[R-meta] Fixed Intercept in mixed effect models Interpretation

[Michael Dewey]

Dear Benedikt

See comments in-line below

On 13/04/2019 11:42, Graf, Benedikt wrote:
> Hello,
> 
> 
> 
> In a seminar a few months ago my interest in meta-analysis was raised. Since then I have been working on a meta-analysis, which I calculate with metafor.
> 
> I have a question for you regarding categorical moderator analysis with metafor. For my core analysis I calculated random effect models. These show a high heritability, which is why I conclude on moderators (which I also coded). Examples would be the type of survey or methodological aspects. I use the following syntax for moderator analyses (example "context" as categorial variable and "gender" as interval/ratio variable):
> 
> 
> 
> mod.context <- rma(yi, vi, weighted=TRUE, method="HE", mods = ~ factor(Context)-1, data=dataset) mod.context

You have told R to fit a model without intercept so you will get one 
coefficient for each level of Context. Your Alternative would be to 
remove the -1 and get the intercept and one fewer coefficient for 
Context. This is not explicitly something to do with metafor, it is how 
linear model functions like lm() and glm() work. Try it and see, you 
will not break anything.

One thing to note is that if you test the moderator variable with the 
two models you are testing two different hypotheses. The way you are 
doing it tests whether the estimated effect is equal to zero, the other 
way tests whether the estimated effect is the same for each level of 
Context.
> 
> confint(mod.context)
> 
> 
> 
> mod.sex <- rma(yi, vi, weighted=TRUE, method="HE", mods = ~ Sex_female-1, data=dataset) mod.sex
> 
> confint(mod.sex)
> 

Have you actually coded Sex as a factor? It would be much better to do 
so if not.

> 
> 
> I partially adopted this syntax from the seminar. I work with Fishers z correlations and a small number of studies. My question refers to the fixation of the intercept and what it means. I want to determine the influence of the categorical factor "context" on my overall effect - do I have to fix the intercept or not? The same applies to gender - assuming I have an effect of x on y, how do I interpret the influence of a fixed or non-fixed intercept on this relationship? (I don't get R� displayed with fixed intercept - is it because the effect x to y is fixed?). I'm new on this field and want to do things right - therefore I would be very grateful for your help.
> 
> 
> 
> Best regards,
> 
> Bene
> 
> 
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> 
> 
> 
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-- 
Michael
http://www.dewey.myzen.co.uk/home.html