I have been trying to model a dataset of variables where each individual is measured a different number of times, and at a different point in time. Most of my variables are counts, but some are not (the target variable is a count). Furthermore there is a bunch of zeros over the count variable.
The closest I was able to find was a Zero-Inflated Poisson model, but as far as I've seen this model assumes that I measured each individual the same amount of times and over the same period. Neither of the two assumptions is true in my case.
I saw a formula (without name), where a regression can be performed such that:
$Y_i$$_t$ = $S_1$$_i$*$a_i$$_j$ + $\epsilon_i$$_t$ + $I_0$$_i$
$I_0$$_i$ = $\alpha_0$ + $\sigma_0$$_i$
$S_1$$_i$ = $\alpha_1$ + $\sigma_1$$_i$
where $i$ indicates individual and $t$ time, around the internet, but the slide simplified $a$ by removing the individual. Furthermore I am not certain if this time would allow different times for each individual.
Since time here is measured in seconds and the amount of measures for an individual can vary from 5 times to over 100 times across years, plotting many constant variables would most likely to a explosion of points as well.
Can statistics address this? I have been having the same issue with data mining and machine learning algorithms as well due to the time constraint. The regression is multivariate and predictors are not necessarily counts.
I appreciate any pointers, books, papers on any substantive field.