Hi there. I'm using metaSEM::meta() to conduct some single-level meta-analyses.
In some subset analyses, as k gets smaller, OpenMX seems to struggle to estimate the variance, estimating Tau2 as low as I will set RE.lbound. I can resolve the error message by running a fixed-effects model by setting RE.constraint = 0. However, when I do this, the standard error for the intercept increases by 33%. This changes the statistical significance of the intercept.
Although I don't have a vested interest in the statistical significance of the intercept, I would like to make a defensible decision whether to constrain Tau2 to zero or not. Is the SE of the intercept still valid given Status1: 5, or should I ignore those numbers and proceed directly to interpreting the fixed-effects model?
Thanks in advance! Reproducible example below.
library(metaSEM) dat <- data.frame(yi = c(0.143581358989816, 0.0454437737469923, 0.508973319897135, -0.140707411290326, 0.13348282996416, 0.169176989775847, 0.329109861753571), vi = c(0.0570362059695423, 0.0428930499852486, 0.0904348502317336, 0.0565782183215856, 0.0607967470232705, 0.0892508158115509, 0.0506686006240954)) # run with defaults mymeta <- meta(y = yi, v = vi, data = dat) summary(mymeta) # Ends in Status1: 5 # Intercept1 estimated as 0.148, SE = 0.069, p = 0.032 # Tau2_1_1 goes to RE.lbound # run with extended lower bound in tau2 mymeta2 <- meta(y = yi, v = vi, data = dat, RE.lbound = 1e-100) summary(mymeta2) # Ends in Status1: 5 # Intercept1 estimated as 0.148, SE = 0.069, p = 0.032 # Tau2_1_1 again goes to RE.lbound # run fixed-effects to restrict (allow?) RE to zero mymeta3 <- meta(y = yi, v = vi, data = dat, RE.constraints = 0) summary(mymeta3) # Ends in Status1: 0 # Intercept1 estimated as 0.148, SE = 0.092, p = 0.110 # SE of intercept increases by 33%!
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You should not trust the results in mymeta and mymeta2 as the status code is 5. See https://openmx.ssri.psu.edu/wiki/errors
A fixed-effect model is a special case of a random-effects model when the heterogeneity variance is 0. Even if you fit a random-effects model, the final result may suggest a fixed-effect model.
Sounds good. I'll avoid interpretation of the random-effects models because of their status code 5. I just thought it was interesting how the fixed-effect and random-effects models reached similar values of Tau^2 but rather different SEs for the intercept!