# meta-regression using metafor

How should I syntax the rma function from metafor package in order to get results in the following example?

My objective is to compare values (means) among species. I have different papers publishing means on different species. I have more than one author publishing on one species, and sometimes the same author published on two species.

My data looks like (this is an example, my dataset is much bigger with more species):

ID, Species, Author, Year, mean, sd, n

1, Eagle, Author 1, 1998, 16.06, 7.34, 46
2, Eagle, Author 2, 1989, 33.37, 8.9, 5
3, Eagle, Author 3, 2005, 15.4, 11.06, 29
4, Eagle, Author 4, 2014, 0.66, 0.03, 24
5, Owl, Author 5, 2008, 2.64, 0.54, 88
6, Owl, Author 6, 2010, 0.68, 0.02, 3
7, Falcon, Author 1, 1998, 0.68, 0.02, 12
8, Falcon, Author 4, 2014, 0.68, 0.02, 25
9, Falcon, Author 7, 2015, 0.68, 0.02, 90
10, Falcon, Author 3, 2005, 0.68, 0.02, 5

What I have done so far is:

model1<-rma(yi=lead_mean,sei=sd,data = Data,mods = ~ Species)
summary(model1)


Results:

Mixed-Effects Model (k = 26; tau^2 estimator: REML)

logLik   deviance        AIC        BIC       AICc
-7.2675    14.5350    60.5350    46.4197  1164.5350

tau^2 (estimated amount of residual heterogeneity):     0 (SE = 0.6600)
tau (square root of estimated tau^2 value):             0
I^2 (residual heterogeneity / unaccounted variability): 0.00%
H^2 (unaccounted variability / sampling variability):   1.00
R^2 (amount of heterogeneity accounted for):            100.00%

Test for Residual Heterogeneity:
QE(df = 4) = 1.5594, p-val = 0.8161

Test of Moderators (coefficients 2:22):
QM(df = 21) = 339.1749, p-val < .0001

Model Results:

estimate        se     zval    pval      ci.lb     ci.ub
intrcpt                       -23.2434    6.0531  -3.8399  0.0001   -35.1073  -11.3795  ***
SpeciesBearded_vulture         12.0634    8.0762   1.4937  0.1353    -3.7655   27.8924
SpeciesCommon_buzzard          11.2611    3.3672   3.3444  0.0008     4.6616   17.8606  ***
SpeciesCommon_kestrel          11.1539    3.3708   3.3090  0.0009     4.5472   17.7606  ***
SpeciesEagle_owl               24.5934    6.0290   4.0792  <.0001    12.7768   36.4100  ***
SpeciesEurasian_sparrowhawk     7.7000    5.1005   1.5097  0.1311    -2.2968   17.6968
SpeciesGolden_eagle            39.1834   12.5607   3.1195  0.0018    14.5648   63.8020   **
SpeciesGreater_spotted         44.6000    4.7005   9.4883  <.0001    35.3871   53.8129  ***
SpeciesImperial_eagle          11.8334    6.8723   1.7219  0.0851    -1.6361   25.3029    .
SpeciesLesser_spotted           5.7000    3.5007   1.6282  0.1035    -1.1612   12.5612
SpeciesLitle_owl               11.8528    3.4044   3.4816  0.0005     5.1803   18.5253  ***
SpeciesLong_eared_owl           6.8000    4.2006   1.6188  0.1055    -1.4330   15.0330
SpeciesMontagu_harrier          2.8000    0.3081   9.0892  <.0001     2.1962    3.4038  ***
SpeciesNorthern_goshawk         7.4000    6.3004   1.1745  0.2402    -4.9485   19.7485
SpeciesOsprey                  23.6434    6.0650   3.8983  <.0001    11.7562   35.5307  ***
SpeciesRough_legged_buzzard   164.6000  308.0000   0.5344  0.5931  -439.0689  768.2689
SpeciesTawny_owl                6.8000    5.5004   1.2363  0.2164    -3.9807   17.5807
SpeciesWestern_marsh_harrier   14.6000   14.0002   1.0428  0.2970   -12.8398   42.0398
SpeciesWhite_tailed_eagle       8.8000    5.5004   1.5999  0.1096    -1.9807   19.5807
countriesNetherlands           17.4823    5.0696   3.4484  0.0006     7.5460   27.4186  ***
countriesPoland                23.6434    6.0527   3.9063  <.0001    11.7803   35.5065  ***
countriesSpain                 14.0500    5.0291   2.7938  0.0052     4.1932   23.9068   **

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


Is the analysis above a methodologically sound approach to solving the stated problem? Here, I am comparing all species with the intercept (Barn owl). There is any method to compare all species among them?

Also, I have YEARS and COUNTRIES for each study, and these factors may also affect the means. Should I introduce them as: (~Species + Years + countries)? How could I know whether they are redundant predictors or correlated?

Thank you!

• Can you clarify whether "I have more than one author publishing on one species" means that more than one mean was obtained from the same dataset? If not, how do you intend to use the author variable in the analysis? – Emily May 16 at 16:58
• I mean that one author publishes data for more than one species. My aim is to compare among species, not among authors, (the authorship is a complementary information). I've seen that in rma the most common thing is to compare data among authors, but my intention is to compare data among species, although in some cases I have different studies publishing on the same species. So, I have 4 papers publishing means for eagles, 2 for owls and 4 for falcons and the aim here is to compare eagles, owls and falcons, examining differences within and between groups. – LauraMon May 17 at 8:20
• Hard to tell but you may want either network meta-analysis or multi-level meta-analysis. – mdewey May 20 at 17:13