# How to correctly interpret rma.uni output?

I am posting this question here after being advised to do so on StackOverflow. I am trying to use the rma.uni function from the metafor package to estimate the impact of fishing gears on my abundance data. Following the method published in Sciberas et al. 2018 (DOI: 10.1111/faf.12283), I think I used correctly the function, however, I am not sure how to interpret the output. In the function, c is the log response ratio and var_cis the associated variance. log2(t+1) represent times in days. In my data, gear is a factor with three levels: CD, QSD and KSD.

As I am not familiar with models in general and especially this type of model, I read online documentation including this : https://faculty.nps.edu/sebuttre/home/R/contrasts.html Thus, I understood that only two levels from my factor gear need to be display in the output.

Below is the output I have when I run the rma.uni function. My questions are:

• if gearCD is considered as a 'reference' in the model then it would mean that the effect of gearKSD is 0.14 more positive (I don't know how to word it) than gearCD and that on the opposite, gearQSD is 0.12 times more damaging ?
• How should I interpret the fact that the pvalues for gearKSD and gearQSD are not significant ? Does it mean that their intercept is not significantly different from the one of gearCD ? If so, is the intercept of gearCD the same thing than intercpt?
• Do you know how I could obtain one intercept value for each level of my factor gear ? I am aiming at distinguishing the intial impact of these three gears so it would be of interest to have one interpect per gear.
• Similarly, if I had interaction terms with log2(t+1) (for example gearKSD:log2(t+1)) the interpreation would be silimar to how we interpret intercept ?

I am sorry I know these are a lot of questions.. Thank you all very much for your help !

rma.uni(c,var_c,mods=~gear+log2(t+1),data=data_AB,method="REML")

Mixed-Effects Model (k = 15; tau^2 estimator: REML)

tau^2 (estimated amount of residual heterogeneity):     0.0585 (SE = 0.0357)
tau (square root of estimated tau^2 value):             0.2419
I^2 (residual heterogeneity / unaccounted variability): 71.00%
H^2 (unaccounted variability / sampling variability):   3.45
R^2 (amount of heterogeneity accounted for):            30.86%

Test for Residual Heterogeneity:
QE(df = 11) = 36.6583, p-val = 0.0001

Test of Moderators (coefficients 2:4):
QM(df = 3) = 6.9723, p-val = 0.0728

Model Results:

estimate      se     zval    pval    ci.lb    ci.ub
intrcpt       -1.0831  0.2540  -4.2644  <.0001  -1.5810  -0.5853  ***
gearKSD        0.0912  0.2002   0.4555  0.6488  -0.3011   0.4835
gearQSD       -0.0654  0.1691  -0.3867  0.6990  -0.3967   0.2660
log2(t + 1)    0.0946  0.0372   2.5449  0.0109   0.0217   0.1675    *

---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


## 1 Answer

if gearCD is considered as a 'reference' in the model then it would mean that the effect of gearKSD is 0.14 more positive (I don't know how to word it) than gearCD and that on the opposite, gearQSD is 0.12 times more damaging ?

It's not multiplicative, so you would sau that gearKSD is associated with an expected increase of 0.15 in the outcome variable, compared to gearCD; and gearQSD is associated with an expected decrease of 0.13 in the outcome variable, compared to gearCD.

How should I interpret the fact that the pvalues for gearKSD and gearQSD are not significant ? Does it mean that their intercept is not significantly different from the one of gearCD ? If so, is the intercept of gearCD the same thing than intercpt?

You would say that, if the true difference associated with the outcome between gearKSD and gearCD was zero, then the probability of obtaining these (or more extreme) results is 0.15. if the true difference associated with the outcome between gearQSD and gearCD was zero, then the probability of obtaining these (or more extreme) results is 0.16.

Do you know how I could obtain one intercept value for each level of my factor gear ? I am aiming at distinguishing the intial impact of these three gears so it would be of interest to have one interpect per gear.

For gearCD the estimated expected value of the outcome is -1.1145 because it is included in the intercept as the reference level. Then you just add the values for the other two: for gearKSD it is -1.1145 + 0.1488 and for gearQSD it is -1.1145 - 0.1274

Similarly, if I had interaction terms with log2(t+1) (for example gearKSD:log2(t+1)) the interpreation would be silimar to how we interpret intercept ?

The intercept is always the estimated expected value for the outcome when the other variables are at zero (or at their reference level in the case of a categorical variable/factor).

However, when a variable is involved in an interaction then the intepretation of the main effects change - the estimates for each of the main effects is conditional on the variable being zero (or at it's reference level in the case of a categorical variable/factor). The interaction term itself then estimates the diffence.

• Thank you very much for your help! I am not sure I followed your explanation for my second question (about the pvalue being not significant). Are you referring for the values of ci.ub with 0.35 and 0.05 ? Also, in my case, the output suggest that the regression line for each of my gear would have the same slope but different intercept, correct ? – Ena Jul 22 '20 at 10:31
• No problem, you're welcome. My explanation was about the meaning of the p values. Statistial significance is a misleading concept, based on arbitrary thresholds (and is affected a lot by sample size). Look at the p value for gearQSD it is very close to 0.05 but is really much different from 0.0499 ? Since this is basically an ANCOVA model (with random effects) the slopes in each group are the same, but they have different intercepts, however there is very little evidence that the intercepts for gearKSD and gearCD are different from each other. – Robert Long Jul 22 '20 at 10:59
• Ok I think I understand better now thank you! But isnt the pvalue of gearQSD= 0.164 ? Also, I found it very confusing to have a R²= 100% with tau=0. I have noticed that the same thing happens when I used log response ratio from species richness data for example (instead of ln(RR) calculated from abundance data as it is the case in my question). I'm wondering if it couldn't be linked to my initial computation of my log response ratio. Do you have any thoughts on this? – Ena Jul 22 '20 at 12:04
• Oh yes, sorry, I was looking at the wrong column for the p values ! I will update the answer. As for the R^2 issue that dos seem strange, but you should ask a new question about that. – Robert Long Jul 22 '20 at 12:08
• In the output, the p-value of gearQSD is 0.6990 (the column with the p-values is labeled pval). And in a meta-regression model, $\tau^2$ is the amount of residual heterogeneity. So if that is 0, then all of the heterogeneity (if there was any to begin with) has been accounted for and hence $R^2 = 100\%$. – Wolfgang Jul 23 '20 at 16:44