Structural Equation Modeling and the Separation of within-Unit Change and between-Unit Variation in Panel Data |
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| Session Organisers | Dr Daniel Seddig (University of Cologne & University of Zurich) Professor Elmar Schlueter (University of Giessen) Mr Nico Seifert (Martin Luther University Halle-Wittenberg) |
| Time | Thursday 18th July, 16:00 - 17:30 |
| Room | D19 |
In many fields of social science, researchers analyze panel data to study change within the units of interest (e.g., persons, groups, organizations, or countries). However, it is not always clear whether the applied statistical models are suitable to identify a causal effect at the within-unit level. Especially the aspect of heterogeneity due to time and due to variation between units may blur statistical estimates and substantive interpretations (Voelkle & Wagner, 2017). In the sociological and econometric literature, between-unit heterogeneity has also been addressed as a problem of omitted unobserved confounders (e.g., Halaby, 2004; Wooldridge, 2002) and fixed-effects regression models (FEM) are recommended as a solution.
Researchers have recently combined the advantages of structural equation modeling (SEM) and FEM by treating the time-invariant unobserved differences between units as latent random variables (e.g., Allison et al., 2017; Bollen & Brand, 2010; Hamaker et al., 2015). The idea of separating within- and between unit variability is not utterly new in SEM (e.g., in latent growth curve modeling) and many features of SEM seem adequate to address particular issues. For example:
(1) The use of lagged dependent and lagged independent variables
(2) Sequential exogeneity and reciprocal causality
(3) Flexible specification and comparison/test of alternative models
(4) Maximum likelihood estimation and handling of missing data
This session aims at presenting studies that use SEM to address unobserved heterogeneity due to time and/or due to differences between units. We welcome (1) applied presentations that make use of survey panel data, and/or that (2) take a methodological approach to address one of the issues listed above or related ones for example by using Monte-Carlo simulations.
Keywords: panel data, unobserved heterogeneity, fixed effects, structural equation modeling
Dr Marco Giesselmann (DIW Berlin) - Presenting Author
Professor Alexander Schmidt-Catran (Goethe University Frankfurt)
An interaction in a fixed effects (FE) regression is usually specified by demeaning the product term. However, algebraic transformations reveal that this strategy does not yield a true within estimator. Instead, the standard FE interaction estimator reflects unit-level differences of interacted variables whose moderators vary within units. This property is desirable whenever the interaction of a time-invariant and a time-varying variable is specified in FE. It may, however, yield unwanted results if both interacted variables vary within units: Monte Carlo experiments confirm that the FE estimator of an interaction is biased if one factor is correlated with an unobserved unit-specific moderator of the other factor. This feature of the standard FE interaction estimator builds on the existence of effect-heterogeneity. Therefore, we discuss several options to deal with this source of heterogeneity between units in panel data analysis.
Mr Nico Seifert (Institute of Medical Sociology (IMS), Martin Luther University Halle-Wittenberg) - Presenting Author
Dr Daniel Seddig (University of Cologne)
Dr Jan Eckhard (University of Koblenz)
Social isolation is a growing threat to public health in aging populations. Previous evidence suggests that social isolation is a major risk factor for early mortality comparable to well-known risk factors such as obesity, physical inactivity, and substance abuse. Furthermore, a lack of social contacts has been associated with an increased risk for a number of health problems as well as subjective measures of health and quality of life. These findings have often been interpreted in terms of the social causation hypothesis, asserting that social isolation has a negative impact on an individual’s health and quality of life. However, most existing studies used research designs that are unable to account for direct selection (health problems leading to a higher risk of social isolation) and indirect selection (confounding by unobserved heterogeneity between individuals). Using data from the German Socio-Economic Panel (GSOEP) study 2004-2012, this study aims to investigate the impact of social isolation on health-related quality of life among older adults (aged 50 years and older) in a novel dynamic panel design with fixed effects. The results show that after addressing sources of endogeneity bias arising from selection processes, social isolation is still associated with lower mental health-related quality of life among men and women, but unrelated to physical health-related quality of life. These findings provide further evidence that social isolation is an important psychosocial risk factor for mental health. However, we find no evidence that social isolation is relevant for physical health.
Ms Nora Huth (GESIS – Leibniz Institute for the Social Sciences, Cologne) - Presenting Author
Mr Elmar Schlüter (Justus-Liebig-University, Gießen)
Strategies for simultaneously modeling within- and between-person relations of two or more constructs over time are of great interest for research on interethnic attitudes. The separation of the intra- and inter-individual components of the relationship between two constructs allows, on the one hand, investigating how the change in one construct affects the intraindividual development of the other construct. On the other hand, it enables to examine differences between persons and the antecedents that can explain these differences. However, so far many common models that aim to investigate reciprocal relationships between two constructs do not allow a clear separation of within- and between-person effects and, therefore, can lead to biased estimates. The Latent Curve Model with Structured Residual (LCM-SR) introduced by Curran et al. (2014)1 overcomes these limits by enabling us to investigate the reciprocal relationship of two constructs simultaneously.
Using the LCM-SR, we examine the within- and between-person relations between perceived discrimination and attitudes towards natives among Turkish adolescents. We take advantage of 5 waves of the IKG-Youth Panel collected among the Youth in West Germany. Controlling for possible reverse relations, we find longitudinal (i.e., within-persons) evidence that increases in perceived discrimination lead to subsequent increases in negative attitudes towards German adolescents. On average (i.e., between-persons), those minority members who report relatively higher levels of perceived discrimination also report greater negativity towards German adolescents. These parallel findings underline the benefits to be achieved from separating within- and between-person levels of analysis while accounting for possible reciprocal relations among the variables of interest.
Mrs Maria-Therese Friehs (Universität Osnabrück) - Presenting Author
Professor Peter Schmidt (Universität Gießen)
Professor Maarten van Zalk (Universität Osnabrück)
Longitudinal survey research analyzing causal effects of intergroup contact on outgroup attitudes and vice versa has often relied on cross-lagged panel models (CLPM; e.g., Binder et al., 2009) or latent growth curve models (e.g., Kotzur & Wagner, 2018) as analytical approaches. Recent critiques (e.g., Hamaker, Kuiper, & Grasman, 2015) point to the potential bias especially in CLPM, arising from the inability of conventional models to separate stable between-person differences and within-person processes over time. This bias has been shown to lead to erroneous findings concerning the presence, sign and predominance of causal effects.
This presentation aims at comparing the results of conventional models analyzing longitudinal causal effects of intergroup contact and outgroup attitudes (i.e., CLPM) with those that account for the differentiation of within- and between-person variance (i.e., random intercept cross lagged panel model (RI-CLPM) as proposed by Hamaker et al., 2015). A four-wave large-scale representative survey (GESIS, 2018; Wagner, Schmidt, & Kauff, 2016) including indicators for positive and negative intergroup contact experiences and outgroup attitudes for four different outgroups is analyzed. We thereby apply the RI-CLPM to an SEM with two indicators per latent variable. Results show considerable differences between the CLPM and the RI-CLPM proposed by Hamaker et al. (2015), mainly characterized through the absence of stability coefficients and cross-lagged effects between the constructs. A discussion of potential explanations for these differences as well as further implications will be presented.
Mr Henrik Andersen (Chemnitz University of Technology ) - Presenting Author
Professor Jochen Mayerl (Chemnitz University of Technology )
Professor Elmar Schlüter (Justus-Liebig-University of Giessen )
Recently, there has been increased interest in the application of fixed-effects regression techniques for panel data within the structural equation modeling (SEM) framework (e.g. Allison, 2017; Bianconcini & Bollen, 2018; Bollen & Brand, 2010; Curran et al., 2013; Hamaker et al., 2015). Fixed-effects regression controls for unobserved heterogeneity and thus eliminates possible confounding by any time-invariant variables (e.g. stable personality traits, sex, birth cohort, place of birth/residence etc.).
Besides this, structural equation modeling with panel data allows for a great deal of flexibility in terms of 1) modeling repeated measures as multiple-indicator latent constructs rather than composite variables to account for measurement error, 2) testing of measurement invariance to ensure observed change is attributable only to real change in the latent constructs, and 3) the use of Likert-style ordered-categorical rather than only continuous indicators without violating assumptions. Furthermore, it is possible to account not only for selection on the level of the x-variable but also its growth/trajectory (Brüderl & Ludwig, 2018). This can be accomplished by applying either multilevel- or growth curve-related concepts to the basic framework (Teachman, 2014).
Using five waves of the German Family Panel (Brüderl et al., 2017; Huinink et al., 2011), we demonstrate such models by examining the (possibly reciprocal) relation between stress and depression. We present a model that is able to account for unobserved heterogeneity (both in terms of level and growth), use multiple-indicator latent constructs to account for measurement error and test for longitudinal measurement invariance. On top of this basic framework, we can examine reciprocal/bidirectional (i.e. cross-lagged) effects, account for autocorrelation (i.e. an autoregressive effect of yt-1 on yt) and address the problem of contemporary vs. lagged effects of x on y and vice versa (Vaisey & Miles, 2017).