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Occasional Paper

Modelling Census Under-Enumeration - A Logistic Regression Perspective

1. Introduction

A Census provides a ‘snapshot’ of the entire national population and has the distinct advantage of providing an opportunity to gather a wealth of information about demographic, economic, social and housing characteristics of the population. Furthermore, unlike surveys, Censuses allow the analysis of these population characteristics right down to very small geographical areas. Population figures are also used by international bodies like the UN (United Nations) and EU (European Union) as a basis for formulating international policy and world population estimates. Therefore, in most countries the requirement to hold a Census, or a least have a methodology in place to obtain up-to-date population figures, is enshrined in the constitutional legislation.

In the UK (United Kingdon), a decennial Census aims to provide an accurate up-to-date count of all the residents. The last Census, held in 2001, estimated that a response rate of 96.1% was achieved in Scotland; which compares favourably with other countries (Boyle and Dorling 2004). However what was particularly noticeable from the Census was the differential response rates that existed between different age-sex groups and areas (see Figure 1.1.1 (53 Kb PDF file)). This is known as “biased under-enumeration”, and the 2001 Census was the first Census that sought to measure this non-uniformity in response.

The 2001 Census sought to accurately account for the differential levels of under-enumeration that existed between different age-sex groups and areas. This was achieved by the One Number Census project which produced an individual level Census database, with synthetic individuals used to fully adjust for the differential levels of under-enumeration.

An important aspect of the project was an independent follow-up survey (the Census Coverage Survey, CCS) carried out after the official Census had taken place. The basic statistical model - called dual system estimation - assumes that a first enumeration, the Census, is followed by a second enumeration (the Census Coverage Survey) which subsequently takes place a few weeks later. Then matching techniques can be used to match records from the Census Coverage Survey to those from the Census.

From the results of the matching (and dual system estimation), an estimate of the people missed by both the Census Coverage Survey and the Census can be made. A key assumption here is that the first and second processes are statistically independent. That is, the probability of enumeration in the second process given enumeration in the first is identical to the probability of enumeration in the second process given the person was missed in the first process. This identity assumption provides a basis for estimating the number that were not enumerated in either the first or second processes – referred to as the undercount or under-enumeration. Consequently, this population undercount is combined with the Census population to give an estimate of the true population.

Therefore, the One Number Census methodology can be thought of as comprising three processes that work together. Firstly, the Census provides a population count. Secondly, the Census Coverage Survey provides an estimate of those missed by the Census. Finally dual system estimation provides an estimate of the people missed by both the Census and Census Coverage Survey. This produces a new estimate of the population that has been adjusted to account for the missing, by imputation.

From Figure 1.1.1 (53 Kb PDF file), it can be seen that females had better response rates overall than males – with males aged 20-24 having the lowest coverage. Furthermore, it was found that, accounting for geographical region, this demographic spread of non-response is much wider, and there was an identification of a broader cross-section of the missed population. As an example, some parts of West Dunbartonshire with a high percentage of social housing stock had a large proportion of young males identified as missing.

Census under-enumeration is a function of a wide range of factors including

1.	demographic
2.	social and economic
3.	housing structure and composition
4.	public attitudes and perceptions
5.	census enumeration strategy
6.	effectiveness of the census under-enumeration measuring instrument

Assuming that (5) and (6) are correctly accounted for by the Census methodology, the other factors can be investigated by looking at the associations and relationships that exist between these factors and under-enumeration. Under-enumeration is likely to be higher in certain areas with particular social, economic and demographic attributes. This paper aims to use logistic regression to model the Census under-enumeration by identifying the attributes that are significant predictors of under-count.

The object of the analyses in this paper is two-fold:

1.	To assess the association between under-enumeration and key deprivation and census variables
2.	To develop one or more models that could be used to predict areas of under-enumeration based on the area attributes and their relationship with under-enumeration

It is important to note that the analysis does not establish any causal relationships with under-enumeration. (Causality can only be determined by carefully controlled experimental study.) Nor does it look at the effect of public perceptions and attitudes to the Census.

The analysis was carried out at a ward level because this level of geography is low enough to avoid any issues of heterogeneity in the population size of council areas, but large enough so that the proportion imputed was greater than zero. Scotland is divided into 1,222 wards. The ward boundaries are of similar size across Scotland with between 650 and 9,200 people in each ward. Figure 1.1.2 (18 Kb PDF file) shows the distribution of residents in as a total and broken down by sex. Although the spread is large the distribution is roughly normal – most wards have a population size of between 3,000 and 5,000 people.

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