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I am trying to joint model longitudinal data with informative observation times. Taking the simpler case, where the outcome and time processes are associated through a random intercept, I already wrote the code to get the EM-algorithm estimates.

Now, I want to calculate the standard errors and p-values of the fixed effects estimates. I am assuming $Var(\hat{\beta})=(X^T V X)^{(-1)}$ with $V=DGD^T+\sigma^2I$. $D$ denotes the random effects design matrix, while G represents the random effects covariance matrix.

All I have are the estimates of the coefficients. How can I get the standard errors for the fixed effects? How to get $D$ and $G$?

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  • $\begingroup$ Not sure if you know this, but Cross Validated supports LaTeX and would make your formula expression more readable. As it is currently written, I can only assume some of what you have noted here. $\endgroup$
    – Shawn Hemelstrand
    Commented Nov 2, 2023 at 22:57
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    $\begingroup$ @ShawnHemelstrand of course (I forgot)! I edited it accordingly. Thank you! $\endgroup$
    – adrimsvieira
    Commented Nov 2, 2023 at 23:10

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