Construction of IHAD

This chapter describes the methods used to construct IHAD, some important technical specifications and basic outputs.

Principal component analysis (PCA) has been used since the first release of SEIFA to summarise Census variables related to socio-economic advantage and disadvantage. The same methodology is used to create the IHAD, modified where necessary to use binary variables.. The aim of PCA is to reduce a large number of correlated variables into a smaller set of transformed variables, called "principal components". Each component is a weighted linear combination of the original. It is possible to extract as many components as there are variables. If the original variables are highly correlated, much of the variation can be summarised by a single principal component.

The first principal component is the weighted linear combination of variables that captures the maximum amount of variation present in the original dataset. This is calculated using the correlations between the variables. In general, variables that are strongly correlated with many others in the list will receive high weights. The first principal component is used to create the IHAD index.

The PCA used the binary candidate variables and the correlation matrix of these variables to give an indication of how significantly each variable contributes to the measurement of the unobserved latent variable of interest, namely socio-economic advantage and disadvantage. Each variable receives a loading that indicates the correlation of that variable with the index. A positive loading indicates an advantaging variable whereas a negative loading indicates a disadvantaging variable. The variables with the highest loadings are the ones that have the highest correlation with the index value.

Polychoric correlations were used instead of the standard Pearson correlations for the correlation matrix; this is appropriate for binary variables to ensure the correlation coefficients used in the PCA are unbiased. Using polychoric correlations is considered to be more accurate when running a PCA on discrete data such as the binary variables used in the IHAD.

The candidate variables listed in Description of candidate IHAD variables were used in the PCA for the IHAD and removed if their loading was less than or equal to 0.3 on the grounds that they were not particularly strong indicators of advantage or disadvantage. This process was performed iteratively, until all of the variables had a loading above 0.3. This is the same procedure used to create the SEIFA. The final variables and their loadings following this process are presented in the Technical details for IHAD: variables and loadings.

The first principal component scores were derived by taking the product of each standardised variable with its respective weight, then taking the sum. For convenience and consistency with the approach taken for SEIFA, these raw component scores were then standardised to a mean of 1,000 and a standard deviation of 100 to produce the index.

The sign of the PCA weights is arbitrary, but intuitively we want more disadvantaged households to have lower scores, for example NOCAR is a disadvantage variable and so should have a negative weight. The weights were multiplied by -1 to give advantage indicators positive weights and loadings, and disadvantage indicators negative weights and loadings. Accordingly, high index scores indicate relative advantage, and low index scores indicate relative disadvantage.

With the preceding two sections providing context, a step-by-step process for constructing IHAD is presented below:

Given the data available, we created a list of variables related to the definition of relative household socio-economic advantage and disadvantage.

We applied the IHAD scope to the dataset, and then identified households with 10 or more applicable missing responses. We removed these households from the dataset, imputed missing responses for most of the required variables, and then applied Hotdeck imputation for HIED and HEAP to create the dataset we used to construct the candidate variables.

We created binary indicators from household, family, and person level variables. These indicators take a value of 1 if the characteristics is present, and 0 if it isn’t.

We removed highly correlated variables to avoid over-representing any specific socio-economic characteristic. When two variables had a correlation coefficient greater than 0.8 in absolute value and were measuring conceptually similar aspects of advantage or disadvantage, we generally removed one of them. However, we applied some discretion, depending on the variables in question and the size of the correlation.

We conducted principal component analysis (PCA) using the binary candidate variables and the correlation matrix of these variables, to obtain the loading for each variable on the first principal component.

We excluded variables with loadings less than 0.3 in absolute value, on the grounds that they were not strong indicators of relative advantage or disadvantage. This limit is an accepted level in the PCA literature and has been used in past releases of SEIFA and IHAD. We removed variables one at a time, starting with the lowest loading variable.

We conducted a PCA on the reduced variable list, and if any other variables loaded below 0.3, we repeated steps six and seven.

This section gives the results of the principal component analysis carried out for IHAD, including variable loadings and percentage of variance explained. A list of variables initially considered for inclusion but removed due to high correlations with other variables or weak loadings is also provided.

IHAD summaries variables that indicate either relative socio-economic advantage or disadvantage, according to the concept described in Defining the concept behind IHAD. The final IHAD variables and loadings are listed below.

IHAD indicators of disadvantage

The following variables are indicators of disadvantage. PUBLIC_RENT is the strongest indicator of disadvantage in the index. 

IHAD indicators of advantage

The following variables are indicators of advantage. DEGREE_DEPENDENT is the strongest indicator of advantage in the index.

In most cases, highly correlated variables were removed from the initial candidate list. This was done to prevent instability in the variable weights and over-representation of any specific socio-economic characteristic. When two variables had a correlation coefficient of size greater than 0.8 in absolute value, one of them was generally removed. However, if they were deemed to be measuring different socio-economic characteristics (e.g. education and occupation), both were retained.

The following variables were initially considered for the index but were excluded when the analysis showed that they were weak indicators of relative advantage or disadvantage.

This section presents the frequency histogram of IHAD scores. The IHAD distributions have generally similar shapes to those from Experimental IHAD 2016.

The scores for IHAD range from 613 to 1,246; the table presents maximum and minimum scores of each IHAD quartile. These show that there is sufficient variation in the IHAD scores to allow for the formation of these groups.

Some households will not have any indicators of advantage or disadvantage (i.e. their values for the final binary candidate variables are all 0). They will still receive an IHAD score reflecting the middle of the IHAD score distribution, which places them in quartile 2.