[R-meta] Omnibus test of moderators in a model with an interaction term

[Michael Dewey]

Dear Gabriele

I would not try to interpret anything about the main effects in the 
presence of an interaction. In effect the interaction is saying that the 
effect of one variable depends on the level of the other.

I would not expect the effects of anything to be strictly additive 
unless they were orthogonal. I suspect that if in your main effects only 
model you look at the variance-covariance matrix of the coefficients 
(which you can get with vcov()) you will find a weak correlation between 
your two main effects (cov2cor() helps to convert to correlations).

Michael

On 04/01/2018 16:46, Gabriele Midolo wrote:
> I am using anova() to perform the ombibus test by setting the "btt"
> argument to estimate the amount of residual heterogeneity reduced for each
> moderator in an rma.mv model. For example, if I interpret this correctly,
> in a model with two moderators (and no interaction) I get the QM of the
> model with:
> 
>> anova(res)
>   Test of Moderators (coefficient(s) 2:3):
> QM(df = 2) = 24.8445, p-val < .0001
> 
> Then I can estimate QM of moderator number 1 and 2 with:
> 
>> anova(res,btt=2)
> Test of Moderators (coefficient(s) 2):
> QM(df = 1) = 15.7282, p-val < .0001
> 
>> anova(res,btt=3)
> Test of Moderators (coefficient(s) 3):
> QM(df = 1) = 9.8144, p-val = 0.0017
> 
> The sum of the two QM values is 25.5, which somehow close to what
> obtained in the "anova(res)", so *is this the way to split the total
> QM and estimate the amount of residual heterogeneity for each
> moderator?*
> 
> But what happens when I want to do the same in a model where there is
> an interaction?
> 
> Suppose I have the following, where sNadd is a continuous variable and
> Fert is a categorical variable:
> 
> topSR<-rma.mv(yi~sNadd*Fert, vi, data=Sr, random =~1|Experiment/ID)
> 
>> topSR
> Multivariate Meta-Analysis Model (k = 193; method: REML)
> 
> Variance Components:
> 
>              estim    sqrt  nlvls  fixed         factor
> sigma^2.1  0.0576  0.2400     83     no     Experiment
> sigma^2.2  0.0065  0.0809    193     no  Experiment/ID
> 
> Test for Residual Heterogeneity:
> QE(df = 189) = 1281.7188, p-val < .0001
> 
> Test of Moderators (coefficient(s) 2:4):
> QM(df = 3) = 56.8972, p-val < .0001
> 
> Model Results:
> 
>                  estimate      se     zval    pval    ci.lb    ci.ub
> intrcpt          -0.2368  0.0387  -6.1122  <.0001  -0.3127  -0.1608  ***
> sNadd            -0.1838  0.0272  -6.7686  <.0001  -0.2370  -0.1306  ***
> FertbNH4          0.1567  0.0612   2.5603  0.0105   0.0367   0.2766    *
> sNadd:FertbNH4    0.1308  0.0335   3.8996  <.0001   0.0651   0.1966  ***
> 
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 
> I want to calculate the contribution that sNadd and Fert have to
> reduce residual heterogeneity individually to show this in a table of
> a paper. I think I should estimate this with:
> 
> 
>> anova(topSR,btt=c(1,3))
> Test of Moderators (coefficient(s) 1,3):
> QM(df = 2) = 40.2180, p-val < .0001
>> anova(topSR,btt=c(2,4))
> Test of Moderators (coefficient(s) 2,4):
> QM(df = 2) = 53.0494, p-val < .0001
> 
> so to split the intercept values and the slope values. Does this makes sense?
> But the sum of the QM values you obtain is much higher than the test
> of moderators found in the model output. I am no longer sure if it
> makes sense to report QM for "Fert" and "sNadd" separately in a model
> where these terms are part of an interaction. Also, the sum of the
> individual factors and the interaction terms is much larger than the
> total QM, indicating that the explained heterogeneity is given by the
> full interactive term, and you cannot really split it between the
> factor ("Fert") in isolation and the interaction between "sNadd" and
> Fert.
> 
> *Is this really the case and, if yes, is there a way to do the same as
> I did for the model without interaction?*
> 
> Hope I explained myself correctly.
> 
> Thank you so much and with my best,
> 
> Gabri
> 
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-- 
Michael
http://www.dewey.myzen.co.uk/home.html