Estimating main effects in a two factorial log linear model when applied to RNA-seq

Hi everybody,

I'm going to apply multiDE, an R package for detection of DEG in multiple treatment conditions, on some RNA-seq time series data... (I wanna assume each time point as a treatment condition)

Let's assume Yidg denotes the normalized read counts for sample "i", in condition "d" for gene "g".

We also assume that Yidg marginally follows the negative binomial distribution with expectation "μdg" and dispersion parameter "ϕg" (i.e., the variance of Yidg is μdg+ϕgμ2dg).

The statistical methodology behind this package is a two factorial log linear model : logμdg = μ + αd + βg + γdg = μ + αd + βg + UdVg,

where μ is the grand mean, αd is the main effect for condition d, βg is the main effect for gene g, and γdg:=UdVg is the interaction effect between gene g and condition d.

My professor has asked me to estimate the main effect for condition (α), the main effect for gene (β) and the effect of interaction between gene and condition (γ). While the package can only show "Ud" in its output...

I'm in grave need of someone to help me please find out how I can estimate those effects...

My main problem is I don't know how I can calculate μdg. Maybe if I can calculate it, then applying a regression strategy would be helpful to estimate those effects...

here it is the link to the full paper:

Thanks in advance