Statistical Methods: Multilevel Modeling (MLM)

When studying certain phenomena in regression analysis, the entities may be subject to some hierarchical (e.g., students-schools) or non-hierarchical structure or membership. Groups and their members can exert influences on each other, suggesting that the variability in dependent variable may have contribution from both individual members and groups. Ignoring grouping effect may give rise to incorrect conclusion, such as differences and relationships that do not exist. The reason may be that individuals within the same group are correlated or clustered.

In our CHES research and teaching, we build various fixed and random (e.g., random intercept only, random intercepts and slopes) effects models to address the aforementioned membership-induced influences that occur at different model components. In particular, we treat multi-time measures of the same individual (e.g., a parcel or pixel in landscape or spatial analysis) as level-1, and individuals as level-2, making MLM able to deal with longitudinal data in general (Guo and Hipp, 2004). We use SAS and MPlus for our MLM modeling work. Below is a list of exemplar papers and teaching notes about multilevel modeling.

Readings and References:

An, L., M. Tsou, S. Crook, B. Spitzberg, J.M. Gawron, and D.K. Gupta (2015). Space-time analysis: Concepts, quantitative methods, and future directions. Annals of Association of American Geographers 105(5):891-914.

Guo, G., Hipp, J., 2004. Longitudinal analysis for continuous outcomes, in: Hardy, M., Bryman, A. (Eds.), The Handbook of Data Analysis. SAGE Publications, Los Angeles, pp. 347–368.

Preacher, K.J., A.L. Wichman, R.C. MacCallum, N.E. Briggs (2008). Latent growth curve modeling, Quantiative Applications in the Social Sciences. SAGE Publications, Los Angeles.

Sullivan, A., A.M. York, L. An, S.T Yabiku, and S.J. Hall (2017). How does perception at multiple levels influence collective action in the commons? The case of Mikania micrantha in Chitwan, Nepal. Forest Policy and Economics 80:1-10.

Yang, S. et al. (in preparation). What influences decisions of local people to out-migrate under Payments for Ecosystem Services (PES)? Evidence from a Nature Reserve in China.

Examples, Models, and/or Documents:

MLM Teaching Notes