easy.binomial.twostage: Fits two-stage binomial for describing depdendence in...

In mets: Analysis of Multivariate Event Times

Fits two-stage binomial for describing depdendence in binomial data using marginals that are on logistic form using the binomial.twostage funcion, but call is different and easier and the data manipulation is build into the function. Useful in particular for family design data.

Description

If clusters contain more than two times, the algoritm uses a compososite likelihood based on the pairwise bivariate models.

Usage

easy.binomial.twostage(
  margbin = NULL,
  data = parent.frame(),
  method = "nr",
  response = "response",
  id = "id",
  Nit = 60,
  detail = 0,
  silent = 1,
  weights = NULL,
  control = list(),
  theta = NULL,
  theta.formula = NULL,
  desnames = NULL,
  deshelp = 0,
  var.link = 1,
  iid = 1,
  step = 1,
  model = "plackett",
  marginal.p = NULL,
  strata = NULL,
  max.clust = NULL,
  se.clusters = NULL
)

Arguments

margbin	Marginal binomial model
data	data frame
method	Scoring method
response	name of response variable in data frame
id	name of cluster variable in data frame
Nit	Number of iterations
detail	Detail for more output for iterations
silent	Debug information
weights	Weights for log-likelihood, can be used for each type of outcome in 2x2 tables.
control	Optimization arguments
theta	Starting values for variance components
theta.formula	design for depedence, either formula or design function
desnames	names for dependence parameters
deshelp	if 1 then prints out some data sets that are used, on on which the design function operates
var.link	Link function for variance
iid	Calculate i.i.d. decomposition
step	Step size
model	model
marginal.p	vector of marginal probabilities
strata	strata for fitting
max.clust	max clusters used for i.i.d. decompostion
se.clusters	clusters for iid decomposition for roubst standard errors

Details

The reported standard errors are based on the estimated information from the likelihood assuming that the marginals are known. This gives correct standard errors in the case of the plackett distribution (OR model for dependence), but incorrect for the clayton-oakes types model. The OR model is often known as the ALR model. Our fitting procedures gives correct standard errors due to the ortogonality and is fast.

Examples

data(twinstut)
twinstut0 <- subset(twinstut, tvparnr<4000)
twinstut <- twinstut0
twinstut$binstut <- (twinstut$stutter=="yes")*1
theta.des <- model.matrix( ~-1+factor(zyg),data=twinstut)
margbin <- glm(binstut~factor(sex)+age,data=twinstut,family=binomial())
bin <- binomial.twostage(margbin,data=twinstut,var.link=1,
		         clusters=twinstut$tvparnr,theta.des=theta.des,detail=0,
	                 method="nr")
summary(bin)
lava::estimate(coef=bin$theta,vcov=bin$var.theta,f=function(p) exp(p))

twinstut$cage <- scale(twinstut$age)
theta.des <- model.matrix( ~-1+factor(zyg)+cage,data=twinstut)
bina <- binomial.twostage(margbin,data=twinstut,var.link=1,
		         clusters=twinstut$tvparnr,theta.des=theta.des,detail=0)
summary(bina)

theta.des <- model.matrix( ~-1+factor(zyg)+factor(zyg)*cage,data=twinstut)
bina <- binomial.twostage(margbin,data=twinstut,var.link=1,
		         clusters=twinstut$tvparnr,theta.des=theta.des)
summary(bina)

out <- easy.binomial.twostage(stutter~factor(sex)+age,data=twinstut,
                              response="binstut",id="tvparnr",var.link=1,
			          theta.formula=~-1+factor(zyg1))
summary(out)

## refers to zygosity of first subject in eash pair : zyg1
## could also use zyg2 (since zyg2=zyg1 within twinpair's))
## do not run t save time
# desfs <- function(x,num1="zyg1",namesdes=c("mz","dz","os"))
#     c(x[num1]=="mz",x[num1]=="dz",x[num1]=="os")*1
#
#out3 <- easy.binomial.twostage(binstut~factor(sex)+age,
#                               data=twinstut, response="binstut",id="tvparnr",
#                               var.link=1,theta.formula=desfs,
#                               desnames=c("mz","dz","os"))
#summary(out3)

 ## Reduce Ex.Timings
n <- 5000
set.seed(100)
dd <- simBinFam(n,beta=0.3)
binfam <- fast.reshape(dd,varying=c("age","x","y"))
## mother, father, children  (ordered)
head(binfam)

########### ########### ########### ########### ########### ###########
####  simple analyses of binomial family data
########### ########### ########### ########### ########### ###########
desfs <- function(x,num1="num1",num2="num2")
{
     pp <- 1*(((x[num1]=="m")*(x[num2]=="f"))|(x[num1]=="f")*(x[num2]=="m"))
     pc <- (x[num1]=="m" | x[num1]=="f")*(x[num2]=="b1" | x[num2]=="b2")*1
     cc <- (x[num1]=="b1")*(x[num2]=="b1" | x[num2]=="b2")*1
     c(pp,pc,cc)
}

ud <- easy.binomial.twostage(y~+1,data=binfam,
     response="y",id="id",
     theta.formula=desfs,desnames=c("pp","pc","cc"))
summary(ud)

udx <- easy.binomial.twostage(y~+x,data=binfam,
     response="y",id="id",
     theta.formula=desfs,desnames=c("pp","pc","cc"))
summary(udx)

########### ########### ########### ########### ########### ###########
####  now allowing parent child POR to be different for mother and father
########### ########### ########### ########### ########### ###########

desfsi <- function(x,num1="num1",num2="num2")
{
    pp <- (x[num1]=="m")*(x[num2]=="f")*1
    mc <- (x[num1]=="m")*(x[num2]=="b1" | x[num2]=="b2")*1
    fc <- (x[num1]=="f")*(x[num2]=="b1" | x[num2]=="b2")*1
    cc <- (x[num1]=="b1")*(x[num2]=="b1" | x[num2]=="b2")*1
    c(pp,mc,fc,cc)
}

udi <- easy.binomial.twostage(y~+1,data=binfam,
     response="y",id="id",
     theta.formula=desfsi,desnames=c("pp","mother-child","father-child","cc"))
summary(udi)

##now looking to see if interactions with age or age influences marginal models
##converting factors to numeric to make all involved covariates numeric
##to use desfai2 rather then desfai that works on binfam

nbinfam <- binfam
nbinfam$num <- as.numeric(binfam$num)
head(nbinfam)

desfsai <- function(x,num1="num1",num2="num2")
{
    pp <- (x[num1]=="m")*(x[num2]=="f")*1
### av age for pp=1 i.e parent pairs
    agepp <- ((as.numeric(x["age1"])+as.numeric(x["age2"]))/2-30)*pp
    mc <- (x[num1]=="m")*(x[num2]=="b1" | x[num2]=="b2")*1
    fc <- (x[num1]=="f")*(x[num2]=="b1" | x[num2]=="b2")*1
    cc <- (x[num1]=="b1")*(x[num2]=="b1" | x[num2]=="b2")*1
    agecc <- ((as.numeric(x["age1"])+as.numeric(x["age2"]))/2-12)*cc
    c(pp,agepp,mc,fc,cc,agecc)
}

desfsai2 <- function(x,num1="num1",num2="num2")
{
    pp <- (x[num1]==1)*(x[num2]==2)*1
    agepp <- (((x["age1"]+x["age2"]))/2-30)*pp ### av age for pp=1 i.e parent pairs
    mc <- (x[num1]==1)*(x[num2]==3 | x[num2]==4)*1
    fc <- (x[num1]==2)*(x[num2]==3 | x[num2]==4)*1
    cc <- (x[num1]==3)*(x[num2]==3 | x[num2]==4)*1
    agecc <- ((x["age1"]+x["age2"])/2-12)*cc ### av age for children
    c(pp,agepp,mc,fc,cc,agecc)
}

udxai2 <- easy.binomial.twostage(y~+x+age,data=binfam,
     response="y",id="id",
     theta.formula=desfsai,
     desnames=c("pp","pp-age","mother-child","father-child","cc","cc-age"))
summary(udxai2)

mets documentation built on Jan. 17, 2023, 5:12 p.m.