[R-sig-eco] Regression when Y has an estimation variance

[Dixon, Philip M [STAT]]

Roy,

One relevant literature is that on meta-regression (a generalization of meta-analysis).  There is a very good handbook by Koricheva, Gurevitch and Mengerson.  Meta analysis mostly deals with Gaussian responses (or transformable to approximately Gaussian).  If there has been any work on non-gaussian responses, I expect it would be summarized in Koricheva.  

The metafor package is one implementation specifically for meta analysis.  A resource on metafor and other R packages is Schwarzer and Carpenter, Meta-analysis with R.  

Other programs can also fit the models as mixed models with heterogenerous specified variances, lme() and lmer() do not let you do this.  lmer() doesn't allow heterogeneous variances; lme() does, but only of the form k_i*sigma^2 (i.e. variances relative to a common scaling factor, not absolutely specified variances).   For a meta analysis, you need to specify the absolute variance for each estimate.  If someone knows how to trick lme() to use exactly the error variances that have been specified, I would love to hear about it.     

Best,
Philip Dixon