where x represents the vector of control variables. Under the assumption that the
disturbances are distributed as iid type I extreme value, this random utility framework
motivates the use of the multinomial logit model. Initially STATA was used to fit a
multinomial logit model with the six PHI categories as the outcome.
All explanatory variables were fitted in the full model in groups of related variables,
specifically demographics, relationship and family formation, education and
occupation, health, wages, benefits and financial assets, health risk and financial risk,
retrospective self-reported life changes, prospective changes in income and financial
assets.
The number of variables in the model from each group of explanatory variables was
reduced using backward elimination from the full model. The objective was to retain
in the model those variables from each group with the greatest explanatory power,
without omitting any important variables from the model. Each group of explanatory
variables was reduced in the presence of all other variables, starting with the least
significant variable in the group. A variable was kept or dropped based on the
likelihood ratio test (alpha = .05) and the next least significant variable was tested and
so on. After all variables had been tested, the next family was then reduced the same
way. Age, sex, health and income are all known important explanatory variables for
health insurance behaviour. Therefore appropriate measure(s) of each of these
characteristics were kept in the model regardless of their significance in the sample.
The final model was tested for adequacy against the full model using the likelihood
ratio test. To ensure that no important explanatory variables had been omitted from
the model, the coefficients in the final model were compared with the full model for
any substantial changes in size.
The final model was tested for the assumption of independence of irrelevant
alternatives, using formal tests and by running a series of binary logit models of each
alternative outcome against the reference outcome “never had private health
insurance” to check any changes in the coefficients.
The variables retained in the final model were age, sex, partner status, number of
children, age of youngest child, occupation, education, language, country of birth,
region of residence, self-assessed health, disability or long-term illness, smoking
status, weekly exercise, individual wages, benefits and financial assets, partner’s
wages and financial assets, total household wages, self-reported prosperity and
attitude to financial risk, recent loss of job, recent illness or disability in the family,
recent worsening of financial situation, recently married, prospective changes in
household wages, benefits and financial assets.
Variables in the final model were inspected for functional form. Age was non-linear
on the logit for the alternatives “joined because of lifetime health cover” and “joined
after lifetime health cover”. Age was therefore entered as spline variables with break-
points at age 31, 46 and 66 to capture the age-related effects of the LHC policy.
Increasing positive financial assets and increasing negative financial assets predicted a
greater probability of having private health insurance relative to no financial assets.
Therefore to capture this non-linear relationship, financial assets was fitted as two
ordinal variables, positive financial assets with 6 ordinal categories ($0 to $9999,
$10,000 to $19,999,.....,$40,000 to $49,999, $50,000 and above) and negative
financial assets with 2 ordinal categories (< -$10,000, $0 to -$9999).