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Multilevel Modeling

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Handbook of Market Research

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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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Notes

  1. 1.

    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 Xij on the dependent variable Yij 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.

  2. 2.

    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).

  3. 3.

    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: Yij = vj + Λjηij + KjXij + εij. The level one structural model can be written as ηij = αj + Βjηij + ΓjXij + ζij and the level two structural model can be expressed as ηj = μ + βηj + γXj + ζj. This notation additionally includes exogenous covariates captured by the vectors Xij and Xj respectively. Furthermore, elements of the matrices vj, Λj, Kj, αj, Βj, and Γj 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).

  4. 4.

    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/)

  5. 5.

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

  6. 6.

    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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Author information

Authors and Affiliations

  1. South Westphalia University of Applied Sciences, Soest, Germany

    Till Haumann

  2. Marketing Group, Warwick Business School, University of Warwick, Coventry, United Kingdom

    Roland Kassemeier

  3. Sales Management Department, University of Bochum, Bochum, Germany

    Jan Wieseke

Authors
  1. Till Haumann
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  2. Roland Kassemeier
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  3. Jan Wieseke
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Corresponding author

Correspondence to Till Haumann .

Editor information

Editors and Affiliations

  1. Universität Mannheim, Mannheim, Germany

    Christian Homburg

  2. Inst. Informations Systems and Marketing Marketing & Sales Research Group, Karlsruher Institut für Technologie, Karlsruhe, Germany

    Martin Klarmann

  3. Faculty of Economics and Business, University of Groningen, Groningen, The Netherlands

    Arnd E. Vomberg

Section Editor information

  1. University of Mannheim, Mannheim, Germany

    Christian Homburg

  2. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Martin Klarmann

  3. University of Groningen, Groningen, Niederlande

    Arnd Vomberg

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Haumann, T., Kassemeier, R., Wieseke, J. (2021). Multilevel Modeling. In: Homburg, C., Klarmann, M., Vomberg, A.E. (eds) Handbook of Market Research. Springer, Cham. https://doi.org/10.1007/978-3-319-05542-8_18-1

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  • DOI: https://doi.org/10.1007/978-3-319-05542-8_18-1

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  • Print ISBN: 978-3-319-05542-8

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