Background:
I'm conducting a multilevel metanalysis to see if different types of magnetic fields, with different intensities and exposure duration, affect plant growth parameters. I have effect sizes (Response ratio, n = 81), nested within outcomes (Fresh weight of the plant, to account for comparisons using the same control group within studies. Fresh weight is also the treatment value), nested within studies and species, which are crossed. A sample of the data looks like this:
Author Species Intensity Exposure Fresh-weight RR NU M PL
1 8 1 1 1 1 1 0 1
1 2 1 1 2 2 1 0 1
2 3 2 2 3 3 0 1 0
2 3 2 3 4 4 0 1 0
2 3 2 4 5 5 0 1 0
3 4 3 2 6 6 1 0 0
3 4 4 2 7 7 1 0 0
3 4 5 2 8 8 1 0 0
3 4 6 2 9 9 1 0 0
4 2 6 3 10 10 0 1 1
4 2 7 4 11 11 0 1 1
4 2 6 3 12 12 0 1 1
4 2 7 4 13 13 0 1 1
... ... ... ... ... ... ... ...
Important All data have unique IDs. For Mods section, I used the raw value of the predictors. NU, M, and PL are dummy variables for whether it is a non-uniform or uniform magnetic field (NU), whether a magnet or electromagnet produced the magnetic field (M), whether exposure initiated in a seed state or a plant state (PL).
Summarising, I have 81 effect sizes, nested within outcomes (fresh weights), nested within 15 studies and 12 species. To model this, I used the following code:
MLM.fw <- rma.mv(RR,
sv,
random = list(~ 1 | Author/Fresh-Weight,
~ 1 | Species),
data = fw2,
method = "REML")
For mods addition, I considered Intensity, Exposure, and the dummy variables as Level 1 predictors. Using AIC to test the models, I found out that it was best to use all the numerical variables and just one dummy variable at a time. For this question, I'll be using NU:
mods = ~ NU*z.int*z.exp
Where z.int and z.exp are the standardized versions of Intensity and Exposure raw values, respectively
This formula gave me the following results:
Multivariate Meta-Analysis Model (k = 81; method: REML)
logLik Deviance AIC BIC AICc
33.5652 -67.1305 -45.1305 -19.9354 -40.8026
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 0.0184 0.1356 15 no Author
sigma^2.2 0.0110 0.1050 74 no Author/Fresh-weight
sigma^2.3 0.0000 0.0000 12 no Species
Test for Residual Heterogeneity:
QE(df = 73) = 402.8025, p-val < .0001
Test of Moderators (coefficients 2:8):
QM(df = 7) = 77.0209, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
intrcpt 0.1863 0.0577 3.2277 0.0012 0.0732 0.2994 **
NU 0.6142 0.1233 4.9805 <.0001 0.3725 0.8559 ***
z.int 0.0554 0.0168 3.3064 0.0009 0.0226 0.0882 ***
z.exp 0.0851 0.0247 3.4456 0.0006 0.0367 0.1336 ***
NU:z.int 0.1828 1.3335 0.1371 0.8910 -2.4309 2.7965
NU:z.exp -0.3095 0.1100 -2.8142 0.0049 -0.5251 -0.0940 **
z.int:z.exp 0.0866 0.0227 3.8205 0.0001 0.0422 0.1311 ***
NU:z.int:z.exp -0.5439 3.2187 -0.1690 0.8658 -6.8523 5.7646
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Questions
¿Is this a good model to try to explain the phenomenon I'm researching? and if so: ¿How can I start building my regression equation? For example, I noticed that NU main effect is rather stronger or more important than NU:z.exp, but the interaction predictor is also significant. ¿Does that mean that NU main effect is no longer needed in the equation?
I wanted to apply robust() to account for correlated standard errors between labs (same authors publishing related articles in different years) or model mis-specification. ¿Would I be over-penalizing my model, considering that nesting ES within outcomes, should be already doing that?
I had a third variable but because of moderate correlation, the model would leave it out. ¿How can I include it anyway?
Thanks in advance for your answers, and don't hesitate to point out any mistakes I may be doing.
