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2022 | OriginalPaper | Buchkapitel

Multilevel Modeling

verfasst von : Till Haumann, Roland Kassemeier, Jan Wieseke

Erschienen in: Handbook of Market Research

Verlag: Springer International Publishing

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Abstract

Many phenomena in marketing involve multiple levels of theory and analysis. Adopting a multilevel lens to marketing phenomena can often yield richer and more rigorous results. However, the consideration of multiple levels of theory and analysis often leads to the challenge to cope with nested data structures in which a lower level unit of analysis is nested within a higher level unit of analysis. Explicitly acknowledging such nested data structures is important as its analysis with single level analysis techniques may result in biased results and thus incorrect conclusions because nested data structures often violate assumptions of conventional single level analysis techniques. A methodological approach which explicitly accounts for multiple levels of analysis and thus the nested structure of data is referred to as multilevel modeling. This chapter attempts to help researchers and practitioners interested in investigating multilevel phenomena by providing an introduction to multilevel modeling. It therefore describes the theoretic fundamentals of multilevel modeling by outlining the conceptual and statistical relevance of multilevel modeling. Furthermore, it provides guidance how to build a multilevel regression model using a step-by-step approach. The chapter also discusses how to assess the fit of multilevel models, how to center variables at different levels of analysis, and how to determine the sample sizes to adequately estimate multilevel models. Moreover, it offers insights how the logic of multilevel regression analysis could be expanded to multilevel structural equation modeling, discusses different statistical software packages that can be employed to estimate multilevel models, and provides a detailed example of building and estimating a multilevel model.

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Vorheriges Kapitel Logistic Regression and Discriminant Analysis

Nächstes Kapitel Panel Data Analysis: A Non-technical Introduction for Marketing Researchers

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Please note that although Equation (10) is labeled as a Level 2 equation where γ₁₀ is a fixed effect reflecting the linear effect of the independent variable X_ij on the dependent variable Y_ij at Level 1 (Raudenbush and Bryk 2002). In step 4 we will allow this regression coefficient to vary between clusters which then results in Equation (18) characterizing a potentially meaningful Level 2 influence.

Note that we focus here on assumptions of multilevel models which are estimated using a maximum likelihood estimator. Other estimation techniques can be helpful if these assumptions are not fulfilled (see section “Model Estimation & Assessing Model Fit” and Hox et al. 2018).

Sometimes a slightly different notation for multilevel structural equation models is employed (Asparouhov and Muthén 2008; Preacher et al. 2010, 2011). Following this notation, the measurement model can be expressed as: Y_ij = v_j + Λ_jη_ij + K_jX_ij + ε_ij. The level one structural model can be written as η_ij = α_j + Β_jη_ij + Γ_jX_ij + ζ_ij and the level two structural model can be expressed as η_j = μ + βη_j + γX_j + ζ_j. This notation additionally includes exogenous covariates captured by the vectors X_ij and X_j respectively. Furthermore, elements of the matrices v_j, Λ_j, K_j, α_j, Β_j, and Γ_j may vary between level two units as expressed by the level two subscripts (j) (for further details of this notation see Preacher et al. 2010).

More detailed reviews of many different software packages that allow the estimation of multilevel models can be found at the homepage of the Centre for Multilevel Modelling at the University of Bristol (www.bristol.ac.uk/cmm/learning/mmsoftware/)

REML = Restricted maximum likelihood; FML = Full maximum likelihood; PQL = penalized quasi-likelihood; AGH = Adaptive Gauss-Hermite quadrature.

Note that we divided the total dollar amount of customer spending within 1 year by 100 to keep the (residual) variance estimates at a lower level, which is helpful to assure a smooth model estimation process.

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Titel: Multilevel Modeling
verfasst von: Till Haumann
Roland Kassemeier
Jan Wieseke
Verlag: Springer International Publishing
Buch: Handbook of Market Research
Print ISBN: 978-3-319-57411-0

Electronic ISBN: 978-3-319-57413-4

Copyright-Jahr: 2022
DOI: https://doi.org/10.1007/978-3-319-57413-4_18