Ignoring a Level in a Multilevel Model: Evidence from UK Census Data

Abstract

Because of the inherent multilevel nature of census data, it is often appropriate to use multilevel models to investigate relationships between census variables. For a local population, the data available from the census allow a three-level nested model to be assumed, with an individual level (level 1), an enumeration district (ED) level (level 2), and a ward level (level 3). The consequences of ignoring one of the three levels in this model are assessed here theoretically. Empirical results, based on 1991 UK Census data, are also provided, comparing the variance components estimated from the three-level model with analyses based on models where the ED or ward level are ignored. The results show how the variation that occurs at the level not included in the models is redistributed to the other levels that the models do include.

The scale of segregation: ancestral groups in Sydney, 2011

“…Not only has this allowed a much finer-grained investigation but it has also facilitated a much more nuanced appreciation of variations in segregation levels. It is widely assumed, as Logan et al (2015aLogan et al ( , 1077 put it, 'that segregation is higher at a finer spatial scale, which is already known' (see also Logan et al, 2015b); the results presented here suggest that this is not always the case -in part, undoubtedly, because (as Tranmer andSteel, 2001, andDuncan et al 1961 brought to our attention some years ago) segregation measures at fine spatial scales necessarily incorporate those at (unobserved) coarser scales.…”

“…(Full details of the modelling procedure are given in Jones et al, 2015. ) Importantly, the MRR values for each scale are net of any segregation at a larger scale, thereby addressing the important issue regarding missing scales raised by Tranmer and Steel (2001). For example, the MRR for Chinese at the SA1 scale indicates how segregated they are at the neighbourhood level, when segregation at each of the three larger scales is held constant: it is thus a 'true' measure of segregation at the micro-scale without any contamination by incorporating an unknown amount of segregation at the larger three scales.…”

Multilevel Modeling of Social Segregation

“…If a higher level is ignored in the multilevel analysis, then as Tranmer and Steel (2001) show, the estimated variance is redistributed to lower levels that the models do include. Thus, including schools at level 2 in a model, but excluding LAs at level 3, will result in a misattribution of any true between LA variation to the school level; the degree of segregation at the school level will be overstated.…”

Spatial scale and measuring segregation: illustrated by the formation of Chicago’s ghetto

“…The other major advantage of this modelling approach is that it takes the non-independence of scales issue raised by Duncan et al (1961) and addressed by Tranmer and Steel (2001) into account. In a two-scale analysis, therefore, at the coarser of the two scales the MOR values are interpreted as discussed above -the average difference in the ratios across all pairs of wards.…”