Results from 17 studies on the association between recidivism and mental health in delinquent juveniles.

dat.assink2016

## Format

The data frame contains the following columns:

 study numeric study id number esid numeric effect size within study id number id numeric row id number yi numeric standardized mean difference vi numeric corresponding sampling variance pubstatus numeric published study (0 = no; 1 = yes) year numeric publication year of the study (approximately mean centered) deltype character type of delinquent behavior in which juveniles could have recidivated (either general, overt, or covert)

## Details

The studies included in this dataset (which is a subset of the data used in Assink et al., 2015) compared the difference in recidivism between delinquent juveniles with a mental health disorder and a comparison group of juveniles without a mental health disorder. Since studies differed in the way recidivism was defined and assessed, results are given in terms of standardized mean differences, with positive values indicating a higher prevalence of recidivism in the group of juveniles with a mental health disorder.

Multiple effect size estimates could be extracted from most studies (e.g., for different delinquent behaviors in which juveniles could have recidivated), necessitating the use of appropriate models/methods for the analysis. Assink and Wibbelink (2016) illustrate the use of multilevel meta-analysis models for this purpose.

## Note

The year variable is not constant within study 3, as this study refers to two different publications using the same data.

## Source

Assink, M., & Wibbelink, C. J. M. (2016). Fitting three-level meta-analytic models in R: A step-by-step tutorial. The Quantitative Methods for Psychology, 12(3), 154--174. https://doi.org/10.20982/tqmp.12.3.p154

## References

Assink, M., van der Put, C. E., Hoeve, M., de Vries, S. L. A., Stams, G. J. J. M., & Oort, F. J. (2015). Risk factors for persistent delinquent behavior among juveniles: A meta-analytic review. Clinical Psychology Review, 42, 47--61. https://doi.org/10.1016/j.cpr.2015.08.002

## Author

Wolfgang Viechtbauer, wvb@metafor-project.org, https://www.metafor-project.org

## Examples

### copy data into 'dat' and examine data
dat <- dat.assink2016
#>   study esid id      yi     vi pubstatus year deltype
#> 1     1    1  1  0.9066 0.0740         1  4.5 general
#> 2     1    2  2  0.4295 0.0398         1  4.5 general
#> 3     1    3  3  0.2679 0.0481         1  4.5 general
#> 4     1    4  4  0.2078 0.0239         1  4.5 general
#> 5     1    5  5  0.0526 0.0331         1  4.5 general
#> 6     1    6  6 -0.0507 0.0886         1  4.5 general
#> 7     2    1  7  0.5117 0.0115         1  1.5 general
#> 8     2    2  8  0.4738 0.0076         1  1.5 general
#> 9     2    3  9  0.3544 0.0065         1  1.5 general

# \dontrun{

library(metafor)

### fit multilevel model
res <- rma.mv(yi, vi, random = ~ 1 | study/esid, data=dat)
res
#>
#> Multivariate Meta-Analysis Model (k = 100; method: REML)
#>
#> Variance Components:
#>
#>             estim    sqrt  nlvls  fixed      factor
#> sigma^2.1  0.1879  0.4334     17     no       study
#> sigma^2.2  0.1120  0.3347    100     no  study/esid
#>
#> Test for Heterogeneity:
#> Q(df = 99) = 809.4611, p-val < .0001
#>
#> Model Results:
#>
#> estimate      se    zval    pval   ci.lb   ci.ub     ​
#>   0.4268  0.1184  3.6038  0.0003  0.1947  0.6589  ***
#>
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>

### use cluster-robust inference methods
robust(res, cluster=dat$study) #> #> Multivariate Meta-Analysis Model (k = 100; method: REML) #> #> Variance Components: #> #> estim sqrt nlvls fixed factor #> sigma^2.1 0.1879 0.4334 17 no study #> sigma^2.2 0.1120 0.3347 100 no study/esid #> #> Test for Heterogeneity: #> Q(df = 99) = 809.4611, p-val < .0001 #> #> Number of estimates: 100 #> Number of clusters: 17 #> Estimates per cluster: 1-22 (mean: 5.88, median: 5) #> #> Model Results: #> #> estimate se¹ tval¹ df¹ pval¹ ci.lb¹ ci.ub¹ ​ #> 0.4268 0.1183 3.6076 16 0.0024 0.1760 0.6776 ** #> #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> 1) results based on cluster-robust inference (var-cov estimator: CR1, #> approx. t-test and confidence interval, dfs = residual method) #> ### LRTs for the variance components res0 <- rma.mv(yi, vi, random = ~ 1 | study/esid, data=dat, sigma2=c(0,NA)) anova(res0, res) #> #> df AIC BIC AICc logLik LRT pval QE tau^2 #> Full 3 153.2654 161.0508 153.5180 -73.6327 809.4611 NA #> Reduced 2 214.0678 219.2581 214.1928 -105.0339 62.8024 <.0001 809.4611 NA #> res0 <- rma.mv(yi, vi, random = ~ 1 | study/esid, data=dat, sigma2=c(NA,0)) anova(res0, res) #> #> df AIC BIC AICc logLik LRT pval QE tau^2 #> Full 3 153.2654 161.0508 153.5180 -73.6327 809.4611 NA #> Reduced 2 233.1313 238.3215 233.2563 -114.5656 81.8658 <.0001 809.4611 NA #> ### examine some potential moderators via meta-regression rma.mv(yi, vi, mods = ~ pubstatus, random = ~ 1 | study/esid, data=dat) #> #> Multivariate Meta-Analysis Model (k = 100; method: REML) #> #> Variance Components: #> #> estim sqrt nlvls fixed factor #> sigma^2.1 0.1712 0.4138 17 no study #> sigma^2.2 0.1128 0.3359 100 no study/esid #> #> Test for Residual Heterogeneity: #> QE(df = 98) = 702.5110, p-val < .0001 #> #> Test of Moderators (coefficient 2): #> QM(df = 1) = 1.8444, p-val = 0.1744 #> #> Model Results: #> #> estimate se zval pval ci.lb ci.ub ​ #> intrcpt 0.8117 0.3056 2.6565 0.0079 0.2128 1.4106 ** #> pubstatus -0.4474 0.3294 -1.3581 0.1744 -1.0930 0.1983 #> #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> rma.mv(yi, vi, mods = ~ year, random = ~ 1 | study/esid, data=dat) #> #> Multivariate Meta-Analysis Model (k = 100; method: REML) #> #> Variance Components: #> #> estim sqrt nlvls fixed factor #> sigma^2.1 0.1351 0.3675 17 no study #> sigma^2.2 0.1128 0.3359 100 no study/esid #> #> Test for Residual Heterogeneity: #> QE(df = 98) = 673.5617, p-val < .0001 #> #> Test of Moderators (coefficient 2): #> QM(df = 1) = 5.4633, p-val = 0.0194 #> #> Model Results: #> #> estimate se zval pval ci.lb ci.ub ​ #> intrcpt 0.4257 0.1040 4.0947 <.0001 0.2219 0.6294 *** #> year -0.0421 0.0180 -2.3374 0.0194 -0.0773 -0.0068 * #> #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> dat$deltype <- relevel(factor(dat$deltype), ref="general") rma.mv(yi, vi, mods = ~ deltype, random = ~ 1 | study/esid, data=dat) #> #> Multivariate Meta-Analysis Model (k = 100; method: REML) #> #> Variance Components: #> #> estim sqrt nlvls fixed factor #> sigma^2.1 0.1899 0.4358 17 no study #> sigma^2.2 0.0847 0.2910 100 no study/esid #> #> Test for Residual Heterogeneity: #> QE(df = 97) = 761.8270, p-val < .0001 #> #> Test of Moderators (coefficients 2:3): #> QM(df = 2) = 14.9760, p-val = 0.0006 #> #> Model Results: #> #> estimate se zval pval ci.lb ci.ub ​ #> intrcpt 0.4702 0.1180 3.9858 <.0001 0.2390 0.7015 *** #> deltypecovert -0.7297 0.1923 -3.7941 0.0001 -1.1066 -0.3527 *** #> deltypeovert -0.2219 0.1392 -1.5939 0.1110 -0.4948 0.0510 #> #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> rma.mv(yi, vi, mods = ~ year + deltype, random = ~ 1 | study/esid, data=dat) #> #> Multivariate Meta-Analysis Model (k = 100; method: REML) #> #> Variance Components: #> #> estim sqrt nlvls fixed factor #> sigma^2.1 0.1493 0.3863 17 no study #> sigma^2.2 0.0853 0.2920 100 no study/esid #> #> Test for Residual Heterogeneity: #> QE(df = 96) = 610.2644, p-val < .0001 #> #> Test of Moderators (coefficients 2:4): #> QM(df = 3) = 19.2399, p-val = 0.0002 #> #> Model Results: #> #> estimate se zval pval ci.lb ci.ub ​ #> intrcpt 0.4656 0.1071 4.3461 <.0001 0.2556 0.6756 *** #> year -0.0380 0.0183 -2.0773 0.0378 -0.0738 -0.0021 * #> deltypecovert -0.7094 0.1914 -3.7069 0.0002 -1.0845 -0.3343 *** #> deltypeovert -0.2040 0.1385 -1.4725 0.1409 -0.4755 0.0675 #> #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> ### assume that the effect sizes within studies are correlated with rho=0.6 V <- vcalc(vi, cluster=study, obs=esid, data=dat, rho=0.6) round(V[dat$study %in% c(1,2), dat$study %in% c(1,2)], 4) #> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] #> [1,] 0.0740 0.0326 0.0358 0.0252 0.0297 0.0486 0.0000 0.0000 0.0000 #> [2,] 0.0326 0.0398 0.0263 0.0185 0.0218 0.0356 0.0000 0.0000 0.0000 #> [3,] 0.0358 0.0263 0.0481 0.0203 0.0239 0.0392 0.0000 0.0000 0.0000 #> [4,] 0.0252 0.0185 0.0203 0.0239 0.0169 0.0276 0.0000 0.0000 0.0000 #> [5,] 0.0297 0.0218 0.0239 0.0169 0.0331 0.0325 0.0000 0.0000 0.0000 #> [6,] 0.0486 0.0356 0.0392 0.0276 0.0325 0.0886 0.0000 0.0000 0.0000 #> [7,] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0115 0.0056 0.0052 #> [8,] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0056 0.0076 0.0042 #> [9,] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0052 0.0042 0.0065 ### fit multilevel model using this approximate V matrix res <- rma.mv(yi, V, random = ~ 1 | study/esid, data=dat) res #> #> Multivariate Meta-Analysis Model (k = 100; method: REML) #> #> Variance Components: #> #> estim sqrt nlvls fixed factor #> sigma^2.1 0.0807 0.2841 17 no study #> sigma^2.2 0.1545 0.3931 100 no study/esid #> #> Test for Heterogeneity: #> Q(df = 99) = 745.4385, p-val < .0001 #> #> Model Results: #> #> estimate se zval pval ci.lb ci.ub ​ #> 0.3678 0.0965 3.8097 0.0001 0.1786 0.5570 *** #> #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> ### use cluster-robust inference methods robust(res, cluster=dat$study)
#>
#> Multivariate Meta-Analysis Model (k = 100; method: REML)
#>
#> Variance Components:
#>
#>             estim    sqrt  nlvls  fixed      factor
#> sigma^2.1  0.0807  0.2841     17     no       study
#> sigma^2.2  0.1545  0.3931    100     no  study/esid
#>
#> Test for Heterogeneity:
#> Q(df = 99) = 745.4385, p-val < .0001
#>
#> Number of estimates:   100
#> Number of clusters:    17
#> Estimates per cluster: 1-22 (mean: 5.88, median: 5)
#>
#> Model Results:
#>
#> estimate     se¹   tval¹  df¹   pval¹  ci.lb¹  ci.ub¹    ​
#>   0.3678  0.0962  3.8210   16  0.0015  0.1637  0.5718  **
#>
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> 1) results based on cluster-robust inference (var-cov estimator: CR1,
#>    approx. t-test and confidence interval, dfs = residual method)
#>

# }