Although a higher education might lead to a higher income we unfortunately do not have the data to look at that but as previously mentioned we have now stressed the importance of parental income, lines 419-428, 503-506, 533-537 and 550-555, thank you for pointing this out.
It also assumes that parents with more educational experience are more likely to have higher incomes and so are more likely to make and avoid healthier food choices for their family.