[R-meta] Random Slope Three-Level Meta-Analysis Model in combination with RVE

[James Pustejovsky]

Hi Martin,

I can confirm that clubSandwich works with random slope models (struct =
"GEN") in metafor. I've added some unit tests to the package to verify that
this is the case.

James

On Wed, Jun 23, 2021 at 4:10 AM Prof. Dr. Martin Brunner <
martin.brunner using uni-potsdam.de> wrote:

> Dear Listmembers,
>
>
>
> I would like to  meta-analyze gender differences in reading achievement.
> My data stem from seven cycles of a triennial large-scale assessment
> program with data from 96 countries, up to seven assessment cycles per
> country and about 4,500 students per cycle within each country. Of note,
> each student participated only in one single cycle. Nevertheless, the data
> are in some sense longitudinal because they allow to examine how the size
> of gender differences developed over time (i.e., cycles) within a certain
> country.
>
>
>
> In my meta-analytic model I would like to examine the linear rate of
> change in standardized mean differences between female and male students'
> reading achievement across time. Given that cycles are separated by a
> three-year time interval, I coded time with 0 for the first cycle, 3 for
> the second cycle, 6 for the third cycle etc.
>
>
>
> Further, some countries implemented educational policies that aimed at
> reducing gender differences in reading achievement. To simplify things, I
> assume that the policies were in effect from the very first cycle and did
> not change over time (i.e., I treat policies as a time-invariant
> covariate). To this end, I coded policy with (0 = no policy to reduce
> gender disparities in a certain country, 1 = policy to reduce gender
> disparities in a certain country). In doing so, I would like to investigate
> the extent to which the educational policies were related to the linear
> rate of change of gender differences.
>
>
>
> To specify my model I would like to use the rma.mv function of metafor
> with SMD_gender depicting the standardized mean differences in reading
> achievement and v_SMD depicting the sampling variance of this effect size.
> The R code was as follows:
>
>
>
> First, I created a variable to represent each available combination of the
> country variable (cnt) and the time variable.
>
>
>
> dat$time_x_cnt <- paste(dat$cnt,dat$time)
>
>
>
> Second, the interaction between time and policy represents a cross-level
> interaction because policy only varies between but not within countries.
> Following Snijders and Bosker (2012)  I therefore specified a random
> intercept and a random slope for the time variable that allows both
> coefficients to vary between countries. Further, I specified a random
> coefficient for the residual term of the true effect size within countries.
>
>
>
> res <- rma.mv(yi = SMD_gender, V = v_SMD,  mods = ~ time*policy,
>
>                                random = list(~ 1 + time | cnt , ~  1 |
> time_x_cnt),
>
>                               struct=c("GEN","GEN"),
>
>                               data=dat, method="REML" )
>
>
>
> In essence I tried to specify a "typical" random-slope growth model to
> study the cross-level interaction. The code works but I am unsure whether I
> correctly specified the model.
>
>
>
> Further, I would like to take advantage of the RVE method to adjust the
> standard errors/95% CIs of the meta-regression coefficients. To this end, I
> used the clubSandwich package.
>
>
>
> conf_int(res, vcov = "CR2")
>
>
>
> The code works. But I am not sure whether RVE provides robust standard
> errors for random-slope models.
>
>
>
> I highly appreciate any advice and comments.
>
>
>
> Best wishes,
>
>
>
> Martin
>
>
>
>
>
> Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel Analysis. An
> introduction to basic and advanced multilevel modeling (2nd edition). SAGE
> Publications.
>
>
>
>
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