Mechanisms of family formation: An application of Hidden Markov Models to a life course process

(2020) - Sapphire Yu Han, Aart C. Liefbroer, Cees H. Elzinga

Journal: Advances in Life Course Research
Link:: https://linkinghub.elsevier.com/retrieve/pii/S1040260818300807
DOI:: 10.1016/j.alcr.2019.03.001
Links::
Tags:: #paper #LifeCourse #SocialTheory
Cite Key:: [@hanMechanismsFamilyFormation2020]

Abstract

Life courses consist of complex patterns of correlated events and spells. The nature and strength of these correlations is known to depend on both micro- and macrocovariates. Life-course models such as event-history analysis and sequence analysis are not well equipped to deal with the processual and latent character of the decision- making process. We argue that Hidden Markov Models satisfy the requirements of a life course model. To illustrate their usefulness, this study will use Hidden Markov chains to model trajectories of family formation. We used data from the Generations and Gender Programme to estimate Hidden Markov Models. The results show the potential of this approach to unravel the mechanisms underlying life-course decision making and how these processes differ both by gender and education.

Notes

"What is lacking, though, are statistical models that allow us to understand how the observed life-course patterns are generated." (Han et al 2020:100265)

"nutshell, an HMM describes a life course as a sequence of observed states that are outcomes of a latent, unobservable decision making process." (Han et al 2020:100265)

"Hidden Markov Models satisfy the requirements of a life course model" (Han et al 2020:100265)

"results show the potential of this approach to unravel the mechanisms underlying life-course decision making and how these processes differ both by gender and education." (Han et al 2020:100265)

"A life course is an individual's narrative of all events or states, ordered in time, that this individual has experienced" (Han et al 2020:100265)

"Event history analysis (EHA) uses regression models to predict the occurrence of particular (combinations of) lifecourse events (Blossfeld, Golsch, & Rohwer, 2007). Sequence analysis (SA) (Cornwell, 2015) is mostly used to find the characteristic patterns in a set of life courses and thereto, SA creates a distance-based representation of this set of life courses. Eventually, this spatial configuration can be used to examine the association between a set of covariates and the final classification (Studer, Ritschard, Gabadinho, & Müller, 2011)." (Han et al 2020:100265)

"However, using HMMs is also very attractive because its characteristics nicely mirror key theoretical assumptions of the life-course paradigm." (Han et al 2020:100265)

"first key assumption of the life-course approach is that individuals exert life-course agency, and thus reflect on their available options and consciously make decisions on appropriate action sequences (Hitlin et al., 2007)." (Han et al 2020:100265)

"Life-course models such as event-history analysis and sequence analysis are not well equipped to deal with the processual and latent character of the decisionmaking process" (Han et al 2020:100265)

"Thus, any model that is to explain the individual life course has to contain a mechanism that represents these unobservable mental processes." (Han et al 2020:100265)

"Second, it is generally held that events and choices made early in life may affect the (non-)occurrence of other" (Han et al 2020:100265)

"events or their outcomes in later life (Bissell, 2000; Gangl, 2004; Mayer, 2009)." (Han et al 2020:100266)

"Third, we know that the life course and its outcomes depend on microand macro-level covariates that are not affected by individual mental processes (Blossfeld, Klijzing, Mills, & Kurz, 2006; Specht, Egloff, & Schmukle, 2011)." (Han et al 2020:100266)

"life-course model should therefore also allow the inclusion of relevant time-constant and time-varying microand macro-level covariates" (Han et al 2020:100266)

"Latent states can be viewed as key nodes in the mental decision-making process, emphasizing the agentic nature of the lifecourse process" (Han et al 2020:100266)

"This paper aims to demonstrate how HMMs can be used, by applying them to modeling the family formation process. Next to the school-to-work transition, family formation is a key aspect of the transition to adulthood (Buchmann & Kriesi, 2011)." (Han et al 2020:100266)

"A Markov-model or Markov-chain is a random process over a set of states such that the probability of being in a particular state at the next observation only depends on the state-history of the process" (Han et al 2020:100266)

"a Hidden Markov Model, the Markov chain is defined over a set of latent, unobservable states." (Han et al 2020:100266)

"When we apply HMMs to model life courses, we know that some states are almost irreversible: for example, once parenthood is entered, it is a lasting state except for the rare cases of child loss. Models in which a return to a previously occupied state is impossible or highly unlikely are called "left-to-right" models" (Han et al 2020:100266)

"A number of key decisions have to be taken if one wants to apply HMMs to life-course research. In this section, we highlight four of these" (Han et al 2020:100267)

"First, we discuss the extent to which a focus on first-order Markov chains (that is a situation where transition probabilities between latent states only depend on the previous latent state) limits the use of HMMs" (Han et al 2020:100267)

"Second, many processes in young adulthood are age-dependent, and we discuss ways in which age-dependency can be accounted for in HMMs. Third, deciding on the number of latent states to be included in a HMM is discussed. Finally, we discuss ways in which covariates can be linked within HMMs." (Han et al 2020:100267)

"The assumption that the process is first-order is a gross simplification: we know that some events early in the life course may have lasting effects long after their occurrence (see e.g. Gangl, 2004, on the scarring effects of unemployment)." (Han et al 2020:100267)

"second important aspect of a basic HMM is the fact that age does not play a role in the parametrization of the model: the transition-rates in the transition-matrix are constant over time whereas we know that certain transitions are highly age-dependent (Fasang, 2012)." (Han et al 2020:100267)

"A third important aspect of an HMM is determining the number k of latent states. This number has to be fixed by the researcher; it is not a free, estimable parameter. So, when we believe that an HMM is a valid model, the next step is to compare HMMs with different numbers of latent states and use the BIC to select the most parsimonious model (see Burnham & Anderson, 2002, Section 6.5.3)." (Han et al 2020:100267)

"Finally, when using covariates in modeling with HMMs, one has to decide how these covariates affect the behavior of the stochastic system as a whole. This system consists of two main parts: the Markov chain over the latent states and the mechanism through which it expresses itself, i.e. the set of emission probability distributions, one for each of the latent states. Covariates may affect either or both of these components." (Han et al 2020:100267)

"With mixture models, model fit is to be judged through evaluating the likelihood of the data , given the model" (Han et al 2020:100268)

"Covariates like gender, SES and religion and macro-variables like welfare regime and the occurrence of natural disasters, economic crises or political instability are generally held to affect demographic decisions in specific, well researched ways (see e.g. Neels, Theunynck, & Wood, 2015; Härkönen & Dronkers, 2006; Sobotka & Toulemon, 2008; Studer, Liefbroer, & Mooyaart, 2018) Thus one should test whether or not the selected k-state model allows for logical inference: i.e. whether or not the model is able to reproduce these effects" (Han et al 2020:100268)

"when the model is capable of reproducing known effects, the model has become one of the nodes in a nomological network (Han, Liefbroer, & Elzinga, 2017; Torgerson, 1958) about life courses and related phenomena" (Han et al 2020:100268)

"The emission probability matrix tells us which observed states are most clearly linked to a latent state, the initial state matrix tells us whether there is a clear starting state or not, and the transition probabilities matrix tells us which transitions between latent states are likely and which are not" (Han et al 2020:100268)

"We feel that our results reveal a number of interesting viewpoints on the family formation process. The 4-state solution represents the transition to adulthood in the family domain as a process that is mainly driven by fertility. The first challenge that young adults face is about when and how to leave parental home." (Han et al 2020:100273)

"Thus, the 4-state HMM suggests a model of the full family cycle starting as a child in a family of origin and ending up as an adult in a next generation family" (Han et al 2020:100273)

"The 5-state HMM provides another interesting view on the family transition into adulthood. Rather than viewing this transition as a linear trajectory where young adults only differ in the likelihood and speed of moving to successive stages as is central to the 4-state HMM, the 5-state HMM distinguishes between two alternative family pathways into adulthood" (Han et al 2020:100273)

"Our analysis also reveals clear differences in the speed and likelihood of transitions when linking covariates to the structural part of the 5-state HMM" (Han et al 2020:100274)

"The interaction of gender and education also offers interesting insights in the switching between the alternative track and the traditional pattern. High educated males are faster in transiting whereas high-educated women are much more likely to delay switching to the traditional family formation pathway" (Han et al 2020:100274)

"Whether one interprets the data on the basis of the 4-state or 5-state HMM solution at least partly depends on one's theoretical interests." (Han et al 2020:100274)

"state HMM offers a succinct interpretation of the traditional family" (Han et al 2020:100274)

"life pattern, pointing at three major decisions to be taken in the course of the family-life cycle (Glick, 1955). The 5-state HMM incorporates more heterogeneity into this family life cycle (Glick, 1989), and offers interesting opportunities to study the process of family change that is often captured under the heading of the Second Demographic Transition (Lesthaeghe, 1995). Furthermore, the analysis with covariates underscores the validity of the 5-state model." (Han et al 2020:100275)

"major advantage of both of these models is that they greatly limit the complexity of the process of transition into adulthood, by reducing the large number of transitions between observable states to a small number of transitions between unobservable, latent states" (Han et al 2020:100275)

"The inclusion of covariates in a HMM serves two purposes. It offers the opportunity to study the influence of covariates at different stages of the life course and to compare their relative importance at these stages." (Han et al 2020:100275)

"Generally, in applying these models to life-course data, researchers have to be aware of both theoretical and practical restrictions on the analyses. Models should not become too complex in order for them to be mathematically feasible to estimate and to be theoretically interpretable" (Han et al 2020:100275)