Micro-macro multilevel latent class models with multiple discrete individual-level variables. (English) Zbl 1414.62228

Bennink, Margot; Croon, Marcel A.; Kroon, Brigitte; Vermunt, Jeroen K.

Adv. Data Anal. Classif., ADAC 10, No. 2, 139-154 (2016).

Summary: An existing micro-macro method for a single individual-level variable is extended to the multivariate situation by presenting two multilevel latent class models in which multiple discrete individual-level variables are used to explain a group-level outcome. As in the univariate case, the individual-level data are summarized at the group-level by constructing a discrete latent variable at the group level and this group-level latent variable is used as a predictor for the group-level outcome. In the first extension, that is referred to as the Direct model, the multiple individual-level variables are directly used as indicators for the group-level latent variable. In the second extension, referred to as the Indirect model, the multiple individual-level variables are used to construct an individual-level latent variable that is used as an indicator for the group-level latent variable. This implies that the individual-level variables are used indirectly at the group-level. The within- and between components of the (co)varn the individual-level variables are independent in the Direct model, but dependent in the Indirect model. Both models are discussed and illustrated with an empirical data example.

MSC:

62H30

Classification and discrimination; cluster analysis (statistical aspects)

Keywords:

latent class analysis; micro-macro analysis; multilevel analysis; discrete data

Software:

Latent GOLD

References:

[1]	Bakk, Z.; Tekle, FB; Vermunt, JK, Estimating the association between latent class membership and external variables using bias adjusted three-step approaches, Sociol Methodol, 43, 272-311, (2013)
[2]	Bank of Italy (2012) Historical database of survey of household income and wealth, 1977-2010
[3]	Bennink, M.; Croon, MA; Vermunt, JK, Micro-macro multilevel analysis for discrete data: a latent variable approach and an application on personal network data, Sociol Methods Res, 42, 431-457, (2013)
[4]	Bolck, A.; Croon, MA; Hagenaars, JAP, Estimating latent structure models with categorical variables: one-step versus three-step estimators, Polit Anal, 12, 3-27, (2004)
[5]	Croon, MA; Veldhoven, MJPM, Predicting group-level outcome variables from variables measured at the individual level: a latent variable multilevel model, Psychol Methods, 12, 45-57, (2007)
[6]	European Commission (2005) The new SME definition: user guide and model declaration. Publication Office, Brussels
[7]	Goldstein H (2011) Multilevel statistical models, 4th edn. Wiley, Chichester · Zbl 1274.62006
[8]	Goss D (1991) Small business and society. Routledge, London
[9]	Guest, DE; Peccei, R., Partnership at work: mutuality and the balance of advantage, Brit J Ind Relat, 39, 207-236, (2001)
[10]	Lukočiene, O.; Varriale, R.; Vermunt, JK, The simultaneous decision(s) about the number of lower- and higher-level classes in multilevel latent class analysis, Sociol Methodol, 40, 247-283, (2010)
[11]	Preacher, KJ; Zyphur, MJ; Zhang, Z., A general multilevel SEM framework for assessing multilevel mediation, Psychol Methods, 15, 209-233, (2010)
[12]	Skrondal A, Rabe-Hesketh S (2004) Generalized latent variable modeling: multilevel, longitudinal and structural equation models. Chapman & Hall/CRC Press, Boca Raton · Zbl 1097.62001
[13]	Snijders TAB, Bosker RJ (2012) Multilevel analysis: an introduction to basic and advanced multilevel modeling, 2nd edn. Sage Publications, London · Zbl 1296.62008
[14]	Van Veldhoven MJPM, Meijman T, Broersen S (2002) Handleiding VBBA: onderzoek naar de beleving van psychosociale arbeidsbelasting en werkstress met behulp van de vragenlijst beleving en beoordeling van de arbeid. Stichting Kwaliteitsbevordering Bedrijfsgezondheidszorg, Amsterdam
[15]	Varriale, R.; Vermunt, JK, Multilevel mixture factor models, Multivar Behav Res, 47, 247-275, (2012)
[16]	Vermunt, JK, Multilevel latent class models, Sociol Methodol, 33, 213-239, (2003)
[17]	Vermunt, JK, Mixed-effects logistic regression models for indirectly observed discrete outcome variables, Multivar Behav Res, 40, 281-301, (2005)
[18]	Vermunt, JK, Latent class modeling with covariates: two improved three-step approaches, Polit Anal, 18, 450-469, (2010)
[19]	Vermunt JK, Magidson J (2005) Technical Guide for Latent GOLD 4.0: basic and advanced. Statistical Innovations, Belmont, MA
[20]	Vermunt JK, Magidson J (2013) LG-Syntax User’s Guide: manual for Latent GOLD 5.0 syntax module. Statistical Innovations, Belmont, MA
[21]	Wilkinson, A., Employment relations in SME’s, Empl Relat, 21, 206-217, (1999)