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National, regional and global trends in marriage and cohabiting unions: Estimates and projections of the proportion of women who are married or in a union by age Mi Hong Yim1, Leontine Alkema2, Vladimira Kantorova3

October 23, 2017

Authors’ affiliations:

1KM Fundamental Research Division, Korea Institute of Oriental Medicine, 1672 Yuseong-daero, Yuseong-gu, Daejeon 34054, Republic of Korea

2Department of Biostatistics and Epidemiology, University of Massachusetts Amherst, Amherst, MA, USA.

3United Nations Population Division, Department of Economic and Social Affairs, New York, NY 10017, USA

This work was supported by Grant No. OPP1110679 Making Family Planning Count from the Bill & Melinda Gates Foundation and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2015R1C1A2A01055428).

The views and opinions expressed in this paper are those of the authors and do not necessarily represent those of the United Nations. This paper has not been formally edited and cleared by the United Nations.

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Abstract (max 200 words) We developed a Bayesian hierarchical model to construct age-specific estimates and projections of the proportion of women who are married or in a union in reproductive ages (15 to 49 years) at the national, regional and global level from 1950 to 2030. We also estimate changes over time in the proportion of women living in consensual unions. The analysis is based on marital and union status data from the World Marriage Data 2015. We show that over the past decades in both developed and developing countries, there have been profound changes in marriage and union patterns, in particular the postponement of marriage and union formation to later ages. In some regions of the world, cohabiting unions have become more common over time, especially in younger age groups, in other regions non-marital unions have remained rare or have always been common. We also provide estimates of the proportion of married and in union women in age group 15 to 19 years indicating the extent of early and child marriages and unions that are still common in parts of the world.

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Introduction

Marriage and union formation patterns have undergone significant transformations in the past decades. Studying trends in marriage and union status provides a reflection of changes in the societies, such as urbanization, globalization, gender equality, rising educational attainment, economic or demographic changes.

In this paper, we provide global comparative estimates of age-specific proportions of women who are married or in a union in reproductive age (15- to 49-years old). The past methodology used to derive estimates and projections of the proportion and number of women of reproductive age who are married or in union was based on interpolation between two observations in each country with the projections combining country and global trajectories and was used by the Population Division since 1996 (United Nations, 1996; Kantorova, 2013; United Nations, 2016). In this paper, we develop a Bayesian hierarchical model to construct age-specific estimates and projections of the proportion of women who are married or in a union in reproductive ages (15 to 49 years) that use all available data sources in each country. We developed a statistical model of the distribution of women into 3 categories - married, in a union, or not married/in-union for each 5-year age group. We combine a parametric function, which gives the expected age pattern of the proportion of married or in-union women for any country-year combination, with a time-series model that captures fluctuations around these outcomes. Similarly, we develop a model to obtain the proportion of women who are in a (non-marital) union, as the ratio to the proportion of married or in-union women of reproductive age.

We prepared a data set based on World Marriage Data 2015 (United Nations, 2015) containing 1549 surveys and censuses from 1954 to 2014 from 230 countries or areas. All data points are used in the fitting of the data model and the estimates are based on the richness of information provided by diverse data sources in our data set. Hertrich, Lardoux and George (2014) demonstrated by studying the quality of data on the age at first marriage in 55 African countries, that surveys and censuses each introduce biases that pull in opposite directions. They conclude that “these inconsistencies originate in reporting errors at the time of data collection and are particular to each type of source. So there is no reason to prefer surveys over censuses when analysing the timing of nuptiality; rather, the two sources should be used in tandem.”

This approach provides global, regional and national annual estimates of age-specific proportions by five-year age groups from around 1970 to the current period. In the result section, we analyze (a) the prevalence of marriage and union (overall proportion of women living in marriage or cohabiting union); (b) the timing of entrance into marriage and union (to assess this dimension, we use the proportion married and in-union in age groups 15-19, 20-24 and 25-29: capturing the time of the onset of union formation and the pace at which union formation then proceed); and (c) the types of unions (we are concerned with the distinction between formal marriages and consensual unions).

Motivation and overview of previous comparative studies

The original motivation for developing annual estimates and projections of the proportion of married or in-union women at the national, regional and global levels was for calculating family planning indicators and informing their projections (United Nations, 1996; Kantorova, 2013; Alkema et al., 2013; Brown et al., 2014). Contraceptive prevalence and unmet need for family planning are most often reported for the base population of married or in-union women of reproductive age (MWRA). In order to estimate the number of contraceptive users or users of particular methods and the number of women with unmet need for family planning, the prevalence rates must be multiplied by the total number of MWRA. To these base numbers for women who are married or in a consensual union, the number of contraceptive users and those who need family planning among unmarried women are added to obtain the number of all contraceptive users and the number of all women with an unmet need for family planning (Singh and Darroch, 2012; Kantorova et al, 2017). Estimates and projections of MWRA are also needed to calculate contraceptive prevalence and unmet need for family planning for global, regional or other aggregate groups and for country-specific annual estimates and projections from

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models (United Nations, 2017).

The age-specific trends in the proportion of married or in-union women at the national, regional and global levels are relevant also for 1) analyzing trends and cross-country comparisons in the marriage and union patterns by age, including trends in early marriages and unions and the patterns of consensual unions; 2) informing analysis of fertility trends and early childbearing patterns; and 3) informing analysis of contraceptive and reproductive behavior.

Review of comparative literature on patterns and trends in marriage and union status of women and men provide insights into striking differences and some commonalities across major areas of the world, but also into differences in the research questions, data and methodologies used. For instance, the increase in cohabitation is one of the trends that has recently attracted growing attention in the demographic and sociological literature. However, comparative research has focused on trends within specific regions. In Europe and Northern America, Perelli-Harris and Lyons-Amos (2015) showed that the changes in partnership patterns have been driven by the postponement of marriage, and cohabitation has emerged as its own partnership form not identical to marriage. Despite increases in all countries, the variation across Europe remains remarkably wide, which is reflected also in policies relating to cohabitation and marriage along a continuum, from countries that have equalized cohabitation and marriage to those that only regulate marriage (Perelli-Harris and Sánchez Gassen, 2012).

In Latin America, studies show that there has been a major increase in cohabitation as a form of union formation (e.g., Castro Martin, 2002; Esteve, García-Román and Lesthaeghe, 2012; Esteve, Lesthaeghe, and Lopez-Gay 2012); however, marriage or cohabiting union among women in Latin America occurs early in life and is nearly universal and the age at entry into marriage or union changed remarkably little over the second half of 20th century (Fussell and Palloni, 2004).

Comparative review of studies on marriage trends in Asia show sharp differences in marriage patterns in terms of marriage timing and the prevalence of marriage persisting throughout the region (Jones 2010), however with a common feature of very low prevalence of cohabitation.

In sub-Saharan Africa, there is a long tradition of studying nuptiality regimes in various parts of Africa (Lesthaeghe, Kaufmann and Meekers, 1989). However, there is the measurement problem because multiple forms of marriage exist in Africa, which make it difficult for researchers to categorize people as being married or unmarried (Bledsoe and Cohen, 1993). Marriage and union are not clearly defined (such as through marriage ceremony as a discreet event in Western societies), and marriage is a process composed of several stages and it is difficult to determine when a union started (Meekers, 1992). The types of marriages and unions are not consistently reflected across the main data sources (Hertrich, Lardoux and George, 2014). In comparative studies for sub-Saharan Africa, the term ‘marriage’ is referring to all various types of marriages and unions (e.g. Hertrich 2017).

Many comparative studies across developing countries looked at the differences in timing of first marriage (United Nations 1988 and 1990; Bledsoe and Cohen, 1993; Singh and Samara, 1996; Mensch, Singh, Casterline, 2005). These studies and research questions get new attention with the 2030 Agenda for Sustainable Development (United Nations General Assembly, 2015) and its target 5.3. to “Eliminate all harmful practices, such as child, early and forced marriage and female genital mutilation”. To measure the progress on the elimination of child and early marriages, the indicator 5.3.1 “Proportion of women aged 20–24 years who were married or in a union before age 15 and before age 18” uses the retrospective questions on first marriage from Demographic and Health Surveys, Multiple Indicators Cluster Surveys and other international surveys (United Nations, 2017).

Marriage and union formations is the demographic event associated with the start of regular sexual relationship and is an important determinant of childbearing and contraceptive behavior. Through the proximate determinants framework for analysis of fertility levels and trends (Bongaarts, 1978; Bongaarts, 2015), the studies have shown a considerable variation among countries in the effects on fertility of major proximate determinants – marriage, contraception and post-partum infecundability. Cleland, Casterline, Singh and Ashurst (1984) found that the fertility-restraining effect of marriage is

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weaker in sub-Saharan African countries compared to that found in Latin America or Asia (though the variations within regions were large). As countries move from high to low fertility, the inhibiting effect of the proximate determinant of marriage becomes stronger (Bongaarts, 2015).

In some regions of the world, declines in childbearing among adolescent and young women and overall fertility levels have been related to rapid declines in the proportion of women in the youngest age groups who are married or in a union. As a result, in these regions the postponement of marriage or union formation has had a large impact on adolescent childbearing and total fertility. Studies for Algeria (Ouadah-Bedidi and Vallin, 2013) and Iran (Abbasi-Shavazi et al., 2009) show that a rise in the marriage age was strongly correlated with declines in fertility.

In Latin America, fertility has declined without a significant change in the age or prevalence of marriage (or cohabiting unions). Rather, the fertility transition has largely occurred as a result of the use of contraception or other means of spacing and stopping births (Moreno & Singh, 1996; Rosero-Bixby, 1996).

In Western and Northern European countries, historically the postponement of marriage resulted in relatively low levels of childbearing. In recent decades, later marriage and union formation has been one of the reasons for the postponement of childbearing in all parts of Europe, which has been unprecedented in its pace, duration and ultimately its impact on fertility trends, explaining a large part of the declines and rises in period total fertility in Europe (Sobotka, 2004; Bongaarts and Sobotka, 2012). In recent years, the attention of researchers turned to the role of the rise of cohabitation on childbearing. While the increasing proportion of births outside formal marriage is observed in all regions of Europe (Klüsener, Perelli-Harris, Gassen, 2013), many of the non-marital births are to women who are living in consensual unions (Perelli-Harris, Sigle-Rushton, Kreyenfeld, Lappegård, Keizer et al. 2010). The changes in the patterns of union formation and childbearing – some couples begin their unions with cohabitation and marry before first conception, some marry during pregnancy or directly after the first birth, some remain in consensual union and some from consensual union to marriage later – and its different trajectories across countries have also been analyzed by researchers (Perelli-Harris, Kreyenfeld, Sigle-Rushton, Keizer, Lappegård et al., 2012).

In East Asia, trends toward later and less marriage and childbearing have been particularly pronounced with rapid decline in marriage and fertility rates that occur in the absence of other major changes in family attitudes or rising individualism (Raymo et al, 2015) and delayed marriage has had substantial role in the low fertility rates currently observed (Jones, 2007).

There has been a wealth of studies on marriage and unions trends and patterns in regional comparative perspective. Our study adds the global perspective based on the comparable estimates for 230 countries and the long-term perspective covering trends from 1970 to 2015.

Data Data sources and data availability

The Population Division provides comparable and up-to-date sets of data on the marital/union status

of the population and produces estimates and reports analysing levels and trends of marriage and union indicators. The data set used in this research is a subset of World Marriage Data 2015 (United Nations, 2016) and contains 1549 surveys and censuses from 1954 to 2014 from 230 countries or areas. A data source (census, survey or registration data) for a given year constitutes a data point.

Overall, among 230 countries or areas, more than two-thirds have five or more observations over the whole period (Figure 1). The period before 1970 is the least represented in our data set, and only 17 per cent of countries have one or two data points available in this period. Therefore, in the interpretation of the results, we concentrate on the period after 1970. Compared to other major areas, Africa and Asia

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have a greater availability of data in our data set, with 81 per cent and 76 per cent of countries, respectively, having five or more data points. The same finding is also true for the most recent period – in the period 1990-2009 48 per cent of countries in Africa and 38 percent of countries in Asia, have 5 or more data points. The richness of the data set for Africa and Asia is partly due to the availability of repeated surveys from international survey programmes, such as DHS and MICS.

Figure 1: Data availability by time period and major area.

Note: ENA = Europe and Northern America. LAC = Latin America and the Caribbean. Source: Data set based on World Marriage Data 2015 (United Nations, 2016).

Definitions of categories of marital/union status For the purpose of this study, women who are currently married or in a union are either 1) women

who have been married and are not divorced, widowed or separated; or 2) women who are living in a cohabiting union. Marital status is defined in relation to the marriage laws or customs of a country (United Nations, 2008). When data on persons living in consensual unions or other types of customary unions are reported in the original data source, they are reported in the present database.

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There is a considerable variation among the definitions of consensual or other customary unions used in surveys. In this paper, there is no distinction made with respect to the terms used in different publications, survey and census reports and tabulations, such as informal unions, consensual unions, unmarried unions, or “living together”. To the extent possible, the category of women in a union includes women living with their partner in the same household and who are not married according to the marriage laws or customs of a country. In World Marriage Data 2015 (United Nations, 2015), for the most recent data points in some countries, marriages and registered unions of same sex partners are reported in the married or consensual union category; this information is presented in data source-specific note. Additionally, changing definitions of consensual unions across sources and over time that preclude analysis of time trends are indicated in a note.

Model

To obtain estimates and projections of the proportion of married or in-union women of reproductive age (MWRA), we developed a statistical model of the distribution of women into 3 categories - married, in a union, or not married/in-union for each 5-year age group. To obtain the proportion of MWRA in 5-year age groups for all country-years, we combine a parametric function, which gives the expected age pattern for any country-year combination, with a time-series model that captures fluctuations around these outcomes. The parametric model is illustrated in Figure 1 (Left). The model has 4 parameters: the age at which the proportion of MWRA starts to increase (a), the age at which the proportion of MWRA peaks (b), the proportion of MWRA at age 50 (c) and the maximum proportion of MWRA (observed at age b) (d). These parameters are likely to change with time and vary across countries.

Figure 2: Left: Parametric model for the proportion of married or in-union women of reproductive age over age. Right: Example of a logistic growth curve to model changes in parameter b (the age at which the proportion of MWRA peaks).

To incorporate differences over time and across countries, for each country or subregion, each of the parameters are modeled with a logistic growth curve, as illustrated in Figure 1 (Right) for parameter b, which represents the age at which the proportion of MWRA peaks. A Bayesian hierarchical model is used to estimate the population-specific parameters of the logistic growth curves, which are the lower asymptote, the upper asymptote, the maximum rate of change and the time point when the rate of change is at its peak. In the Bayesian hierarchical modeling approach, the estimates are based on the observations in the population (being country or subregion) of interest, as well as observations in other populations. We have fitted hierarchical models that include country-specific parameters as well as models with subregional parameters only. Trials with country-specific parameters only suggested that such models may be overparametrized due to data sparsity and limited variation across countries within subregions. The final model will be a compromise between country-specific parameters for those indicators that display variability across countries within subregions, and subregional parameters for the remaining indicators.

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To obtain the proportion of women who are in a union, we developed the model for the ratio of the proportion of in-union women of reproductive age to the proportion of married or in-union women of reproductive age (MWRA). The model set-up for the ratio is similar to the model for the proportion of MWRA. The parametric model for the ratio is illustrated in Figure 2 (Left). The model has 3 parameters: the age at which the ratio starts to stop moving (e), the ratio at age e (f) and the ratio at age 15 (g). These parameters are likely to change with time and vary across countries. Each of the parameters are modeled with a logistic growth curve and a Bayesian hierarchical model is used to estimate the country- or subregion-specific parameters of the logistic growth curves like constructing estimates and projections of the proportion of MWRA. The logistic growth curve is illustrated in Figure 2 (Right) for parameter g.

Figure 3: Left: Parametric model for the ratio of the proportion of in-union women to the proportion of MWRA over age. Right: Example of a logistic growth curve to model changes in parameter g (the ratio at age 15).

A Markov Chain Monte Carlo (MCMC) algorithm was used to generate samples of the posterior distributions of the parameters using JAGS software (Plummer M, 2003) and the analysis was carried out in R (R Development Core Team, 2013).

Detailed methodology and specification of the statistical model is described in the appendix (available from the authors upon request).

Results

Trends in the proportion of women married or in a union

Country-specific observations for each age group (dots) together with the estimates and projections of the age-specific proportion of women who are married or in a union are presented in Figure 4 for selected countries. The estimates are presented as medians (lines) with 95% confidence intervals (dotted lines).

The largest differences among countries in Figure 4 are in the proportion of married/in-union women in the age groups 15-19 and 20-24. In sub-Saharan Africa, the selected countries cover diverse regions of Africa - Ghana and Senegal (Western Africa), Malawi and Rwanda (Eastern Africa) and Democratic Republic of the Congo (Middle Africa), and the results show that large proportions of women in the age group 15-19 were married/in-union (above 20%) in the 1970s, reaching above 40% in Malawi and Senegal. Since the 1980s, while in Ghana, Malawi and Senegal the proportion of married/in-union women in the age groups 15-19 declined, there were less changes observed in Democratic Republic of the Congo. The diversity of trends is also seen in the age group 20-24 – in Malawi above 70% of women are married/in-union with minimal changes over time, while marriage has become less common in Ghana and Rwanda and only around 40% of women are married/in-union in 2010. Some signs of the postponement of marriage and union formation are observed also in the age group 25-29 in Ghana and Senegal.

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Figure 4 also shows two countries in South America: Colombia and Chile. In both countries it can be observed that around 10 to 18% of 15-19 years old and 40% of 20-24 years old are married/in-union in 2015. However, while in Chile, there has been a postponement of marriage and unions formation apparent from the declines of 20-24 and 25-29 years old who are married/in-union, the patterns of early marriage/union formation are still present in Colombia.

For many countries in other regions, the postponement of marriage and union formation became apparent over the 1980s and 1990s. The last two examples in Figure 4, Hungary and Canada, document this transition. In Hungary, until the early 1980s, 60% of women aged 20-24 were married/in-union; since 1990s, the fast postponement of marriage and union formation took place and only 20% of women aged 20-24 are married or in-union in the 2010s. Moreover, while until 1980s formal marriage was predominant, in the 2010s most of women who were married or in a union were in non-marital union (around 75%). In Canada the postponement started earlier – in the late 1970s.

Figure 4: Observations and estimates for selected countries. Observed proportions of married/in-union women (dots) plotted over time for all age groups, together with estimates of the proportion of married women (lines) and 95% CIs (dotted lines). Note: Only observations that report both the proportion married and in union are included in the display. For each country, additional census and survey observations that report only data on marriage are included in the model. The year 2015 has a white column to separate the past and future trajectories.

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Figure 5 represents comparison of the model-based estimates and projections of the proportions of married/in-union between 1970 and 2010 by individual age groups for all countries and areas of the world. The results show a profound decline in early marriages and unions in age groups 15-19 and a postponement in marriage and union formation among women aged 20-24 and 25-29 in many parts of the world. The greatest diversity of patterns is observed in the age group 20-24, where in some countries of Europe, Asia, Africa and Oceania, less than 20% are married/in-union, while there are still countries in Africa and few in Asia, where more than 70% of women in this age group are married/in-union. Generally, when looking at changes over time from 1970 to 2010, the smallest changes across all age groups happened in Latin America and the Caribbean countries (most countries of this region are in the age-specific figures located close to the identity line representing no change).

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Figure 5: Estimates of the proportions of married/in-union women (dots) for 1970 (y-axis) and 2010 (x-axis) for age groups 15-19 (Left) and 25-29 (Right), by major area.

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Trends in the proportion of married women

Figures 6 represent estimates of the proportion of married women for selected countries. For countries where non-formal unions are rare, we present two country pairs showing the diversity within regions (Algeria and Egypt in Northern Africa, and Bangladesh and Pakistan in Southern Asia). In Algeria and Egypt around 20% of women aged 15-19 and 60% of women aged 20-24 were married in the 1970s. While in Egypt situation remained nearly unchanged, in Algeria, by the 2010s, marriage among 15-19 years old is rare and only 20% of 20-24 years-old were married (and similar changes were apparent also among 25-34 years-old women). Interestingly, both countries show slight increase in the proportion married in younger age groups according to the latest data available.

Examples of Canada, Hungary and Italy show fast declines in the proportion married in all age groups, but most prominently among those aged 20-29; depending on the country situations, the

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decline in marriages is partly replaced by an increase in prevalence of cohabiting union – in Canada to some degree and in Italy minimally (see Figure 7).

Figure 6: Observations and estimates for selected countries. Observed proportions of married women (dots) plotted over time for all age groups, together with estimates of the proportion of in-union women (lines) and 95% CIs (dotted lines). Note: Only observations that report both the proportion in-union are included in the display. For each country, additional census and survey observations that report data for married/in-union only are included in the model.

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Trends in the proportion of women in cohabiting unions

The results of this study highlight that cohabitation is not a phenomenon exclusive to specific regions. Consensual unions in each region have some distinctive features: their historical roots, their pervasiveness among all age groups, and their status as a socially accepted context for childbearing. Its prevalence is highest in parts of Latin America and the Caribbean, where the proportion of women in cohabiting unions ranges from around 20 per cent in Chile to above 50 per cent in the Dominican Republic in the age groups 25-29 and 30-34 years old (Figure 7). While in most countries, the prevalence of cohabiting unions has been increasing over time, there are countries where it has always been high and other countries where the prevalence remains extremely low (e.g. example of Cambodia and Senegal in Figure 7 with data available from surveys).

Figure 7: Observations and estimates for selected countries. Observed proportions of in-union women (dots) plotted over time for all age groups, together with estimates of the proportion of in-union women (lines) and 95% CIs (dotted lines). Note: Only observations that report both the proportion in-union are included in the display. For each country, additional census and survey observations that report data for married/in-union and married only are included in the model.

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Discussion

We developed a Bayesian hierarchical model to construct age-specific estimates and projections of the proportion of women who are married or in-union in reproductive ages (15 to 49 years) at the national, regional and global level from 1950 to 2060. We also estimated changes over time in the proportion of women living in consensual unions. The statistical model combines a parametric function, which gives the expected age pattern of the proportion of married or in-union women for any country-year combination, with a time-series model that captures fluctuations around these outcomes. In the Bayesian hierarchical modeling approach, the estimates are based on the observations in the population (being country or subregion) of interest, as well as observations in other populations. The hierarchical structure of the model enables producing estimates for periods where few or no data are available based on the information from parameters at the regional and global level.

We prepared a data set based on the World Marriage Data 2015 (United Nations, 2015) containing 1549 surveys and censuses from 1954 to 2014 from 230 countries or areas. All data points are used in the fitting of the data model and the estimates are based on the richness of information provided by diverse data sources in our data set.

The advantage of the model-based estimates of the number and proportion of married or in-union women at the national, regional and global levels is that the results provide gradual changes over time, which are not limited to snapshots of years represented by selected census or survey data.

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Furthermore, the regional and global aggregates are results of the country-specific estimates for a specific year and weighted by the population size of that year.

Constructing estimates and projections of the proportion of women who are married or in a union is challenging not only because of limited data availability and data quality for many countries, but also of limited availability and comparability of data on non-marital unions in some regions. In addition, there are challenges with finding and using comparable definitions across countries and data sources. Our statistical model based on the distribution of women into 3 categories - married, in a union, or not married/in-union for each 5-year age group might be too simplistic for describing situation in marriage and union patterns across countries and over time. Furthermore, more attention needs to be given to difference between data sources – one example is data for Bangladesh in 2011 – according to DHS 44.7% of 15-19 years old women were married, while according to the census data only 32.4%. Data compilations that contain all diverse data sources help to find and analyze these inconsistencies.

In general, we show that over the past decades in both developed and developing countries, there have been profound changes in marriage and union patterns. In some regions of the world, cohabiting unions have become more common over time, especially in younger age groups, in other regions non-marital unions have remained rare or have always been common. To assess the changes in the timing of entrance into marriage and union, we analyzed the differences in the proportion married and in-union in age groups 15-19, 20-24 and 25-29: capturing the time of the onset of union formation and the pace at which union formation then proceed.

Acknowledgements The dataset used in this analysis is based on the data compilations World Marriage Data 2015 (United Nations, 2015; prepared by Stephen Kisambira, Kyaw Kyaw Lay, Kirill Andreev, Ann Biddlecom, Camille Dorion, Vladimíra Kantorová and Petra Nahmias) and World Marriage Data 2017 (forthcoming; prepared by Stephen Kisambira, Kyaw Kyaw Lay, Vladimíra Kantorová, Ching Yee Lin, Nadia Soerjanto and Philipp Ueffing). References

Abbasi-Shavazi, Mohammad Jalal, Peter McDonald and Meimanat Hosseini-Chavoshi (2009). The Fertility Transition in Iran: Revolution and Reproduction. Springer Verlag.

Alkema, L., V. Kantorova, C. Menozzi and A. Biddlecom (2013). National, regional, and global rates and trends in contraceptive prevalence and unmet need for family planning between 1990 and 2015: a systematic and comprehensive analysis. The Lancet, Vol. 381, No. 9878, pp. 1642-1652.

Bledsoe, Caroline H. and Barney Cohen (Eds.) (1993). Social Dynamics of Adolescent Fertility in Sub-Saharan Africa. National Academies Press.

Bongaarts, John (1978). A framework for analyzing the proximate determinants of fertility. Population and Development Review, Vol. 4, No. 1, pp. 105-132.

Bongaarts, John. (2015). “Modeling the fertility impact of the proximate determinants: Time for a tune-up,” Demographic Research 33: 535–560.

Bongaarts, J. and Sobotka, T. (2012), A Demographic Explanation for the Recent Rise in European Fertility. Population and Development Review, 38: 83–120.

Brown, Win et al. (2014). “Developing the ‘120 by 20’ goal for the global FP2020 initiative,” Studies in Family Planning 45(1): 73–84.

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Castro Martin, Teresa (2002). Consensual Unions in Latin America: Persistence of a Dual Nuptiality System. Journal of Comparative Family Studies Vol. 33, No. 1, pp. 35-55

Cleland, John, John B. Casterline, Susheela Singh and Hazel Ashurst (1984). The Effects of Nuptiality, Contraception and Breastfeeding On Fertility in Developing Countries. International Family Planning Perspectives, Vol. 10, No. 3, pp. 86-93

Esteve, Albert, Joan García-Román and Ron Lesthaeghe (2012). The Family Context of Cohabitation and Single Motherhood in Latin America. Population and Development Review, Vol. 38, No. 4 (DECEMBER 2012), pp. 707-727

Esteve, Albert, Ron Lesthaeghe, and Antonio Lopez-Gay (2012). The Latin American cohabitation boom, 1970-2007," Population and Development Review 38

Fussell, Elizabeth and Alberto Palloni (2004). Persistent Marriage Regimes in Changing Times. Journal of Marriage and Family, Vol. 66, No. 5, Special Issue: International Perspectives on Families and Social Change.

Hertrich, Véronique, Solène Lardoux and Karen George (2014). Estimating Age at First Union in Africa. Are Census and Survey Data Comparable? Population Vol. 69, No. 3 (2014 July-September), pp. 357-389

Jones, Gavin W. (2007). Delayed Marriage and Very Low Fertility in Pacific Asia. Population and Development Review, 33: 453–478.

Jones, Gavin W (2010). Changing Marriage Patterns in Asia. Working Paper Series No. 131. Asia Research Institute. http://www.ari.nus.edu.sg/wps/wps10_131.pdf

Kantorová, V. (2013). National, regional and global estimates and projections of the number of women age 15 to 49 who are married or in a union, 1970-2030. Technical paper 2013/2. United Nations: New York.

Kantorová, V., Dasgupta, A. N. Z., Ueffing, P., and Wheldon, M. C. (2017). Adding Unmarried Women: National, Regional, and Global Estimates of Family Planning Indicators for All Women. Poster presented at the Population Association of America Annual Conference, Chicago, Illinois. https://paa.confex.com/paa/2017/meetingapp.cgi/Paper/16058 [retrieved 28 September 2017].

Klüsener, S, B Perelli-Harris, NS Gassen (2013). Spatial aspects of the rise of nonmarital fertility across Europe since 1960: The role of states and regions in shaping patterns of change. European Journal of Population/Revue européenne de Démographie 29 (2), 137-165

Lesthaeghe, Ron, Georgia Kaufmann, and Dominique Meekers (1989). “The nuptiality regimes in sub-Saharan Africa,” in Ron Lesthaeghe (ed.), Reproduction and Social Organization in Sub-Saharan Africa, Berkeley/Los Angeles: University of California Press, pp. 238–337.

Lloyd, Cynthia B. (ed.). (2005). Growing Up Global: The Changing Transitions to Adulthood in Developing Countries. Washington, DC: The National Academies Press.

Meekers, Dominique (1992). “The process of marriage in African societies: A multiple indicator approach,” Population and Development Review 18(1): 61–79.

Mensch, Barbara S., Susheela Singh, John B. Casterline (2006). Trends in the Timing of First Marriage Among Men and Women in the Developing World. In: Cynthia B. Lloyd, Jere R. Behrman, Nelly P. Stromquist and Barney Cohen (Eds.) The Changing Transitions to Adulthood in Developing Countries: Selected Studies. National Research Council.

http://www.ari.nus.edu.sg/wps/wps10_131.pdfjavascript:void(0)javascript:void(0)

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Moreno, L., & Singh, S. (1996). Fertility decline and changes in proximate determinants in the Latin American and Caribbean regions. In J. M. Guzman, S. Singh, G. Rodriguez, & E. A. Pantelides (Eds.), The fertility transition in Latin America (pp. 113- 134). Oxford, England: Clarendon Press.

Ouadah-Bedidi, Z. and Vallin, J. (2013), Fertility and Population Policy in Algeria: Discrepancies between Planning and Outcomes. Population and Development Review, 38: 179–196. doi: 10.1111/j.1728-4457.2013.00559.x

Perelli-Harris, B., M Lyons-Amos (2015). Changes in partnership patterns across the life course: An examination of 14 countries in Europe and the United States. Demographic Research 33, 145.

Perelli-Harris, B., W Sigle-Rushton, M Kreyenfeld, T Lappegård, R Keizer et al. (2010). The educational gradient of childbearing within cohabitation in Europe. Population and Development Review 36 (4), 775-801.

Perelli-Harris, B,. M Kreyenfeld, W Sigle-Rushton, R Keizer, T Lappegård et al. (2012). Changes in union status during the transition to parenthood in eleven European countries, 1970s to early 2000s. Population studies 66 (2), 167-182.

Perelli-Harris, B., N Sánchez Gassen (2012). How similar are cohabitation and marriage? Legal approaches to cohabitation across Western Europe. Population and Development Review 38 (3), 435-467.

Plummer M (2003). JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In: Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003). March 20–22, Vienna, Austria.

R Development Core Team (2013). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.

Raymo, James M., Hyunjoon Park, Yu Xie, Wei-jun Jean Yeung (2015). Marriage and Family in East Asia: Continuity and Change. Annu. Rev. Sociol. 2015. 41:471–92

Rosero-Bixby, L. (1996). Nuptiality trends and fertility transition in Latin America. In J. M. Guzman, S. Singh, G. Rodriguez, & E. A. Pantelides (Eds.), The fertility transition in Latin America (pp. 135- 150). Oxford, England: Clarendon Press

Singh, Susheela and Jaqueline E. Darroch (2012). Adding It Up: Costs and Benefits of Contraceptive Services—Estimates for 2012. New York: Guttmacher Institute.

Singh, Susheela and Renee Samara. (1996). Early Marriage Among Women in Developing Countries. International Family Planning Perspectives, Vol. 22, No. 4, pp. 148-157

Sobotka, Tomáš (2004). Is Lowest-Low Fertility in Europe Explained by the Postponement of Childbearing? Population and Development Review, Vol. 30, No. 2, pp. 195-220

United Nations (1988). First Marriage: Patterns and Determinants. New York: Department of International Economic and Social Affairs of the United Nations Secretariat.

United Nations (1990). Patterns of First Marriage: Timing and Prevalence. New York: Department of International Economic and Social Affairs of the United Nations Secretariat.

United Nations (1996). Levels and Trends of Contraceptive Use as Assessed in 1994. New York: United Nations.

javascript:void(0)javascript:void(0)

19

United Nations, Department of Economic and Social Affairs, Population Division (2015). World Marriage Data 2015. New York: United Nations. http://www.un.org/en/development/desa/population/theme/marriage-unions/WMD2015.shtml

United Nations, Department of Economic and Social Affairs (2016). SDG Indicators. Global indicator framework for the Sustainable Development Goals and targets of the 2030 Agenda for Sustainable Development. United Nations: New York. https://unstats.un.org/sdgs/indicators/indicators-list/

United Nations, Department of Economic and Social Affairs, Population Division (2016). Estimates and Projections of the Number of Women Aged 15-49 Who Are Married or in a Union: 2016 Revision. New York: United Nations. http://www.un.org/en/development/desa/population/theme/marriage-unions/marriage_estimates.shtml

United Nations, Department of Economic and Social Affairs, Population Division (2017). Model-based Estimates and Projections of Family Planning Indicators 2017. New York: United Nations. http://www.un.org/en/development/desa/population/theme/family-planning/cp_model.shtml

United Nations General Assembly. 2015. Transforming Our World: The 2030 Agenda for Sustainable Development. Resolution adopted by the General Assembly on 25 September 2015 (A/RES/70/1). New York. https://sustainabledevelopment.un.org/post2015/transformingourworld

http://www.un.org/en/development/desa/population/theme/marriage-unions/WMD2015.shtmlhttps://unstats.un.org/sdgs/indicators/indicators-list/https://unstats.un.org/sdgs/indicators/indicators-list/http://www.un.org/en/development/desa/population/theme/marriage-unions/marriage_estimates.shtmlhttp://www.un.org/en/development/desa/population/theme/marriage-unions/marriage_estimates.shtmlhttp://www.un.org/en/development/desa/population/theme/family-planning/cp_model.shtmlhttps://sustainabledevelopment.un.org/post2015/transformingourworld

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Appendix National, regional and global trends in marriage and cohabiting unions: Estimates and projections of the proportion of women who are married or in a union by age Mi Hong Yim1, Leontine Alkema2, Vladimira Kantorova3

October 19, 2017

METHODS 1 Total proportion model and the ratio model 1.1 Total proportion and the ratio

To obtain estimates and projections of the proportion of married or in-union women of reproductive age (MWRA), we developed a statistical model of the distribution of women into 3 categories - married, in a union, or not married/in-union for each 5-year age group. 𝑚𝑚𝑐𝑐,𝑡𝑡,𝑥𝑥 denotes the proportion of women who are married and 𝑢𝑢𝑐𝑐,𝑡𝑡,𝑥𝑥 denotes the proportion of women in a union in country 𝑐𝑐, year 𝑡𝑡 and age group 𝑥𝑥. 5-year period was used for year 𝑡𝑡 and age group 𝑥𝑥. If 𝑃𝑃𝑐𝑐,𝑡𝑡,𝑥𝑥 denotes total proportion of MWRA and 𝑅𝑅𝑐𝑐,𝑡𝑡,𝑥𝑥 denotes the ratio of the proportion of in-union women of reproductive age to total proportion of MWRA in country 𝑐𝑐, year 𝑡𝑡 and age group 𝑥𝑥,

𝑃𝑃𝑐𝑐,𝑡𝑡,𝑥𝑥 = 𝑚𝑚𝑐𝑐,𝑡𝑡,𝑥𝑥 + 𝑢𝑢𝑐𝑐,𝑡𝑡,𝑥𝑥,

𝑅𝑅𝑐𝑐,𝑡𝑡,𝑥𝑥 = 𝑢𝑢𝑐𝑐,𝑡𝑡,𝑥𝑥/(𝑚𝑚𝑐𝑐,𝑡𝑡,𝑥𝑥 + 𝑢𝑢𝑐𝑐,𝑡𝑡,𝑥𝑥),

with 0 ≤ 𝑃𝑃𝑐𝑐,𝑡𝑡,𝑥𝑥,𝑅𝑅𝑐𝑐,𝑡𝑡,𝑥𝑥 ≤ 1. To obtain 𝑃𝑃𝑐𝑐,𝑡𝑡,𝑥𝑥 and 𝑅𝑅𝑐𝑐,𝑡𝑡,𝑥𝑥 in 5-year age groups for all country-years, we combine a parametric function, which gives the expected age pattern for any subregion-year combination, with a time-series model that captures fluctuations around these outcomes. 𝑃𝑃𝑐𝑐,𝑡𝑡,𝑥𝑥 and 𝑅𝑅𝑐𝑐,𝑡𝑡,𝑥𝑥 are modelled on logit-scale by parametric functions over age with autocorrelated distortions:

𝑃𝑃𝑐𝑐,𝑡𝑡,𝑥𝑥 = logit−1(logit(𝑘𝑘𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥) + 𝑞𝑞𝑐𝑐,𝑡𝑡,𝑥𝑥),

𝑅𝑅𝑐𝑐,𝑡𝑡,𝑥𝑥 = logit−1(logit(𝑓𝑓𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥) + 𝑔𝑔𝑐𝑐,𝑡𝑡,𝑥𝑥),

where 𝑘𝑘𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 and 𝑓𝑓𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 are subregion-year specific parametric functions over age 𝑥𝑥 in subregion 𝑠𝑠𝑠𝑠 and year 𝑡𝑡. 𝑞𝑞𝑐𝑐,𝑡𝑡,𝑥𝑥 and 𝑔𝑔𝑐𝑐,𝑡𝑡,𝑥𝑥 are the distortions in country 𝑐𝑐, year 𝑡𝑡 and age group 𝑥𝑥. The distortions are modelled by autoregressive process of order 1 with autoregressive parameters 𝜌𝜌𝑞𝑞,𝑥𝑥 and 𝜌𝜌𝑔𝑔,𝑥𝑥, the same distortions of one time period ago 𝑞𝑞𝑐𝑐,𝑡𝑡−1,𝑥𝑥 and 𝑔𝑔𝑐𝑐,𝑡𝑡−1,𝑥𝑥 and variances 𝜎𝜎𝑞𝑞,𝑥𝑥2 and 𝜎𝜎𝑔𝑔,𝑥𝑥2 :

𝑞𝑞𝑐𝑐,𝑡𝑡,𝑥𝑥~𝑁𝑁�𝜌𝜌𝑞𝑞,𝑥𝑥 ⋅ 𝑞𝑞𝑐𝑐,𝑡𝑡−1,𝑥𝑥,𝜎𝜎𝑞𝑞,𝑥𝑥2 �,

𝑔𝑔𝑐𝑐,𝑡𝑡,𝑥𝑥~𝑁𝑁(𝜌𝜌𝑔𝑔,𝑥𝑥 ⋅ 𝑔𝑔𝑐𝑐,𝑡𝑡−1,𝑥𝑥,𝜎𝜎𝑔𝑔,𝑥𝑥2 ),

with 0 < 𝜌𝜌𝑞𝑞,𝑥𝑥 ,𝜌𝜌𝑔𝑔,𝑥𝑥 < 1. The distortion at 𝑡𝑡 = 1 in country 𝑐𝑐 and age group 𝑥𝑥 are given by:

𝑞𝑞𝑐𝑐,1,𝑥𝑥~𝑁𝑁�0,𝜎𝜎𝑞𝑞,𝑥𝑥2

1 − 𝜌𝜌𝑞𝑞,𝑥𝑥2�,

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𝑔𝑔𝑐𝑐,1,𝑥𝑥~𝑁𝑁�0,𝜎𝜎𝑔𝑔,𝑥𝑥2

1 − 𝜌𝜌𝑔𝑔,𝑥𝑥2�.

1.2 Parametric functions in total proportion and the ratio over age The parametric function in total proportion over age

The parametric function 𝑘𝑘𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 in total proportion of women who are married or in a union is given over age by:

𝑘𝑘𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 = 𝐾𝐾𝑠𝑠𝑠𝑠,𝑡𝑡 �𝐸𝐸𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 + 𝐴𝐴𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥

2�,

𝐾𝐾𝑠𝑠𝑠𝑠,𝑡𝑡(𝑎𝑎) =

⎩⎪⎨

⎪⎧3 ⋅ 𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡 ⋅ (𝑎𝑎 − 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡)

2

𝛥𝛥1𝑠𝑠𝑠𝑠,𝑡𝑡2−

2 ⋅ 𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡 ⋅ (𝑎𝑎 − 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡)3

𝛥𝛥1𝑠𝑠𝑠𝑠,𝑡𝑡3, for 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡 ≤ 𝑎𝑎 ≤ 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡 + 𝛥𝛥1𝑠𝑠𝑠𝑠,𝑡𝑡

�𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡 − 𝑣𝑣𝑠𝑠𝑠𝑠,𝑡𝑡� −𝑣𝑣𝑠𝑠𝑠𝑠,𝑡𝑡

50 − �𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡 + 𝛥𝛥1𝑠𝑠𝑠𝑠,𝑡𝑡�⋅ (𝑎𝑎 − 50), for 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡 + 𝛥𝛥1𝑠𝑠𝑠𝑠,𝑡𝑡 < 𝑎𝑎 ≤ 50,

with parameters 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡,Δ1𝑠𝑠𝑠𝑠,𝑡𝑡 ,𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡 and 𝑣𝑣𝑠𝑠𝑠𝑠,𝑡𝑡 in subregion 𝑠𝑠𝑠𝑠 and year 𝑡𝑡 , where 𝑎𝑎 denotes age, 𝐴𝐴𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 and 𝐸𝐸𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 denote the start age and the end age of age group 𝑥𝑥. 𝑘𝑘𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 was approximated at the midpoint of the age group 𝑥𝑥. 𝐾𝐾𝑠𝑠𝑠𝑠,𝑡𝑡(𝑎𝑎) is illustrated in Figure 1 (Left). It has 4 parameters: the age at which the proportion of MWRA starts to increase (𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡), the age at which the proportion of MWRA peaks (𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡 + Δ1𝑠𝑠𝑠𝑠,𝑡𝑡), the proportion of MWRA at age 50 (𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡 − 𝑣𝑣𝑠𝑠𝑠𝑠,𝑡𝑡) and the maximum proportion of MWRA (observed at age 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡 + Δ1𝑠𝑠𝑠𝑠,𝑡𝑡) (𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡).

The parametric function in the ratio over age

The parametric function 𝑓𝑓𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 in the ratio of the proportion of in-union women of reproductive age to total proportion is given over age by:

𝑓𝑓𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 = 𝐹𝐹𝑠𝑠𝑠𝑠,𝑡𝑡 �𝐸𝐸𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 + 𝐴𝐴𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥

2�,

𝐹𝐹𝑠𝑠𝑠𝑠,𝑡𝑡(𝑎𝑎) = �logit−1 �

ℎ𝑠𝑠𝑠𝑠,𝑡𝑡𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡2

⋅ (𝑎𝑎 − (15 + 𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡))2 + 𝑏𝑏𝑠𝑠𝑠𝑠,𝑡𝑡� , for 𝑎𝑎 ≤ 15 + 𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡

logit−1�𝑏𝑏𝑠𝑠𝑠𝑠,𝑡𝑡�, for 𝑎𝑎 > 15 + 𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡 ,

with parameters ℎ𝑠𝑠𝑠𝑠,𝑡𝑡 ,𝑏𝑏𝑠𝑠𝑠𝑠,𝑡𝑡 and 𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡 in subregion 𝑠𝑠𝑠𝑠 and year 𝑡𝑡, where 𝑎𝑎 denotes age, 𝐴𝐴𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 and 𝐸𝐸𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 denote the start age and the end age of age group 𝑥𝑥. 𝑓𝑓𝑠𝑠𝑠𝑠,𝑡𝑡,𝑥𝑥 was approximated at the midpoint of the age group 𝑥𝑥. 𝐹𝐹𝑠𝑠𝑠𝑠,𝑡𝑡(𝑎𝑎) is illustrated in Figure 1 (Right). It has 3 parameters: the age at which the ratio starts to stop moving (15 + 𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡), the ratio at age 15 + 𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡 (logit−1�𝑏𝑏𝑠𝑠𝑠𝑠,𝑡𝑡�) and the ratio at age 15 (logit−1�𝑏𝑏𝑠𝑠𝑠𝑠,𝑡𝑡 + ℎ𝑠𝑠𝑠𝑠,𝑡𝑡�).

22

Figure 1: Left: Parametric model in the proportion of MWRA over age. Right: Parametric model in the ratio of the proportion of in-union women to the proportion of MWRA over age. 1.3 Systematic trends in parameters of total proportion and the ratio The systematic trends in parameters of total proportion

The parameters 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡 ,Δ1𝑠𝑠𝑠𝑠,𝑡𝑡 ,𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡 and 𝑣𝑣𝑠𝑠𝑠𝑠,𝑡𝑡 of 𝐾𝐾𝑠𝑠𝑠𝑠,𝑡𝑡(𝑎𝑎) are likely to change with time and vary across subregions. To incorporate differences over time and across subregions, each of the parameters is modelled with a logistic growth curve over time for each subregion. The systematic trends in parameters 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡,Δ1𝑠𝑠𝑠𝑠,𝑡𝑡 and 𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡 of 𝐾𝐾𝑠𝑠𝑠𝑠,𝑡𝑡(𝑎𝑎) are given by logistic curves over time:

𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡 = 𝑧𝑧𝑠𝑠𝑠𝑠,min +𝛿𝛿𝑠𝑠𝑠𝑠,𝑧𝑧 ⋅ (20 − 𝑧𝑧𝑠𝑠𝑠𝑠,min)

1 + exp(−𝜔𝜔𝑠𝑠𝑠𝑠 ⋅ (𝑡𝑡 − Ω𝑠𝑠𝑠𝑠)),

Δ1𝑠𝑠𝑠𝑠,𝑡𝑡 = Δ1𝑠𝑠𝑠𝑠,min +𝛿𝛿𝑠𝑠𝑠𝑠,1 ⋅ (25 − Δ1𝑠𝑠𝑠𝑠,min)

1 + exp(−𝜔𝜔𝑠𝑠𝑠𝑠 ⋅ (𝑡𝑡 − Ω𝑠𝑠𝑠𝑠)),

𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡 = 𝑑𝑑𝑠𝑠𝑠𝑠,min +𝛿𝛿𝑠𝑠𝑠𝑠,𝑑𝑑 ⋅ (1 − 𝑑𝑑𝑠𝑠𝑠𝑠,min)

1 + exp(𝜔𝜔𝑠𝑠𝑠𝑠 ⋅ (𝑡𝑡 − Ω𝑠𝑠𝑠𝑠)),

where same pace parameter 𝜔𝜔𝑠𝑠𝑠𝑠 and same timing parameter Ω𝑠𝑠𝑠𝑠 for all logistic curves are given. Logistic curve in 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡 is increasing over time at pace 𝜔𝜔𝑠𝑠𝑠𝑠 from 𝑧𝑧𝑠𝑠𝑠𝑠,min to 𝑧𝑧𝑠𝑠𝑠𝑠,min + 𝛿𝛿𝑠𝑠𝑠𝑠,𝑧𝑧 ⋅ (20 −𝑧𝑧𝑠𝑠𝑠𝑠,min) and centered in year Ω𝑠𝑠𝑠𝑠. Logistic curve in Δ1𝑠𝑠𝑠𝑠,𝑡𝑡 is similar to 𝑧𝑧𝑠𝑠𝑠𝑠,𝑡𝑡. Logistic curve in 𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡 is decreasing over time at pace 𝜔𝜔𝑠𝑠𝑠𝑠 from 𝑑𝑑𝑠𝑠𝑠𝑠,min + 𝛿𝛿𝑠𝑠𝑠𝑠,𝑑𝑑 ⋅ (1 − 𝑑𝑑𝑠𝑠𝑠𝑠,min) to 𝑑𝑑𝑠𝑠𝑠𝑠,min and centered in year Ω𝑠𝑠𝑠𝑠. Figure 2 (Left) shows the logistic curve in parameter 𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡. The systematic trend in parameter 𝑣𝑣𝑠𝑠𝑠𝑠,𝑡𝑡 is given by linear function over time:

𝑣𝑣𝑠𝑠𝑠𝑠,𝑡𝑡 = 𝑚𝑚𝑎𝑎𝑥𝑥 �−𝛿𝛿𝑠𝑠𝑠𝑠,𝑣𝑣

2050− 1950⋅ (𝑡𝑡 − 2050),0�,

where 𝑣𝑣𝑠𝑠𝑠𝑠,𝑡𝑡 is decreasing from 𝛿𝛿𝑠𝑠𝑠𝑠,𝑣𝑣 to 0 over time and 𝑣𝑣𝑠𝑠𝑠𝑠,𝑡𝑡 has 𝛿𝛿𝑠𝑠𝑠𝑠,𝑣𝑣 at year 1950 and 0 at year 2050.

The systematic trends in parameters of the ratio

The parameters ℎ𝑠𝑠𝑠𝑠,𝑡𝑡, 𝑏𝑏𝑠𝑠𝑠𝑠,𝑡𝑡 and 𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡 of 𝐹𝐹𝑠𝑠𝑠𝑠,𝑡𝑡(𝑎𝑎) are likely to change with time and vary across subregions. To incorporate differences over time and across subregions, each of the parameters is modelled with a logistic growth curve over time for each subregion. The systematic trends in parameters ℎ𝑠𝑠𝑠𝑠,𝑡𝑡,𝑏𝑏𝑠𝑠𝑠𝑠,𝑡𝑡 and 𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡 of 𝐹𝐹𝑠𝑠𝑠𝑠,𝑡𝑡(𝑎𝑎) are given by logistic curves over time:

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ℎ𝑠𝑠𝑠𝑠,𝑡𝑡 = ℎ𝑠𝑠𝑠𝑠,min +𝛿𝛿𝑠𝑠𝑠𝑠,ℎ

1 + exp(−𝛼𝛼𝑠𝑠𝑠𝑠(𝑡𝑡 − Λ𝑠𝑠𝑠𝑠)),

𝑏𝑏𝑠𝑠𝑠𝑠,𝑡𝑡 = 𝑏𝑏𝑠𝑠𝑠𝑠,min +𝛿𝛿𝑠𝑠𝑠𝑠,𝑏𝑏

1 + exp(−𝛼𝛼𝑠𝑠𝑠𝑠(𝑡𝑡 − Λ𝑠𝑠𝑠𝑠)),

𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡 = 𝑒𝑒𝑠𝑠𝑠𝑠,min +𝛿𝛿𝑠𝑠𝑠𝑠,𝑒𝑒

1 + exp(−𝛼𝛼𝑠𝑠𝑠𝑠(𝑡𝑡 − Λ𝑠𝑠𝑠𝑠)),

where same pace parameter 𝛼𝛼𝑠𝑠𝑠𝑠 and same timing parameter Λ𝑠𝑠𝑠𝑠 for all logistic curves are given. Logistic curve in ℎ𝑠𝑠𝑠𝑠,𝑡𝑡 is increasing over time at pace 𝛼𝛼𝑠𝑠𝑠𝑠 from ℎ𝑠𝑠𝑠𝑠,min to ℎ𝑠𝑠𝑠𝑠,min + 𝛿𝛿𝑠𝑠𝑠𝑠,ℎ and centered in year Λ𝑠𝑠𝑠𝑠. Logistic curves in 𝑏𝑏𝑠𝑠𝑠𝑠,𝑡𝑡 and 𝑒𝑒𝑠𝑠𝑠𝑠,𝑡𝑡 are similar to ℎ𝑠𝑠𝑠𝑠,𝑡𝑡. Figure 2 (Right) shows the logistic curve in parameter ℎ𝑠𝑠𝑠𝑠,𝑡𝑡.

Figure 2: Left: Example of a logistic growth curve to model changes in parameter 𝑑𝑑𝑠𝑠𝑠𝑠,𝑡𝑡. Right: Example of a logistic growth curve to model changes in parameter ℎ𝑠𝑠𝑠𝑠,𝑡𝑡. 2 Bayesian hierarchical model

Different levels hierarchies are used for different sets of parameters to estimate the subregion-

specific parameters of systmatic trends. The parameters related to the lower and upper asymptotes in logistic curves are estimated with a hierarchical model with one level:

𝑧𝑧𝑠𝑠𝑠𝑠,𝑚𝑚𝑚𝑚𝑛𝑛∗ = logit(𝑧𝑧𝑠𝑠𝑠𝑠,𝑚𝑚𝑚𝑚𝑚𝑚−520−5

)~𝑁𝑁(𝑧𝑧𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛∗ ,𝜅𝜅𝑧𝑧𝑚𝑚𝑚𝑚𝑚𝑚(𝑠𝑠𝑠𝑠) ),

𝛥𝛥1𝑠𝑠𝑠𝑠,𝑚𝑚𝑚𝑚𝑛𝑛∗ = logit(𝛥𝛥1𝑠𝑠𝑠𝑠,𝑚𝑚𝑚𝑚𝑚𝑚−5

25−5)~𝑁𝑁(𝛥𝛥1𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛∗ ,𝜅𝜅𝛥𝛥1𝑚𝑚𝑚𝑚𝑚𝑚

(𝑠𝑠𝑠𝑠) ),

𝑑𝑑𝑠𝑠𝑠𝑠,𝑚𝑚𝑚𝑚𝑛𝑛∗ = logit(𝑑𝑑𝑠𝑠𝑠𝑠,𝑚𝑚𝑚𝑚𝑚𝑚−0.3

1−0.3)~𝑁𝑁(𝑑𝑑𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛∗ , 𝜅𝜅𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚

(𝑠𝑠𝑠𝑠) ),

ℎ𝑠𝑠𝑠𝑠,𝑚𝑚𝑚𝑚𝑛𝑛~𝑁𝑁(ℎ𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛,𝜅𝜅ℎ𝑚𝑚𝑚𝑚𝑚𝑚(𝑠𝑠𝑠𝑠) )𝑇𝑇(0, ),

𝑏𝑏𝑠𝑠𝑠𝑠,𝑚𝑚𝑚𝑚𝑛𝑛~𝑁𝑁(𝑏𝑏𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛,𝜅𝜅𝑏𝑏𝑚𝑚𝑚𝑚𝑚𝑚(𝑠𝑠𝑠𝑠) ),

𝑒𝑒𝑠𝑠𝑠𝑠,𝑚𝑚𝑚𝑚𝑛𝑛~𝑁𝑁(𝑒𝑒𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛, 𝜅𝜅𝑒𝑒𝑚𝑚𝑚𝑚𝑚𝑚(𝑠𝑠𝑠𝑠) )𝑇𝑇(0,100),

𝛿𝛿𝑠𝑠𝑠𝑠,𝑧𝑧∗ = logit(𝛿𝛿𝑠𝑠𝑠𝑠,𝑧𝑧−01−0

)~𝑁𝑁(𝛿𝛿𝑤𝑤,𝑧𝑧∗ , 𝜅𝜅𝛿𝛿𝑧𝑧(𝑠𝑠𝑠𝑠)),

𝛿𝛿𝑠𝑠𝑠𝑠,1∗ = logit(𝛿𝛿𝑠𝑠𝑠𝑠,1−01−0

)~𝑁𝑁(𝛿𝛿𝑤𝑤,1∗ ,𝜅𝜅𝛿𝛿1(𝑠𝑠𝑠𝑠)),

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𝛿𝛿𝑠𝑠𝑠𝑠,𝑑𝑑∗ = logit(𝛿𝛿𝑠𝑠𝑠𝑠,𝑑𝑑−01−0

)~𝑁𝑁(𝛿𝛿𝑤𝑤,𝑑𝑑∗ ,𝜅𝜅𝛿𝛿𝑑𝑑(𝑠𝑠𝑠𝑠)),

𝛿𝛿𝑠𝑠𝑠𝑠,ℎ~𝑁𝑁(𝛿𝛿𝑤𝑤,ℎ ,𝜅𝜅𝛿𝛿ℎ(𝑠𝑠𝑠𝑠))𝑇𝑇(0, ),

𝛿𝛿𝑠𝑠𝑠𝑠,𝑏𝑏~𝑁𝑁(𝛿𝛿𝑤𝑤,𝑏𝑏 ,𝜅𝜅𝛿𝛿𝑏𝑏(𝑠𝑠𝑠𝑠))𝑇𝑇(0, ),

𝛿𝛿𝑠𝑠𝑠𝑠,𝑒𝑒~𝑁𝑁(𝛿𝛿𝑤𝑤,𝑒𝑒 , 𝜅𝜅𝛿𝛿𝑒𝑒(𝑠𝑠𝑠𝑠))𝑇𝑇(0,100).

For pace parameters, two-level hierarchical models are used:

𝜔𝜔𝑠𝑠𝑠𝑠∗ = logit(𝜔𝜔𝑠𝑠𝑠𝑠−0.010.5−0.01

)~𝑁𝑁(𝜔𝜔𝑠𝑠[𝑠𝑠𝑠𝑠]∗ ,𝜅𝜅𝜔𝜔(𝑠𝑠𝑠𝑠)),

𝜔𝜔𝑠𝑠∗~𝑁𝑁(𝜔𝜔𝑤𝑤∗ ,𝜅𝜅𝜔𝜔(𝑠𝑠)),

𝛼𝛼𝑠𝑠𝑠𝑠∗ = logit(𝛼𝛼𝑠𝑠𝑠𝑠−0.010.5−0.01

)~𝑁𝑁(𝛼𝛼𝑠𝑠[𝑠𝑠𝑠𝑠]∗ , 𝜅𝜅𝛼𝛼(𝑠𝑠𝑠𝑠)),

𝛼𝛼𝑠𝑠∗~𝑁𝑁(𝛼𝛼𝑤𝑤∗ ,𝜅𝜅𝛼𝛼(𝑠𝑠)).

For the timing parameter Ωsr in total proportion for developed subregions, one-level hierarchical model is used:

𝛺𝛺𝑠𝑠𝑠𝑠∗ = logit �𝛺𝛺𝑠𝑠𝑠𝑠−19102090−1910

�,

𝛺𝛺𝑠𝑠𝑠𝑠∗ ~𝑁𝑁�𝛺𝛺𝐷𝐷∗ ,𝜅𝜅𝛺𝛺(𝐷𝐷)� , 𝑠𝑠𝑠𝑠 ∈ D(developed subregions),

while for the timing parameter Ωsr in total proportion for developing subregions, two-level hierarchical model is used:

𝛺𝛺𝑠𝑠𝑠𝑠∗ = logit(𝛺𝛺𝑠𝑠𝑠𝑠−19102090−1910

),

𝛺𝛺𝑠𝑠𝑠𝑠∗ ~𝑁𝑁�𝛺𝛺𝑠𝑠[𝑠𝑠𝑠𝑠]∗ , 𝜅𝜅𝛺𝛺

(𝑠𝑠𝑠𝑠)� , 𝑠𝑠𝑠𝑠 ∈ L(developing subregions)

𝛺𝛺𝑠𝑠∗~𝑁𝑁(𝛺𝛺𝑤𝑤∗ ,𝜅𝜅𝛺𝛺(𝑠𝑠)).

For the timing parameter Λsr in the ratio for all subregions, two-level hierarchical model is used:

𝛬𝛬𝑠𝑠𝑠𝑠∗ = logit(𝛬𝛬𝑠𝑠𝑠𝑠−19102050−1910

)~𝑁𝑁(𝛬𝛬𝑠𝑠[𝑠𝑠𝑠𝑠]∗ , 𝜅𝜅𝛬𝛬(𝑠𝑠𝑠𝑠)),

𝛬𝛬𝑠𝑠∗~𝑁𝑁(𝛬𝛬𝑤𝑤∗ ,𝜅𝜅𝛬𝛬(𝑠𝑠)).

For the parameter δsr,v in linear function, one-level hierarchical model is used:

𝛿𝛿𝑠𝑠𝑠𝑠,𝑣𝑣∗ = logit(𝛿𝛿𝑠𝑠𝑠𝑠,𝑣𝑣−00.3−0

)~𝑁𝑁(𝛿𝛿𝑤𝑤,𝑣𝑣∗ ,𝜅𝜅𝛿𝛿𝑣𝑣(𝑠𝑠𝑠𝑠))

3 Data model

Observation 𝑦𝑦𝑠𝑠,𝑗𝑗,1 denotes the observed proportion of women in marriage and observation 𝑦𝑦𝑠𝑠,𝑗𝑗,2

25

denotes the observed proportion of women in a union for survey 𝑠𝑠 and age group 𝑗𝑗. Observation 𝑦𝑦𝑠𝑠,𝑗𝑗,3 denotes the observed proportion of women in marriage or in a union for survey 𝑠𝑠 and age group 𝑗𝑗. 𝑐𝑐[𝑠𝑠] denotes country, 𝑡𝑡[𝑠𝑠] denotes year and 𝑥𝑥[𝑠𝑠, 𝑗𝑗] denotes age group of 5-year period for survey 𝑠𝑠 and age group 𝑗𝑗. The data model for the proportion of women in marriage is given by:

𝑦𝑦𝑠𝑠,𝑗𝑗,1~𝑁𝑁(𝑚𝑚𝑐𝑐[𝑠𝑠],𝑡𝑡[𝑠𝑠],𝑥𝑥[𝑠𝑠,𝑗𝑗],𝜎𝜎𝑚𝑚2 ).

The data model for the proportion of women in a union is given by:

𝑦𝑦𝑠𝑠,𝑗𝑗,2~𝑁𝑁(𝑢𝑢𝑐𝑐[𝑠𝑠],𝑡𝑡[𝑠𝑠],𝑥𝑥[𝑠𝑠,𝑗𝑗],𝜎𝜎𝑢𝑢2).

The data model for the proportion of women in marriage or in a union is given by:

𝑦𝑦𝑠𝑠,𝑗𝑗,3~𝑁𝑁(𝑃𝑃𝑐𝑐[𝑠𝑠],𝑡𝑡[𝑠𝑠],𝑥𝑥[𝑠𝑠,𝑗𝑗],𝜎𝜎𝑝𝑝2).

4 Prior distributions

Spread-out prior distributions were used for world-level mean parameters for total proportion model and the ratio model:

𝜎𝜎𝑚𝑚~𝑈𝑈(0,0.05)

𝜎𝜎𝑢𝑢~𝑈𝑈(0,0.05)

𝜎𝜎𝑝𝑝~𝑈𝑈(0,0.05)

𝜌𝜌𝑞𝑞,𝑥𝑥~𝑈𝑈(0,1)

𝜎𝜎𝑞𝑞,𝑥𝑥~𝑈𝑈(0,5)

𝜌𝜌𝑔𝑔,𝑥𝑥~𝑈𝑈(0,1)

𝜎𝜎𝑔𝑔,𝑥𝑥~𝑈𝑈(0,5)

𝑧𝑧𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛∗ ~𝑁𝑁(0,10)

𝛿𝛿𝑤𝑤,𝑧𝑧∗ ~𝑁𝑁(0,20)

𝛥𝛥1𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛∗ ~𝑁𝑁(0,10)

𝛿𝛿𝑤𝑤,1∗ ~𝑁𝑁(0,10)

𝑑𝑑𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛∗ ~𝑁𝑁(0,10)

𝛿𝛿𝑤𝑤,𝑑𝑑∗ ~𝑁𝑁(0,10)

𝜔𝜔𝑤𝑤∗ ~𝑁𝑁(−1,10)

𝛺𝛺𝑤𝑤∗ ~𝑁𝑁(0,10)

𝛺𝛺𝐷𝐷∗ ~𝑁𝑁(0,10)

𝛿𝛿𝑤𝑤,𝑣𝑣∗ ~𝑁𝑁(0,20)

𝜅𝜅𝑧𝑧𝑚𝑚𝑚𝑚𝑚𝑚(𝑠𝑠𝑠𝑠) ~𝑈𝑈(0,5)

𝜅𝜅𝛿𝛿𝑧𝑧(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,10)

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𝜅𝜅𝛥𝛥1𝑚𝑚𝑚𝑚𝑚𝑚(𝑠𝑠𝑠𝑠) ~𝑈𝑈(0,5)

𝜅𝜅𝛿𝛿1(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,5)

𝜅𝜅𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚(𝑠𝑠𝑠𝑠) ~𝑈𝑈(0,5)

𝜅𝜅𝛿𝛿𝑑𝑑(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,5)

𝜅𝜅𝜔𝜔(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,20)

𝜅𝜅𝜔𝜔(𝑠𝑠)~𝑈𝑈(0,20)

𝜅𝜅𝛺𝛺(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,5)

𝜅𝜅𝛺𝛺(𝑠𝑠)~𝑈𝑈(0,5)

𝜅𝜅𝛺𝛺(𝐷𝐷)~𝑈𝑈(0,5)

𝜅𝜅𝛿𝛿𝑣𝑣(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,5)

ℎ𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛~𝑈𝑈(0,10)

𝛿𝛿𝑤𝑤,ℎ~𝑈𝑈(0,10)

𝑏𝑏𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛~𝑈𝑈(−10,10)

𝛿𝛿𝑤𝑤,𝑏𝑏~𝑈𝑈(0,10)

𝑒𝑒𝑤𝑤,𝑚𝑚𝑚𝑚𝑛𝑛~𝑈𝑈(0,100)

𝛿𝛿𝑤𝑤,𝑒𝑒~𝑈𝑈(0,100)

𝛼𝛼𝑤𝑤∗ ~𝑁𝑁(−1,50)

𝛬𝛬𝑤𝑤∗ ~𝑁𝑁(0,10)

𝜅𝜅ℎ𝑚𝑚𝑚𝑚𝑚𝑚(𝑠𝑠𝑠𝑠) ~𝑈𝑈(0,5)

𝜅𝜅𝛿𝛿ℎ(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,5)

𝜅𝜅𝑏𝑏𝑚𝑚𝑚𝑚𝑚𝑚(𝑠𝑠𝑠𝑠) ~𝑈𝑈(0,5)

𝜅𝜅𝛿𝛿𝑏𝑏(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,10)

𝜅𝜅𝑒𝑒𝑚𝑚𝑚𝑚𝑚𝑚(𝑠𝑠𝑠𝑠) ~𝑈𝑈(0,100)

𝜅𝜅𝛿𝛿𝑒𝑒(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,100)

𝜅𝜅𝛼𝛼(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,20)

𝜅𝜅𝛼𝛼(𝑠𝑠)~𝑈𝑈(0,20)

27

𝜅𝜅𝛬𝛬(𝑠𝑠𝑠𝑠)~𝑈𝑈(0,5)

𝜅𝜅𝛬𝛬(𝑠𝑠)~𝑈𝑈(0,5)

5 Computation

A Markov Chain Monte Carlo (MCMC) algorithm was used to generate samples of the posterior distributions of the parameters using JAGS software (Plummer M, 2003) and the analysis was carried out in R (R Development Core Team, 2013). Results were obtained from 4 chains. After discarding the first 30,000 iterations as burn-in, 840,000 iterations was obtained in each chain, keeping every 600th iteration. Convergence of the MCMC algorithm was checked through visual inspection of trace plots and convergence diagnostics of Gelman and Rubin.