# Fixed Effects vs Multilevel Models

In social science we are often dealing with data that is hierarchically structured. For example, people are located within neighbourhoods, pupils within schools, observations over time are nested within individuals or countries.

Multilevel models are used to recognize hierarchically structured data such as these. However though multilevel modeling can provide a flexible way of modeling variation in the social world, it has a number of potential weaknesses.

## Concerns

A common concern encountered with using multilevel models is that they require strong assumptions in order to make causal inference from the results. For instance, without assuming that people are random allocated to neighbourhoods it is difficult to make causal inferences about the effect of neighbourhood variables on people within them.

A second concern that manifests itself commonly in cross national studies is that some datasets do not have enough higher level units for the multilevel approach to be appropriate.

## Solution

A solution to both of these concerns is to use ‘fixed effects’ models that remove all variation between higher level units from the parameter estimation. This has the advantage of removing all potential unobserved confounding variables at the higher level from the analysis and thus aids causal inference.

The drawback being that much useful and/or interesting variation is removed. This talk will illustrate the advantages and disadvantages of both approaches and discuss ways you might use them in your research.

## Background Reading

- Allison, P. (2009) Fixed Effects Regression Models, Sage Quantitative Applications in the Social Sciences, vol. 160.
- Clarke, P., Crawford, C., Steele, F. & Vignoles, A. (2010) The choice between fixed and random effects models: some considerations for educational research, Institute of Education DoQSS Working Paper No. 10-10
- Goldstein, H. (2010) Multilevel Statistical Models, 4th Edition, Wiley.

## PDF slides

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