4.3 Modelling health
This section provides some additional details that are supplementary to the regression models. These details inform parts of the results from the core models.
4.3.1 Health failures and the health survey models
Wealth was measured at Wave 2 whereas measures of physical discomfort and psychological distress were recorded in Wave 3. This may be problematic if enough individuals experienced a substantial change in health between Waves 2 and 3. Deteriorating health between these waves could push some respondents from moderate (in Wave 2) to high discomfort and distress (in Wave 3). Alternatively, an improvement in health could lead to some individuals experiencing a reduction in their levels of discomfort and distress between Waves 2 and 3.
SoFIE contains a variable that may enable some of those in the former group to be identified.[13] Respondents were asked in Wave 3 whether they experienced an injury or illness, which restricted their usual activities, lasting seven days or more in the 12 months preceding the interview. Those who answered “yes” to this question were assumed to have experienced a health “failure”. For these respondents, their Wave 3 health is less likely to be a suitable proxy for their unobserved health in Wave 2.
This was incorporated by decomposing the measures of physical discomfort and psychological distress by the presence of a health failure. In the core models the health variable being considered changed from:
H = {physical discomfort, psychological distress}
to:
H = {physical discomfort by failure, psychological discomfort by failure}
4.3.2 Independence of the chronic conditions
Independence of the chronic conditions was tested before including multiple conditions together in the core models. This was done by treating the occurrence of each chronic condition as a Bernoulli event. Seven of these conditions (excluding depression and schizophrenia) were combined to form a single multinomial model. The model has the following form:
The proportion of the longitudinal population with each condition was used as the best estimator for the probability of having the condition:
(ci = 1) = proportion of the longitudinal population with ci = 1
where ci = 1 if the respondent has the ith chronic condition.
From this, the probability of being diagnosed with every number and combination of conditions was calculated:
P(C = j) = Σ
with: Σci = j
where: C = the total number of chronic conditions for a respondent
These were grouped by the number of conditions in the diagnosis and multiplied by the weighted population total to give estimates for the entire longitudinal population.
Table 5 shows the results of this model and the actual observed results.
| Number of chronic conditions | Zero | 1 | 2 | 3 | 4 | 5–7 |
|---|---|---|---|---|---|---|
| Estimated | 1,223,200 | 1,105,100 | 399,100 | 73,300 | 7,200 | 400 |
| Actual | 1,449,300 | 826,700 | 347,500 | 131,600 | 40,300 | 12,900 |
Source: SoFIE Waves 1–3, OSMs, longitudinal weights, supplied by Statistics New Zealand
Inspection of the results shows the theoretical model to be a poor fit; this was confirmed by a goodness-of-fit test. The model overestimates the proportion of the longitudinal population with one or two conditions and underestimates the proportion of the longitudinal population with zero or three to seven conditions.
The failure of this model highlights the lack of independence among the conditions. This was not investigated further. A successful model would be expected to include age because older respondents are seen or seem to have a higher likelihood of developing all conditions.[14]
The lack of independence between chronic conditions means that including multiple conditions in the analysis tends to make one or more of the conditions redundant. Each core model was run once for each chronic condition, so as to avoid this. A summary variable that indicated how many chronic conditions each respondent suffered from was considered, but was discarded owing to poor fit.
4.3.3 Receipt of a health tested benefit
SoFIE respondents were asked about the amount and sources of income they received over the last 12 months, including all forms of benefits. These benefits were separated into health and non-health benefits based on the requirements to qualify for each benefit.[15] SoFIE estimates 10% of the longitudinal population receive some form of health tested benefit.
An attempt was made to include the receipt of a health tested benefit in the core models. This resulted in many of the health descriptors becoming no longer significant at the 10% level and the coefficients of those variables that were still significant becoming significantly lower.
Much of the change caused by the inclusion of a health tested benefit will be due to colinearity. Because the receipt of a health tested benefit is dependent on a large number of factors including health, income and wealth, it is not a truly independent variable. Results from its inclusion can be found in Appendix C, Appendix Table 19.
Notes
- [13]No means of detecting an improvement in health between Wave 2 and Wave 3 was found.
- [14]So a 60-year-old woman is more likely to have been diagnosed with heart disease than a 50-year-old woman. A 60-year-old woman is also more likely to have been diagnosed with high cholesterol than a 50-year-old woman. The chances increase for both conditions.
- [15]Illness-based benefits include Sickness Benefit, Invalid’s Benefit, Disability Allowance, Amputee Assistance, Residential Support Subsidy and Rehabilitation Allowance.
