logit.normal.mle: Logistic-Normal Maximum Likelihood Estimation for Binary Data
In swihart/lnMLE_1.0-2: Logistic-Normal Model for Clustered Binary (Binomial) Data

Description Usage Arguments Details Value Author(s) References See Also Examples

logit.normal.mle allows for a more general model than the simple logistic-normal model since the scale parameter, sigma, may depend on cluster level characteristics.

1 2	logit.normal.mle(meanmodel, logSigma, id, n=NULL, beta=NULL, alpha=NULL, model="marginal", lambda=0.0, r = 20, maxits=50, tol = 1e-3, data = sys.frame(sys.parent()) )

`meanmodel`	a symbolic description of the marginal model to be fit that generally takes the form `y ~ x`. Further details of model specification are provided below.
`logSigma`	a symbolic description of the model used to estimate the dependence of `sigma` on covariates `z`, where `z` is a subset of covariates `x`. In general, `random` has the form `~ z`.
`id`	Cluster identification variable.
`n`	Number of responses per binomial trial.
`beta`	Initial estimate of mean parameter.
`alpha`	Initial estimate of log variance component parameter.
`model`	"conditional" for classic GLMM, "marginal" for the marginalized model.
`lambda`	A likelihood penalty parameter (>= 0) for `alpha`
`r`	Number of Gauss-Hermite quadrature points. The user may choose r=3, 5, 10, 20, or 50. The default value is r=20.
`maxits`	Maximum number of iterations for convergence. The default is maxits=50.
`tol`	Convergence criterion that specifies the absolute change in parameter estimates.
`data`	an optional data frame containing the variables in the model. If not found in `data`, the variables are taken from `environment(marginal)`, typically the environment from which `logit.normal.mle` is called.

logit.model.mle assumes that longitudinal binary measurements of y and possibly time-dependent exogenous covariates x are collected at times t(i,1), t(i,2),..., t(i,n(i)) for i = 1,2,...,N subjects or clusters. Each of the clusters or individuals (id) need not have measurements at every interval.

The meanmodel is specified symbolically as a formula. A typical marginal model has the form y ~ x. The covariates x are a series of terms separated by + which specify the marginal linear predictor for the longitudinal (binary) response vector y. The parameter(s) beta denote the contrast in log odds of success for subgroups defined by covariates x(t) The user may provide initial estimate(s) for beta.

The parameter alpha describes how the individual-level heterogeneity sigma_i in the log odds varies as a function of covariates z_i. The random model statement (logSigma) has the form ~ z. The covariates z are a subset of x, possibly just an intercept. The user may provide initial estimates(s) for alpha.

All formulas have an implied intercept term. To remove this, include -1 on the right-hand side of the formula statement. See formula for more details.

Returns an object of class logit.normal.mle. The function print.logit.normal.mle may used to obtain and print a summary of the results. See below for an example.

Patrick Heagerty heagerty@u.washington.edu

Diggle, P.J. Heagerty, P. Liang, K.Y. and Zeger, S.L. (2002) "Analysis of Longitudinal Data", 2nd Edition, Oxford University Press.

Heagerty, P.J. (1999) "Marginally Specified Logistic-Normal Models for Longitudinal Binary Data", Biometrics 55, 688-98.

print.logit.normal.mle

#
## Madras data example:
#
#data(madras)
#attach(madras)
#model1 <- logit.normal.mle(meanmodel = y ~ gender+month+age+monthXage, logSigma = ~ 1 + age, id=id, model="marginal", data=madras)
#		print.logit.normal.mle(model1)
#
## Eye and Race Example
#
data(eye_race)
attach(eye_race)
marg_model <- logit.normal.mle(meanmodel = value ~ black,
                           logSigma= ~1,
                           id=eye_race$id,
                           model="marginal",
                           data=eye_race,
                           tol=1e-5,
                           maxits=100,
                           r=50)
marg_model
cond_model <- logit.normal.mle(meanmodel = value ~ black,
                           logSigma= ~1,
                           id=eye_race$id,
                           model="conditional",
                           data=eye_race,
                           tol=1e-5,
                           maxits=100,
                           r=50)
cond_model
compare<-round(cbind(marg_model$beta, cond_model$beta),2)
colnames(compare)<-c("Marginal", "Conditional")
compare