mtm.lag2 {mtm}R Documentation

Fit a (lag 2) Marginal Transition Model

Description

Fit a lag-2 marginal transition model for longitudinal binary outcome data.

Usage

mtm.lag2(marginal, trans1, trans2, id, beta=NULL, alpha1=NULL, alpha2=NULL, tol = 1e-4, iter = 50, data=sys.frame(sys.parent()))

Arguments

marginal a symbolic description of the model to be fit that generally takes the form y ~ x. Further details of model specification are provided below.
trans1 covariates used to estimate the dependence of y(t) on y(t-1). The model specification of the z1 is a subset of covariates x.
trans2 covariates used to estimate the dependence of y(t) on y(t-2). In general, z2 is a subset of covariates x.
id a vector that identifies the clusters which correspond to the binary response vector given by y.
beta initial parameter estimate(s) optionally provided by the user of how the covariates x(t) influence the average response y(t). The number of estimates provided in beta should correspond to the number of covariates in x, including an intercept.
alpha1 initial estimate(s) optionally provided by the user of how the dependence of y(t) on y(t-1) varies as a function of covariate(s) z1. The number of estimates provided in alpha1 should correspond to the number of covariates in z1 used to assess the serial dependence in the outcome measure.
alpha2 initial estimate(s) optionally provided by the user of how the dependence of y(t) on y(t-2) varies as a function of covariate(s) z2. The number of estimates provided in alpha2 should correspond to the number of covariates in z2 used to assess the serial dependence in the outcome measure.
tol tolerance is a measure used in the numerical calculations to determine whether or not convergence of the point estimates has occurred. The default is 1e-4.
iter number of iterations to obtain convergence of estimates with the limits specified by tol. The default is 50 iterations.
data an optional 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 mtm.lag2 is called.

Value

Returns an object of class mtm.lag2. The function print.mtm2 is used to obtain and print a summary of the results. See below for an example.

DETAILS

mtm.lag2 assumes that the longitudinal measurements of y and x are collected at equally spaced intervals, though each of the N clusters or individuals need not have measurements at every interval. y is the longitudinal (binary) response vector measured on clusters or individuals specified by id.

The marginal model is specified symbolically as a formula. A typical model has the form y ~ x The covariates x are a series of terms separated by + which specify the marginal linear predictor for y. The parameter(s) beta denote the marginal dependence of y(t) on covariates x(t) The user may provide initial estimate(s) for beta.

The transitional model statement (trans1) has the form ~ z1 where trans1. The parameter(s) alpha1 determine how the dependence of y(t) on y(t-1) varies as a function of covariates z1(t-1). The covariates z1 are generally a subset of x, possibly just an intercept. An initial estimate of alpha1 may be provided by the user.

The transitional model statement (trans2) has the form ~ z2 where trans2. The parameter(s) alpha2 determine how the dependence of y(t) on y(t-2) varies as a function of covariates z2(t-2). The covariates z2 are generally a subset of x, possibly just an intercept. An initial estimate of alpha2 may be provided by the user.

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.

References

P. Heagerty (2002), Marginalized transition models and likelihood inference for longitudinal categorical data. Biometrics, 58, 342-51.

A. Azzalini (1994), Logistic regression for autocorrelated data with application to repeated measures. Biometrika, 81, 767-75 (correction: 1997. 84, 989).

See Also

mtm.lag1

Examples

#
## Data for this example may be found in the dataset 'madras.rda'.
#
        data(madras)    
        attach(madras)
#
## lag-2 MTM model call -- Model 5 of Heagerty (2002):
#
        model2 <- mtm.lag2(marginal = y ~ month + age + gender + monthXage + monthXgender, 
                         trans1 = ~ initial + month,
                         trans2 = ~ 1, 
                         id=id, beta=NULL, alpha1=NULL, alpha2=NULL, data=madras)
        print.mtm2(model2)

[Package mtm version 1.0 Index]