Paper prepared for the conference on
“Divorce in Cross-National Perspective: A European Research Network”
European University Institute, Florence, Italy
November 14 & 15, 2002
DRAFT
A Meta-Analysis of German Research on Divorce Risks
Michael Wagner
and
Bernd Weiß
Research Institute for Sociology
University of Cologne
Greinstr. 2
50939 Cologne
mwagner@wiso.uni-koeln.de
bernd.weiss@wiso.uni-koeln.de
Abstract
The aim of the paper is to evaluate divorce studies in Germany and to apply metaanalytic techniques in order to summarize the results of this research. Literature
research identified 42 studies published between 1987 and 2001. These studies use
longitudinal data from seven projects and all studies estimate event history models
with the divorce rate as dependent variable. In sum, they examine 399 different risk
factors and report 3730 effects. Results of the meta-analysis are threefold. First, there
are methodological problems in the field of meta-analysis that are not resolved in a
very satisfactory way. Second, no theory of divorce has been tested in detail, rather
single hypotheses have been examined which were derived from exchange or
microeconomic theory. Third, divorce research can be improved by a more cumulative
design which means that we need more studies conducting a replication of existing
empirical findings.
1
1 Problem1
During the past twenty years German sociology experienced a boom of divorce
studies. This development was mainly caused by methodological innovations that
enabled a reliable longitudinal assessment of marital histories, e.g. retrospectively in
life course research or prospectively in panel studies. The aim of this paper is to
evaluate the studies on divorce risks in Germany. So many divorce risks have been
reported that it became unclear what we really know about the determinants of marital
instability (Hartmann 1989; Dorbritz/Gärtner 1998). Which theories or hypotheses
have been confirmed by empirical findings? Is research undertaken cumulatively? Are
empirical 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 serious
ones result from non-systematical and incomplete literature research as well as from
an inadequate integration and interpretation of diverging quantitative results
(Wagner/Weiß 2001). In order to overcome these disadvantages, we apply metaanalytic methods. Besides primary and secondary research, this method stands for a
third type of empirical social research. Meta-analysis is primarily concerned with the
quantitative integration of published empirical findings (Glass 1976). However, it
allows not only their integration but also the explanation of their heterogeneity.
Meta-analysis is rather unknown, especially in German sociology. Only Künzler (1994)
and Engelhardt (2000) mention it, the latter as part of a survey of study designs in
demography. Some others call their study a meta-analysis, as in fact they summarize
characteristics of numerous publications, but without systematically investigating
quantitative results (Bretschneider 1997; Hartmann 1999). In other disciplines than
sociology, like medical science, psychology and educational science, meta-analysis
has 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 „Evidence
Based Medicine“ has already been institutionalized (Altman 2000; Petitti 2000; Sutton
et al. 2000). Numerous handbooks and monographies on meta-analysis underline the
importance of this research area (Bortz/Olkin 1985; Hunter/Schmidt 1990;
Lipsey/Wilson 2001; Rosenthal 1991; Schultz-Gambard 1987; Sutton et al. 2000).
1
This research was supported by the German Science Foundation from July
2000 to July 2001 (WA 1502/1-1). We thank Hans-Peter Blossfeld (Bamberg) for
helpful comments on an earlier version of the manuscript.
2
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 by
Cooper (1982):
1. Problem/research question
2. Literature research
3. Data evaluation and coding
4. Data analysis
5. Presentation of results
2.1 Literature Research
The population of our meta-analysis is defined as the totality of empirical studies from
Germany investigating marital stability and using the divorce rate as the dependent
variable. These studies use longitudinal data on marriages and partnerships. Before
1990, only studies of West Germany, after 1990 studies of West and East Germany
were included.
A comprehensive literature research is necessary for any meta-analysis, including all
types of publications and research reports. A detailed description of literature research
procedures 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 social
science 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 research
was finished in spring 2001 (for details see Wagner/Weiß 2001; Weiß 2001).
Finally, 42 publications could be identified that matched the search criteria. They were
published 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 of
the Mannheim Research Project „Determinants of Divorces“ had been released.
In Germany, the relevant divorce studies use data samples from seven larger projects
of the Social Sciences. These are the Mannheim Research Project ‘Determinants of
Divorce’, the German Socio-Economic Panel, the Family Survey of the German Youth
Institute, the German Life History Study (Max Planck Institute for Human
3
Development), the Family and Fertility Survey of Germany, the General Social Survey
of the Social Sciences and the Cologne Longitudinal Study of Gymnasium graduates.
Most of the publications are taken from the Mannheim Research Project, followed by
the Family Survey (Table 1).
Table 1: Number of publications by year of publication and study
Year
Study
DoD1
GSEP
FS
GLHS
FFS
GSS
1987
0
0
0
0
0
1
1989
0
1
0
0
0
0
1991
0
1
0
1
0
0
1992
0
3
0
0
0
0
1993
0
0
0
1
0
0
1994
0
1
0
0
0
0
1995
0
0
2
0
0
0
1996
0
0
1
0
0
0
1997
3
0
2
1
0
0
1998
2
1
1
0
2
0
1999
10
0
4
1
0
0
2000
2
0
1
0
0
0
2001
0
0
0
0
0
0
Total
17
7
11
4
2
1
Total2
KLS
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
3
1
1
2
1
6
6
15
3
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 Life
History Study (MPI, Berlin); FFS: Family and Fertility Survey; GSS: General Social Survey of the Social
Studies; KLS: Cologne Longitudinal Study of Gymnasium Graduates.
2
Klein‘s (1999; No. 32 and 33) study has been counted twice, so the total number of publications has
been artificially increased by an additional publication.
Literature research revealed a number of anomalies. We ignored double publications
of identical or nearly identical texts (cf. publication No. 232 and Diekmann/Klein 1993
as well as publication No. 2 and Babka von Gostomski 1999). If a paper has been
published 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 is
possible that publications include empirical results which are based on two different
samples. These publications have been registered as two independent cases (cf.
publications No. 32 and 33).
2
See the number of identification as it is found in the bibliography of the studies
that have been included in the meta-analysis.
4
2.2
Levels of Analysis
We distinguish between three basic concepts: study, publication and effect size.
These concepts are ordered hierarchically (figure 1): ‘study’ is defined as the data
source or data sample, ‘publications’ report empirical results that are based on
individual studies, and an ‘effect size’ is a standardized research outcome which refers
to statistics that capture the degree of association between variables (Hedges/Olkin
1985). In our case, the only type of research outcomes are regression coefficients.
Figure 1: Levels of Meta-Analysis
S tudy
Sampling unit
P ublicatio n A
Unit of analysis
P ublicatio n B
S ubgro up A
P ublicatio n C
S ubgro up B
M o del A
M o del B
D ivo rce risk A
E ffect size A
E ffect size A
D ivo rce risk B
E ffect size B
E ffect size B
D ivo rce risk C
E ffect size C
D ivo rce risk D
E ffect size D
E ffect size D
In meta-analysis, single publications can be regarded as the sampling units and
reported effect sizes can be regarded as the units of analysis. The state of research
could 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 different
marriage cohorts. Rather often for every single subgroup several event history models
are estimated. Each of these models includes a different combination of covariates.
5
Consequently, the effect sizes do not only depend on the studies or on the
characteristics of the underlying sample, but also on the particular subgroup and on
the 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 that
some of them only differ with respect to value categorization or reference groups,
although they measure the same theoretical concept. The variables and their effects
have been estimated in 515 models (Cox-model 71.3%; sickle model 11.8%;
exponential model 9.7%; generalized log-logistic model 4.1%; remaining model
specifications 3.1%). On an average, 7.2 covariate effects have been observed for
each model and 9.3 covariate effects were counted for each variable.
2.3 Collecting and Coding Data
It is not only justified to collect data on reported statistical results like single
coefficients, levels of significance, or standard errors. As study characteristics might
affect statistical results and therefore account for their heterogeneity, also study
variables like type of institutional affiliation, type of financial support, or year of start
and end of the project are of interest (Lipsey 1994; Lipsey/Wilson 2000).
In all publications divorce rates are analyzed by multivariate methods of eventanalysis. However, each analysis is based on different variables. The theoretical and
technical problem is to identify, to define and to sort this variety of variables and to
assign effect sizes. It was necessary to develop a detailed schema which merges
variables of the same meaning, operationalization and reference group. Based on 15
divorce studies, a preleminary classification was developed. The categorization
schema broadly followed the ‘ Thesaurus Social Sciences’ of the Informationszentrum
Sozialwissenschaften (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 into
several subgroups. Altogether, 399 codes had been assigned which means that we
identified 399 different determinants of divorce.
The hierarchical arrangement of data corresponds to a special type of data storage
and 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 allows
a 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/Weiß
6
(2001) and Weiß (2001). The statistical analyses have been realized by the software
“R: A Language for Data Analysis and Graphics” (Ihaka/Gentleman 1996). Some of
the already existing analysis functions could be taken over, in other cases the
programming of new functions was necessary.
2.4 Data Analysis
Data analysis is performed in four steps: preparation of data, integration of effect
sizes, tests for homogeneity and detailed subgroup analysis. The outcome of effect
size integration is a set of different and pooled divorce factors. An analysis of
graphical curves has not been realized (Weiß 2001). Integration will be done by using
two different methods: vote-counting and calculating mean effect sizes.
2.4.1 Vote-counting
Vote-counting is somewhere in between qualitative and quantitative review. It counts
significant positive, significant negative and non-significant effects. The modal
category is regarded to be the best estimator concerning the direction of the effect
between 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 votecounting does not consider the magnitude of the correlation between two variables.
2.4.2 Estimation of mean effect sizes
Many authors describe meta-analytical methods for pooling bivariate statistics (e.g.
correlation coefficients, rank order correlations etc.) (Bortz/Döring 1995). Less
information exists on synthesizing regression coefficients from multivariate event
history models (cf. Greenland 1987). Many meta-analysts use such regression
coefficients 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 models
that are differently specified. Coefficients from bivariate or multivariate methods differ
according 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 this
methodological problem (Amato 2001; Lipsey/Wilson 2001: 67 ff. and other metaanalyses cited in this book).
7
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 order
to get a comparable effect size (Amato/Gilbreth 1999; Karney/Bradbury 1995). We do
not know of any meta-analysis that ignores an effect size because coefficients were
estimated in multivariate models. Because it is common to aggregate effect sizes
which is related to different subgroups (cohorts, geographical regions, years), and
which also estimates different parameters, it is reasonable to use this method. In the
present study we exclusively use regression coefficients. The pooled effect sizes are
realized through the computation of the weighted means of all effect sizes. In this
context, three requirements are important :
a)
b)
c)
It is only meaningful to aggregate effect sizes if at least two individual effect
sizes are documented;
effect sizes have to be statistically independent (Fricke/Treinies 1995;
Lipsey/Wilson 2000);
effect sizes are weighted according to their reliability.
A consequence of the first requirement is that only a small sample of all variables is
included in meta-analysis (see below). To realize condition b), it is important only to
integrate those effect sizes that are derived from different studies or subsamples. To
meet these criteria, in a first step effect sizes for similar variables are aggregated for
each study. In a second step mean effect sizes are pooled across studies
(Beelmann/Bliesener 1994; Bortz/Döring 1995).
To achieve the third requirement, we weighted the single effect sizes by their inverse
variance (the squared standard error) of each effect size. As suggested by many
authors, we use the weighted arithmetic mean (Hedges/Olkin 1985; Lipsey/Wilson
2000; Normand 1999; Shadish/Haddock 1994).”Hence, larger weights are assigned to
effect 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 E S , weighted by their inverse variance vi is calculated for n
independent effects sizes ESi as follows:
n
ES =
∑w
i =1
i
× ESi
n
∑w
i =1
, where w i =
i
8
1
1
.
=
vi SE 2
The inverse variance vi is a weight assigned to the study and equals the inverse
squared standard error (see appendix).
2.4.3 Effect size distributions
Two 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 estimates
only one population effect size and differences of effect sizes between studies are
ignored. The random effects model assumes the population parameters to be
randomly distributed and located around a so-called “superpopulation”. The total
variance of effect size estimates reflects both a study-within-variance and a studybetween-variance (Shadish/Haddock 1994):
v i* = σθ2 + v i (see appendix) .
In the present case, the pooled effect sizes are expected to be heterogeneous,
because the different effect sizes are based on different subgroups or model
specifications (cf. above). Especially, the integration of partial coefficients is not
successfully solved. Coefficients from different models do not estimate the same
parameter. Therefore, we particularly make use of random effects models and expect
results of strong heterogeneity. We cannot address the question to what extent
heterogeneity analyses could assess how the variety of model specifications affect the
mean effect size.
Homogeneity tests are applied to decide whether a distribution model with random or
with fixed effects is appropriate. In many cases these tests are based on the so-called
Q-statistic (cf. Hedges/Olkin 1985; Normand 1999; White 1999). We do not consider
other homogeneity tests like for example the Likelihood Ratio Test (Hedges/Olkin
1985). With k-1 degrees of freedom, the Q-statistic follows a Chi2 distribution with k
effect sizes:
Q =
k
∑ w (ES
i
i =1
i
− ES )2 .
If Q exceeds the critical value of the Chi2 distribution, the null hypothesis of a
homogeneous distribution has to be rejected. Hence, the distribution of effect sizes
would be assumed to be heterogeneous. It would be possible to conduct further
analyses that identify the determinants of heterogeneity. Those analyses are restricted
9
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 random
effects model.
2.4.4 Estimation of weights
Serious problems emerge if publications do not report sufficient information to conduct
a meta-analysis. This is especially true in case of missing standard errors of the effect
sizes: only nine publications (21.4 percent of all publications) report standard errors or
t-values. The remaining publications only offer information about significance levels
using the well known ‘ star symbolism’. To estimate the standard errors the given
information should be used at the best possible degree. Therefore, different estimation
methods can be found which basically refer to three different levels of information:
(1) At best, publications report exact information on standard errors, and the methods
described in section 2.4.2. can be applied. Only effect sizes of the same type can be
aggregated ( - 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 no
difference between - or -coefficients, because the computation of a t-value does not
depend 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 (that
is 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-value
of 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 very
roughly. Another method is to set -coefficients to zero. It is not known which of the
two methods produces less errors.
The whole decision process of finding an appropriate estimation procedure can be
visualized as a flowchart (figure 2). It also includes the so-called percent effects that
can be computed from ( -1) x 100.The figure shows the three already mentioned
information levels which follow a hierarchical order. Within these three levels, it is
important to distinguish between types of effect sizes in order to choose the
10
appropriate estimation method. To avoid confusion not all connections are shown
(instead we use an encircled A).
11
Figure 2: Flow chart of the process of estimating standard errors
S ta rt
S ta n d a rd e rr o r s (S E ) o r o th e r
u se fu l sta tistics fo r co m p u tin g
we ig h ts
In fo rm a tio n o n
sta n d a r d e rr o r s?
no
no
t-v a lu e s ?
p - va lu e s?
ye s
ye s
ye s
W h ich typ e o f
e ffe ct?
W h ich typ e o f
e ffe ct?
W h ich typ e o f
e ffe ct?
β-e ffe c t ?
ye s
β-e ffe c t ?
β-e ffe c t ?
ye s
ye s
S E = β/z
S E = β/t
A
ye s
no
no
α-e ffe c t ?
ye s
A
(1 ) t= α/S E
(2 ) β= ln (α)
(3 ) S E = β/t
α-e ffe c t ?
α-e ffe c t ?
no
ye s
ye s
(1 ) β= ln (α)
(2 ) S E = β/t
(1 ) β= ln (α)
(2 ) S E = β/z
A
A
no
% -e ffe c t ?
ye s
(1 )
(2 )
(3 )
(4 )
α=%/100+1
t= α/S E
β= ln ( α)
S E = β/t
A
no
% -e ffe c t ?
% -e ffe c t ?
ye s
S q u a re S E a n d we ig h t β' s
ye s
(1 )
α=%/100+1
(2) β= ln ( α)
(3 ) S E = β/z
(1 ) α=%/100+1
(2) β= ln (α)
(3 ) S E = β/t
A
End
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 is
described. Second, we report the results for the divorce risks in detail. Only those
12
variables are integrated that are related to a common theoretical concept that is an
element of a theory of marital stability. For that reason we shortly present the main
theories of marital stability.
3.1 Theories of marital stability
Based on the theory of action, two approaches are primarly used for explaining marital
stability: exchange theory and microeconomic theory (cf. Engelhardt 2002). Exchange
theory has been founded by George C. Homans, Peter M. Blau, John W. Thibaut and
Harold H. Kelly. It is assumed that actors achieve their aims through an exchange of
material and immaterial resources where rewards are maximized and costs are
minimized. The exchange of resources is regulated by norms of reciprocity and justice
which enhance the progression of trust and commitment (Sabatelli/Shehan 1993).
Exchange theory has been applied to marital stability by Levinger (1965, 1982) and
Lewis/Spanier (1979). It is hypothesized that marital stability depends on the quality of
relationship, on the alternatives to the existing marriage, and on external social
barriers which are opposed to divorce. Marital quality is attributed to social and
personal resources, to satisfaction with the life style, and to rewards of spousal
interaction. In accordance with the microeconomic theory, several authors emphasized
marital investments because they increase the costs for divorce. Couples break up if
the quality of relationship falls below the aspiration level and if the expected gain from
alternatives (for example a relationship with another partner) exceeds the costs of
divorce.
Based on the studies of Gary S. Becker, the microeconomic theory of the family suits
exchange theory in many aspects. Microeconomic theory of divorce assumes persons
to organize their household in such a way that the utility of commodities is maximized.
If the collective utility of marriage is less than the expected utility of the alternatives,
the marriage will be divorced. Among other things, the rewards of marriage are
dependent on the mode of division of labor, investments in marital capital, and the
“partner-match”. If the marriage market would be perfect, partner would have no
reason for leaving their spouses. Because micro-economic theory gives up the the
neoclassical fiction of a perfect market, conceptions like search costs and subjective
insecurity are implemented into the theory. Search costs arise because individuals
need information about potential spouses. At the time of marriage not all qualities of
the partners are known (Hill/Kopp 1995).
Newly, a framing model of marriage has been proposed by Esser (1999, 2002) which
combines microeconomic theory and theories about subjective ‘ realities’ as they are
13
proposed by Schütz, Berger/Luckmann and Goffmann. ‘ Marriage frames’ are relatively
stable mental models of a marriage which offer basic orientations for the spouses. The
existence of a frame of a “good marriage” is an important condition for marital
investments 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 two
partners.
We consider the household economy to be the theory of divorce which was quoted
most often. In fact, only a crude rating of the theoretical orientations was possible. But
microeconomic 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 all
publications, we could not identify a definite theoretical framework. Despite of many
authors do not develop specific hypotheses, it seems to be obvious that German
divorce research favors microeconomic theory.
3.2 Sample
Only independent effect sizes should be synthesized in meta-analysis. As the
publications are rooted in seven single studies a maximum of seven effects per
variable can be integrated. Effect size were pooled if the corresponding effect was
reported 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 two
reasons. First, the number of variables would have been oversized. Second, it is
questionable whether effects which have not been replicated are important
(Karney/Bradbury 1995). For the remaining 63 variables, between two and five
independent effect sizes have been observed. Thus, no variable has been used either
in 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 from
the fact that some variables had different reference categories, whereas other
variables had been aggregated to a more general variable. Also the gender variable
was sorted out as it is only useful for methodological reasons. The remaining 45
variables “produced” 1550 effects which resulted in 136 independent effect sizes after
their aggregation at the study level.
14
Table 2: Divorce factors (in %) by number of independent effect sizes
Number of independent
effect sizes
Divorce factors (in %)
(n)
1
2
3
4
5
6
7
Total
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 been
grouped according to theoretical concepts. These classifications are hypothetical and
cannot always been justified in a satisfying way. Only very few of the publications we
analyzed included explicit arguments about the assignment of variables to theoretical
constructs (for example Brüderl/Kalter 2001).
In addition to that, variable descriptions often are far from being optimal. Variables are
not described precisely in nearly one-third of the publications. Sometimes the meaning
of variables is not clear, sometimes the categories of the variables are not at all or not
correctly explained. In most of these cases, other publications are mentioned that are
supposed to offer more detailed information about the variables. Hence, we tried to
find missing variable information in other publications. Sometimes, data coding had to
operate with plausible assumptions about missing variable information.
Initially, calculations are made for all determinants of divorce applying a fixed effects
model. In case of heterogenous effect sizes, integrated effects are reported that are
based on a random effects model.
15
Table 3: Pooled divorce risks
sig <0
Divorce risk
Premarital information about the spouse
Premarital cohabitation
Duration of cohabitation
Duration until start of relationship
Duration until common household
k
n
5
2
2
2
74 48 13
9 4 4
8 7 8
11 10 11
0 61 0,098 10,296 *** 0,010
2 3 0,002 0,200
0,005
0 0 -0,094 -8,972 *** 0,013
0 0 -0,022 -2,176 *** 0,004
Search costs
Early marriage (marriage before 21)
Child birth at time of marriage
Age at marriage
Wife‘ s age at marriage
Husband‘ s age at marriage
Wife‘ s age at start of relationship
Husband‘ s age at start of relationship
4
3
5
5
3
2
2
31
10
66
87
67
5
5
28 0
8 8
52 63
73 81
24 63
3 3
2 4
Marital investments
Birth of first child
Birth of second child
Birth of third child
Common parenthood
Number of children
Premarital birth
Common home-ownership of the spouses
Home-ownership
4
4
4
4
4
5
2
3
60
27
19
73
41
79
42
31
40
13
7
49
37
25
27
29
External barriers
Catholic
Number of church attendances
3
2
13 12 13
17 14 14
56
25
10
69
38
30
41
31
0 >0
Fixed effects model
beta
in % sig SE
Random effects model
beta
in % sig SE
-0,123 -11,574
0 31 0,647 90,980 *** 0,037
0 2 -0,394 -32,565 *** 0,038
0 3 -0,011 -1,094 *** 0,001
1 5 -0,056 -5,446 *** 0,003
1 3 -0,019 -1,911 *** 0,002
0 2 -0,048 -4,687 *** 0,007
0 1 -0,023 -2,274 *** 0,007
0,711 103,603 ***
-0,454 -36,492
-0,044 -4,305 **
-0,070 -6,658 ***
-0,023 -2,274 ***
-0,031 -3,052
0,099
0,316
0,016
0,011
0,006
0,042
0,353 16,61
0,886 124,04
0,068 162,78
0,056 49,45
0,017
9,68
0,084 28,60
0,016
0,95
0 4 -0,107 -10,147
0 2 -0,015 -1,489
0 9 -0,004 -0,399
0 4 -0,167 -15,380
0 3 -0,235 -20,943
2 47 -0,003 -0,300
0 1 -0,456 -36,619
0 0 -0,797 -54,932
*** 0,013
0,010
0,034
*** 0,015
*** 0,019
0,004
*** 0,035
*** 0,052
-0,259
-0,039
-0,019
-0,518
-0,210
0,021
-0,776
-0,832
-22,818
-3,825
-1,882
-40,429
-18,942
2,122
-53,976
-56,482
0,103
0,032
0,063
0,174
0,099
0,018
0,371
0,103
0,441
0,444
0,770
0,961
0,358
0,634
0,743
0,512
62,81
13,44
4,95
34,87
67,67
51,94
18,44
4,43
0 -0,411 -33,701 *** 0,056
3 -0,031 -3,052 *** 0,008
-0,086
-8,241
0,189
0,065 0,131
1,77
14,30
16
14,798
Q
0,097 1,341 168,21
0,096
0,00
0,033
1,63
0,113 0,227 154,19
0
0
0,138
Range
**
***
**
**
***
Church wedding
Reform of divorce law
2
3
29 27 29
10 4 10
0
0
Division of labor
Not employed
Wife‘ s employment
Husband’s employment
4
2
2
35 11 13
33 24 6
19 17 17
0 22 -0,007 -0,698
0,009
0 27 0,221 24,732 *** 0,023
0 2 -0,569 -43,391 *** 0,073
Social context
Year of marriage
Large city
Size of birthplace
Marriage in GDR
4
2
2
4
50 46
61 48
6 4
22 18
0 48 0,024 2,429 *** 0,002
0 61 0,317 37,300 *** 0,021
0 4 0,011 1,106
0,018
0 17 0,127 13,542 *** 0,046
Homogamy
Educational homogamy
Wife is better educated than husband
Both catholic
Wife older than husband
2
3
2
2
30 18 30
10 10 6
22 8 18
18 0 5
0 0
0 4
0 4
0 13
-0,308 -26,508 *** 0,035
0,000 0,000
0,033
-0,053 -5,162 *** 0,015
-0,004 -0,399
0,014
Social and personal resources
High level of father’s education
Wife‘ s education in years
Husband‘ s education in years
Abitur
Mittlere Reife
Educational level of wife: Abitur
2
2
2
4
3
2
23 17 1
30 14 11
27 4 21
34 5 13
24 12 11
6 0 1
1
1
2
0
0
0
0,485 62,418 ***
0,003 0,300
-0,009 -0,896 **
0,006 0,602
0,010 1,005
0,023 2,327
0,051
0,002
0,004
0,009
0,014
0,026
0,497
0,027
64,378 ***
2,737
0,197
0,192
21,774
21,167
Transmission of divorce risk
Parent‘ s divorce
Grown up without biological parents
Grown up with one parent
5
2
2
90 71 5
50 14 3
57 7 30
0 85 0,432 54,034 *** 0,023
0 47 0,028 2,840 *** 0,009
0 27 0,023 2,327 *
0,014
0,415
0,249
0,069
51,437 ***
28,274
7,144
2
0
2
5
0 -0,497 -39,165 *** 0,039
0 -0,426 -34,688 *** 0,100
21
18
4
21
13
5
17
-0,502 -39,468 **
0,013
1,308
-0,137 -12,803
0,015
0,362
0,236
0,316
1,511
43,620 ***
26,617
37,163
-0,696 -50,142
0,373 45,208
-0,192 -17,469
0,155
0,235 0,639
1,64
8,12
0,263 1,283
0,155
0,674 1,349
28,94
4,28
48,71
0,012
0,092
0,250
0,233
0,098
0,189
0,501
2,240
88,18
14,51
14,35
49,83
0,436 0,874
0,262 1,386
0,170 0,340
0,039
15,38
51,30
38,66
0,12
0,094 0,187
0,030 0,060
0,003
0,160 0,836
0,164 0,405
0,107
3,27
49,76
0,23
13,45
57,02
0,56
0,088 0,606
0,237 0,474
0,075 0,151
50,43
75,16
16,89
Marriage experience
First marriage
Remarriage
5
3
61 32 55
28 12 1
0 6 -0,132 -12,366 *** 0,024
0 27 0,323 38,127 *** 0,056
*p<0,10; **p<0,05; ***p<0,01
18
-0,288 -25,024 ***
0,112 0,614
0,041
49,46
0,03
Tabelle 4 : Divorce risks
Determinant
Premarital information
about the spouse
Premarital cohabitation
Duration of cohabitation
Duration until start of
relationship
Duration until common
household
Search costs
Early marriage (marriage
before 21)
Child birth at time of
marriage
Age at marriage
Wife‘ s age at marriage
Husband‘ s age at marriage
W ife‘ s age at start of
relationship
Husband‘ s age at start of
relationship
Code
d
m
m
m
d
Annotation
Spouses were living together for at least four months before
marriage. Some authors estimate effect sizes for ‚non
premarital cohabitation‘ . Because of dummy coding, this
variable has been multiplied by -1 and now represents the
effect size for „premarital cohabitation“.
Duration of cohabitation in years
Time between first aquantance and start of the relationship
in years
in years
At least one of the spouses is younger than 21 years at the
time of marriage.
d
m
m
m
m
in years
in years
in years
in years
m
in years
Marital investments
Birth of first child
Birth of second child
Birth of third child
Common parenthood
d
d
d
d
Number of children
m
Premarital birth
Common home-ownership
of the spouses
Home-ownership
d
d
time dependent covariate
time dependent covariate
time dependent covariate
Both spouses are biological parents for at least one of the
children
In one out of four cases the variable is time dependent
coded
Birth of first child before marriage
d
External barriers
Catholic
d
No. of church attendances
m
Church wedding
Reform of divorce law
d
d
Division of labor
Not employed
d
Respondent belongs to the catholic church at the time of
interview
Frequency of church attendance is coded 1 (never) to 5
(weekly attendances)
Coded as 1 if year of marriage is 1977 or 1978, otherwise 0.
The respondent was either not or never employed. To
increase the number of cases, the variable „employed“ was
added and multiplied with the factor (-1). Employment was
coded either time dependently or time independently.
19
Determinant
Code
Wife‘ s employment
Husband‘ s employment
d
d
Social context
Year of marriage
Large city
m
d
Size of birthplace
Marriage in GDR
m
d
Annotation
Wife is gainfully employed (partially time dependent)
Husband is gainfully employed (partially time dependent)
At time of marriage spouses live in a city with at least
100.000 inhabitants
Number of inhabitants of birthplace
Homogamy
Educational homogamy
Wife is better educated
than husband
Both catholic
d
d
Equal educational level of both spouses
d
Wife older than husband
d
At the time of interview both spouses belong to the catholic
church
Wife is at least two years older than husband
So ci al and p erso n al
resources
High lev el of f at her’s
education
Wife‘ s education in years
Husband’s education in
years
Abitur
Mittlere Reife
Educational level of wife:
‚Abitur‘
Transmission of divorce
risk
Divorce of parents
Gr own up without
biological parents
Grown up with only one
parent
d
m
m
d
V/H
d
d
Respondent’s highest educational level is ‚Abitur‘ .
Resondent’s highest educational level is ‚Mittlere Reife‘
At least one of the spouses experienced a divorce before
age of eighteen
d
d
Marriage experience
First marriage
d
Respondent’s first marriage
Remarriage
d
At least one of the spouses experienced a remarriage
d: dummy-coding; m: metric variable; V/H: category of reference: Volks-/Hauptschule
20
First, we regard indicators of the level of information about the spouse before
marriage: cohabitation, duration of cohabitation, duration of time between first contact
and beginning of the relationship, duration of time until the start of a common
household. Whereas the effects of cohabitation and of duration of cohabitation are not
significant, the duration of the premarital relationship (whether the partners have a
common household or not) reduces the risk of divorce. Time duration between the
date 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 only
matter if ‘ a marriage is on trial’, but also whether potential partners take their time
before starting a partnership. Another explanation favours the idea of relationships,
which took a long time to be established because social barriers against a partnership
exist. If partnerships are established despite of such barriers this would indicate a
special ‘ seriousness’ or an outstandingly promising ‘match’.
Second, we have indicators of costs for searching a partner: early marriage, age of
marriage of interviewed person, age of marriage (husband or wife), age of beginning
a relationship (husband or wife). It is quite open whether the ‘ forced marriage’ (child
birth at time of marriage, ‘ Mussehe’) indicates search costs. All of these variables are
negatively related to the divorce rate. The higher the search costs, the more stable is
the marriage. Early marriages get separated very often. Every year of waiting time until
marriage reduces the divorce risk by four percent. Wife’s age at marriage is more
important than husband’s 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 second
child, birth of third child, common child, number of children and premarital child. On
the other hand, the variables home-ownership and common home-ownership are
included. 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 the
results show, it is important that the child is a common child of both spouses. If not
both 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 of
marriages. The influence of the reform of the divorce law, affiliation to the catholic
church, frequency of church visits, and the church wedding are related to the validity
and internalization of these standards. It is almost certain that the affiliation to the
catholic church or a church wedding reduce the divorce risk. If the frequency of church
21
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 resulted
in a strong reduction of divorce rates during the years 1977/1978.
Also the division of household labor can be understood as a marital investment. The
more efficient the division of labor is, the higher are the gains of marriage. Admittedly,
a positive effect of wife’s employment on the rate of divorce is only based on two
studies. We do not find significant influences of other variables like non-employment
or husband’s employment.
There are a number of variables which can be allocated in an unspecific way to the
social context or more specific to marital alternatives: Living in a large city, size of
birth place, marriage in GDR and year of marriage. The rate of divorce is significantly
higher in large cities, even though the size of birth place is irrelevant. The integrated
effect of the year of marriage, which has been estimated in four studies, positively
affects the divorce rate under the assumption of a fixed effects model. However, this
model is inadequate, obviously relevant differences in effect sizes exist between the
studies. According to the random effects model year of marriage is no longer
significant.
Similar results arise from comparing former East and West Germany. According to
official statistics, the divorce rate of GDR exceeded that of the FRG. As our results
show, this fact is asserted if we follow a model with fixed effects. But a larger
heterogeneity of results is ascertained as well, presumably because the effect of this
variable strongly depends on control variables that are included into the specific
models. We therefore have to assume a model with random effects, which shows
differences between East and West to be statistically insignificant.
A number of different indicators capture the amount of social homogamy: wife older
than husband, educational homogamy, a relatively high level of wife’s education, both
spouses being catholic. None of these variables significantly corresponds to the risk
of 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 of
the father’s education. It was not possible to include measures of household or
personal income into meta-analysis. Whereas the level of father’s education strongly
increases the divorce risk, husband’s level of education is positively related to marital
22
stability. The educational level of the wife and the educational level which is not
differentiated 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 not
possible to relate the stability of the parental marriage to a single theoretical construct.
The transmission effect sizes have been integrated throughout five studies into a
statistically significant mean effect size. The divorce risk increases up to 50% if the
parental marriage had been separated. Other variables that measure whether the
interviewed persons grew up either without parents or with only one parent do not
reach an integrated effect size which is different from zero.
Finally, also variables concerning the first or the second marriage are listed
separately, without a correspondence to a single theoretical construct. Assumably,
these variables capture selection effects. Nevertheless, these variables are
meaningful in a statistical sense: the divorce risk of first marriages is about 25% lower
than for marriages of a higher order.
4 Summary and discussion
The aim of this paper was to evaluate German divorce studies by means of metaanalytic methods. We discuss the results with respect to
1)
2)
3)
the applicability of meta-analysis,
the evaluation of the present state of research,
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 of
appropriate weighting factors and the handling of publications whith incomplete data.
Some of these problems could be solved if the quality of research and of publications
would be improved. Almost all of the evaluated studies present incomplete statistical
data. Especially unfavourable is that bivariate effects and the standard errors of effect
sizes often are not reported.
The present analyses has pointed out that the construction of independent variables
23
widely differs between authors. In this situation an integration of results is only
achievable by a broader definition of categories. Nevertheless, in this case one might
run 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 can
also be an advantage for meta-analysis: the benefit of a meta-analytical integration
results out of the diversity of studies (Glass 1977). Different operationalizations or
research 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 to
integrative reviews in general. The special advantage of a quantitative integration
compared to a qualitative one is indeed to be found in the systematic and explicit
procedure. For instance, a quantitative review allows an analysis of study differences
and of their influence on meta-analytical results.
These points in mind one has to be careful when evaluating the state of research. We
are far away from an adequate testing of a theory of marital stability. Only selected
constructs or single hypotheses from exchange or microeconomic theory have been
considered in empirical research. Our meta-analysis clearly shows that variables
influence the divorce risk that are related to search costs, marital investments and
external barriers. The division of labor between spouses, social homogamy, and own
resources really do not affect the risk of divorce. In contrast, the transmission
hypothesis is clearly supported, and first marriages are more stable than marriages of
a higher order. However, it is in turn not very evident how these empirical associations
can be interpreted in the light of exchange or microeconomic theory.
Very few attempts have been undertaken to measure the opportunities of remarriages
or more general the alternatives to an existing marriage. These central hypothetical
constructs 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 mentioned
shortcomings. Research is hardly organized in a cumulative way. Replications are not
really done and much too often different variables and measures are used. New
studies are carried out without relating them systematically to the results of already
existing research. Meta-analysis should become part of the methodological canon in
24
sociology. This would be facilitated by an improvement of research and a higher
quality of publications. If the future development of sociology will be similar to that in
the medical sciences or in psychology, the demand for meta-analyses will strongly
increase 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 increase
the more studies and publications on a certain topic are available.
25
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Appendix
As mentioned in section 2.4.2 it is necessary to use independent effect sizes for
integration. Therefore calculation of weighted means will be done in a two-stage
process. At the second stage standard errors are computed as follows:
SE ES =
1
k
∑ wi
, with k number of studies.
i =1
The between-studies variance σ θ (cf. section 2.4.3) is calculated as follows :
2
 ∑k w 2 
i
Q − ( k − 1) mit c = ∑k w − i =1 .
2
σθ =
k

i
i =1
c
 ∑ wi 
 i =1 
35