[R-meta] Replicating Three-Level Model with Fixed Effects

[Viechtbauer, Wolfgang (SP)]

This may be one explanation. But I think the district-level value of 'year' was used to center. So:

> mean(aggregate(dat$year, list(dat$district), FUN=mean)$x)
[1] 1990.591

Then:

> res <- rma.mv(yi, vi, mods = ~ I(year-1990.591), random = ~ 1 | district/study, data=dat, method="ML")
> print(res, digits=3)

Multivariate Meta-Analysis Model (k = 56; method: ML)

Variance Components:

           estim   sqrt  nlvls  fixed          factor 
sigma^2.1  0.056  0.238     11     no        district 
sigma^2.2  0.033  0.181     56     no  district/study 

Test for Residual Heterogeneity:
QE(df = 54) = 550.260, p-val < .001

Test of Moderators (coefficient 2):
QM(df = 1) = 0.355, p-val = 0.551

Model Results:

                    estimate     se   zval   pval   ci.lb  ci.ub 
intrcpt                0.183  0.080  2.298  0.022   0.027  0.340  * 
I(year - 1990.591)     0.005  0.009  0.596  0.551  -0.012  0.022    

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

These are now the same results as in Table 5.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-
>project.org] On Behalf Of Michael Dewey
>Sent: Tuesday, 11 December, 2018 10:13
>To: Andrew Loignon; r-sig-meta-analysis using r-project.org
>Subject: Re: [R-meta] Replicating Three-Level Model with Fixed Effects
>
>Dear Andrew
>
>The difference you report is about 2.5%. With possibly different
>hardware, different fitting algorithm, ..., I would not be too concerned
>myself. Other readers on this site might have a different view though.
>
>Michael
>
>On 10/12/2018 18:01, Andrew Loignon wrote:
>> Hi everyone,
>>
>> As part of a separate project, I've been familiarizing myself with
>multi-level meta-analyses. While working through the example provided on
>the metafor package's website (http://www.metafor-
>project.org/doku.php/analyses:konstantopoulos2011), I ran into some
>difficulties replicating the three-level model described by
>Konstantopolous (2011, "Fixed effects and variance components estimation
>in
>> three-level meta-analysis").
>>
>> Specifically, I can replicate Konstantopolous' two-level model using
>year as a fixed effect (Table 4 in the research article) using the
>following code:
>>
>> m0.ml <- rma.mv(yi, vi,
>>                  random = ~ 1| study,
>>                  mods = ~ I(year-mean(year)),
>>                  method="ML",
>>                  digits=3,
>>                  data=dat.konstantopoulos2011
>>                  )
>> summary(m0.ml)
>>
>> However, when I extend the model to include the higher-level nesting
>variable (i.e., district), the intercept diverges from what
>Konstantopolous reports (Table 5 in the research article). Right now, I'm
>using the following code:
>>
>> m1.ml <- rma.mv(yi, vi,
>>                  random = ~ 1| district/study,
>>                  mods = ~ I(year-mean(year)),
>>                  method="ML",
>>                  digits = 3,
>>                  data=dat.konstantopoulos2011)
>> summary(m1.ml)
>>
>> With this model, I find an intercept of .178, while Konstantopolous
>reports a value of .183.
>>
>> Any suggestions for how to reconcile these differences would be very
>much appreciated.
>>
>> Best,
>>
>> Andrew
>> Andrew C. Loignon
>> Assistant Professor
>> 2716 Business Education Complex
>> Rucks Department of Management
>> E. J. Ourso College of Business
>> Louisiana State University
>> Baton Rouge, LA 70808
>> Email: aloignon using lsu.edu<mailto:aloignon using lsu.edu>
>> Phone: 225-578-6148