Meta-Analysis Divorce German

8/10/2019 Meta-Analysis Divorce German

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Paper prepared for the conference onDivorce in Cross-National Perspective: A European Research Network

European University Institute, Florence, ItalyNovember 14 & 15, 2002

DRAFT

A Meta-Analysis of German Research on Divorce Risks

Michael Wagner

and

Bernd Wei

Research Institute for SociologyUniversity of Cologne

Greinstr. 250939 Cologne

[email protected]

[email protected]


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Abstract

The aim of the paper is to evaluate divorce studies in Germany and to apply meta-

analytic techniques in order to summarize the results of this research. Literatureresearch identified 42 studies published between 1987 and 2001. These studies uselongitudinal data from seven projects and all studies estimate event history modelswith the divorce rate as dependent variable. In sum, they examine 399 different riskfactors and report 3730 effects. Results of the meta-analysis are threefold. First, thereare methodological problems in the field of meta-analysis that are not resolved in avery satisfactory way. Second, no theory of divorce has been tested in detail, rathersingle hypotheses have been examined which were derived from exchange ormicroeconomic theory. Third, divorce research can be improved by a more cumulativedesign which means that we need more studies conducting a replication of existingempirical findings.


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1This research was supported by the German Science Foundation from July2000 to July 2001 (WA 1502/1-1). We thank Hans-Peter Blossfeld (Bamberg) for

helpful comments on an earlier version of the manuscript.2

1 Problem 1

During the past twenty years German sociology experienced a boom of divorcestudies. This development was mainly caused by methodological innovations that

enabled a reliable longitudinal assessment of marital histories, e.g. retrospectively inlife course research or prospectively in panel studies. The aim of this paper is toevaluate the studies on divorce risks in Germany. So many divorce risks have beenreported that it became unclear what we really know about the determinants of maritalinstability (Hartmann 1989; Dorbritz/Grtner 1998). Which theories or hypotheseshave been confirmed by empirical findings? Is research undertaken cumulatively? Areempirical findings presented in such a way that their evaluation is possible?

The evaluation of empirical research is usually done by qualitative reviews. However,this kind of research synthesis shows various shortcomings. The two most seriousones result from non-systematical and incomplete literature research as well as froman inadequate integration and interpretation of diverging quantitative results(Wagner/Wei 2001). In order to overcome these disadvantages, we apply meta-analytic methods. Besides primary and secondary research, this method stands for athird type of empirical social research. Meta-analysis is primarily concerned with thequantitative integration of published empirical findings (Glass 1976). However, itallows not only their integration but also the explanation of their heterogeneity.

Meta-analysis is rather unknown, especially in German sociology. Only Knzler (1994)and Engelhardt (2000) mention it, the latter as part of a survey of study designs indemography. Some others call their study a meta-analysis, as in fact they summarizecharacteristics of numerous publications, but without systematically investigatingquantitative results (Bretschneider 1997; Hartmann 1999). In other disciplines thansociology, like medical science, psychology and educational science, meta-analysishas gained much more popularity, in Germany as well as elsewhere. In psychology,the outcomes of a great number of studies that are interested in the success of certain

therapies have been summarized by meta-analyses. In medical science, the EvidenceBased Medicine has already been institutionalized (Altman 2000; Petitti 2000; Suttonet al. 2000). Numerous handbooks and monographies on meta-analysis underline theimportance of this research area (Bortz/Olkin 1985; Hunter/Schmidt 1990;Lipsey/Wilson 2001; Rosenthal 1991; Schultz-Gambard 1987; Sutton et al. 2000).


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2 Meta-analysis

To perform a meta-analysis does not differ much from other types of social research

(Diekmann 1997; Schnell et al. 1995). We apply a five stage-model proposed byCooper (1982):

1. Problem/research question2. Literature research3. Data evaluation and coding4. Data analysis5. Presentation of results

2.1 Literature ResearchThe population of our meta-analysis is defined as the totality of empirical studies fromGermany investigating marital stability and using the divorce rate as the dependentvariable. These studies use longitudinal data on marriages and partnerships. Before1990, only studies of West Germany, after 1990 studies of West and East Germanywere included.

A comprehensive literature research is necessary for any meta-analysis, including alltypes of publications and research reports. A detailed description of literature researchprocedures is given by Lipsey/Wilson (2001) and White (1994). In the present case,we started with a stock of 15 studies. Then a systematical search using several socialscience literature databases was undertaken (Family Studies Database, Popline,SSCI, SOLIS, FORIS, Sociological Abstracts, IHS, PsycINFO and PSYNDEX).References of publications were examined for further studies. The literature researchwas finished in spring 2001 (for details see Wagner/Wei 2001; Wei 2001).

Finally, 42 publications could be identified that matched the search criteria. They werepublished between 1987 and 2001. Half of all publications appeared before 1998.Many articles were published after 1997, because at this point of time the results ofthe Mannheim Research Project Determinants of Divorces had been released.

In Germany, the relevant divorce studies use data samples from seven larger projectsof the Social Sciences. These are the Mannheim Research Project Determinants ofDivorce, the German Socio-Economic Panel, the Family Survey of the German YouthInstitute, the German Life History Study (Max Planck Institute for Human


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2See the number of identification as it is found in the bibliography of the studies

that have been included in the meta-analysis.4

Development), the Family and Fertility Survey of Germany, the General Social Surveyof the Social Sciences and the Cologne Longitudinal Study of Gymnasium graduates.Most of the publications are taken from the Mannheim Research Project, followed bythe Family Survey (Table 1).

Table 1: Number of publications by year of publication and studyYear Study Total 2

DoD 1 GSEP FS GLHS FFS GSS KLS1987 0 0 0 0 0 1 0 11989 0 1 0 0 0 0 0 11991 0 1 0 1 0 0 0 21992 0 3 0 0 0 0 0 31993 0 0 0 1 0 0 0 11994 0 1 0 0 0 0 0 1

1995 0 0 2 0 0 0 0 21996 0 0 1 0 0 0 0 11997 3 0 2 1 0 0 0 61998 2 1 1 0 2 0 0 61999 10 0 4 1 0 0 0 152000 2 0 1 0 0 0 0 32001 0 0 0 0 0 0 1 1Total 17 7 11 4 2 1 1 43

1 DoD: Mannheim Research Project Determinants of Divorce` ;GSEP: German Socio-Economic Panel(DIW, Berlin); FS: Family Survey of the German Youth Institute (DJI, Munich); GLHS: German LifeHistory Study (MPI, Berlin); FFS: Family and Fertility Survey; GSS: General Social Survey of the SocialStudies; KLS: Cologne Longitudinal Study of Gymnasium Graduates.

2 Kleins (1999; No. 32 and 33) study has been counted twice, so the total number of publications hasbeen artificially increased by an additional publication.

Literature research revealed a number of anomalies. We ignored double publicationsof identical or nearly identical texts (cf. publication No. 23 2 and Diekmann/Klein 1993as well as publication No. 2 and Babka von Gostomski 1999). If a paper has beenpublished twice with substantial modifications this was counted as two publications

and both went into the meta-analysis (cf. publications No. 7 and 34). Moreover, it ispossible that publications include empirical results which are based on two differentsamples. These publications have been registered as two independent cases (cf.publications No. 32 and 33).


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Study

Pub lica tion A Pub lication B Publication C

Subgroup A Subgroup B

M odel A M odel B

Unit of analysis

Sampling unit

Divo rce risk A

Divo rce risk B

Divorce risk C

Divo rce risk D

Effect size A

Effect size B

Effect s ize C

Effect size D

Effect size A

Effect size B

Effect size D

2.2 Levels of AnalysisWe distinguish between three basic concepts: study, publication and effect size.These concepts are ordered hierarchically (figure 1): study is defined as the datasource or data sample, publications report empirical results that are based on

individual studies, and an effect size is a standardized research outcome which refersto statistics that capture the degree of association between variables (Hedges/Olkin1985). In our case, the only type of research outcomes are regression coefficients.

Figure 1: Levels of Meta-Analysis

In meta-analysis, single publications can be regarded as the sampling units andreported effect sizes can be regarded as the units of analysis. The state of researchcould be related to the study level.

It is important to note that empirical results might be valid only for specific subgroups.Sometimes, divorce risks are reported for West or for East Germany or for differentmarriage cohorts. Rather often for every single subgroup several event history modelsare estimated. Each of these models includes a different combination of covariates.


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Consequently, the effect sizes do not only depend on the studies or on thecharacteristics of the underlying sample, but also on the particular subgroup and onthe particular specification of the model.

Altogether 3730 effects have been coded which have been reported for 399 variables -the determinantes of divorce. This huge number of variables results from the fact thatsome of them only differ with respect to value categorization or reference groups,although they measure the same theoretical concept. The variables and their effectshave been estimated in 515 models (Cox-model 71.3%; sickle model 11.8%;exponential model 9.7%; generalized log-logistic model 4.1%; remaining modelspecifications 3.1%). On an average, 7.2 covariate effects have been observed foreach model and 9.3 covariate effects were counted for each variable.

2.3 Collecting and Coding DataIt is not only justified to collect data on reported statistical results like singlecoefficients, levels of significance, or standard errors. As study characteristics mightaffect statistical results and therefore account for their heterogeneity, also studyvariables like type of institutional affiliation, type of financial support, or year of startand end of the project are of interest (Lipsey 1994; Lipsey/Wilson 2000).

In all publications divorce rates are analyzed by multivariate methods of event-analysis. However, each analysis is based on different variables. The theoretical andtechnical problem is to identify, to define and to sort this variety of variables and toassign effect sizes. It was necessary to develop a detailed schema which mergesvariables of the same meaning, operationalization and reference group. Based on 15divorce studies, a preleminary classification was developed. The categorizationschema broadly followed the Thesaurus Social Sciences of the InformationszentrumSozialwissenschaften (1999) that uses eight categories: demography and other;marriage, family or kin and other networks; education; occupation; religion; nationality;

spatial environment; property. Each of these categories was further divided intoseveral subgroups. Altogether, 399 codes had been assigned which means that weidentified 399 different determinants of divorce.

The hierarchical arrangement of data corresponds to a special type of data storageand data organization. Instead of storing data in an inappropriate rectangle matrix,which is done by MS-EXCEL or SPSS, we made use of a relational database. It allowsa more flexible use of data, and data retrieval account for different levels of analysis.A detailed description of data coding and data organization is given by Wagner/Wei


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(2001) and Wei (2001). The statistical analyses have been realized by the softwareR: A Language for Data Analysis and Graphics (Ihaka/Gentleman 1996). Some ofthe already existing analysis functions could be taken over, in other cases theprogramming of new functions was necessary.

2.4 Data AnalysisData analysis is performed in four steps: preparation of data, integration of effectsizes, tests for homogeneity and detailed subgroup analysis. The outcome of effectsize integration is a set of different and pooled divorce factors. An analysis ofgraphical curves has not been realized (Wei 2001). Integration will be done by usingtwo different methods: vote-counting and calculating mean effect sizes.

2.4.1 Vote-countingVote-counting is somewhere in between qualitative and quantitative review. It countssignificant positive, significant negative and non-significant effects. The modalcategory is regarded to be the best estimator concerning the direction of the effectbetween the independent and the dependent variable (Light/Smith 1971).

This method shows some serious statistical shortcomings (Fricke/Treinies 1985;Hedges/Olkin 1985; Wolf 1986). Additionally, Glass (1976) points out that vote-counting does not consider the magnitude of the correlation between two variables.

2.4.2 Estimation of mean effect sizesMany authors describe meta-analytical methods for pooling bivariate statistics (e.g.correlation coefficients, rank order correlations etc.) (Bortz/Dring 1995). Lessinformation exists on synthesizing regression coefficients from multivariate eventhistory models (cf. Greenland 1987). Many meta-analysts use such regressioncoefficients without giving any reasons (Karney/Bradbury 1995; Amato/Keith 1991;Amato 2001).

Another difficulty has to do with the aggregation of effect sizes that stem from modelsthat are differently specified. Coefficients from bivariate or multivariate methods differaccording to their magnitudes and standard errors. Following Lipsey/Wilson (2001),meta-analysis misses adequate procedures of multivariate result integration (e.g.factor analysis or multiple regression). Only very few authors discuss thismethodological problem (Amato 2001; Lipsey/Wilson 2001: 67 ff. and other meta-analyses cited in this book).


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Some authors simply aggregate effect sizes of coefficients from multivariate models.For example t- and p-values can be transformed into a correlation coefficient r in orderto get a comparable effect size (Amato/Gilbreth 1999; Karney/Bradbury 1995). We donot know of any meta-analysis that ignores an effect size because coefficients were

estimated in multivariate models. Because it is common to aggregate effect sizeswhich is related to different subgroups (cohorts, geographical regions, years), andwhich also estimates different parameters, it is reasonable to use this method. In thepresent study we exclusively use regression coefficients. The pooled effect sizes arerealized through the computation of the weighted means of all effect sizes. In thiscontext, three requirements are important :

a) It is only meaningful to aggregate effect sizes if at least two individual effectsizes are documented;

b) effect sizes have to be statistically independent (Fricke/Treinies 1995;Lipsey/Wilson 2000);

c) effect sizes are weighted according to their reliability.

A consequence of the first requirement is that only a small sample of all variables isincluded in meta-analysis (see below). To realize condition b), it is important only tointegrate those effect sizes that are derived from different studies or subsamples. Tomeet these criteria, in a first step effect sizes for similar variables are aggregated foreach study. In a second step mean effect sizes are pooled across studies(Beelmann/Bliesener 1994; Bortz/Dring 1995).

To achieve the third requirement, we weighted the single effect sizes by their inversevariance (the squared standard error) of each effect size. As suggested by manyauthors, we use the weighted arithmetic mean (Hedges/Olkin 1985; Lipsey/Wilson2000; Normand 1999; Shadish/Haddock 1994).Hence, larger weights are assigned toeffect sizes from studies with smaller variances and larger within-study sample sizes(Shadish/Haddock 1994). Effect sizes based on a large sample show a higher

reliability and will therefore get higher weights.

The mean effect size , weighted by their inverse variance v i is calculated for n E S

independent effects sizes ES i as follows:

, where . E S w E S

w

i ii

n

ii

n=

=

=

1

1

wv S E

i

i

= =

1 12


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The inverse variance v i is a weight assigned to the study and equals the inversesquared standard error (see appendix).

2.4.3 Effect size distributionsTwo distribution models of effect sizes have to be distinguished. The fixed effects model assumes all effect sizes to come from one study population. It thus estimatesonly one population effect size and differences of effect sizes between studies areignored. The random effects model assumes the population parameters to berandomly distributed and located around a so-called superpopulation. The totalvariance of effect size estimates reflects both a study-within-variance and a study-between-variance (Shadish/Haddock 1994):

(see appendix) .v vi i* = +

2

In the present case, the pooled effect sizes are expected to be heterogeneous,because the different effect sizes are based on different subgroups or modelspecifications (cf. above). Especially, the integration of partial coefficients is notsuccessfully solved. Coefficients from different models do not estimate the sameparameter. Therefore, we particularly make use of random effects models and expectresults of strong heterogeneity. We cannot address the question to what extent

heterogeneity analyses could assess how the variety of model specifications affect themean effect size.

Homogeneity tests are applied to decide whether a distribution model with random orwith fixed effects is appropriate. In many cases these tests are based on the so-calledQ-statistic (cf. Hedges/Olkin 1985; Normand 1999; White 1999). We do not considerother homogeneity tests like for example the Likelihood Ratio Test (Hedges/Olkin1985). With k-1 degrees of freedom, the Q-statistic follows a Chi 2 distribution with k effect sizes:

.Q w E S E S i ii

k

= =

( )21

If Q exceeds the critical value of the Chi 2 distribution, the null hypothesis of ahomogeneous distribution has to be rejected. Hence, the distribution of effect sizeswould be assumed to be heterogeneous. It would be possible to conduct furtheranalyses that identify the determinants of heterogeneity. Those analyses are restricted


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to large sample sizes and could therefore not be applied in the present study. Instead,we compute the weighting factor as the weighted average mean based on a randomeffects model.

2.4.4 Estimation of weightsSerious problems emerge if publications do not report sufficient information to conducta meta-analysis. This is especially true in case of missing standard errors of the effectsizes: only nine publications (21.4 percent of all publications) report standard errors ort-values. The remaining publications only offer information about significance levelsusing the well known star symbolism. To estimate the standard errors the giveninformation should be used at the best possible degree. Therefore, different estimationmethods can be found which basically refer to three different levels of information:

(1) At best, publications report exact information on standard errors, and the methodsdescribed in section 2.4.2. can be applied. Only effect sizes of the same type can beaggregated (

- or -coefficients). We decided to aggregate

-coefficients. Hence, -coefficients had to be converted following

=ln( ) with SE=

/t , where t= /SE .

(2) The equation above can also be used if t-values are reported. There is nodifference between - or

-coefficients, because the computation of a t-value does notdepend on effect size types.

(3) As already stated, some publications only report intervals of significance levels,e.g. 0.01 < p < 0.05 . In this case, the appropriate z-value can still be computed (thatis the upper bound of the interval) and we get SE=

/Z .

We define effect sizes as non-significant if no significance levels are reported.Following Rosenthal (1991), we assign a p -value of 0.5 and the corresponding z -valueof 0.0 (one-tailed) as non-significant. In our case, a two-tailed question is given, so

that z is set to 0.67. The estimation of the standard error can only be done veryroughly. Another method is to set

-coefficients to zero. It is not known which of thetwo methods produces less errors.

The whole decision process of finding an appropriate estimation procedure can bevisualized as a flowchart (figure 2). It also includes the so-called percent effects thatcan be computed from ( -1) x 100 .The figure shows the three already mentionedinformation levels which follow a hierarchical order. Within these three levels, it isimportant to distinguish between types of effect sizes in order to choose the


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appropriate estimation method. To avoid confusion not all connections are shown(instead we use an encircled A).


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Star t

S t a n da r d e r r o r s ( S E ) o r o t h e r

useful statistics for computingweights

Informat ion o ns tandard er rors?

-effec t?

-effec t?

Which type ofeffect?

%-effec t?

Square SE and weight ' s

( 1) t = /S E(2 ) =ln( )(3) SE=/ t

(1 ) =%/100+1( 2 ) t= /S E(3 ) =ln( )(4) SE=/ t

t -va lues?

-effec t?

-effec t?

%-effec t?

(1 ) =ln( )(2) SE=/ t

(1 ) =%/100+1(2) =ln( )(3) SE=/t

SE =/ t

p-va lues?

-effec t?

-effec t?

%-effec t?

(1 ) =ln( )(2) SE=/ z

(1 )=%/100+1(2) =ln( )(3) SE=/ z

SE =/ z

W h i c h t y p e o feffect?

Which type ofeffect?

A

A

A

A

A

Aye s

ye s

ye s

ye s

ye s

ye s

ye s

ye s

ye s

ye s

ye s

no no

ye sye s

no

n o

n o

no

no

En d

Figure 2: Flow chart of the process of estimating standard errors

3 Theories of marital stability and results of the meta-analysis

The results of the meta-analyses are presented in three steps. First, the sample isdescribed. Second, we report the results for the divorce risks in detail. Only those


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proposed by Schtz, Berger/Luckmann and Goffmann. Marriage frames are relativelystable mental models of a marriage which offer basic orientations for the spouses. Theexistence of a frame of a good marriage is an important condition for maritalinvestments which in turn strengthen the frame. If the frame loses relevance caused by

serious marital problems, the frame gets redefined in a kind of self-dynamic process.Now, the stability of marriage depends on the utility balances made up by the twopartners.

We consider the household economy to be the theory of divorce which was quotedmost often. In fact, only a crude rating of the theoretical orientations was possible. Butmicroeconomic theory has been accentuated in more than half of the publications,whereas exchange theory only in every tenth of all publications. In nearly 30% of allpublications, we could not identify a definite theoretical framework. Despite of manyauthors do not develop specific hypotheses, it seems to be obvious that Germandivorce research favors microeconomic theory.

3.2 SampleOnly independent effect sizes should be synthesized in meta-analysis. As thepublications are rooted in seven single studies a maximum of seven effects pervariable can be integrated. Effect size were pooled if the corresponding effect wasreported at least in two cases.

As table 2 shows, 399 variables stem from 42 publications. For 336 variables only one independent effect size has been observed. We disregard these variables for tworeasons. First, the number of variables would have been oversized. Second, it isquestionable whether effects which have not been replicated are important(Karney/Bradbury 1995). For the remaining 63 variables, between two and fiveindependent effect sizes have been observed. Thus, no variable has been used eitherin all or in six of the seven studies. Out of the 63 variables with more than one

independent effect size, 45 went into the meta-analysis. This reduction resulted fromthe fact that some variables had different reference categories, whereas othervariables had been aggregated to a more general variable. Also the gender variablewas sorted out as it is only useful for methodological reasons. The remaining 45variables produced 1550 effects which resulted in 136 independent effect sizes aftertheir aggregation at the study level.


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Table 2: Divorce factors (in %) by number of independent effect sizes

Number of independenteffect sizes

1 2 3 4 5 6 7 Total

Divorce factors (in %)(n) 84,2(336) 9,3(37) 3,3(13) 2,3(9) 1,0(4) 0 0 100(399)

3.3 Integrated divorce risks

The results of the meta-analysis are presented in table 3. Variables have beengrouped according to theoretical concepts. These classifications are hypothetical andcannot always been justified in a satisfying way. Only very few of the publications we

analyzed included explicit arguments about the assignment of variables to theoreticalconstructs (for example Brderl/Kalter 2001).

In addition to that, variable descriptions often are far from being optimal. Variables arenot described precisely in nearly one-third of the publications. Sometimes the meaningof variables is not clear, sometimes the categories of the variables are not at all or notcorrectly explained. In most of these cases, other publications are mentioned that aresupposed to offer more detailed information about the variables. Hence, we tried tofind missing variable information in other publications. Sometimes, data coding had tooperate with plausible assumptions about missing variable information.

Initially, calculations are made for all determinants of divorce applying a fixed effectsmodel. In case of heterogenous effect sizes, integrated effects are reported that arebased on a random effects model.


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Table 3: Pooled divorce risksFixed effects model Random effects model

Divorce risk k n sig 0 beta in % sig SE beta in % sig Premarital information about the spouse

Premarital cohabitation 5 74 48 13 0 61 0,098 10,296 *** 0,010 0,138 14,798 0,09Duration of cohabitation 2 9 4 4 2 3 0,002 0,200 0,005 Duration until start of relationship 2 8 7 8 0 0 -0,094 -8,972 *** 0,013 Duration until common household 2 11 10 11 0 0 -0,022 -2,176 *** 0,004 -0,123 -11,574 0,113

Search costsEarly marriage (marriage before 21) 4 31 28 0 0 31 0,647 90,980 *** 0,037 0,711 103,603 *** 0,099Child birth at time of marriage 3 10 8 8 0 2 -0,394 -32,565 *** 0,038 -0,454 -36,492 0,3Age at marriage 5 66 52 63 0 3 -0,011 -1,094 *** 0,001 -0,044 -4,305 ** 0,Wifes age at marriage 5 87 73 81 1 5 -0,056 -5,446 *** 0,003 -0,070 -6,658 *** 0,0Husband s age at marriage 3 67 24 63 1 3 -0,019 -1,911 *** 0,002 -0,023 -2,274 *** 0,00Wife s age at start of relationship 2 5 3 3 0 2 -0,048 -4,687 *** 0,007 -0,031 -3,052 0,04Husbands age at start of relationship 2 5 2 4 0 1 -0,023 -2,274 *** 0,007

Marital investments Birth of first child 4 60 40 56 0 4 -0,107 -10,147 *** 0,013 -0,259 -22,818 ** 0Birth of second child 4 27 13 25 0 2 -0,015 -1,489 0,010 -0,039 -3,825 0,0Birth of third child 4 19 7 10 0 9 -0,004 -0,399 0,034 -0,019 -1,882 0,Common parenthood 4 73 49 69 0 4 -0,167 -15,380 *** 0,015 -0,518 -40,429 *** 0,1Number of children 4 41 37 38 0 3 -0,235 -20,943 *** 0,019 -0,210 -18,942 ** 0,0Premarital birth 5 79 25 30 2 47 -0,003 -0,300 0,004 0,021 2,122 0,0Common home-ownership of the spouses 2 42 27 41 0 1 -0,456 -36,619 *** 0,035 -0,776 -53,976 ** 0,371 Home-ownership 3 31 29 31 0 0 -0,797 -54,932 *** 0,052 -0,832 -56,482 *** 0,

External barriers Catholic 3 13 12 13 0 0 -0,411 -33,701 *** 0,056 Number of church attendances 2 17 14 14 0 3 -0,031 -3,052 *** 0,008 -0,086 -8,241 0,065


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Church wedding 2 29 27 29 0 0 -0,497 -39,165 *** 0,039 Reform of divorce law 3 10 4 10 0 0 -0,426 -34,688 *** 0,100 -0,502 -39,468 ** 0,2

Division of labor Not employed 4 35 11 13 0 22 -0,007 -0,698 0,009 0,013 1,308 0,2

Wifes employment 2 33 24 6 0 27 0,221 24,732 *** 0,023 Husbands employment 2 19 17 17 0 2 -0,569 -43,391 *** 0,073 -0,137 -12,803 0,67

Social context Year of marriage 4 50 46 2 0 48 0,024 2,429 *** 0,002 0,015 1,511 0,Large city 2 61 48 0 0 61 0,317 37,300 *** 0,021 0,362 43,620 *** 0Size of birthplace 2 6 4 2 0 4 0,011 1,106 0,018 0,236 26,617 0,2Marriage in GDR 4 22 18 5 0 17 0,127 13,542 *** 0,046 0,316 37,163 0,

Homogamy Educational homogamy 2 30 18 30 0 0 -0,308 -26,508 *** 0,035 -0,696 -50,142 0,43Wife is better educated than husband 3 10 10 6 0 4 0,000 0,000 0,033 0,373 45,208 0,262 Both catholic 2 22 8 18 0 4 -0,053 -5,162 *** 0,015 -0,192 -17,469 0Wife older than husband 2 18 0 5 0 13 -0,004 -0,399 0,014

Social and personal resources High level of fathers education 2 23 17 1 1 21 0,485 62,418 *** 0,051 0,497 64,378 *** 0,0Wife s education in years 2 30 14 11 1 18 0,003 0,300 0,002 0,027 2,737 0,03Husbands education in years 2 27 4 21 2 4 -0,009 -0,896 ** 0,004 Abitur 4 34 5 13 0 21 0,006 0,602 0,009 0,197 21,774 0Mittlere Reife 3 24 12 11 0 13 0,010 1,005 0,014 0,192 21,167 0,Educational level of wife: Abitur 2 6 0 1 0 5 0,023 2,327 0,026

Transmission of divorce risk Parent s divorce 5 90 71 5 0 85 0,432 54,034 *** 0,023 0,415 51,437 *** 0,Grown up without biological parents 2 50 14 3 0 47 0 ,028 2,840 *** 0,009 0,249 28,274 0,23Grown up with one parent 2 57 7 30 0 27 0,023 2,327 * 0,014 0,069 7,144 0,07


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Marriage experience First marriage 5 61 32 55 0 6 -0,132 -12,366 *** 0,024 -0,288 -25,024 *** 0,1Remarriage 3 28 12 1 0 27 0,323 38,127 *** 0,056

*p


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Tabelle 4 : Divorce risksDeterminant Code AnnotationPremarital informationabout the spousePremarital cohabitation d Spouses were living together for at least four months before

marriage. Some authors estimate effect sizes for nonpremarital cohabitation. Because of dummy coding, thisvariable has been multiplied by -1 and now represents theeffect size for premarital cohabitation.

Duration of cohabitation m Duration of cohabitation in yearsDuration until start ofrelationship

m Time between first aquantance and start of the relationshipin years

Duration until commonhousehold

m in years

Search costsEarly marriage (marriage

before 21)

d At least one of the spouses is younger than 21 years at the

time of marriage.Child birth at time ofmarriage

d

Age at marriage m in yearsWifes age at marriage m in yearsHusband s age at marriage m in yearsWifes age at start ofrelationship

m in years

Husbands age at start ofrelationship

m in years

Marital investments

Birth of first child d time dependent covariateBirth of second child d time dependent covariateBirth of third child d time dependent covariateCommon parenthood d Both spouses are biological parents for at least one of the

childrenNumber of children m In one out of four cases the variable is time dependent

codedPremarital birth d Birth of first child before marriageCommon home-ownershipof the spouses

d

Home-ownership d

External barriers Catholic d Respondent belongs to the catholic church at the time of

interviewNo. of church attendances m Frequency of church attendance is coded 1 (never) to 5

(weekly attendances)Church wedding dReform of divorce law d Coded as 1 if year of marriage is 1977 or 1978, otherwise 0.

Division of laborNot employed d The respondent was either not or never employed. To

increase the number of cases, the variable employed wasadded and multiplied with the factor (-1). Employment was

coded either time dependently or time independently.


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Determinant Code Annotation

20

Wife s employment d Wife is gainfully employed (partially time dependent)Husbands employment d Husband is gainfully employed (partially time dependent)

Social context

Year of marriage mLarge city d At time of marriage spouses live in a city with at least

100.000 inhabitantsSize of birthplace m Number of inhabitants of birthplaceMarriage in GDR d

HomogamyEducational homogamy d Equal educational level of both spousesWife is better educatedthan husband

d

Both catholic d At the time of interview both spouses belong to the catholicchurch

Wife older than husband d Wife is at least two years older than husbandSocial and personalresourcesHigh level of father seducation

d

Wife s education in years mHusbands education inyears

m

Abitur d Respondents highest educational level is Abitur .Mittlere Reife V/H Resondents highest educational level is Mittlere ReifeEducational level of wife:

Abitur

d

Transmission of divorceriskDivorce of parents d At least one of the spouses experienced a di vorce before

age of eighteenG r o w n u p w i t h o u tbiological parents

d

Grown up with only oneparent

d

Marriage experience

First marriage d Respondents first marriageRemarriage d At least one of the spouses experienced a remarriaged: dummy-coding; m: metric variable; V/H: category of reference: Volks-/Hauptschule


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First, we regard indicators of the level of information about the spouse before marriage : cohabitation, duration of cohabitation, duration of time between first contactand beginning of the relationship, duration of time until the start of a commonhousehold. Whereas the effects of cohabitation and of duration of cohabitation are not

significant, the duration of the premarital relationship (whether the partners have acommon household or not) reduces the risk of divorce. Time duration between thedate of becoming acquainted and the beginning of a relationship is rather important.Each year reduces the divorce risk by about nine percent. It presumably does not onlymatter if a marriage is on trial, but also whether potential partners take their timebefore starting a partnership. Another explanation favours the idea of relationships,which took a long time to be established because social barriers against a partnershipexist. If partnerships are established despite of such barriers this would indicate aspecial seriousness or an outstandingly promising match.

Second, we have indicators of costs for searching a partner : early marriage, age ofmarriage of interviewed person, age of marriage (husband or wife), age of beginninga relationship (husband or wife). It is quite open whether the forced marriage (childbirth at time of marriage, Mussehe) indicates search costs. All of these variables arenegatively related to the divorce rate. The higher the search costs, the more stable isthe marriage. Early marriages get separated very often. Every year of waiting time untilmarriage reduces the divorce risk by four percent. Wifes age at marriage is moreimportant than husbands age at marriage.

The third block of variables are assumed to indicate the amount of marital investments . Marital investments increase the costs for divorce. On the one hand,integrated effect sizes are available for the variables birth of first child, birth of secondchild, birth of third child, common child, number of children and premarital child. Onthe other hand, the variables home-ownership and common home-ownership areincluded. The birth of a second or a third child does actually not affect the divorce risk.Only the birth of the first child affects the stability of marriage, although this effect is

not homogeneous. Thus effect sizes between the studies vary systematically. As theresults show, it is important that the child is a common child of both spouses. If notboth spouses are the parents of the child, the divorce risk is very high.

External barriers against divorce result from social norms that regulate the break up ofmarriages. The influence of the reform of the divorce law, affiliation to the catholicchurch, frequency of church visits, and the church wedding are related to the validityand internalization of these standards. It is almost certain that the affiliation to thecatholic church or a church wedding reduce the divorce risk. If the frequency of church


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attendances is high, we find significant effects only for the model with fixed effects.However, these effects are not homogeneous. Moreover, the new divorce law resultedin a strong reduction of divorce rates during the years 1977/1978.

Also the division of household labor can be understood as a marital investment. Themore efficient the division of labor is, the higher are the gains of marriage. Admittedly,a positive effect of wifes employment on the rate of divorce is only based on twostudies. We do not find significant influences of other variables like non-employmentor husbands employment.

There are a number of variables which can be allocated in an unspecific way to thesocial context or more specific to marital alternatives: Living in a large city, size ofbirth place, marriage in GDR and year of marriage. The rate of divorce is significantlyhigher in large cities, even though the size of birth place is irrelevant. The integratedeffect of the year of marriage, which has been estimated in four studies, positivelyaffects the divorce rate under the assumption of a fixed effects model. However, thismodel is inadequate, obviously relevant differences in effect sizes exist between thestudies. According to the random effects model year of marriage is no longersignificant.

Similar results arise from comparing former East and West Germany. According toofficial statistics, the divorce rate of GDR exceeded that of the FRG. As our resultsshow, this fact is asserted if we follow a model with fixed effects. But a largerheterogeneity of results is ascertained as well, presumably because the effect of thisvariable strongly depends on control variables that are included into the specificmodels. We therefore have to assume a model with random effects, which showsdifferences between East and West to be statistically insignificant.

A number of different indicators capture the amount of social homogamy : wife olderthan husband, educational homogamy, a relatively high level of wifes education, both

spouses being catholic. None of these variables significantly corresponds to the riskof divorce. Hence, no effect of social homogamy on marital stability could be identified.

Only a few measures of the social and economic resources of couples were available:We do have information about the level of education of husband and wife as well as ofthe fathers education. It was not possible to include measures of household orpersonal income into meta-analysis. Whereas the level of fathers education stronglyincreases the divorce risk, husbands level of education is positively related to marital


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stability. The educational level of the wife and the educational level which is notdifferentiated by gender show no significant effects.

Many times the hypothesis of the intergenerational transmission of divorce has been

tested. It presumes a divorce of parents to reduce the marital stability of their children.So far, it is not completely clear why this association exists. For that reason it is notpossible to relate the stability of the parental marriage to a single theoretical construct.The transmission effect sizes have been integrated throughout five studies into astatistically significant mean effect size. The divorce risk increases up to 50% if theparental marriage had been separated. Other variables that measure whether theinterviewed persons grew up either without parents or with only one parent do notreach an integrated effect size which is different from zero.

Finally, also variables concerning the first or the second marriage are listedseparately, without a correspondence to a single theoretical construct. Assumably,these variables capture selection effects. Nevertheless, these variables aremeaningful in a statistical sense: the divorce risk of first marriages is about 25% lowerthan for marriages of a higher order.

4 Summary and discussion

The aim of this paper was to evaluate German divorce studies by means of meta-analytic methods. We discuss the results with respect to

1) the applicability of meta-analysis,2) the evaluation of the present state of research,3) the quality of publications and methods of analyzing divorce risks.

The applicability of meta-analysis in divorce research is limited because of three

problems: the comparability of bivariate and multivariate effects, the calculation ofappropriate weighting factors and the handling of publications whith incomplete data.

Some of these problems could be solved if the quality of research and of publicationswould be improved. Almost all of the evaluated studies present incomplete statisticaldata. Especially unfavourable is that bivariate effects and the standard errors of effectsizes often are not reported.

The present analyses has pointed out that the construction of independent variables


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widely differs between authors. In this situation an integration of results is onlyachievable by a broader definition of categories. Nevertheless, in this case one mightrun into the risk of comparing apples and oranges. Such a procedure can only be

justified if fruits are an appropriate construct. But such theoretical integrative

procedures could possibly also improve the present study. Different measures canalso be an advantage for meta-analysis: the benefit of a meta-analytical integrationresults out of the diversity of studies (Glass 1977). Different operationalizations orresearch contexts enhance the generalization level of the effect to be integrated(Drinkmann 1990).

One might object that the problem of comparing apples and oranges applies tointegrative reviews in general. The special advantage of a quantitative integrationcompared to a qualitative one is indeed to be found in the systematic and explicitprocedure. For instance, a quantitative review allows an analysis of study differencesand of their influence on meta-analytical results.

These points in mind one has to be careful when evaluating the state of research. Weare far away from an adequate testing of a theory of marital stability. Only selectedconstructs or single hypotheses from exchange or microeconomic theory have beenconsidered in empirical research. Our meta-analysis clearly shows that variablesinfluence the divorce risk that are related to search costs, marital investments andexternal barriers. The division of labor between spouses, social homogamy, and ownresources really do not affect the risk of divorce. In contrast, the transmissionhypothesis is clearly supported, and first marriages are more stable than marriages ofa higher order. However, it is in turn not very evident how these empirical associationscan be interpreted in the light of exchange or microeconomic theory.

Very few attempts have been undertaken to measure the opportunities of remarriagesor more general the alternatives to an existing marriage. These central hypotheticalconstructs that are part of all divorce theories were only measured in a very crude way

through variables like year of marriage, size of place or marriage in the GDR or FRG.The effects of marriage cohort or of East/West marriage are very heterogenous.Obviously, effect sizes of these variables strongly depend on model specifications.

The quality of divorce research does not only show the already mentionedshortcomings. Research is hardly organized in a cumulative way. Replications are notreally done and much too often different variables and measures are used. Newstudies are carried out without relating them systematically to the results of alreadyexisting research. Meta-analysis should become part of the methodological canon in


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sociology. This would be facilitated by an improvement of research and a higherquality of publications. If the future development of sociology will be similar to that inthe medical sciences or in psychology, the demand for meta-analyses will stronglyincrease also in sociology. As many studies from the US show, meta-analysis is

possible and necessary within sociology and the need for its application will increasethe more studies and publications on a certain topic are available.


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3 Identification number of each publication can be found in square brackets.

31

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Babka von Gostomski, Ch., 1998: Machen Kinder Ehen glcklich? Eine empirischeUntersuchung mit der Mannheimer Scheidungsstudie zum Einfluss von Kindern auf

das Ehescheidungsrisiko. Zeitschrift fr Bevlkerungswissenschaft 23: 151-177. [2]3

Babka von Gostomski, Ch./Hartmann, J./Kopp, J., 1998: SoziostrukturelleBestimmungsgrnde der Ehescheidung: Eine empirische berprfung einigerHypothesen der Familienforschung. Zeitschrift fr Soziologie der Erziehung undSozialisation 18: 117-133. [1]

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Brderl, J./Diekmann, A./Engelhardt, H., 1997: Erhht eine Probeehe dasScheidungsrisiko? Eine empirische Untersuchung mit dem Familiensurvey. KlnerZeitschrift fr Soziologie und Sozialpsychologie 49: 205-222. [4]


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Brderl, J./Diekmann, A./Engelhardt, H., 1999: Premarital Cohabitation and MaritalStability in Western Germany.http://www.sowi.uni-mannheim.de/lehrstuehle/lessm/papers/kohab.pdf (28. September2000). [19]

B r d e r l , J . / D i e k m a n n , A . / E n g e l h a r d t , H . , 1 9 9 9 : A r t e f a k t e i n d e rScheidungsursachenforschung? Eine Erwiderung auf einen Artikel von YaseminNiephaus. Klner Zeitschrift fr Soziologie und Sozialpsychologie 51: 744-753. [24]

Diefenbach, H., 1999: Geschichte wiederholt sich nicht!? Der Zusammenhang vonEhescheidung in der Eltern- und in der Kindgeneration. pp. 91-118 in: T. Klein/Kopp,J. (Eds.): Scheidungsursachen aus soziologischer Sicht. Wrzburg: Ergon.[35]

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Diekmann, A./Engelhardt, H., 1995: Die soziale Vererbung des Scheidungsrisikos:Eine empirische Untersuchung der Transmissionshypothese mit dem deutschenFamiliensurvey. Zeitschrift fr Soziologie 24: 215-228. [5]

Diekmann, A./Engelhardt, H., 1999: The Social Inheritence of Divorce: Effects ofParent' sFamily Type in Postwar Germany. American Sociological Review 64:783-793. [16]

Diekmann, A./Klein, T., 1991: Bestimmungsgrnde des Ehescheidungsrisikos. Eineempirische Untersuchung mit den Daten des soziokonomischen Panels. KlnerZeitschrift fr Soziologie und Sozialpsychologie 43: 271-290. [23]

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GDR and FRG. Berlin: Max-Planck-Institut fr Bildungsforschung. [6]

Esser, H., 1999: Heiratskohorten und die Instabilitt von Ehen. pp. 260-288 in: J.Gerhards/R. Hitzler (Eds.): Eigenwilligkeit und Rationalitt sozialer Prozesse.Opladen: Westdeutscher Verlag. [18]

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(Eds.): Familie und Lebensverlauf im gesellschaftlichen Umbruch. Stuttgart: Enke. [10]

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Klein, T./Stauder, J., 1999: Der Einfluss ehelicher Arbeitsteilung auf die Ehestabilitt.pp. 159-177 in: T. Klein/J. Kopp (Eds.): Scheidungsursachen aus soziologischer Sicht.Wrzburg: Ergon. [31]

Klein, T./Niephaus, Y./Diefenbach, H./Kopp, J., 1996: Entwicklungsperspektiven vonElternschaft und ehelicher Stabilitt in den neuen Bundeslndern seit 1989. pp. 60-81in: W. Bien (Ed.): Familie an der Schwelle zum neuen Jahrtausend. Wandel undEntwicklung familialer Lebensformen. Opladen: Leske + Budrich. [39]

Klein, T./ Esser, H./ Babka von Gostomski, Ch./Hartmann, J./Jinschek, R./Keller, M./ Kopp, J., 1997: Abschlussbericht des Forschungsprojektes Determinanten derEhescheidung" 1995 bis 1997. Mannheim: Mannheimer Zentrum fr europischeSozialforschung. [41]

Kopp, J., 1997: Die Notwendigkeit von Paarinformationen: Empirische Ergebnisse derScheidungsforschung und ihre theoretische Begrndung. pp. 57-84 in: J. Kopp (Ed.):Methodische Probleme der Familienforschung. Zu den praktischen Schwierigkeitenbei der Durchfhrung einer empirischen Untersuchung. Frankfurt/Main: Campus. [25]

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fr Bevlkerungswissenschaft 23: 39-54. [42]

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Stauder, J., 2000: Eheliche Arbeitsteilung und Ehestabilitt. Dissertation. Heidelberg.[22]

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Allmendinger/J. Huinink (Eds.): Vom Regen in die Traufe: Frauen zwischen Beruf undFamilie. Frankfurt/Main: Campus. [13]

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Perspektive des Lebensverlaufs. pp. 372-393 in: A. Diekmann/S. Weick (Eds.): DerFamilienzyklus als sozialer Proze. Bevlkerungssoziologische Untersuchungen mitden Methoden der Ereignisanalyse. Berlin: Duncker & Humblot. [14]

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AppendixAs mentioned in section 2.4.2 it is necessary to use independent effect sizes forintegration. Therefore calculation of weighted means will be done in a two-stageprocess. At the second stage standard errors are computed as follows:

, with k number of studies.SE w

E S

ii

k =

=

1

1

The between-studies variance (cf. section 2.4.3) is calculated as follows :2

mit . ( )

2 1= Q k

cc w

w

wi

ii

k

ii

k i

k

= =

=

=

2

1

1

1

Meta-Analysis Divorce German

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