# Trying to understand coef column (and how to convert it to fold change)

Hi everyone!

I just performed an expression analysis with transcripts, and I’m trying to understand what exactly means “coef” column. I read in the Tutorial this:

`coef` : the model coefficient value (effect size).

So, ok, it’s the effect size, but I’m used to read about fold changes and log2 fold changes in this kind of analyses. So how can be this coefficient value transformed to fold change (in case this coefficient wasn’t fold change, which is a possibility I don’t discard)?

If it helps, I used these parameters:
transform = “LOG”, analysis_method = “LM”, correction = “BH”, normalization = “TSS”, standardize = FALSE

Thank you very much in advance.

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Hello, I am also interested in this post. Thanks a lot, Gabri

Hi @dts (and @mrgambero),
Thanks for the question! In a previous response, we showed how to convert the coef to log2 fold change. This is also something that we are thinking of implementing more clearly in the next major iteration of MaAsLin. We haven’t done it to date because it is confusing to implement/interpret within the multivariable infrastructure of MaAsLin. In the future, we are thinking of allowing a call for the main variable of interest within the model which will allow the results of a log2 fold change to be more interpretable.
I hope this helps!
Kelsey

Thanks @Kelsey_Thompson !

I am sorry to be annoying, but I still have doubts about how to do that.
That question explains how to convert the coefficient to log2fold change in case of a glm with poisson distribution. But I usually use either 'lm" or “negative binomial”. Would that be the same?

I think in case of lm, I do not need to do the following step:
fc<- exp(fit\$coefficients[2]) ## Antilog coef #2

Thanks for considering this implementation for the future.
I think it is a good idea to have it has fold change, so it is better quantifiable.
Now we have this coefficient but we do not really know how to biologically interpret it.

Gabri

Hi @mrgambero - it’s the same as the Poisson GLM for the negative binomial. In fact, you can use the same formula for any GLM with a log link. Thanks!

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Thank you both! It helped a lot. I saw that previous response, but I was not sure at all if it would fit for the parameters I was using (in fact, I deduce from @himel.mallick answer that this formula is not proper for linear model, right?). Now I changed the analysis_method to CPLM and transform to NONE, and following the formula I guess I get the log2 fold change correctly.

Thanks again, and keep on doing your excellent job.

Thanks, all. Just to add to the rationale for not doing a similar back transformation for linear models: with a log2 transformation in place (default in MaAsLin 2, similar to limma), the coefficients can be interpreted as the log2 fold-changes themselves, as explained here. Note that, the interpretation is not quite the same without a log2 transformation for a linear model. This goes back to @Kelsey_Thompson’s comment on why we opted to report coefficients instead which are generally more universal across models and they are likewise much easier to interpret in our multi-model, multivariable setup.

Hello Himel.mallick.

I am so sorry, you got me a little even more confused.
When you say “log2 transformation in place (default in MaAsLin 2”.
it means, that, if I use Maaslin with default parameters (so that would be
analysis_method = “LM”)
The “coef” column is already a log2fold change?
I DO NOT need to do any further operation on the data.

not even the: x<- log2(coef) step.

Is that correct?

I am sorry to be annoying. I just want to make sure I am reporting and explaining the value correctly.

Thanks!
Gabri

Hi @mrgambero - that is correct. This is simply because the data is already log2-transformed and based on the math provided above, it will be approximately the same as the log2 fold-change value as shown below.

Actual log2(FC) = log2(mean(Group1/Group2))
MaAsLin 2 coefficient or “Log2(FC)” for the default model = mean(log2(Group1)) - mean(log2(Group2)).

Does this make sense?

It makes sense to me. Thanks again for your detailed explanations.

yes! thanks!
Better to be sure I was not understanding pears for apples!

Thanks a lot!