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[R-meta] Metafor modeling question

4 messages · Yuhang Hu, Wolfgang Viechtbauer

Yuhang Hu
# 
Dear All,

I have two questions about the following model:

mm <- rma.mv(y ~ SES, V, random = list(~SES|study, ~SES|outcome), struct =
c("GEN","GEN"))

fit to a dataset structurally similar to:

study outcome SES
1     A       1.5
1     A       1.7
1     B       1.5
1     B       1.7
2     A       2.1
3     A       1.1
3     A       2.3
3     B       1.1
3     B       2.3

Question 1: I know, if I used: "random = list(~1 | study, ~1| outcome)",
then 'study' and 'outcome' would be crossed, random effects. But are
'study' and 'outcome' in model 'mm' still crossed,
random effects? (In other words, can crossed random-effects have varying
coefficients in them)

Question 2: Is it possible (or useful) to plot residuals vs. fitted values
for model 'mm'? If yes, how can we do that in metafor?

Many thanks for your help,
Yuhang
1 day later
Wolfgang Viechtbauer
# 
Dear Yuhang,

Please see below for my answers.

Best,
Wolfgang
Yes, they are crossed in this example.
fitted(mm) gives you the fitted values and resid(mm) gives you the residuals, so you can just plot them against each other with plot(fitted(mm), resid(mm)) or you can use the standardized residuals on the y-axis with plot(fitted(mm), rstandard(mm)$z), since the residuals themselves are heteroscedastic, but the standardized residuals are ... well, standardized!

Whether such a plot is useful is difficult to say in general, but I suppose it can be used in the same manner as it is used with primary data.
Yuhang Hu
# 
Dear Wolfgang,

Thanks you so much for your response. Regarding the fitted vs residuals
plot, if we see a violation (e.g., heteroskedasticity and/or non-random
pattern in residuals' distribution around the regression line) as in the
case below, what should we do?

I would imagine that if I was working with an rma.uni() model, I could
model the heteroskedasticity using the 'scale=' argument?

Thanks,
Yuhang

mm <- rma.mv(yi ~ SES, vi, random = list(~SES|study, ~SES|outcome),
             struct = c("GEN","GEN"), data = dat)

plot(fitted(mm), resid(mm))

dat <- structure(list(study = c(1L, 1L, 2L, 2L, 3L, 3L, 4L, 5L, 6L,
7L, 7L, 8L, 8L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L, 11L, 12L,
13L, 13L, 14L, 14L, 15L, 15L, 16L, 16L, 17L, 18L, 18L, 18L, 18L,
18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L,
18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L,
18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 19L, 19L, 20L,
20L), group = c(1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,
2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1), outcome = c("A",
"A", "B", "B", "B", "B", "B", "A", "A", "A", "B", "A", "A", "A",
"B", "A", "B", "A", "B", "A", "B", "B", "A", "A", "B", "B", "B",
"A", "A", "B", "B", "A", "B", "B", "B", "B", "B", "B", "B", "B",
"B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B",
"B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B",
"B", "B", "B", "B", "B", "B", "A", "B", "A", "B"), SES = c(1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 13, 10, 8, 16, 3, 2, 18, 1,
5, 4, 20, 11, 9, 14, 17, 15, 6, 12, 19, 7, 13, 10, 8, 16, 3,
2, 18, 1, 5, 4, 20, 11, 9, 14, 17, 15, 6, 12, 19, 1, 1, 1, 1),
    yi = c(0.661693, 0.594366, 1.199301, 1.626664, 1.216272,
    -0.751534, -1.170659, 0.959518, 0.353214, 1.595024, 1.689419,
    0.462459, 1.324527, 0.61639, 0.615806, 0.616544, 0.617199,
    1.420133, 1.542125, 1.338082, 1.523729, 0.569801, 1.041618,
    6.796397, 3.241257, 0.97541, 1.369298, 1.706266, 1.964219,
    1.554362, 1.693888, 0.939487, 0.349941, 0.364232, 0.41826,
    0.37037, 0.378151, 0.265958, 0.250613, 0.32379, 0.318541,
    0.331738, 0.373367, 0.242215, 0.420524, 0.153225, 0.287845,
    0.43818, 0.315411, 0.264576, 0.33054, 0.35668, 0.393478,
    0.468176, 0.342097, 0.39018, 0.332325, 0.414179, 0.303209,
    0.290351, 0.398231, 0.283192, 0.290464, 0.352266, 0.323642,
    0.357534, 0.18504, 0.349599, 0.322425, 0.330017, 0.273626,
    0.484511, 3.087989, -0.427958, 1.133235, 1.073414), vi = c(0.030703,
    0.355305, 0.190678, 0.525746, 0.257342, 0.371465, 0.65578,
    0.970636, 0.605049, 0.584372, 0.185532, 0.140877, 0.618397,
    0.880055, 0.29737, 0.186943, 0.376905, 0.327622, 0.232547,
    0.288472, 0.88999, 0.203553, 0.202477, 0.94609, 0.694122,
    0.79155, 0.260697, 0.689051, 0.332882, 0.883863, 0.265871,
    0.443643, 0.71795, 0.325523, 0.720786, 0.905436, 0.777423,
    0.424495, 0.449885, 0.436236, 0.551392, 0.412329, 0.841006,
    0.03359, 0.592244, 0.159267, 0.430026, 0.044465, 0.341106,
    0.163984, 0.037114, 0.9678, 0.215364, 0.111536, 0.292115,
    0.548628, 0.25953, 0.217442, 0.615006, 0.108288, 0.80669,
    0.789254, 0.312538, 0.996466, 0.277414, 0.975438, 0.710994,
    0.028242, 0.488088, 0.921909, 0.622881, 0.145062, 0.240907,
    0.461285, 0.881521, 0.974101)), row.names = c(NA, -76L), class =
"data.frame")

On Mon, Mar 27, 2023 at 12:49?AM Viechtbauer, Wolfgang (NP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

            

      
      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Wolfgang Viechtbauer
    

    

      
      #
    

  


  

      
I would start by running:

par(mfrow=c(3,2))
profile(mm)

which will indicate that none of the var-cor components are identifiable.

The only study with any variability in SES is study 18 (all other studies have SES = 1), which makes analyzing the association between the effect sizes and SES a difficult endeavor.

Not sure how I would approach this. Possibly, I might consider just looking at study 18 by itself to examine this relationship:

plot(yi ~ SES, data=dat, subset=study==18, pch=21, bg="gray", cex=0.5/sqrt(vi))

Best,
Wolfgang