{"title":"Getting the Within Estimator of Cross-Level Interactions in Multilevel Models with Pooled Cross-Sections: Why Country Dummies (Sometimes) Do Not Do the Job","authors":"Marco Giesselmann, Alexander W. Schmidt-Catran","doi":"10.1177/0081175018809150","DOIUrl":"https://doi.org/10.1177/0081175018809150","url":null,"abstract":"Multilevel models with persons nested in countries are increasingly popular in cross-country research. Recently, social scientists have started to analyze data with a three-level structure: persons at level 1, nested in year-specific country samples at level 2, nested in countries at level 3. By using a country fixed-effects estimator, or an alternative equivalent specification in a random-effects framework, this structure is increasingly used to estimate within-country effects in order to control for unobserved heterogeneity. For the main effects of country-level characteristics, such estimators have been shown to have desirable statistical properties. However, estimators of cross-level interactions in these models are not exhibiting these attractive properties: as algebraic transformations show, they are not independent of between-country variation and thus carry country-specific heterogeneity. Monte Carlo experiments consistently reveal the standard approaches to within estimation to provide biased estimates of cross-level interactions in the presence of an unobserved correlated moderator at the country level. To obtain an unbiased within-country estimator of a cross-level interaction, effect heterogeneity must be systematically controlled. By replicating a published analysis, we demonstrate the relevance of this extended country fixed-effects estimator in research practice. The intent of this article is to provide advice for multilevel practitioners, who will be increasingly confronted with the availability of pooled cross-sectional survey data.","PeriodicalId":48140,"journal":{"name":"Sociological Methodology","volume":"49 1","pages":"190 - 219"},"PeriodicalIF":3.0,"publicationDate":"2018-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/0081175018809150","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44725827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Comment: The Inferential Information Criterion from a Bayesian Point of View","authors":"O. Vassend","doi":"10.1177/0081175018794489","DOIUrl":"https://doi.org/10.1177/0081175018794489","url":null,"abstract":"1. The Bayesian information criterion (BIC) has been proposed as a way to carry out Bayesian hypothesis testing when there are no clear expectations. However, the BIC rests on a particular prior distribution, for which there is rarely any justification. See Raftery (1995) on the case for the BIC and Weakliem (1999) for a critique. 2. The assumption that the sample is of the same size is important. To obtain the expected prediction error in a sample of arbitrary size, it is necessary to know the true model. Consequently, there is no method of model selection that uniformly leads to better out-of-sample predictions. 3. Schultz proposes that the value should be exp(AIC2 – AIC1), or about .0025 in this example. I think this is mistaken, and it should be exp{(AIC2 – AIC1)/2}. The general point about considering the theoretical probability of a nonzero value applies regardless of which formula is correct.","PeriodicalId":48140,"journal":{"name":"Sociological Methodology","volume":"48 1","pages":"91 - 97"},"PeriodicalIF":3.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/0081175018794489","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44420171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Prologue","authors":"Anonymous","doi":"10.1177/0081175018799359","DOIUrl":"https://doi.org/10.1177/0081175018799359","url":null,"abstract":"Readers who leaf through this journal's pages in early 2021 or connect to it online will, sadly, need no reminder of how COVID-19-the respiratory illness caused by a novel strain of coronavirus-spread illness, death, and fear around the world, culminating in the declaration of a pandemic by the World Health Organization on 11 March 2020 Just as spring daffodils and orange blossoms burst forth last spring in the Mediterranean region that is our shared literary-cultural patria, we found ourselves involuntarily immersed in lockdowns Last but not least, we gratefully acknowledge Editorial Board members for continuing to provide detailed and rigorous article evaluations within the requested time frame, authors at all career stages for their submissions of exciting new work, and book reviewers for keeping our readers abreast of current scholarship in comedia studies and beyond","PeriodicalId":48140,"journal":{"name":"Sociological Methodology","volume":"48 1","pages":"xi - xxv"},"PeriodicalIF":3.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/0081175018799359","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47395063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dedication: Allan McCutcheon: Latent Class Analyst","authors":"A. McCutcheon, Allan Lee","doi":"10.1177/0081175018791565","DOIUrl":"https://doi.org/10.1177/0081175018791565","url":null,"abstract":"","PeriodicalId":48140,"journal":{"name":"Sociological Methodology","volume":"48 1","pages":"ix - x"},"PeriodicalIF":3.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/0081175018791565","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47514789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mattis van den Bergh, Geert H van Kollenburg, Jeroen K Vermunt
{"title":"Deciding on the Starting Number of Classes of a Latent Class Tree.","authors":"Mattis van den Bergh, Geert H van Kollenburg, Jeroen K Vermunt","doi":"10.1177/0081175018780170","DOIUrl":"https://doi.org/10.1177/0081175018780170","url":null,"abstract":"<p><p>In recent studies, latent class tree (LCT) modeling has been proposed as a convenient alternative to standard latent class (LC) analysis. Instead of using an estimation method in which all classes are formed simultaneously given the specified number of classes, in LCT analysis a hierarchical structure of mutually linked classes is obtained by sequentially splitting classes into two subclasses. The resulting tree structure gives a clear insight into how the classes are formed and how solutions with different numbers of classes are substantively linked to one another. A limitation of the current LCT modeling approach is that it allows only for binary splits, which in certain situations may be too restrictive. Especially at the root node of the tree, where an initial set of classes is created based on the most dominant associations present in the data, it may make sense to use a model with more than two classes. In this article, we propose a modification of the LCT approach that allows for a nonbinary split at the root node, and we provide methods to determine the appropriate number of classes in this first split, based either on theoretical grounds or on a relative improvement of fit measure. This novel approach also can be seen as a hybrid of a standard LC model and a binary LCT model, in which an initial, oversimplified but interpretable model is refined using an LCT approach. Furthermore, we show how to apply an LCT model when a nonstandard LC model is required. These new approaches are illustrated using two empirical applications: one on social capital and the other on (post)materialism.</p>","PeriodicalId":48140,"journal":{"name":"Sociological Methodology","volume":"48 1","pages":"303-336"},"PeriodicalIF":3.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/0081175018780170","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36859532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Comment: Some Challenges When Estimating the Impact of Model Uncertainty on Coefficient Instability","authors":"Robert M. O’Brien","doi":"10.1177/0081175018790569","DOIUrl":"https://doi.org/10.1177/0081175018790569","url":null,"abstract":"","PeriodicalId":48140,"journal":{"name":"Sociological Methodology","volume":"48 1","pages":"34 - 39"},"PeriodicalIF":3.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/0081175018790569","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44241112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Comment: Bayes, Model Uncertainty, and Learning from Data","authors":"B. Western","doi":"10.1177/0081175018799095","DOIUrl":"https://doi.org/10.1177/0081175018799095","url":null,"abstract":"Robert M. O’Brien is a professor emeritus at the University of Oregon. He specializes in criminology and quantitative methods. Within criminology, he focuses on the methods used to gather criminological data, on the analysis of crime rates, and on the task of extricating the effects of ages, periods, and cohorts on crime rates. His most recent publication on that topic, “Homicide Arrest Rate Trends in the United States: The Contributions of Periods and Cohorts (1965–2015),” appeared in 2018 in the Journal of Quantitative Criminology. In quantitative methods, some of his contributions involve the effects of using interval data as ordinal, generalizability theory, identification in structural equation modeling measurement models, the use of multicollinearity indices, and an obsession with age-period-cohort models. In 2015 he published a book on this topic, Age-Period-Cohort Models: Approaches and Analyses with Aggregate Data (Chapman & Hall, 2015).","PeriodicalId":48140,"journal":{"name":"Sociological Methodology","volume":"48 1","pages":"39 - 43"},"PeriodicalIF":3.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/0081175018799095","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48945486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonlinear Autoregressive Latent Trajectory Models","authors":"Shawn Bauldry, K. Bollen","doi":"10.1177/0081175018789441","DOIUrl":"https://doi.org/10.1177/0081175018789441","url":null,"abstract":"Autoregressive latent trajectory (ALT) models combine features of latent growth curve models and autoregressive models into a single modeling framework. The development of ALT models has focused primarily on models with linear growth components, but some social processes follow nonlinear trajectories. Although it is straightforward to extend ALT models to allow for some forms of nonlinear trajectories, the identification status of such models, approaches to comparing them with alternative models, and the interpretation of parameters have not been systematically assessed. In this paper we focus on two forms of nonlinear autoregressive latent trajectory (NLALT) models. The first form allows for a quadratic growth trajectory, a popular form of nonlinear latent growth curve models. The second form derives from latent basis models, or freed loading models, that allow for arbitrary growth processes. We discuss details concerning parameterization, model identification, estimation, and testing for the two forms of NLALT models. We include a simulation study that illustrates potential biases that may arise from fitting alternative models to data derived from an autoregressive process and individual-specific nonlinear trajectories. In addition, we include an extended empirical example modeling growth trajectories of weight from birth through age 2.","PeriodicalId":48140,"journal":{"name":"Sociological Methodology","volume":"48 1","pages":"269 - 302"},"PeriodicalIF":3.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/0081175018789441","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42277749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rejoinder: Can We Weight Models by Their Probability of Being True?","authors":"John Muñoz, Cristobal Young","doi":"10.1177/0081175018796841","DOIUrl":"https://doi.org/10.1177/0081175018796841","url":null,"abstract":"Draper, David. 1995. “Assessment and Propagation of Model Uncertainty.” Journal of the Royal Statistical Society, Series B 57:45–97. Freedman, David A. 1983. “A Note on Screening Regression Equations.” American Statistician 37:152–55. Leamer, Edward E. 1983. “Let’s Take the Con out of Econometrics.” American Economic Review 73:31–43. Raftery, Adrian E. 1996. “Approximate Bayes Factors and Accounting for Model Uncertainty in Generalised Linear Models.” Biometrika 83:251–66. Young, Cristobal, and Katherine Holsteen. 2017. “Model Uncertainty and Robustness: A Computational Framework for Multimodel Analysis.” Sociological Methods and Research 46:3–40.","PeriodicalId":48140,"journal":{"name":"Sociological Methodology","volume":"48 1","pages":"43 - 51"},"PeriodicalIF":3.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1177/0081175018796841","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46160602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"社会学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}