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Factor moderators in metafor

3 messages · Viechtbauer Wolfgang (STAT), John Hodgson

John Hodgson
# 
I'm puzzled by the behaviour of factors in rma models, see example and
comments below. I'm sure there's a simple explanation but can't see it... 

Thanks for any input

John Hodgson


------------------------------------- code/selected output -----------------


library(metafor)

##    Set up data (from Lenters et al  A Meta-analysis of Asbestos and Lung
Cancer...
##    Environmental Health Perspectives ? volume 119 | number 11 | November
2011)
 
KL = c(0.02905, 0.06929, -0.1523, 1.6441, 0.1215, 0.3975, 1.0566, 0.1257,
0.2277, 0.06791, 0.08164, 0.2526, 0.07577, 0.03266, 0.1141, 0.1836, 1.8276,
0.4149, 15.4974)
SE = c(0.006633, 0.09335, 0.08909, 0.4297, 0.07858, 0.1753, 0.3679, 0.1837,
0.2172, 0.2775, 0.4201, 0.1976, 0.7688, 0.06507, 0.06239, 0.09061, 0.9509,
0.2181, 7.331)

VL = SE*SE

amph =   c(0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
mix =    c(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
ftype =  c(0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2) 


factor(amph)
factor(ftype)
factor(mix)

##  Fit ftype...
Mixed-Effects Model (k = 19; tau^2 estimator: REML)

tau^2 (estimate of residual amount of heterogeneity): 0.0111 (SE = 0.0095)
tau (sqrt of the estimate of residual heterogeneity): 0.1054

Test for Residual Heterogeneity: 
QE(df = 17) = 43.0937, p-val = 0.0005

Test of Moderators (coefficient(s) 2): 
QM(df = 1) = 1.1069, p-val = 0.2928

Model Results:

         estimate      se    zval    pval    ci.lb   ci.ub   
intrcpt    0.0811  0.0606  1.3380  0.1809  -0.0377  0.2000   
mods       0.0473  0.0449  1.0521  0.2928  -0.0408  0.1353   


Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 


##   why only one df for the 2-level factor?
##   in other words, why isn't the above model the same as the following...
Mixed-Effects Model (k = 19; tau^2 estimator: REML)

tau^2 (estimate of residual amount of heterogeneity): 0.0030 (SE = 0.0046)
tau (sqrt of the estimate of residual heterogeneity): 0.0549

Test for Residual Heterogeneity: 
QE(df = 16) = 37.5762, p-val = 0.0017

Test of Moderators (coefficient(s) 2,3): 
QM(df = 2) = 6.9220, p-val = 0.0314

Model Results:

         estimate      se    zval    pval    ci.lb   ci.ub   
intrcpt    0.0380  0.0402  0.9448  0.3447  -0.0408  0.1169   
amph       0.2879  0.1163  2.4754  0.0133   0.0599  0.5158  *
mix        0.0888  0.0625  1.4199  0.1556  -0.0338  0.2114   

---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
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Viechtbauer Wolfgang (STAT)
# 
There is a simple explanation:

1) The command:

factor(ftype)

does not actually turn 'ftype' permanently into a factor, since you are not re-assigning it back to the object 'ftype'. You have to use:

ftype <- factor(ftype)

2) If you want to use the formula interface for specifying moderators, you have to use mods = ~ <formula>, so in other words:

rma(KL, VL, mods = ~ ftype)

after you have made 'ftype' a factor (see 1).

Or you can simply use:

rma(KL, VL, mods = ~ factor(ftype))

which does the conversion of 'ftype' into a factor within the model formula.

Best,

Wolfgang

--   
Wolfgang Viechtbauer, Ph.D., Statistician   
Department of Psychiatry and Psychology   
School for Mental Health and Neuroscience   
Faculty of Health, Medicine, and Life Sciences   
Maastricht University, P.O. Box 616 (VIJV1)   
6200 MD Maastricht, The Netherlands   
+31 (43) 388-4170 | http://www.wvbauer.com