mtm.lag1 {mtm} | R Documentation |
Fit a lag-1 marginal transition model for longitudinal binary outcome data.
mtm.lag1(marginal, trans1, id, beta=NULL, alpha1=NULL, offset=NULL, data = sys.frame(sys.parent()), tol = 1e-4)
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) . In general, trans1 has the form ~ z1 where z1 may or may not be 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) of how the covariates x(t) influence the average response y(t) . The estimates may be provided by the user and number of estimates provided in beta should correspond to the number of covariates in x , including an intercept.
|
alpha1 |
initial estimate(s) of how the dependence of y(t) on y(t-1) varies as a function of covariate(s) z1 . The number of estimates may be provided by the user and the number of estimates in alpha1 should correspond to the number of covariates in z1 used to assess the serial dependence in the outcome measure.
|
offset |
this can be used to specify an a priori known component to be included in the linear predictor during fitting |
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. |
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 mtm.lag1 is called.
|
Returns an object of class mtm.lag1
. The function print.mtm1
may used to obtain and print a summary of the results. See below for an example.
mtm.lag1
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 marginal 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 parameter alpha1
determines how the dependence of y(t)
on y(t-1)
varies as a function of covariates z1(t)
. The transitional model statement (trans1
) has the form ~ z1
. The covariates z1
are generally a subset of x
, possibly just an intercept.
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.
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).
# ## Data for this example may be found in the dataset 'madras.rda'. # data(madras) attach(madras) # ## lag-1 MTM model call -- Model 1 of Heagerty (2002): # model1 <- mtm.lag1(marginal=y ~ month + age + gender + monthXage + monthXgender, trans1 = ~ 1, id=id, beta=NULL, alpha1=NULL, data=madras) print.mtm1(model1)