# [R-meta] multivariate meta-analysis or mixed model approach

Juan Pablo Edwards Molina edwardsmolina at gmail.com
Tue Aug 8 18:46:26 CEST 2017

```Dear list,

I need to estimate the intercept and slope of two variables relationship
(across 38 studies), let's say: y ~ x.

Based on this tutorial (http://www.metafor-project.
org/doku.php/tips:two_stage_analysis#mixed-effects_model_approach)

I don't know which of the two possible approaches is most suitable:

- Two-stage ultivariate approach: Estimating (est) at first stage each
study terms (intercept-slope), var-cov  matrix (V) and then

mv1 <- rma.mv(est, V, mods = ~ term -1, random = ~ term | study,
struct="UN", data=df1, method="ML")

with this output:

> print(mv1, digits=3)

Multivariate Meta-Analysis Model (k = 76; method: ML)

Variance Components:

outer factor: study (nlvls = 38)
inner factor: term  (nlvls = 2)

estim     sqrt  k.lvl  fixed  level
tau^2.1    424427.426  651.481     38     no     b0
tau^2.2       221.540   14.884     38     no     b1

rho.b0  rho.b1    b0  b1
b0       1  -0.020     -  no
b1  -0.020       1    38   -

Test for Residual Heterogeneity:
QE(df = 74) = 14135.101, p-val < .001

Test of Moderators (coefficient(s) 1:2):
QM(df = 2) = 1070.927, p-val < .001

Model Results:

estimate       se    zval   pval     ci.lb     ci.ub
termb0  3475.110  107.220  32.411  <.001  3264.963  3685.257  ***
termb1   -17.733    2.620  -6.768  <.001   -22.869   -12.598  ***

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

========================================================

or simply go into mixed model approach:

library(lme4)

mix1  <- lmer(y ~ x + ( x |study), data=df, REML=F)

with this output

> summary(mix1)
Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: yield ~ sev + (sev | study)
Data: longs

AIC      BIC   logLik deviance df.resid
20196.8  20228.3 -10092.4  20184.8     1423

Scaled residuals:
Min      1Q  Median      3Q     Max
-4.6511 -0.5715  0.0155  0.5255  3.7780

Random effects:
Groups   Name        Variance Std.Dev. Corr
study    (Intercept) 422064.2 649.66
sev            159.4  12.63   0.04
Residual              65708.3 256.34
Number of obs: 1429, groups:  study, 38

Fixed effects:
Estimate Std. Error t value
(Intercept) 3456.186    106.967   32.31
sev          -16.460      2.328   -7.07

Correlation of Fixed Effects:
(Intr)
sev -0.032

================================================================

The mixed model approach yields lower SE of the effects: is it a good point
to decide among both
approaches?

I'm also interested on test moderator variables than can improve the models:

mv2 <- rma.mv(est, V, mods = ~ term + term:year - 1,
random = ~ term | study,
struct="UN", data=df1, method="ML")

Is it right under multivariate approach?

or

mix2  <- lmer(y ~ x * year + (x|study), data=df, REML=T)

I really appreciate your advices!

*Juan Edwards​*

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