maop {maop}R Documentation

Mixed Autoregressive Ordered Probit Models

Description

Fits mixed autoregressive ordered probit models to a longitudinal data set by maximum pairwise likelihood.

Usage

maop(formula, subjects, periods=subjects, randomEffect=FALSE, 
dynamics=NULL, startValues=NULL, distance=2, print.info=TRUE)

Arguments

formula a formula expression of form response ~ predictors. The response must be an ordinal factor. The model fitted is a dynamic generalization of the ordered probit regression model and it must have an intercept. See the documentation of formula for other details.
subjects identifier for the different subjects in the longitudinal study. This is a vector of the same length of the response containing identifiers for the different subjects. See the example.
periods identifier for the different measurement periods of the subjects in the longitudinal study. The default value is equal to that of subjects assuming one single measurement period for each patient. Otherwise, periods is a vector of the same length of the response containing identifiers for the different measurement periods. See the example.
randomEffect logical. Should a subject-specific random effect be included?
dynamics a factor whose levels correspond to different autocorrelation parameters. The default value is NULL indicating an unique autocorrelation parameter.
startValues starting values. The default value is NULL meaning that starting values are computed automatically by the maop function
distance maximal distance within pairs of observations included in the pseudolikelihood.
print.info logical. Should information about computation status be printed?.

Details

MAOP stands for mixed autoregressive ordered probit models, as described in Varin and Czado (2009). Model fitting is performed by maximum pairwise likelihood (Varin, 2008).

Value

An object of class maop. The components of an object of the class maop are

formula fitted model.
subjects factor denoting different subjects.
periods factor denoting different measurement periods.
isRandomEffect whether a subject-specific random effect is included in the model.
dynamics factor denoting different autocorrelation parameters.
distance maximal admissible distance between pairs of observations.
startValues starting values.
coeff maximum pairwise likelihood estimator.
stdErr estimated standard errors.
varMatrix estimated variance-covariance matrix of the parameter estimates.
logPair maximized log-pairwise likelihood.
clic composite likelihood information criterion (Varin and Vidoni, 2005).
convergence integer code as in optim function.

Author(s)

Cristiano Varin

References

Varin, C. and Vidoni, P. (2005). A note on composite likelihood inference and model selection. Biometrika, 92, 519–528.

Varin, C. (2008). On composite marginal likelihoods. Advances in Statistical Analysis, 92, 1–28.

Varin, C. and Czado, C. (2009). A mixed autoregressive probit model for ordinal longitudinal data. Biostatistics, to appear.

See Also

migraine, optim, polr

Examples

# Fits a MAOP model to migraine data (Varin and Czado, 2009)
data(migraine)
attach(migraine)
# covariates
university <-rep(0,length(HA))
university[ED==5]<-1
university[ED==6]<-1
university[ED==7]<-1
university <- as.factor(university==1)
analgesics <- as.factor(MEDANALG=="Y")
# weather covariates
wc <- factor(cut(MINWC, breaks=c(-50, -10, 0, 10, 30)))
high.pressure <- PMN>10130
high.pressure.yesterday <- PMN1P>10130
change <- rep("persistence", length(high.pressure))
change[(!high.pressure & high.pressure.yesterday)] <- "worse"
change[(high.pressure & !high.pressure.yesterday)] <- "better"
change <- factor(change)
humidity <- cut(RHMN, breaks=c(0, 60, 80, 100))
# model
m <- HA~university+analgesics+wc+humidity+change
# fit model m with different autocorrelation parameters 
# for patients with analgesics intake and those who not 
# try with pairwise likelihood with maximal distance 2
maop2 <- maop(m, subjects=SUBJECT, periods=PERIOD, randomEffect=TRUE, 
dynamics=analgesics, distance=2)
summary(maop2, digits=2)
# pairwise likelihood with maximal distance equals to 6 
maop6 <- maop(m, subjects=SUBJECT, periods=PERIOD, randomEffect=TRUE,
dynamics=analgesics, distance=6, startValues=maop2$coeff)
summary(maop6, digits=2)

[Package maop version 0.2 Index]