In Twisk (2013) on the equation describing a generalized estimating equation (GEE), why is there a subscripted '1' after beta? In his book on Applied Longitudinal Data Analysis for Epidemiology, page 60 there is an equation that describes a generalized estimating equations (GEE) model.
"
This equation models the relationship between an outcome variable ($Y$) and a set of covariates ($X_1$, $X_2$ ... $X_j$) for $i$ persons at different timepoints $t$. It adjusts for repeated measurements (i.e. within-subject correlation) by assuming a 'working' correlation structure for the repeated measurements of the outcome variable $Y$ (i.e. the correlation structure $CORR$).
With GEE analysis the relationships between the variables of the model at different time-points are analyzed simultaneously.The estimated $\beta_1$
reflects the longitudinal relationship between the outcome variable $Y$ and the corresponding covariates $X$:
$$Y_{it}  = \beta_0 + \sum_{j=1}^J \beta_{1j}\chi_{itj} + ... + CORR_{it} + \epsilon_{it}$$
where $Y_{it}$ are observations for subject i at time t, $\beta_0$ is the intercept, $X_{ijt}$ is the
covariate j for subject i at time t, $\beta_1$ is the regression coefficient for covariate j, J is the number of covariates, $CORR_{it}$ is the working correlation structure, and $\epsilon$ is the “error” for subject i at time t. "
Is the 1 in beta1 just there to denote that it is related to vector of the first covariate?
If so, why does it not also say X1?

Yes, basically. The 1 subscript just means that vector of (time independent) betas comprise the "slope" terms in the mean model of the GEE. Why not subscript with $X_1$? Then you'd have a double subscript, and it's hard to read in printed text if not impossible to typeset.
