Micro–Macro Multilevel Analysis for Discrete Data

A multilevel regression model is proposed in which discrete individual-level variables are used as predictors of discrete group-level outcomes. It generalizes the model proposed by Croon and van Veldhoven for analyzing micro–macro relations with continuous variables by making use of a specific type of latent class model. A first simulation study shows that this approach performs better than more traditional aggregation and disaggreagtion procedures. A second simulation study shows that the proposed latent variable approach still works well in a more complex model, but that a larger number of level-2 units is needed to retain sufficient power. The more complex model is illustrated with an empirical example in which data from a personal network are used to analyze the interaction effect of being religious and surrounding yourself with married people on the probability of being married.

[1]  A. Agresti.  An introduction to categorical data analysis , 1997 .

[2]  M. Croon,et al.  Researching individual well-being and performance in context : Multilevel mediational analysis for bathtub models , 2015 .

[3]  Jeroen K. Vermunt,et al.  Multilevel Mixture Factor Models , 2012, Multivariate behavioral research.

[4]  K. R. Milner,et al.  A multiple-goal, multilevel model of feedback effects on the regulation of individual and team performance. , 2004, The Journal of applied psychology.

[5]  C. Judd,et al.  Statistical difficulties of detecting interactions and moderator effects. , 1993, Psychological bulletin.

[6]  B. Muthén,et al.  The multilevel latent covariate model: a new, more reliable approach to group-level effects in contextual studies. , 2008, Psychological methods.

[7]  Marcel Croon,et al.  Estimating Latent Structure Models with Categorical Variables: One-Step Versus Three-Step Estimators , 2004, Political Analysis.

[8]  Harvey Goldstein,et al.  Multilevel Structural Equation Models for the Analysis of Comparative Data on Educational Performance , 2007 .

[9]  Jeroen K. Vermunt,et al.  Multilevel latent variable modeling : An application in educational testing , 2008 .

[10]  J. Kyle Roberts,et al.  Handbook of advanced multilevel analysis , 2011 .

[11]  José G. Dias,et al.  A bootstrap-based aggregate classifier for model-based clustering , 2008, Comput. Stat..

[12]  S. Vansteelandt.  Estimation of Direct and Indirect Effects , 2012 .

[13]  S. Rabe-Hesketh,et al.  Generalized multilevel structural equation modeling , 2004 .

[14]  J. Fox.  Bayesian Item Response Modeling: Theory and Applications , 2010 .

[15]  Jacques A. Hagenaars,et al.  Categorical Longitudinal Data: Log-Linear Panel, Trend, and Cohort Analysis , 1990 .

[16]  A. Alas,et al.  BAYESIAN ESTIMATION OF A MULTILEVEL IRT MODEL USING GIBBS SAMPLING JEAN-PAUL FOX AND CEES , 2005 .

[17]  Cristina B. Gibson,et al.  The Effect Of Individual Perceptions of Deadlines on Team Performance , 2001 .

[18]  Jeffrey P. Dew,et al.  The Role of Religion in Adolescence for Family Formation in Young Adulthood. , 2009, Journal of marriage and the family.

[19]  H. Goldstein,et al.  The limitations of using school league tables to inform school choice , 2009 .

[20]  T. Snijders,et al.  The Use of Multilevel Modeling for Analysing Personal Networks: Networks of Cocaine Users in an Urban Area. , 1995 .

[21]  J. Vermunt.  Mixed-Effects Logistic Regression Models for Indirectly Observed Discrete Outcome Variables , 2005, Multivariate behavioral research.

[22]  Jeroen K. Vermunt,et al.  Latent class modeling with covariates : Two improved three-step approaches 1 , 2012 .

[23]  Kristopher J Preacher,et al.  A general multilevel SEM framework for assessing multilevel mediation. , 2010, Psychological methods.

[24]  Leo A. Goodman,et al.  The analysis of multidimensional contingency tables when some variables are posterior to others: a modified path analysis approach , 1973 .

[25]  H. Pan,et al.  A Multilevel Analysis of School Examination Results , 1993 .

[26]  Peter M. Bentler,et al.  EQS : structural equations program manual , 1989 .

[27]  Jeroen K. Vermunt,et al.  Multilevel Growth Mixture Models for Classifying Groups , 2010 .

[28]  R. Peccei,et al.  Partnership at Work: Mutuality and the Balance of Advantage , 2001 .

[29]  M. Croon,et al.  Predicting group-level outcome variables from variables measured at the individual level: a latent variable multilevel model. , 2007, Psychological methods.

[30]  L. A. Goodman.  Exploratory latent structure analysis using both identifiable and unidentifiable models , 1974 .

[31]  S. Embretson,et al.  Item response theory for psychologists , 2000 .

[32]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[33]  D P MacKinnon,et al.  Multilevel Mediation Modeling in Group-Based Intervention Studies , 1999, Evaluation review.

[34]  P. Fayers.  Item Response Theory for Psychologists , 2004, Quality of Life Research.

[35]  P. Deb.  Finite Mixture Models , 2008 .

[36]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[37]  J. Broersen,et al.  Handleiding VBBA: onderzoek naar de beleving van psychosociale arbeidsbelasting en werkstress met behulp van de vragenlijst beleving en beoordeling van de arbeid , 1997 .

[38]  J. Fox,et al.  Bayesian estimation of a multilevel IRT model using gibbs sampling , 2001 .

[39]  James Algina,et al.  An Empirical Comparison of Statistical Models for Value-Added Assessment of School Performance , 2004 .

[40]  J. Pearl.  The Mediation Formula: A Guide to the Assessment of Causal Pathways in Nonlinear Models , 2011 .

[41]  Jeroen K. Vermunt,et al.  AVOIDING BOUNDARY ESTIMATES IN LATENT CLASS ANALYSIS BY BAYESIAN POSTERIOR MODE ESTIMATION , 2006 .

[42]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .

[43]  Patrick J Curran,et al.  Have Multilevel Models Been Structural Equation Models All Along? , 2003, Multivariate behavioral research.

[44]  Jean-Paul Fox,et al.  Bayesian modeling of measurement error in predictor variables using item response theory , 2003 .

[45]  Roel Bosker,et al.  Multilevel analysis : an introduction to basic and advanced multilevel modeling , 1999 .

[46]  Jeroen K. Vermunt,et al.  7. Multilevel Latent Class Models , 2003 .

[47]  Kevin M. Murphy,et al.  Estimation and Inference in Two-Step Econometric Models , 1985 .

[48]  A. Wilkinson.  Employment relations in SMEs , 1999 .

[49]  Jeroen K. Vermunt,et al.  Estimating the Association between Latent Class Membership and External Variables Using Bias-adjusted Three-step Approaches , 2013 .

[50]  Jeroen K. Vermunt,et al.  6. The Simultaneous Decision(s) about the Number of Lower- and Higher-Level Classes in Multilevel Latent Class Analysis , 2010 .

[51]  J. Vermunt,et al.  Measuring Student Ability, Classifying Schools, and Detecting Item Bias at School Level, Based on Student-Level Dichotomous Items , 2014 .

[52]  Sophia Rabe-Hesketh,et al.  Multilevel Structural Equation Modeling , 2009 .

[53]  Marc van Veldhoven,et al.  Financial performance and the long-term link with HR practices, work climate and job stress , 2005 .

[54]  T. Keith.  Multiple Regression and Beyond , 2005, Principles & Methods of Statistical Analysis.

[55]  Risto Lehtonen,et al.  Multilevel Statistical Models , 2005 .

[56]  Jay Magidson,et al.  LG-Syntax user's guide: Manual for Latent GOLD 4.5 Syntax module , 2008 .

[57]  G. McClelland,et al.  Designing, testing, and interpreting interactions and moderator effects in family research. , 2005, Journal of family psychology : JFP : journal of the Division of Family Psychology of the American Psychological Association.

[58]  J. Vermunt,et al.  Latent Gold 4.0 User's Guide , 2005 .

[59]  X M Tu,et al.  Power analyses for longitudinal trials and other clustered designs , 2004, Statistics in medicine.

[60]  Lex Borghans,et al.  The Role of Noncognitive Skills in Explaining Cognitive Test Scores , 2006, SSRN Electronic Journal.

[61]  Matthijs Kalmijn,et al.  Homogeneity of social networks by age and marital status: A multilevel analysis of ego-centered networks , 2007, Soc. Networks.

[62]  J-P Fox,et al.  Multilevel IRT using dichotomous and polytomous response data. , 2005, The British journal of mathematical and statistical psychology.

[63]  L. A. Goodman.  The Analysis of Systems of Qualitative Variables When Some of the Variables Are Unobservable. Part I-A Modified Latent Structure Approach , 1974, American Journal of Sociology.

[64]  Jeroen K. Vermunt,et al.  Relating Latent Class Assignments to External Variables: Standard Errors for Correct Inference , 2014, Political Analysis.

[65]  Michael Rutter,et al.  School Effectiveness Findings 1979–2002 , 2002 .

[66]  Ulrich Trautwein,et al.  A 2 × 2 taxonomy of multilevel latent contextual models: accuracy-bias trade-offs in full and partial error correction models. , 2011, Psychological methods.

[67]  Bengt Muthén,et al.  Beyond multilevel regression modeling: Multilevel analysis in a general latent variable framework. , 2011 .

[68]  Tom A B Snijders,et al.  Power and sample size in multilevel modeling , 2006 .

[69]  D. Mackinnon.  Introduction to Statistical Mediation Analysis , 2008 .

[70]  Michael C Neale,et al.  People are variables too: multilevel structural equations modeling. , 2005, Psychological methods.

[71]  K. Muller,et al.  Power Calculations for General Linear Multivariate Models Including Repeated Measures Applications. , 1992, Journal of the American Statistical Association.

[72]  Alan Agresti,et al.  Categorical Data Analysis , 2003 .

[73]  Stan Lipovetsky,et al.  Generalized Latent Variable Modeling: Multilevel,Longitudinal, and Structural Equation Models , 2005, Technometrics.

[74]  Tom A. B. Snijders,et al.  Multilevel analysis of personal networks as dependent variables , 1999, Soc. Networks.

[75]  J. Hox.  Multilevel analysis: Techniques and applications, 2nd ed. , 2010 .