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I would like to ask if you can help me in interpreting the results of my analysis or if perhaps you know a paper or a book where this is nicely explained. I am conducting an analysis in order to check whether the experimental method (Field or pot) has an influence on the crop response to zinc fertilizations. Here below, I put the model B4 I used: RR response ratio, RRv variance of response ratio, mods experiment type (field, pot or aqua).

Model: B4 = rma.mv(RR,RRv,mods=~factor(exp),random=list(~ 1| Paper), intercept = FALSE, data=DataZn,sparse=TRUE)

Multivariate Meta-Analysis Model (k = 1968; method: REML)

      logLik      Deviance           AIC           BIC          AICc  
-613607.7310  1227215.4621  1227223.4621  1227245.7950  1227223.4825  

Variance Components: 

            estim    sqrt  nlvls  fixed  factor
sigma^2    0.0639  0.2529     56     no   Paper

Test for Residual Heterogeneity: 
QE(df = 1965) = 2169043.4451, p-val < .0001

Test of Moderators (coefficient(s) 2,3): 
QM(df = 2) = 12.6162, p-val = 0.0018

Model Results:

                  estimate      se     zval    pval    ci.lb   ci.ub    
intrcpt             0.7342  0.2532   2.8993  0.0037   0.2379  1.2306 
factor(exp)Field   -0.3896  0.2562  -1.5206  0.1284  -0.8917  0.1126    
factor(exp)Pot     -0.1063  0.2645  -0.4020  0.6877  -0.6247  0.4121 
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  • $\begingroup$ I am a bit surprised that you specified intercept = FALSE but still got an estimated intercept. This may not matter, but what happens if you specify mods = ~ factor(exp) - 1 instead? Incidentally it is not that good an idea to name your variables with existing function names like exp. $\endgroup$
    – mdewey
    Oct 20 '16 at 14:36
  • $\begingroup$ Indeed, I was also wondering why I get an intercept if I specified FALSE. If I specify mod= factor(exp)-1 is still for intercept=0? $\endgroup$ Oct 20 '16 at 14:45
  • $\begingroup$ Yes, what happens when you try it? $\endgroup$
    – mdewey
    Oct 20 '16 at 15:25
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    $\begingroup$ See help(rma.mv). To quote: "When specifying a model formula via the mods argument, the intercept argument is ignored. Instead, the inclusion/exclusion of the intercept term is controlled by the specified formula." $\endgroup$
    – Wolfgang
    Oct 20 '16 at 16:57
  • $\begingroup$ Are you sure you do not need to specify exp in your random formula and possibly also specify struct as well? See the Berkey example in the metafor documentation. $\endgroup$
    – mdewey
    Oct 23 '16 at 11:28
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So this one does not go unanswered.

The confusion over the role of the intercept was answered by @Wolfgang in comments, it is ignored in this function, as documented.

The test for residual heterogeneity tests whether the variation between studies is larger than expected. With so many studies it has power to detect quite small differences. In any event it is better to inspect the data to establish the source of the heterogeneity.

The test for moderators is a test for their overall effect. In this case since there is a single moderator with three levels it tests for the overall effect of that moderator.

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