# [R-sig-ME] Estimated dependent variable in GL(M)Ms

Viechtbauer, Wolfgang (SP) wolfg@ng@viechtb@uer @ending from m@@@trichtuniver@ity@nl
Sun Jan 13 22:36:12 CET 2019

```Hi Roy,

I took a look at the paper by Lewis and Linzer. As Torsten already indicated, what they describe *is* meta-analysis (except that they make no reference to this at all). Meta-analytic method allow you to model outcomes that are estimates with know variances / standard errors. Packages metafor (of which I am the author) or meta (by Guido Schwarzer) are good starting points. As a simple example, let's say you have the following estimates and variances:

yi <- c(-0.889, -1.585, -1.348, -1.442, -0.218, -0.786, -1.621, 0.012, -0.469, -1.371, -0.339, 0.446, -0.017)
vi <- c(0.326, 0.195, 0.415, 0.02, 0.051, 0.007, 0.223, 0.004, 0.056, 0.073, 0.012, 0.533, 0.071)

Then you can analyze (i.e., pool) these estimates with:

library(metafor)
res <- rma(yi, vi)
res

Predictors can be added as well:

xi <- c(44, 55, 42, 52, 13, 44, 19, 13, 27, 42, 18, 33, 33)
res <- rma(yi ~ xi, vi)
res

This is essentially approach 4.3 in the paper, except that this uses REML estimation instead of the (rather inefficient) estimator of sigma^2 described in the paper.

The OLS + robust standard errors approach described in the paper would be:

id <- 1:13
res <- rma(yi ~ xi, vi, weights=1)
robust(res, cluster=id)

But the estimates of the model coefficients are not efficient (since they are estimated using OLS). This would be better:

res <- rma(yi ~ xi, vi)
robust(res, cluster=id)

Best,
Wolfgang

--
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD
Maastricht, The Netherlands | +31 (43) 388-4170 | http://www.wvbauer.com

>-----Original Message-----
>From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces using r-
>project.org] On Behalf Of Torsten Hauffe
>Sent: Friday, 11 January, 2019 20:08
>To: Roy Averill-Murray
>Cc: r-sig-mixed-models using r-project.org
>Subject: Re: [R-sig-ME] Estimated dependent variable in GL(M)Ms
>
>Sounds like you are looking for meta-analysis. But I'm not 100% sure
>this.
>
>Cheers!
>
>On Fri, 11 Jan 2019 at 19:57, Roy Averill-Murray
><royaverillmurray using gmail.com>
>wrote:
>
>> How does one estimate beta parameters and appropriate SEs when the
>> dependent variable consists of estimated values with known variances?
>My
>> case involves modeling factors affecting animal home ranges that were
>> estimated separately (i.e., individual home ranges are the dependent
>> variable, each of which has its own variance). I found the paper by
>Lewis
>> and Linzer (2005. Estimating regression models in which the dependent
>> variable is based on estimates. Political Analysis 13:345-364), which
>> describes feasible generalized least squares, but I have been unable to
>> find R code for this or a description of how to apply it in nlme, lme4,
>> glmmTMB, etc.
>>
>> Thanks for any help,
>> Roy Averill-Murray

```