14, 315-332.

Tests of Zero Correlations Among P Variables

Description

This function computes Wilcox H-test and the Steiger-Hakstian-Test for testing H0: R = I.

Usage

WilcoxH(x, use = "pairwise.complete.obs")

Arguments

x

Data frame or matrix of dimension n*p with survival times (NA's allowed).

use

Treatment of NA's for the computation of the correlation matrix (see cor()). Either "all.obs", "complete.obs", or "pairwise.complete.obs"

Details

This test is robust against violations of normality. Since phmclust() assumes independence across pages, this test can be used to explore the appropriateness of the data.

Value

Returns an object of class "wilcoxh" with the following values:

Rmat

Correlation matrix

SH.res

Results for Steiger-Hakstian-Test

WH.res

Results for Wilcox H-test

References

Wilcox, R. (1997). Tests of independence and zero correlations among P variables. Biometrical Journal, 2, 183-193.

See Also

phmclust

Examples


data(webshop)
res <- WilcoxH(webshop)
res

PHM model selection with BIC

Description

This function fits models for different proportionality restrictions.

Usage

msBIC(x, K, method = "all", Sdist = "weibull", cutpoint = NULL, 
EMoption = "classification", EMstop = 0.01, maxiter = 100)

Arguments

x

Data frame or matrix of dimension n*p with survival times (NA's allowed).

K

A vector with number of mixture components.

method

A vector with the methods provided in phmclust: With "separate" no restrictions are imposed, "main.g" relates to a group main effect, "main.p" to the variables main effects. "main.gp" reflects the proportionality assumption over groups and variables. "int.gp" allows for interactions between groups and variables. If method is "all", each model is fitted.

Sdist

Various survival distrubtions such as "weibull", "exponential", and "rayleigh".

cutpoint

Cutpoint for censoring

EMoption

"classification" is based on deterministic cluster assignment, "maximization" on deterministic assignment, and "randomization" provides a posterior-based randomized cluster assignement.

EMstop

Stopping criterion for EM-iteration.

maxiter

Maximum number of iterations.

Details

Based on the output BIC matrix, model selection can be performed in terms of the number of mixture components and imposed proportionality restrictions.

Value

Returns an object of class BICmat with the following values:

BICmat

Matrix with BIC values

K

Vector with different components

method

Vector with proportional hazard methods

Sdist

Survival distribution

See Also

screeBIC

Examples


##Fitting 3 Weibull proportional hazard models (over groups, pages) for K=2,3 components
data(webshop)
res <- msBIC(webshop, K = c(2,3), method = c("main.p","main.g"), maxiter = 10)
res

Fits mixtures of proportional hazard models

Description

This function allows for the computation of proportional hazards models with different distribution assumptions on the underlying baseline hazard. Several options for imposing proportionality restrictions on the hazards are provided. This function offers several variations of the EM-algorithm regarding the posterior computation in the M-step.

Usage

phmclust(x, K, method = "separate", Sdist = "weibull", cutpoint = NULL, EMstart = NA, 
EMoption = "classification", EMstop = 0.01, maxiter = 100)

Arguments

x

Data frame or matrix of dimension n*p with survival times (NA's allowed).

K

Number of mixture components.

method

Imposing proportionality restrictions on the hazards: With "separate" no restrictions are imposed, "main.g" relates to a group main effect, "main.p" to variable main effects. "main.gp" reflects the proportionality assumption over groups and variables. "int.gp" allows for interactions between groups and variables.

Sdist

Various survival distrubtions such as "weibull", "exponential", and "rayleigh".

cutpoint

Integer value with upper bound for observed dwell times. Above this cutpoint, values are regarded as censored. If NULL, no censoring is performed

EMstart

Vector of length n with starting values for group membership, NA indicates random starting values.

EMoption

"classification" is based on deterministic cluster assignment, "maximization" on deterministic assignment, and "randomization" provides a posterior-based randomized cluster assignement.

EMstop

Stopping criterion for EM-iteration.

maxiter

Maximum number of iterations.

Details

The method "separate" corresponds to an ordinary mixture model. "main.g" imposes proportionality restrictions over variables (i.e., the group main effect allows for free-varying variable hazards). "main.p" imposes proportionality restrictions over groups (i.e., the variable main effect allows for free-varying group hazards). If clusters with only one observation are generated, the algorithm stops.

Value

Returns an object of class mws with the following values:

K

Number of components

iter

Number of EM iterations

method

Proportionality restrictions used for estimation

Sdist

Assumed survival distribution

likelihood

Log-likelihood value for each iteration

pvisit

Matrix of prior probabilities due to NA structure

se.pvisit

Standard errors for priors

shape

Matrix with shape parameters

scale

Matrix with scale parameters

group

Final deterministic cluster assignment

posteriors

Final probabilistic cluster assignment

npar

Number of estimated parameters

aic

Akaike information criterion

bic

Bayes information criterion

clmean

Matrix with cluster means

se.clmean

Standard errors for cluster means

clmed

Matrix with cluster medians

References

Mair, P., and Hudec, M. (2009). Multivariate Weibull mixtures with proportional hazard restrictions for dwell time based session clustering with incomplete data. Journal of the Royal Statistical Society, Series C (Applied Statistics), 58(5), 619-639.

Celaux, G., and Govaert, G. (1992). A classification EM algorithm for clustering and two stochastic versions. Computational Statistics and Data Analysis, 14, 315-332.

See Also

stableEM, msBIC

Examples


data(webshop)

## Fitting a Weibll mixture model (3 components) is fitted with classification EM 
## Observations above 600sec are regarded as censored

res1 <- phmclust(webshop, K = 3, cutpoint = 600)
res1
summary(res1)

## Fitting a Rayleigh Weibull proportional hazard model (2 components, proportional over groups)
res2 <- phmclust(webshop, K = 2, method = "main.p", Sdist = "rayleigh") 
res2
summary(res2)

Plot functions

Description

Plotting functions for hazard rates, survival times and cluster profiles.

Usage

plot_hazard(x, gr.subset, var.subset, group = TRUE, xlim = NA, ylim = NA, 
xlab = "Survival Time", ylab = "Hazard Function", main = "Hazard Functions", type = "l", 
lty = 1, lwd = 1, col = NA, legpos = "right", ...)

plot_survival(x, gr.subset, var.subset, group = TRUE, xlim = NA, ylim = NA, 
xlab = "Survival Time", ylab = "Survival Function", main = "Survival Functions", 
type = "l", lty = 1, lwd = 1, col = NA, legpos = "right", ...)

plot_profile(x, method = "mean", type = "b", pch = 19, lty = 1, lwd = 1, col = NA, 
xlab = "Variables", leglab = NA, ylab = NA, main = NA, legpos = "topright", ...)

Arguments

x

object of class mws from phmclust

gr.subset

Optional vector for plotting subset of clusters

var.subset

Optional vector for plotting subset of variables

group

if TRUE hazard/survival plots are produced for each group, if FALSe for each variable

method

"mean" for cluster mean profile plot and "median" for cluster median profile plot

xlim

limits for x-axis

ylim

limits for y-axis

xlab

label for x-axis

ylab

label for y-axis

main

title of the plot

leglab

label for the legend

type

type of plot

lty

line type

lwd

line width

pch

type of plotting points

col

colors; if NA it is determined in the function

legpos

position of the legend; "topright","topleft","bottomright", "bottomleft","left","right","top", or "center"

...

Additional plot options

See Also

phmclust

Examples


##Plots for mixture Weibull model with 3 components
data(webshop)
res <- phmclust(webshop, 3)

##Hazard plot for first and third group, all pages
plot_hazard(res, gr.subset = c(1,3), group = TRUE, xlab = "Dwell Time")

##Survival plot for each group, first 6 pages
plot_survival(res, var.subset= 1:6, group = FALSE, xlab = "Dwell Time")

##Cluster profile plot
plot_profile(res, xlab = "Pages", ylab = "Mean Dwell Time", main = "Cluster Profile")

Scree plot of BIC's

Description

This function produces a scree plot on the basis of the BIC values in msBIC.

Usage

screeBIC(x, lty = 1, col = NA, pch = 19, type = "b", main = "BIC Screeplot", 
xlab = "Number of Components", ylab = "BIC", legpos = "topright", ...)

Arguments

x

Object of class mws from msBIC

lty

Line type

col

Line colors; if NA, colors are determined automatically

pch

Value for plotting points

type

Type of plot

main

Plot title

xlab

Label for x-axis

ylab

Label for y-axis

legpos

position of the legend

...

Additional plot parameters

See Also

msBIC

Examples


##Fitting all Weibull proportional hazard models for K=2,3,4 components
data(webshop)
res <- msBIC(webshop, K = c(2,3,4), method = "all", maxiter = 5)
screeBIC(res)

Stable EM solution

Description

This function performs the clustering for different EM starting values in order to find a stable solution.

Usage

stableEM(x, K, numEMstart = 5, method = "separate", Sdist = "weibull", cutpoint = NULL,
EMoption = "classification", EMstop = 0.0001, maxiter = 1000, print.likvec = TRUE)

Arguments

x

Data frame or matrix of dimension n*p with survival times (NA's allowed).

K

Number of mixture components.

numEMstart

Number of different starting solutions

method

Imposing proportionality restrictions on the hazards: With separate no restrictions are imposed, main.g relates to a group main effect, main.p to the variables main effects. main.gp reflects the proportionality assumption over groups and variables. int.gp allows for interactions between groups and variables.

Sdist

Various survival distrubtions such as weibull, exponential, and rayleigh.

cutpoint

Integer value with upper bound for observed dwell times. Above this cutpoint, values are regarded as censored. If NULL, no censoring is performed

EMoption

classification is based on deterministic cluster assignment, maximization on deterministic assignment, and randomization provides a posterior-based randomized cluster assignement.

EMstop

Stopping criterion for EM-iteration.

maxiter

Maximum number of iterations.

print.likvec

If TRUE the likelihood values for different starting solutions are printed.

Details

After the computation of the models for different starting solutions using the function phmclust the best model is chosen, i.e., the model with the largest likelihood value. The output values refer to this final model.

Value

Returns an object of class mws with the following values:

K

Number of components

iter

Number of EM iterations

method

Method with propotionality restrictions used for estimation

Sdist

Assumed survival distribution

likelihood

Log-likelihood value for each iteration

pvisit

Matrix of prior probabilities due to NA structure

se.pvisit

Standard errors for priors

shape

Matrix with shape parameters

scale

Matrix with scale parameters

group

Final deterministic cluster assignment

posteriors

Final probabilistic cluster assignment

npar

Number of estimated parameters

aic

Akaike information criterion

bic

Bayes information criterion

clmean

Matrix with cluster means

se.clmean

Standard errors for cluster means

clmed

Matrix with cluster medians

See Also

phmclust,msBIC

Examples


## Exponental mixture model with 2 components for 4 different starting solutions
data(webshop)
res <- stableEM(webshop, K = 2, numEMstart = 4, Sdist = "exponential")
res
summary(res)

Webshop dataset for mixPHM package

Description

This artificial data set represents dwell times in seconds of 333 sessions on 7 webpage categories of a webshop. Missing values indicate that the corresponding session did not visit a particular page.

Usage

data(webshop)

Format

Numeric matrices of data frames with subjects as rows and variables as columns. Missing values are coded as NA (which corresponds to 0 survival time).

Examples

data(webshop)
str(webshop)