Dear Allstatsters, 

The following questions refer to some comments made in the book 'Analysis 
of Longitudinal Data' by Diggle, Liang, and Zeger (1994) concerning the 
modelling of longitudinal data by splitting a covariate to a 
cross-sectional and a longitudinal element. Say b_c is the coefficient for 
the x-sect element, and b_l is the coefficient for the longitudinal 
element. 

It says: 

We want to distinguish the contributions of cross-sectional and 
longitudinal information to the estimated relationship of respiratory 
infection and age... Note that the distinction between b_c and b_l defined 
for linear models holds only approximately for logistic and other 
non-linear models. (p161)

What is the authors referring to when they seem to suggest that this 
technique is more accurate for linear model than for non-linear models? 

Also I read in the second chapter the following: 

The orthogonality between x_i1 and x_ij for each j is achieved if x_ij - 
x_i1 = delta_j, independent of i. That is, the least-squares estimator, 
beta-hat, will be an unbiased estimate of beta_L if the spacings in x 
between two consecutive visits are the same for all subjects. (p 25)

I don't understand it. If x_ij - x_i1 is independent of i, then we have 
x_i1 being independent of (x_ij - x_i1), but it doesn't mean x_i1 is 
independent of x_ij. In any case, the authors seem to be suggesting that 
if our x_ij are things like age taken at regular intervals, then the OLS 
estimator, without breaking down age into cross-sectional and longitudinal 
components, will give the same estimates as the longitudinal beta if we 
break down age into x-sect and longitudinal components. Which, I've shown 
on a simple dataset, is not true. Perhaps the confusing bit is the 'for 
each j' in the first sentence, which I can't figure out what it's 
referring to. 

Any help would be appreciated. 

Thanks, 

Timothy Mak