lbm {lbm}

Log binomial regression model in Exact method

Description

If the maximum likelihood (ML) solution lies on the boundary of the parameter space in log binomial model, a special method is needed since the standard fitting algorithm may meet numerical difficulties. Exact method can overcome the difficulties and address the ML solution when it lies on the boundary of the parameter space.lbm implemented the exact method to address the ML solution in the log binomial model.

Usage

lbm(formula, data,contrasts = NULL,subset,na.action,lfv=0.95,
           vce = "oim",rescode=NULL,control=lbm.control(),...)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under ‘Details’.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lbm is called.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

subset

a specification of the rows to be used: defaults to all rows. This can be any valid indexing vector (see [.data.frame] for the rows of data or if that is not supplied, a data frame made up of the variables used in formula.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of na.action, and is na.fail if that is unset. The 'factory-fresh' default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

lfv

a testing range option which decides the range of boundary vector candidates included for testing. The default value is 0.95, which means the covariate vectors with probability greater than 0.95 will be included into boundary pairing system as boundary vector candidates.

vce

the type of the information matrix used to attain the variance-covariance matrix. Two options could be selected, observed information matrix (OIM) and expected information matrix (EIM). The default vce is "OIM". This argument only works in the data with boundary vector. If there is no boundary vector included in the data, the results are from glm. In the glm, the standard error is calculated by expected information matrix.

rescode

is an option to code the response variable if it is a factor.

control

The control argument of lbm is by default passed to the arguments of lbm.control.

...

For lbm, arguments to be used to form the default control argument if it is not supplied directly.

Details

A typical predictor has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with any duplicates removed. A specification of the form first:second indicates the set of terms obtained by taking the interactions of all terms in first with all terms in second. The specification first*second indicates the cross of first and second. This is the same as first + second + first:second. The terms in the formula will be re-ordered so that main effects come first, followed by the interactions, all second-order, all third-order and so on: to avoid this pass a terms object as the formula.

Value

lbm returns an object of class inheriting from "lbm" which inherits from the class "lbm". The function summary (i.e., summary.lbm) can be used to obtain or print a summary of the estimates and the relevant confidence interval. The argument CF.lvl in summary represents the level of confidence interval claimed in the model. The default value is CF.lvl=0.95. Optionally, Risk ratio estimates and their related confidence interval are offered as an argument RR in the summary. The default RR=FALSE is not to display them.

An object of class "lbm" is a list containing at least the following components:

coefficients

a named vector of coefficients

residuals

the working residuals, that is the residuals in the final iteration of the IWLS fit.

fitted.values

the fitted mean values, obtained by transforming the linear predictors by the inverse of the log link function.

linear.predictors

the linear fit on log scale.

deviance

twice the absolute value of maximized log-likelihood.

aic

A version of Akaike's An Information Criterion, minus twice the maximized log-likelihood plus twice the number of parameters, computed by the aic component of the family. For the binomial model, the dispersion is fixed at one and the number of parameters is the number of coefficients.

null.deviance

The deviance for the null model, comparable with deviance. The null model will only include an intercept if there is one in the model.

df.residual

the residual degrees of freedom.

df.null

the residual degrees of freedom for the null model.

response

the response vector used in the mode.l

vcov

the unscaled (dispersion = 1) estimated covariance matrix of the estimated coefficients.

vce

the type of information matrix applied.

call

the matched call.

na.action

(where relevant) information returned by stats::model.frame on the special handling of NA.

contrasts

(where relevant) the contrasts used.

formula

the formula supplied.

factor

the order of factors used in the response variable.

bvector

the matrix of boundary vectors.

bv

logical. Determines whether the model has boundary vectors.

References

Petersen, M. R. & Deddens, J. A. (2010). Maximum likelihood estimation of the log-binomial model. Communications in Statistics - Theory and Methods, 39: 5, 874 - 883.

See Also

glm, lm.

Examples

## Two examples are from Petersen, M. R. & Deddens, J. A. (2010).

## Example 1.
x<-c(1:10)
y<-c(0,0,0,0,1,0,1,1,1,1)
data<-data.frame(x,y)
a<-lbm(formula=y~x,data=data,vce="eim")

## Example 2.
x1<-c(1:11)
x2<-x1^2
y<-c(10,6,4,3,3,2,3,3,4,6,10)
dat<-cbind(x1,x2,y)
dat1<-apply(dat, 1, function(t) {
  temp<-data.frame(x1=rep(t[1],10),x2=rep(t[2],10),y=0)
  temp$y[1:t[3]]<-1
  return(temp)
})
data<-do.call(rbind, dat1)
a<-lbm(formula=y~x1+x2,data=data)
summary(a)