T. Lai and D. Small: Marginal Regression Analysis of Longitudinal Data
with Time-Dependent Covariates.

The file 'rprograms_timedependcov.R' contains R functions that use
two-step GMM to fit a linear model with time-dependent covariates.
The functions assume that each unit is observed for T time periods.
The data should be arranged into three matrices ymat, xmat, zmat,
where ymat is an NxT matrix containing the outcome, with each unit's
outcomes at times 1,..., T in a row; xmat is an Nx(T*number of time
dependent covariates) matrix, with the rows arranged as first time
dependent covariate for times 1,...,T for the unit, second time
dependent covariate for times 1,...,T for the unit, ..., last time
dependent covariate for times 1,...,T for the unit; zmat is an 
Nx(number of time-independent covariates), with each unit's
time-independent covariates arranged in a row.  The functions assume
that an intercept is to be  included in the model; the intercept
should not be included in the time independent covariates.  

To fit a two-step GMM model, the user must first classify the types of
the time-dependent covariates (the function only allows Type 2 or Type 3)
and use the function validmomcondticovfunc to specify which moment
conditions will be considered.  Then the user fits the two-step GMM model with
the specified moment conditions using the function
twostepgmmticovfunc.  The other functions in the file need to be read
into R in order for the function twostepgmmticovfunc to work.  The
function twostepgmmticovfunc outputs a list with three values:
betahat: the coefficient vector -- the ordering of the coefficients is
the intercept, the time- dependent coefficients and the time-independent 
coefficients.
gmmobjmin: The value of the GMM objective function, i.e., Q_N(beta) in
the paper
asycovest: the estimated covariance matrix of the estimates

Example: Suppose T=5 and there are 3 time-dependent covariates and 
2-time-independent covariates,  and the 3 time-dependent covariates
are classified as Type 2, Type 3 and Type 2.  We would fit the model by: 
momsel=validmomcondticovfunc(5,c(1,0,1),2)
modelfit=twostepgmmticovfunc(ymat,xmat,zmat,momsel)

For more information, please contact:
Dylan Small
Department of Statistics
The Wharton School, University of Pennsylvania
400 Huntsman Hall, 3730 Walnut St.
Philadelphia, PA 19104
e-mail: dsmall@wharton.upenn.edu