poisson model for normalized values

[BenxiaHu]

Hello

I am still confused this model:
x and y are normliazed values, not count. why are they applied to poisson regression model?

Originally posted by @BenxiaHu in #5 (comment)

[lzj1769]

I have the same question.

Isn't the Poisson regression mode supposed to model count data?

In the method section, it says, "Gene expression values are normalized by counts per million".

[snehamitra]

Apologies for the confusion. It is "counts per 10,000", and not "million", as mentioned in Fig. 1f and g, the "Data preprocessing" section, as well as in scarlink_processing.

The scRNA-seq data sets will still retain count-like non-negative values after scaling to 10k counts per cell. So we can use the Poisson (pseudo/quasi) likelihood function. Previous studies have shown that Poisson pseudo/quasi maximum likelihood estimation works well with data containing lots of zeros where the data does not necessarily need to be count data. That being said, it is sensitive to the scaling factor. We have started exploring that scaling by median may yield improved results in some data sets instead of scaling by 10,000. We added 'median' as a scaling factor in the scarlink_processing function.

[BenxiaHu]

Please show me references

[snehamitra]

"pseudo maximum likelihood method with Poisson family may be applied even if Yt is any real number", Theorem 1 in https://www.jstor.org/stable/1913471?seq=5

Poisson pseudo maximum likelihood estimator is generally well behaved for data having a large proportion of zeros: https://personal.lse.ac.uk/TENREYRO/ppml-fsr.pdf