Faculty of Social and Behavioural Sciences
Graduate School of Child Development and Education
A Comparison of Meta-Analytic Structural Equation
Modeling and Univariate Meta-Analysis: An Application in
Forensic Child and Youth Care Sciences
Research Master Child Development and Education Research Master Thesis
Student: T. (Tessa) van den Berg, 10003459
Supervisors: Dr. S. (Suzanne) Jak & Dr. M. (Machteld) Hoeve February 7, 2018
Contents
Abstract 3
A Comparison of Meta-Analytic Structural Equation Modeling and Univariate
Meta-Analysis 4
Application: The Potential Mediating Role of Parenting on Intergenerational
Continuity of Criminal Behavior 9
Methods 10
Results 17
Discussion 30
References 37
Appendix A: Additional Information about the Application 42
Appendix B: Tests for Publication Bias 60
Appendix C: Additional Univariate Meta-Analyses 69
Abstract
Meta-analysis is a widely used statistical technique to integrate research findings of a large collection of studies, which results in a summary effect size and measures of moderation effects by study characteristics. The most used approach of meta-analysis, univariate meta-analysis, tests a hypothesis about one association between two variables. However, more complex research questions that include mediation effects cannot be answered using univariate meta-analysis. Meta-analytic structural equation modeling (MASEM), combining meta-analysis and structural equation modeling, can answer these questions by testing entire models of sets of variables at once and is therefore more elaborate and precise. The advantages and disadvantages of both methods were illustrated by the research project ‘The potential mediating role of parenting on intergenerational continuity of criminal behavior’. Results (k = 88 studies) showed that
univariate meta-analysis resulted in larger and significant effect sizes, while MASEM showed smaller and sometimes nonsignificant effect sizes for the same associations. Because univariate meta-analysis cannot control for any other variables, it leads to seemingly larger effect sizes. Regarding moderator analysis of continuous variables, univariate meta-analysis is more suitable than MASEM, since MASEM can only investigate moderators as categorical variables. In conclusion, different research methods lead to different types of effect sizes, which may in turn lead to different conclusions. Therefore, it is very important to choose the most appropriate research method, taking the advantages and disadvantages of univariate meta-analysis and MASEM that were illustrated in this study into account.
Keywords: Meta-Analytic Structural Equation Modeling, Univariate Meta-Analysis,
A Comparison of Analytic Structural Equation Modeling and Univariate Meta-Analysis
Meta-analysis is a statistical technique to integrate research findings of a large collection of studies (Glass, 1976), which is widely used in social sciences (Rosenthal & DiMatteo, 2001). It tests a hypothesis by statistically combining the results of several independent studies, which generates a summary effect size. Combining data of a large collection of studies results in more precision of estimates and therefore also in higher statistical power. This gives us the opportunity to look at the larger picture without relying on one single study and see the differences and similarities among methodologies and results of separate studies. In addition, to explore the differences between studies, moderator variables can be investigated. This may help to
understand why studies with different samples result in inconsistent research findings (Rosenthal & DiMatteo, 2001).
Univariate Meta-Analysis
In univariate meta-analysis, a summary effect size is estimated for the relationship between two variables. Although this may be the most popular approach of meta-analysis, it has had criticisms. The examination of the relationship between two variables is often insufficient in social sciences, as research questions frequently involve more complex relations, such as
mediation effects. These research questions cannot be answered using univariate meta-analysis. For example, when one wants to investigate to what extent the relationship between parental delinquency and juvenile delinquency is mediated by parenting behaviors, the indirect effect cannot be estimated by univariate analysis. Moreover, when conducting a univariate meta-analysis on the effect of one variable on the other, one cannot control for other variables that
might influence the outcome variable as well. Thus, research questions that involve several variables are hard to answer using univariate meta-analysis.
Figure 1. A. Path model of the relationship between parental delinquency and juvenile
delinquency, partially mediated by parenting behavior. B. Factor model of the latent variable ‘Parenting’, which explains the covariances between several parenting behaviors.
Meta-Analytic Structural Equation Modeling
A different kind of meta-analysis that can answer these questions is called meta-analytic structural equation modeling (MASEM; Viswesvaran & Ones, 1995). This method combines meta-analysis and structural equation modeling (SEM). SEM is a confirmatory technique to test path models, factor models or a combination of both (Jöreskog, 1970). Those models are based on theory. Figure 1 shows an example of a path model and a factor model. Squares represent observed variables, ellipses represent latent variables, one-headed arrows represent direct effects, and two-headed, curved arrows represent (co)variances. The latent variables ε represent residual
factors. Path models describe directional relationships between observed variables. In factor models, latent variables explain the covariances between observed variables. Both path and factor models estimate parameters while holding the other predictor variables that were included in the model constant. Model fit indices provide information about how well the model fits to the data, and hence whether the hypothesized model should be rejected or not. In short, SEM gives us the opportunity to estimate indirect effects and control for several variables when estimating effects.
Conducting SEM requires large samples. When studies have small samples, this often results in different models provided by separate studies (Jak, 2015). No clear-cut conclusion can be drawn by comparing these studies. Therefore, it would be useful to combine all studies to use all available data and apply MASEM to a theoretically based model. Additionally, competing models could be compared. Model fit indices indicate which model fits best to the data and is the most representative of the population.
A great advantage of MASEM is that the included studies do not need to provide information about all effects in the hypothesized model (Viswesvaran & Ones, 1995). For example, several studies may have investigated the relationship between parental delinquency and parenting behavior, other studies may have investigated the relationship between parenting behavior and juvenile delinquency, and a third collection of studies may have investigated the relationship between parental delinquency and juvenile delinquency. The bivariate correlations provided by the studies can be taken together to test the hypothesized path model in Figure 1, although the mediating effect of parenting behavior in this model may never have been tested before. Thus, because MASEM uses bivariate associations in a multivariate model, questions
that were not addressed in earlier research can be answered by combining information from earlier studies.
Although MASEM gives a more elaborate and precise examination of reality than univariate meta-analysis, there are disadvantages as well. For example, when testing moderators with MASEM, the moderator needs to be categorical to conduct a subgroup analysis (Jak & Cheung, under review). Comparing the model in different subgroups will indicate whether the moderator has a significant influence on the effect sizes in the model. In univariate meta-analysis, a moderator can be a continuous variable as well (Shadish & Sweeney, 1991;
Thompson & Higgins, 2002). This means that moderators can contain much more information in univariate meta-analysis than in MASEM.
In conclusion, univariate meta-analysis can test the relationship between two variables, whereas MASEM can test several relationships between a set of variables at once. Moreover, MASEM can investigate research questions that were not explored before. On the other hand, univariate meta-analysis can investigate all kinds of moderator variables, while MASEM can only examine categorical variables as a moderator.
The Present Study
In contrast to univariate meta-analysis, MASEM is a relatively new type of meta-analysis and not yet applied very often. Therefore, researchers may not be acquainted with and not be aware of the advantages and disadvantages of MASEM. The purpose of the current study is to create more insight in this and help researchers to choose the most appropriate method for conducting their research.
Thus, this study investigates the differences between MASEM and univariate meta-analysis, and the advantages and disadvantages of both methods. MASEM has several
approaches: univariate MASEM (Hedges & Olkin, 1985), Maximum Likelihood MASEM (Oort & Jak, 2016), the generalized least squares approach (Becker, 1992), and the Two Stage SEM approach (see Jak, 2015). According to Cheung and Chan (2005), the Two Stage SEM approach performs best in the second stage, when proposed models are tested, compared to the other approaches. Maximum Likelihood MASEM performs equally well, but the Two Stage SEM approach is, unlike Maximum Likelihood MASEM, able to examine random-effects models. Since a random-effects model is preferred in this study, the research question of this study considers the Two Stage SEM approach and the term MASEM refers to that approach. The differences between MASEM and univariate meta-analysis will be illustrated with data from the research project ‘The potential mediating role of parenting on intergenerational continuity of criminal behavior’, which will be explained in the next section. The application of both methods may give more insight in the differences between the methods.
It is expected that univariate meta-analysis and MASEM result in different estimates of the effect sizes. MASEM controls for other variables in the model and therefore provides multiple regression coefficients, while univariate meta-analysis provides bivariate correlations. As a consequence, the data analysis for univariate meta-analysis and MASEM respectively may result in different conclusions about which variable has the strongest association with the outcome variable (juvenile delinquency). Besides, MASEM can specifically answer questions about mediation effects, whereas univariate meta-analysis can only investigate direct effects between two variables at a time. Furthermore, the moderator analysis may provide different results. This is due to the fact that moderators in MASEM need to be categorical, while moderators in univariate analysis can be continuous as well. Therefore, univariate meta-analysis may be able to examine moderators more precisely.
Application: The Potential Mediating Role of Parenting on Intergenerational Continuity of Criminal Behavior
The application regards a study in which the relationship between parental delinquency and juvenile delinquency is tested. Studies showed evidence for intergenerational continuity of criminal behavior (Besemer, Axelsson, & Sarnecki, 2016), and suggested that nurture may play a larger role in intergenerational continuity than hereditary mechanisms (Bijleveld & Wijkman, 2009). Furthermore, a meta-analysis showed significant relationships between several parenting behaviors and criminal behavior in children (Hoeve et al., 2009). In a study from Dannerbeck (2005), parents who have been incarcerated display lower levels of effective parenting and their children show longer and more serious delinquent histories of themselves than children of parents without a history of incarceration. The level of ineffective parenting significantly contributed to juvenile delinquency. However, the study did not evaluate the mediating role of parenting.
The current study focuses on the hypothesis that the relationship between parental delinquency and juvenile delinquency is partially mediated by several variables that represent parenting behavior, based on some of the most important theories about parenting: support (Maccoby & Martin, 1983), authoritarian control (Baumrind, 1971), behavioral control (Barber, Olsen, & Shagle, 1994), psychological control (Barber et al., 1994), and indirect parenting behavior (knowledge about the child’s whereabouts; Kerr & Stattin, 2000). Figure 2 shows the hypothesized path model of the research project. As shown in the figure, it is also hypothesized that the residual factors of the parenting variables are correlated, because parental delinquency will not explain all the covariance between the variables.
Figure 2. Hypothesized model: The mediating role of parenting on the intergenerational
continuity of criminal behavior.
Methods Procedure
The data was collected using several electronic databases: ERIC, PsycINFO, Sociological Abstracts, and Criminal Justice Abstracts. The databases were searched for articles, books, chapters, paper presentations, dissertations, and reviews. Several search terms that were used in different combinations are ‘delinquency’, ‘delinquent’, ‘crime’, ‘criminal’, ‘criminality’, ‘offending’, ‘parenting’, ‘parent-influence’, ‘child-rearing’, and ‘intergenerational continuity’. Besides, reference lists of articles were checked to find studies that were not found in the
databases. To deal with a possible publication bias, experts in the field were approached in order to find relevant unpublished articles. The search script, flow diagram for the selection of studies,
reference list of included studies, and a table with their characteristics can be found in Appendix A.
Sample
Since the data collection is still in progress, the first studies that were fully coded were included in the meta-analyses. This subsample of the original dataset consists of 88 samples from 83 published studies about the relationships between parental delinquency, parenting, and
juvenile delinquency. Usually, researchers would attempt to achieve as much studies as possible in order to conduct a reliable and valid meta-analysis. However, the use of a smaller subsample would not have any impact on the comparison of research methods, and can therefore be used for this study without concerns. The inclusion and exclusion criteria that were used in the study are described below.
Inclusion criteria. The selection of the studies was based on the following criteria regarding operationalization of delinquency and parenting, and presence of bivariate
associations. Delinquency was defined as behavior prohibited by the law. For both parents and juveniles, the same definition of delinquency was used. Parenting was defined as behavior of the parent that is directed toward the child (e.g., neglect, punishment, monitoring, affection, and communication). The studies reported on one or more bivariate associations between
delinquency in parents, parenting, and child delinquency. When studies only reported multivariate associations, the authors were contacted to obtain bivariate data. Finally, the included studies were prospective and provided information about at least one relationship between variables in the past year.
Exclusion criteria. Investigations solely focusing on behavior of the parent which is not directed towards the child, such as marital problems, violent dating, intellectual functioning, and
parental depression were excluded. Studies that focus on specific crimes, such as sex crimes, theft or fire setting were excluded as well. Furthermore, retrospective studies and studies with non-Western samples were not included.
Classification and Coding
The effect sizes that were collected in this study are bivariate correlations between
delinquency in parents, several variables that represent parenting behavior (support, authoritarian control, behavioral control, psychological control, and indirect parenting), and delinquency in children. The effect size that was used in the data-analyses was Pearson’s r correlation
coefficient. This effect size was either directly coded or transformed from other types of effect sizes which were reported in the primary studies. Study characteristics were examined as moderators. The effect sizes and study characteristics were coded by two students, using a coding scheme.
Moderators. Several variables were examined as moderators in this study, to test
whether they influence the effect sizes in the model. First, the gender and age of both the parents and the juveniles were considered. The type of crime was coded as overt, covert or general. Furthermore, some characteristics of the study were taken into account, such as study design (cross-sectional or longitudinal), source for data collection (self-report, official records or both), and informant (parents, adolescents or other). Finally, methodological characteristics regarding the quality of the studies were coded: publication status, impact factor of the journal, sample size, sampling frame, and the number of items and reliability of the questionnaires that were used for the data collection. Because the current study used the data as an illustration, only two of the moderators were investigated; one categorical variable with three levels (socio-economic status) and one continuous variable (juvenile’s age).
Interrater reliability. Ten studies were scored by both coders in order to assess
agreement between the coders. The interrater reliability was analyzed by calculating percentage of agreement for the study variables, Cohen’s Kappa (κ) for categorical variables, and intraclass correlation (ICC) for continuous variables. The interrater reliability was good for the coded effect sizes (ICC = 0.995; 88.2% agreement) and for the age of the juveniles (ICC = 0.997; 94.1% agreement). For socio-economic status, the interrater reliability was in the moderate range (κ = 0.444; 70% agreement).
Analyses
The research question of the application was answered using two different kinds of data analysis: univariate meta-analysis and MASEM. R software was used to analyze the data, with the R packages metaSEM (Cheung, 2015) and metafor (Viechtbauer, 2010). Prior to the main analyses, a funnel plot was created for all associations between the variables of the research project to evaluate signs of a publication bias (e.g., Light & Pillemer, 1984; Egger, Smith, Schneider, & Minder, 1997). Publication bias refers to the tendency of either journals to reject studies with no significant results, or authors to not submit studies with null results. In addition, the trim and fill method was applied (see Duval & Tweedie, 2000).
Overall analyses. First, the overall analyses were carried out with both methods. This means that pooled bivariate correlations in univariate meta-analysis and the parameter estimates in MASEM were estimated. Significance of effect sizes was tested with 95% confidence
intervals (α = .05).
Univariate meta-analysis. For each effect in the hypothesized model of the application, a
univariate meta-analysis was conducted. First, an effect size was observed and sampling variance was estimated for each primary study. Then, a weighted mean of the effect sizes was calculated
(r), using maximum likelihood estimation in order to make the estimation method similar to the one that was used for MASEM. This is the summary effect size, for which more weight was assigned to the more precise studies, based on the inverse of their sampling variances. For the estimation of the summary effect size, a random-effects model was used. A fixed-effects model assumes that the population effect sizes are equal across studies, while a random-effects model assumes that the selected primary studies are random samples from a larger population and allows the effects sizes to be different across studies. In the research project that was used for this study, it is assumed that there is variability between the effect sizes of different studies. Besides, it is argued that random-effects models should be the norm in real-world data in the social sciences (Field & Gillett, 2010).
Several test statistics provide information about the variance between the studies. The between-study variance of the pooled effect size (τ²) and the proportion of total variability that is due to differences between studies (I²) were estimated. I² values of .25 were interpreted as low, .50 as medium, and .75 as high levels of heterogeneity (Higgins, Thompson, Deeks, & Altman, 2003).
MASEM. In the first stage of the Two Stage SEM approach of MASEM, each primary
study is represented by a correlation matrix that includes the variables of the hypothesized model. A pooled correlation matrix was estimated using random effects MASEM (Cheung, 2014). For this, maximum likelihood estimation was used. To determine the consistency of the pooled effect sizes, the same test statistics as in univariate meta-analysis were used. Each pooled correlation is provided with τ² and I².
In the second stage, the hypothesized model was fitted to the pooled correlation matrix of stage 1. Weighted least squares (WLS) estimation was used in stage 2. The WLS procedure takes
care of the weights of the pooled correlations. Pooled correlations that were based on more studies, and were thus estimated with more precision, get more weight in stage 2. The output provided the estimates for each parameter in the model: regression coefficients (β), covariances (ѱ), and (residual) variances (ѱ). Usually, the output also provides information about evaluation of model fit. However, the proposed model of the research project is just identified, which means that all possible parameters are included in the model (df = 0). As a consequence, the model fit indices imply by definition that the model perfectly fits to the data. Thus, although the proposed model may not be the model that represents reality best, model fit cannot be evaluated.
Moderator analyses. Additionally, moderator analyses were carried out to explain study-level variance of the pooled bivariate correlations in univariate meta-analysis and the parameter estimates in MASEM. Two moderator variables were separately examined to be able to compare the results of univariate meta-analysis and MASEM.
Univariate meta-analysis. For each univariate meta-analysis, meta-regression was
conducted to examine the effect of two possible moderators on the pooled correlations
(Thompson & Higgins, 2002). The moderators juvenile’s age when parenting was measured and socio-economic status were investigated in two separate mixed-effects models, with the effect size as outcome variable. The regression coefficients (β) of the juvenile’s age and socio-economic status on the effect size represent the size of the moderating effects and 95%
confidence intervals were used to test the statistical significance of the moderating effects. Since categorical moderator variables are only allowed to have two categories, the variable socio-economic status was transformed from a three-level variable into two dummy variables, high (high = 1; moderate and low = 0) and moderate (moderate = 1; high and low = 0).
MASEM. The same two possible moderators, juvenile’s age when parenting was
measured and socio-economic status, were separately investigated in MASEM using subgroup analysis (Jak & Cheung, under review). Because only categorical variables can be examined as moderators, the continuous variable juvenile’s age was transformed into a categorical variable. Then, the model was fitted to each subgroup, using multigroup analysis. In a second multigroup model, equality constraints were added across groups for each effect. This means that the effect sizes are constrained to be equal across groups. Difference in model fit between the two
multigroup models was evaluated using Δχ². When the model with equality constraints fits significantly worse than the model without equality constraints, this indicates that the effects are not equal across groups. In that case, the juvenile’s age has a significant effect on at least one of the parameter estimates in the model. The next step would be to examine the difference in model fit between the two multigroup models with equality constraints on each parameter estimate separately, in order to identify the association(s) on which the moderator has an effect. The second moderator, socio-economic status, already is a categorical variable (with three categories). Hence, subgroup analysis as explained above can be directly applied to this moderator.
Since subgroup analysis was applied, the hypothesized model was tested in smaller samples than the sample that was used for the overall analyses. This led to a lack of data in some of the subgroups; not every association had data about the association itself and about the
moderator variables as well. Therefore, the respective associations had to be removed from the model and could not be tested for a moderating effect. The model that was tested for moderating effects is shown in Figure 4. To keep the results of MASEM comparable to the results of
univariate meta-analysis, the associations that were not tested in MASEM, were not tested in univariate meta-analysis for moderating effects either.
Results
For both analyses, univariate meta-analysis and MASEM, the same dataset was used. A total of 88 studies were included in the study, which together have a total sample size of N = 154,176. Table 1 shows the number of studies (k) and total sample size (N) for each association in the model of the research project.
Table 1
Sample Sizes and Numbers of Studies
1 2 3 4 5 6 7 1. Parental delinquency 6,580 746 6,593 1,919 3,038 51,768 2. Support 6 4,220 47,908 19,116 14,208 77,303 3. Authoritarian control 2 4 1,359 484 704 6,927 4. Behavioral control 6 16 3 2,810 12,687 63,132 5. Psychological control 1 7 1 3 1,919 19,116 6. Indirect parenting 2 9 1 11 1 33,206 7. Juvenile delinquency 19 39 10 39 7 25
Note. Numbers of studies are shown below the diagonal and total sample sizes are shown above
the diagonal. Publication Bias
Only the association between indirect parenting and juvenile delinquency showed signs of publication bias. Other associations showed (almost) no signs of publication bias or were based on too few studies that it was not possible to investigate publication bias. Figures of funnel plots with applied trim and fill method can be found in Appendix B. The presence of any
publication bias is not expected to influence differences between univariate meta-analysis and MASEM, and has therefore no effect on the comparison of methods in this study.
Overall Results
When the analyses for MASEM were carried out, the model did not converge because the between-studies variance (τ²) was too small and could not be estimated. Therefore, for some associations τ² was manually set to 0 using OpenMx in R (Boker et al., 2011). For the same associations, a fixed-effects model was used in univariate meta-analysis, in order to keep the results of univariate meta-analysis and MASEM comparable. Study-level variance was evaluated using τ² and I² from the univariate meta-analyses, but would have the same results in MASEM, and can be found in Table 2. For the associations between parental delinquency and the parenting variables, there was little to no variance at the study-level. However, for the associations
between the parenting variables and juvenile delinquency, the study-level variance was higher and can be considered heterogeneous. Moreover, these associations were investigated with more primary studies and larger samples compared to the associations between parental delinquency and parenting, and may therefore show more variability. A large proportion of the total
variability of these effect sizes was due to differences between studies.
Univariate Meta-Analysis. The first column of Table 2 presents the pooled bivariate correlations and 95% confidence intervals for the univariate meta-analyses of the associations that were of interest for the research project. First of all, parental delinquency showed small but significant relationships with two of the parenting variables. Authoritarian control correlated positively with parental delinquency (r = 0.08) and indirect parenting correlated negatively with parental delinquency (r = −0.07). In addition, parental delinquency had a small to medium positive and significant correlation with juvenile delinquency (r = 0.19).
Table 2
Results and Descriptive Statistics of Univariate Meta-Analyses and Meta-Analytic Structural Equation Modeling
Associations with parental delinquency Univariate
meta-analysis (r) MASEM (β) N k τ² I²
Support −0.019 [−0.044, 0.005] −0.021 [−0.045, 0.003] 6,580 6 0 0 Authoritarian control 0.080 [0.008, 0.151] 0.075 [0.005, 0.146] 746 2 0 0 Behavioral control −0.029 [−0.059, 0.001] −0.030 [−0.062, 0.001] 6,593 6 0 0.211 Psychological control 0.040 [−0.005, 0.085] 0.042 [−0.003, 0.086] 1,919 1 - - Indirect parenting −0.072 [−0.107, −0.037] −0.072 [−0.106, −0.038] 3,038 2 0 0
Associations with juvenile delinquency Univariate
meta-analysis (r) MASEM (β) N k τ² I²
Parental delinquency 0.189 [0.128, 0.249] 0.171 [0.110, 0.231] 51,768 19 0.016 0.986 Support −0.149 [−0.185, −0.112] −0.075 [−0.128, −0.022] 77,303 39 0.012 0.956 Authoritarian control 0.151 [0.097, 0.204] 0.107 [0.037, 0.178] 6,927 10 0.005 0.773 Behavioral control −0.161 [−0.207, −0.116] −0.111 [−0.177, −0.045] 63,132 39 0.019 0.966 Psychological control 0.079 [0.020, 0.137] −0.011 [−0.102, 0.080] 19,116 7 0.005 0.922 Indirect parenting −0.178 [−0.251, −0.105] −0.093 [−0.186, 0.001] 33,206 25 0.033 0.980
Note. r = pooled bivariate correlation; β = regression coefficient; N = sample size; k = number of studies;
τ² = study-level variance; I² = proportion of total variability that is due to differences between studies. 95% confidence intervals are shown below effect sizes.
Considering the parenting variables, all were significantly correlated to juvenile delinquency. Support (r = −0.15), behavioral control (r = −0.16), and indirect parenting (r = −0.18) showed small to medium negative correlations, which means that these parenting
practices may decrease juvenile delinquency. On the other hand, authoritarian control (r = 0.15; small to medium) and psychological control (r = 0.08; small) showed positive correlations, which means that these may increase juvenile delinquency. If one would draw conclusions about the relevance of variables from the comparison of the sizes of bivariate correlations, indirect parenting would seem to be the most important variable in the prediction or prevention of juvenile delinquency.
Additional univariate meta-analyses were carried out for the associations between the parenting variables. These were not part of the hypotheses of the research project and will therefore not be further discussed. The results can be found in Appendix C.
Meta-Analytic Structural Equation Modeling. Table 3 presents the weighted pooled correlation matrix that was constructed in the first stage of the analysis. In the second stage, the hypothesized model of the research project was fitted to this matrix. Figure 3 shows the
hypothesized model with the parameter estimates. Since the model is saturated, the model fits perfectly by definition. The residual variance of juvenile delinquency was ѱ = 0.907, which means that 9.3% of the variance in juvenile delinquency was explained by the model. The direct effects of parental delinquency on the parenting variables were all small and only two were significant. First, parental delinquency significantly increased authoritarian control (β = 0.075). Second, parental delinquency significantly decreased indirect parenting (β = −0.072). Thus, delinquent parents tend to use more authoritarian control in their children’s upbringing and have less knowledge about their children’s whereabouts than non-delinquent parents.
Table 3
Weighted Pooled Correlation Matrix for the Relationships between the Study Variables
1 2 3 4 5 6 1. Parental delinquency 2. Support −0.021 3. Authoritarian control 0.075* −0.166* 4. Behavioral control −0.030 0.202* −0.036 5. Psychological control 0.042 −0.187 0.265* −0.246 6. Indirect parenting −0.072* 0.325* −0.178* 0.298* −0.150* 7. Juvenile delinquency 0.190* −0.147* 0.150* −0.160* 0.080* −0.180* Note. *p < .05.
Furthermore, parental delinquency had a significant effect on juvenile delinquency, controlling for parenting. The more delinquent the parent, the more delinquent their offspring (β = 0.171) while holding the parenting variables constant. Besides, three of the five parenting variables were significant predictors of juvenile delinquency. Parenting behaviors that could decrease juvenile delinquency, controlling for parental delinquency and all other parenting variables in the model, are support (β = −0.075) and behavioral control (β = −0.111). On the other hand, authoritarian control could increase juvenile delinquency (β = 0.107), holding parental delinquency and the other parenting variables constant. Psychological control and indirect parenting (which seemed to be the most important parenting variable in the prediction of juvenile delinquency according to univariate meta-analysis) seem to have no significant effect on juvenile delinquency when controlling for parental delinquency and the other parenting
Figure 3. Meta-Analytic Structural Equation Model results. Note: *p < .05, **p < .01, ***p <
.001.
Indirect effects from parental delinquency on juvenile delinquency through parenting were calculated from the model by multiplying the direct effects (Table 4), and their significance was tested using likelihood-based confidence intervals (Neale & Miller, 1997). Only
authoritarian control seems to be a significant mediator between parental delinquency and
juvenile delinquency. Although the indirect effect is very small (β = 0.008), parental delinquency leads to more authoritarian control from the parent, which in turn leads to more juvenile
delinquency.
In conclusion, parental delinquency has a positive direct effect on juvenile delinquency, also when controlling for five kinds of parenting behaviors. This means that there is no full
mediation by parenting. However, the effect is partially mediated by authoritarian control from the parent.
Table 4
Meta-Analytic Structural Equation Modeling: Indirect Effects of Parental Delinquency on Juvenile Delinquency β 95% CI Support 0.002 [−0.0002, 0.004] Authoritarian control 0.008 [0.001, 0.019] Behavioral control 0.003 [−0.0002, 0.009] Psychological control −0.001 [−0.008, 0.004] Indirect parenting 0.007 [−0.0002, 0.015]
Note. Indirect or mediation effects are shown from parental delinquency through each parenting
Table 5
Meta-Analytic Structural Equation Modeling: Residual Variances and Covariances
Residual variances ѱ 95% CI Support 1.000 [0.998, 1.000] Authoritarian control 0.994 [0.979, 1.000] Behavioral control 0.999 [0.996, 1.000] Psychological control 0.998 [0.993, 1.000] Indirect parenting 0.995 [0.989, 0.999] Juvenile delinquency 0.907 [0.873, 0.934] Covariances ѱ 95% CI
Support – Authoritarian control −0.164 [−0.268, −0.060] Support – Behavioral control 0.202 [0.102, 0.301] Support – Psychological control −0.186 [−0.386, 0.014] Support – Indirect parenting 0.324 [0.241, 0.406] Authoritarian control – Behavioral control −0.034 [−0.182, 0.115] Authoritarian control – Psychological control 0.262 [0.180, 0.344] Authoritarian control – Indirect parenting −0.173 [−0.244, −0.102] Behavioral control – Psychological control −0.245 [NA, 0.148] Behavioral control – Indirect parenting 0.296 [0.193, 0.398] Psychological control – Indirect parening −0.147 [−0.190, −0.103]
Note. ѱ = residual variance or covariance; CI = confidence interval.
Comparison of results. To start, the pooled correlations from the first stage in MASEM (Table 3) could be compared to the results of the univariate meta-analyses (first column of Table 2), since these both regard bivariate correlations. Small differences can be seen on the second or
third decimal places of the correlations, which are due to the fact that MASEM is a multivariate analysis. It takes the dependency of effect sizes that came from the same study into account.
However, the final results of MASEM are more different from the results of the univariate meta-analyses. Table 2 presents the results of both analyses. Effects from parental delinquency to parenting were similar and the same conclusions can be drawn. On the other hand, the effects from parenting to juvenile delinquency and from parental delinquency to
juvenile delinquency showed large differences. All parameter estimates in MASEM were smaller than the pooled correlations in univariate meta-analysis. In some cases, this even leads to
different conclusions about the research questions. For example, the relationship between support and juvenile delinquency could be considered as a small to medium correlation according to univariate meta-analysis, but only as a small effect according to MASEM. In
particular the relationships between psychological control and juvenile delinquency, and between indirect parenting and juvenile delinquency showed large differences. Both parameter estimates were not significant in MASEM, while they were significant correlations in univariate meta-analysis. Apparently, the effect of these parenting variables on juvenile delinquency disappears when controlling for other parenting variables and parental delinquency.
This can be explained by the fact that univariate meta-analysis leads to bivariate correlations, while MASEM leads to multiple regression coefficients. Since psychological control and indirect parenting also correlate to other parenting variables (as can be seen in Table 5), some of the variance in juvenile delinquency that would be explained by psychological control and indirect parenting may already be explained by the other variables. Thus, the effects that psychological control and indirect parenting have on juvenile delinquency according to
univariate meta-analysis, are not visible in MASEM because they correlate with other parenting behaviors that have a significant effect on juvenile delinquency as well.
Moderator Analyses
Since there was a lack of data, a smaller model was tested for moderator effects (Figure 4). Only the associations between parental delinquency, support, behavioral control, and juvenile delinquency were examined.
Univariate meta-analysis. Although in univariate meta-analysis several moderators can be examined at once, the moderators will be examined separately in order to be able to compare the results with the results of MASEM. First, the continuous variable juvenile’s age (M = 13.56,
SD = 2.87) was investigated as a moderator (Table 6). For the relation between parental
delinquency and behavioral control, the effect of age of the juvenile was positive and significant (β = 0.013). The relation between parental delinquency and behavioral control was negative (r = −0.029), so the younger the juvenile, the stronger this relationship was. For the relationship between support and juvenile delinquency, age had a significant negative effect (β = −0.015). Thus, the older the juvenile, the stronger the negative relationship between support and juvenile delinquency, and the more important support becomes in the prediction of juvenile delinquency. The age of the juvenile also has a moderating effect on the intergenerational continuity of criminal behavior: the older the juvenile, the smaller the relationship between parental delinquency and juvenile delinquency (β = −0.043).
Table 6
Univariate Meta-Analysis: Moderator Analysis of Continuous Variable Juvenile’s Age
Intercept β
Parental delinquency – Support 0.142 [−0.063, 0.348]
−0.013 [−0.029, 0.003] Parental delinquency – Behavioral control −0.187
[−0.343, −0.031]
0.013 [0.001, 0.026] Parental delinquency – Juvenile delinquency 0.681
[0.246, 1.117]
−0.043 [−0.079, −0.008] Support – Juvenile delinquency 0.052
[−0.105, 0.208]
−0.015 [−0.026, −0.004] Behavioral control – Juvenile delinquency 0.039
[−0.212, 0.290] [−0.032, 0.004] −0.014
Note. β = regression coefficient. 95% confidence intervals are shown below effect sizes.
Next, the categorical variable socio-economic status was turned into two dummy
variables, high and moderate, and examined as a moderator (Table 7). No significant moderating effects were found for neither of the two dummy variables. Thus, socio-economic status seems to have no moderating effect on the relationships between parental delinquency, support, behavioral control, and juvenile delinquency.
Additionally, as univariate meta-analysis can investigate several moderators at a time, both moderators were included in a second model. The effects of each moderator are now
controlled for the effect of the other moderator, which leads to different results. These results can be found in Appendix D.
Table 7
Univariate Meta-Analysis: Moderator Analysis of Categorical Variable Socio-Economic Status
Moderate SES High SES
Intercept β β Parental delinquency – Support −0.004 [−0.042, 0.035] −0.030 [−0.245, 0.184] −0.012 [−0.066, 0.042] Parental delinquency – Behavioral control −0.044 [−0.083, −0.005] −0.039 [−0.189, 0.110] 0.052 [−0.002, 0.106] Parental delinquency – Juvenile delinquency 0.060 [−0.135, 0.255] 0.155 [−0.080, 0.389] 0.128 [−0.118, 0.374] Support – Juvenile delinquency −0.108 [−0.251, 0.035] −0.077 [−0.250, 0.096] 0.042 [−0.201, 0.284] Behavioral control – Juvenile delinquency −0.156 [−0.262, −0.051] −0.004 [−0.139, 0.132] −0.034 [−0.195, 0.126]
Note. β = regression coefficient. 95% confidence intervals are shown below effect sizes.
Meta-Analytic Structural Equation Modeling. Because continuous moderator
variables cannot be investigated in MASEM, the moderator juvenile’s age was transformed into a categorical variable. The dataset was divided into two groups: studies with juveniles with a mean age above the grand mean (M = 13.56, SD = 2.87; k = 36), and studies with juveniles with a mean age below the mean (k = 23).
To test for a moderating effect of age, a multigroup model was tested that includes the two age groups. Equality constraints were added on all direct effects in the model, assuming that all effects in the model are equal across the two groups. This resulted in no significant difference in model fit when compared to the model without equality constraints: Δχ²(5) = 9.140, p = 0.104. Thus, the age of the juveniles did not have a moderating effect on any direct effect in the model.
Figure 4. Model tested for moderators.
Furthermore, the categorical variable socio-economic status was investigated as a moderator as well. This variable has three categories: high (k = 6), moderate (k = 16), and low socio-economic status (k = 8). Again, a multigroup model was tested, this time with three groups, and equality constraints were added on all effects in the model across the three groups. When compared to the model without equality constraints, this resulted in no significant difference in model fit: Δχ²(10) = 16.312, p = 0.091. Thus, socio-economic status had no moderating effect on the associations between parental delinquency, support, behavioral control, and juvenile
delinquency.
Comparison of results. The moderator analysis of juvenile’s age in univariate meta-analysis and MASEM resulted in different outcomes. This variable was investigated as a continuous variable in univariate meta-analysis, but as a categorical variable in MASEM. The significant effects that resulted from univariate meta-analysis were not found with MASEM. Since the continuous variable had to be transformed into a categorical variable for the analysis in MASEM, information about the age of the juveniles was lost. As a consequence, MASEM has less power to detect moderating effects than univariate meta-analysis. However, the possible
moderator socio-economic status, which was investigated as a categorical variable in both univariate meta-analysis and MASEM, showed similar results across methods.
Discussion
This study investigated the differences between the outcomes of univariate meta-analysis and MASEM. As expected, the two research methods resulted in different estimates of the effect sizes, for both the overall analyses and moderator analyses. Results showed that parameter estimates in MASEM are generally smaller than the pooled bivariate correlations in univariate meta-analysis. For several reasons, which will be explained below, the parameter estimates in MASEM are more precisely examined and therefore more accurate than the bivariate
correlations in univariate analysis. Contrarily, in moderator analyses, univariate meta-analysis seemed to perform more accurately in case of a continuous moderator variable, since MASEM has to transform this into a categorical variable in order to be able to examine it. However, in case of a categorical moderator variable, MASEM and univariate meta-analysis result in the same conclusions. Altogether, the differences in outcomes showed that both
methods have their own characteristics which can be an advantage or disadvantage. An overview of characteristics of both methods is shown in Table 8. The advantages and disadvantages of these characteristics, with corresponding numbers, will be explained below.
Table 8
Characteristics of Meta-Analytic Structural Equation Modeling and Univariate Meta-Analysis
MASEM Univariate Meta-Analysis
(1) Examines a set of variables in a hypothesized model
Examines one association between two variables
(2) Results in multiple regression coefficients
Results in pooled bivariate correlations
(3) Can control for other variables Cannot control for other variables (4) Can estimate indirect / mediation
effects
Can only estimate bivariate relationships
(5) Can answer research questions that were not explored before
Can only give a summary effect size of associations that were examined before (6) Is a multivariate analysis Is a univariate analysis
(7) Can do moderator analysis with only categorical variables
Can do moderator analysis with all kinds of variables
(8) Investigates rather one moderator at a time
Can investigate several moderators at a time
Differences between Parameter Estimates and Pooled Correlations
The main difference between MASEM and univariate meta-analysis is that univariate meta-analysis investigates one association between two variables, while MASEM can investigate an entire model of a set of variables at once (1). This study examined a path model, but factor models can be examined with MASEM as well (see Jak, 2015; for examples, see Norton et al., 2013, and Fan et al., 2010). Because of this difference, univariate meta-analysis results in pooled bivariate correlations, while MASEM results in multiple regression coefficients, which can also be interpreted as a kind of partial correlations (2). This relates to the fact that MASEM can control for other variables that are included in the model that is investigated, while univariate
meta-analysis cannot (3). Hence, variance in an outcome variable (e.g., juvenile delinquency) is explained by several variables in MASEM, but only by one variable in univariate meta-analysis. Since different variables (e.g., psychological control and authoritarian control) may have a shared explained variance in the outcome variable, this reduces the effect sizes of the predictor variables on the outcome variable. This would be explained by the correlation between the two parenting variables.
Thus, for example, psychological control and authoritarian control correlate to each other; parents who use psychological control may use authoritarian control as well. Variance in juvenile delinquency that would be explained by psychological control may actually already be explained by authoritarian control of the parent. As a consequence, the relationship between psychological control and juvenile delinquency that was visible in univariate meta-analysis, disappeared when controlling for authoritarian control (and other variables) in MASEM. In conclusion, univariate meta-analysis seems to overestimate effect sizes of relationships between variables, because no other variables are taken into account. The parameter estimates in MASEM provide the estimated unique effects of the predictor variables. Since behavior of individuals will always be influenced by several variables, it would in social sciences be more accurate to use MASEM instead of univariate meta-analysis.
The differences in effect sizes led to different conclusions about the research questions as well. First of all, this was because the associations between psychological control and juvenile delinquency and between indirect parenting and juvenile delinquency were not significant in MASEM, while significant correlations were obtained in univariate meta-analysis. Second, although it is incorrect, researchers tend to compare bivariate correlations to draw conclusions about which variable has the largest influence on the outcome variable (e.g., Bartel, Gradisar, &
Williamson, 2015; Cottle, Lee, & Heilbrun, 2001; Gendreau, Little, & Goggin, 1996; Hanson & Bussiere, 1998; Hoeve et al., 2009; Ozer et al., 2003). For example, Bartel et al. (2015) explain their table with results of their univariate meta-analyses as follows: “Variables are ranked from the largest negative correlation, to the largest positive correlation, indicating the most protective to the least beneficial, respectively” (p. 76). If the results of our own univariate meta-analyses would be interpreted that way, it would be concluded that indirect parenting has the largest influence on juvenile delinquency, compared to the other parenting variables. In contrast, according to MASEM it would be concluded that indirect parenting has no effect at all and behavioral control has the largest influence on juvenile delinquency. Thus, different research methods may lead to different conclusions. In turn, this could lead to inadequate future implications (e.g., inadequate recommendations may be made about parenting-targeted interventions).
Furthermore, MASEM is able to estimate indirect or mediation effects (4). Although univariate meta-analysis does not have this advantage, researchers tend to incorrectly estimate indirect effects from univariate analyses as well (e.g., Verhage et al., 2016). Thus, when a
research question for a meta-analysis involves a mediation effect, MASEM should be used as the research method. In line with this, MASEM can investigate research questions that were not explored before (5). Because not every primary study needs to include all variables in the hypothesized model of the meta-analysis (Viswesvaran & Ones, 1995), the combination of different studies about different associations may give new insights. Finally, small differences in effect sizes between the methods could be due to the fact that MASEM is a multivariate analysis and takes into account that some effect sizes came from the same study and therefore depend on
each other (6). This leads to more accurate effect sizes in MASEM than in univariate meta-analysis (Jackson, Riley, & White, 2011).
Moderator Analysis
The advantage of MASEM that it can investigate many variables at once also means that more data is needed for the analysis, which is not always available. For this reason, the
moderator analyses in this study had to be narrowed down to a few associations, namely between parental delinquency, support, authoritarian control, and juvenile delinquency. Because MASEM uses subgroup analysis to investigate moderators (Jak & Cheung, under review), all associations between all variables – even when they are not included in the hypothesized model – need to have data available about the association itself and about the moderator. When this data is not available, moderator analysis is not possible. To deal with this problem, the model could be narrowed down to less variables. However, this does not rectify the fact that this is a
disadvantage of MASEM.
Since subgroup analysis is used for moderator analyses, MASEM can only investigate moderators as categorical variables (7). Continuous variables therefore need to be transformed into categorical variables in order to be able to examine their effects on the hypothesized model. This leads to a loss of information about the continuous variable. Because univariate meta-analysis can investigate all kinds of variables as moderators (Shadish & Sweeney, 1991), this would lead to more accurate outcomes than in MASEM. However, a categorical variable can be examined as a moderator just as well in MASEM as in univariate meta-analysis.
Finally, univariate meta-analysis can investigate several moderators at a time in one model (8). The effects of the moderators on the association between the two variables of interest are then multiple regression coefficients. The effect of one moderator is controlled for the effect
of the other moderator. This is an advantage of univariate meta-analysis. MASEM could do this as well by creating more subgroups and combinations of subgroups, but this would lead to a very small number of studies (k) in each subgroup, which may cause a lack of data in one or more subgroups.
Strengths and Limitations
This study illustrated important differences between two research methods: univariate meta-analysis and MASEM. Since MASEM is a relatively new approach, this gave insights in the advantages of this method, compared to univariate meta-analysis, which is a more common approach of meta-analysis. It illustrates that choosing one of these research methods over the other could have an important impact on the outcomes. By using illustrative data, the different characteristics of the two methods became clear. The explanation of the advantages and disadvantages will help researchers to choose the most appropriate method for their research.
However, this study has some limitations as well. The moderator analysis in MASEM showed no significant effect on the hypothesized model. Therefore, the illustration of this analysis is not entirely complete. When an effect would have been found, the study could have shown the next steps of moderator analysis in MASEM. With a larger dataset or with simulated data it may have been possible to make the illustration more complete. On the other hand, this shows exactly the pitfalls that researchers would have to deal with when using actual data. Future Research
Now that the advantages and disadvantages of both methods are clear, recommendations can be made about the improvement of the research methods. The main disadvantage of
MASEM is that it can investigate moderators only as categorical moderators. Parameter-based MASEM would be an option to solve this problem (Cheung & Cheung, 2016), but is unrealistic
to apply on real data. Thus, an important suggestion for future research would be to improve the moderator analysis in MASEM in a way that it can investigate continuous moderator variables as well.
Conclusion
In sum, MASEM seems to examine relationships between variables more accurately. It also gives a more elaborate and precise examination of reality than univariate meta-analysis, because it can test hypothesized models and estimate mediation effects. On the other hand, univariate meta-analysis is more precise when it comes to moderator analysis. It is very important to keep in mind that differences in effect sizes, as were shown in this study between univariate meta-analysis and MASEM, lead to differences in conclusions about the research questions. This affects everything that depends on these conclusions, such as clinical
implications. Therefore, it is very important to choose the most appropriate research method to investigate specifically your research question. Although both methods have their advantages and disadvantages, in social sciences it may be preferred to take several variables into account – since behavior of individuals will always be affected by more than one aspect – and use MASEM as a research method.
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Appendix A: Additional Information about the Application Search Script
The search script that was used for the database PsycINFO is shown below. This script was translated to scripts for the databases ERIC, Sociological Abstracts, and Criminal Justice Abstracts. First, scripts were written for each of the (sets of) variables: parenting, juvenile delinquency, and parental delinquency, and were later combined to find studies about the associations between the variables. Since data was available from a previous meta-analysis (Hoeve et al., 2009), the search script for the combination of parenting and juvenile delinquency was limited to 2008-current.
#1 parenting
parental involvement/ OR parenting style/ OR parenting skills/ OR transgenerational patterns/ OR (parenting OR child?rearing OR parent* influenc* OR parent* style* OR ((parent* OR mother* OR maternal OR father* OR paternal) ADJ3 (acceptance OR authorita* OR control* OR discipline OR disclosure OR harsh OR knowledge OR monitoring OR neglect OR
permissive* OR rejection OR supervision OR support OR warmth)) OR intergeneration* OR second generation* OR transgenerat*).ti,ab,id.
#2 juvenile delinquency
juvenile delinquency/ OR juvenile justice/ OR ((child* OR adolesc* OR youth* OR juvenile) ADJ3 (delinq* OR devian* OR crim* OR offend*)).ti,ab,id.
#3 parental delinquency
((parent* OR mother* OR maternal OR father* OR paternal) ADJ3 (delinq* OR devian* OR crim* OR offend*)).ti,ab,id.
Combination of search scripts
(1 AND 2) OR (1 AND 3) OR (2 AND 3)
Figure A1. Flow diagram for the selection of studies for the entire project ‘The potential
mediating role of parenting on intergenerational continuity of criminal behavior’. The coding of studies and the manual search are still in progress, which is why a subset of k = 88 studies was included in this study.
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