cl1: OPTIMIZATION ROUTINE FOR BIVARIATE COMPOSITE LIKELIHOOD FOR...
In weightedScores: Weighted Scores Method for Regression Models with Dependent Data
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Optimization routine for bivariate composite likelihood for MVN copula.
Usage
1
2
Arguments
b
The regression coefficients.
gam
The uinivariate parameters that are not regression coefficients. That is the parameter γ of negative binomial distribution or the q-dimensional vector of the univariate cutpoints of ordinal model. γ is NULL for Poisson and binary regression.
xdat
(\mathbf{x}_1 , \mathbf{x}_2 , … , \mathbf{x}_n )^\top,
where the matrix \mathbf{x}_i,\,i=1,…,n for a given unit will
depend on the times of observation for that unit (j_i) and will have
number of rows j_i, each row corresponding to one of the j_i elements
of y_i and p columns where p is the number of covariates including
the unit first column to account for the intercept (except for ordinal regression where there is no intercept). This xdat matrix is
of dimension (N\times p), where N =∑_{i=1}^n j_i is the total
number of observations from all units.
ydat
(y_1 , y_2 , … , y_n )^\top, where
the response data vectors y_i,\,i=1,…,n
are of possibly different lengths for different units. In particular,
we now have that y_i is (j_i \times 1), where j_i is the number of
observations on unit i. The total number of observations from all units
is N =∑_{i=1}^n j_i. The ydat are the collection of data vectors
y_i, i = 1,…,n one from each unit which summarize all the data
together in a single, long vector of length N.
id
An index for individuals or clusters.
tvec
A vector with the time indicator of individuals or clusters.
margmodel
Indicates the marginal model.
Choices are “poisson” for Poisson, “bernoulli” for Bernoulli,
and “nb1” , “nb2” for the NB1 and NB2 parametrization
of negative binomial in Cameron and Trivedi (1998).
corstr
Indicates the latent correlation structure of normal copula.
Choices are “exch”, “ar”, and “unstr” for exchangeable, ar(1)
and unstructured correlation structure, respectively.
link
The link function.
Choices are “log” for the log link function, “logit” for
the logit link function, and “probit” for
the probit link function.
Details
The
CL1 composite likelihood method in Zhao and Joe (2005). The
univariate parameters are estimated
from the sum of univariate marginal log-likelihoods and then the dependence
parameters are estimated from the sum of bivariate marginal log-likelihoods
with the univariate parameters fixed from the first step.
Note that bcl.ord is a variant of the code for ordinal (probit and logistic) regression.
Value
A list containing the following components:
minimum
The negative value of the sum of bivariate marginal log-likelihoods at
CL1 estimates.
estimate
The CL1 estimates.
gradient
The gradient at the estimated minimum of CL1.
code
An integer indicating why the optimization process terminated,
same as in nlm.
Author(s)
Aristidis K. Nikoloulopoulos A.Nikoloulopoulos@uea.ac.uk
Harry Joe harry.joe@ubc.ca
References
Zhao, Y. and Joe, H. (2005)
Composite likelihood estimation in multivariate data analysis.
The Canadian Journal of Statistics, 33, 335–356.
See Also
Examples
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################################################################################
# NB1 regression for count data
################################################################################
################################################################################
# read and set up data set
################################################################################
data(childvisit)
# covariates
season1<-childvisit$q
season1[season1>1]<-0
xdat<-cbind(1,childvisit$sex,childvisit$age,childvisit$m,season1)
# response
ydat<-childvisit$hosp
#id
id<-childvisit$id
#time
tvec<-childvisit$q
################################################################################
# select the marginal model
################################################################################
margmodel="nb1"
################################################################################
# select the correlation structure
################################################################################
corstr="exch"
################################################################################
# perform CL1 estimation
################################################################################
i.est<-iee(xdat,ydat,margmodel)
cat("\niest: IEE estimates\n")
print(c(i.est$reg,i.est$gam))
est.rho<-cl1(b=i.est$reg,gam=i.est$gam,xdat,ydat,id,tvec,margmodel,corstr)
cat("\nest.rho: CL1 estimates\n")
print(est.rho$e)
################################################################################
# Ordinal regression
################################################################################
################################################################################
# read and set up data set
################################################################################
data(arthritis)
nn=nrow(arthritis)
bas2<-bas3<-bas4<-bas5<-rep(0,nn)
bas2[arthritis$b==2]<-1
bas3[arthritis$b==3]<-1
bas4[arthritis$b==4]<-1
bas5[arthritis$b==5]<-1
t2<-t3<-rep(0,nn)
t2[arthritis$ti==3]<-1
t3[arthritis$ti==5]<-1
xdat=cbind(t2,t3,arthritis$trt,bas2,bas3,bas4,bas5,arthritis$age)
ydat=arthritis$y
id<-arthritis$id
#time
tvec<-arthritis$time
################################################################################
# select the link
################################################################################
link="logit"
################################################################################
# select the correlation structure
################################################################################
corstr="exch"
################################################################################
# perform CL1 estimation
################################################################################
i.est<-iee.ord(xdat,ydat,link)
cat("\niest: IEE estimates\n")
print(c(i.est$reg,i.est$gam))
est.rho<-cl1.ord(b=i.est$reg,gam=i.est$gam,xdat,ydat,id,tvec,corstr,link)
cat("\nest.rho: CL1 estimates\n")
print(est.rho$e)
weightedScores documentation built on March 24, 2020, 1:07 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Optimization routine for bivariate composite likelihood for MVN copula.
Usage
1 2 |
Arguments
b |
The regression coefficients. |
gam |
The uinivariate parameters that are not regression coefficients. That is the parameter γ of negative binomial distribution or the q-dimensional vector of the univariate cutpoints of ordinal model. γ is NULL for Poisson and binary regression. |
xdat |
(\mathbf{x}_1 , \mathbf{x}_2 , … , \mathbf{x}_n )^\top, where the matrix \mathbf{x}_i,\,i=1,…,n for a given unit will depend on the times of observation for that unit (j_i) and will have number of rows j_i, each row corresponding to one of the j_i elements of y_i and p columns where p is the number of covariates including the unit first column to account for the intercept (except for ordinal regression where there is no intercept). This xdat matrix is of dimension (N\times p), where N =∑_{i=1}^n j_i is the total number of observations from all units. |
ydat |
(y_1 , y_2 , … , y_n )^\top, where the response data vectors y_i,\,i=1,…,n are of possibly different lengths for different units. In particular, we now have that y_i is (j_i \times 1), where j_i is the number of observations on unit i. The total number of observations from all units is N =∑_{i=1}^n j_i. The ydat are the collection of data vectors y_i, i = 1,…,n one from each unit which summarize all the data together in a single, long vector of length N. |
id |
An index for individuals or clusters. |
tvec |
A vector with the time indicator of individuals or clusters. |
margmodel |
Indicates the marginal model. Choices are “poisson” for Poisson, “bernoulli” for Bernoulli, and “nb1” , “nb2” for the NB1 and NB2 parametrization of negative binomial in Cameron and Trivedi (1998). |
corstr |
Indicates the latent correlation structure of normal copula. Choices are “exch”, “ar”, and “unstr” for exchangeable, ar(1) and unstructured correlation structure, respectively. |
link |
The link function. Choices are “log” for the log link function, “logit” for the logit link function, and “probit” for the probit link function. |
Details
The CL1 composite likelihood method in Zhao and Joe (2005). The univariate parameters are estimated from the sum of univariate marginal log-likelihoods and then the dependence parameters are estimated from the sum of bivariate marginal log-likelihoods with the univariate parameters fixed from the first step.
Note that bcl.ord is a variant of the code for ordinal (probit and logistic) regression.
Value
A list containing the following components:
minimum |
The negative value of the sum of bivariate marginal log-likelihoods at CL1 estimates. |
estimate |
The CL1 estimates. |
gradient |
The gradient at the estimated minimum of CL1. |
code |
An integer indicating why the optimization process terminated,
same as in |
Author(s)
Aristidis K. Nikoloulopoulos A.Nikoloulopoulos@uea.ac.uk
Harry Joe harry.joe@ubc.ca
References
Zhao, Y. and Joe, H. (2005) Composite likelihood estimation in multivariate data analysis. The Canadian Journal of Statistics, 33, 335–356.
See Also
Examples
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 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 | ################################################################################
# NB1 regression for count data
################################################################################
################################################################################
# read and set up data set
################################################################################
data(childvisit)
# covariates
season1<-childvisit$q
season1[season1>1]<-0
xdat<-cbind(1,childvisit$sex,childvisit$age,childvisit$m,season1)
# response
ydat<-childvisit$hosp
#id
id<-childvisit$id
#time
tvec<-childvisit$q
################################################################################
# select the marginal model
################################################################################
margmodel="nb1"
################################################################################
# select the correlation structure
################################################################################
corstr="exch"
################################################################################
# perform CL1 estimation
################################################################################
i.est<-iee(xdat,ydat,margmodel)
cat("\niest: IEE estimates\n")
print(c(i.est$reg,i.est$gam))
est.rho<-cl1(b=i.est$reg,gam=i.est$gam,xdat,ydat,id,tvec,margmodel,corstr)
cat("\nest.rho: CL1 estimates\n")
print(est.rho$e)
################################################################################
# Ordinal regression
################################################################################
################################################################################
# read and set up data set
################################################################################
data(arthritis)
nn=nrow(arthritis)
bas2<-bas3<-bas4<-bas5<-rep(0,nn)
bas2[arthritis$b==2]<-1
bas3[arthritis$b==3]<-1
bas4[arthritis$b==4]<-1
bas5[arthritis$b==5]<-1
t2<-t3<-rep(0,nn)
t2[arthritis$ti==3]<-1
t3[arthritis$ti==5]<-1
xdat=cbind(t2,t3,arthritis$trt,bas2,bas3,bas4,bas5,arthritis$age)
ydat=arthritis$y
id<-arthritis$id
#time
tvec<-arthritis$time
################################################################################
# select the link
################################################################################
link="logit"
################################################################################
# select the correlation structure
################################################################################
corstr="exch"
################################################################################
# perform CL1 estimation
################################################################################
i.est<-iee.ord(xdat,ydat,link)
cat("\niest: IEE estimates\n")
print(c(i.est$reg,i.est$gam))
est.rho<-cl1.ord(b=i.est$reg,gam=i.est$gam,xdat,ydat,id,tvec,corstr,link)
cat("\nest.rho: CL1 estimates\n")
print(est.rho$e)
|
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