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Occasional Paper

Modelling Census Under-Enumeration - A Logistic Regression Perspective

Results - Deprivation Models

Table 4.1.1 (11 Kb PDF file) shows the Multiple Depravation Index while Model 1 (18 Kb PDF file) provides the formula used to calculate the SIMD score. 

The slope of 0.015 represents the change in log odds for one unit increase in the SIMD score. Similarly, its odds ratio of 1.016 is the ratio for one unit change in the SIMD score. It would be more significant to look at increments other than one unit. For example, an increase in SIMD by 10 units increases the imputation probability by 17%[Footnote 1].

Looking at the component domains of the SIMD score, the model is shown in Model 2 (19 Kb PDF file).

All the deprivation variables entered into the model yield significant probabilities, implying that there is a significant relationship. As it is assumed that the relationship between log odds of an event and the deprivation score is linear, this model tells us that a 10-unit increment in the income deprivation score (holding everything else fixed) increases the probability of imputation by 40%.

Table 4.1.2 (12 Kb PDF file) shows the Singular Deprivation Indices.

It is peculiar that the education and employment deprivation domain maximum likelihood estimates are negative, although they are positively correlated with the income domain. A likely explanation could be that the assumption of linearity might be flawed and this is investigated later on.

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Footnote 1

Assuming that the logit is linear in the continuous covariate, then (1.016) ¹⁰ = 1.17