Title: Testing models empirically: Path diagram for two variables
Course: UGQuants (SSPS) > Section: Causality

Testing models empirically: Path diagram for two variables

We can describe the relationship between income and health more precisely using the difference in proportions method, and focusing on those who say their health is very good. We will take low income and very bad health as our base categories.

First looking at all respondents of all ages and taking those on low (up to median) incomes as our base category for our independent variable, we can see that  .239 of them said they had very good health. In addition, .367 of those in high (above median) incomes said they had very good health. The difference in proportions between the two categories is 128. The total proportion in very good health is therefore the proportion in the 'base' category (low income) in very good health plus the extra proportion in the non-base category (high income) who were in very good health multiplied by the proportion of respondents in the non-base category. This is shown in the diagram below.

This causal path diagram keeps us clear about what relationships we have to measure. It is also dependent on our theory, or model, of where the causal directions might lie. The arrows in the diagram represent the direct effect of one variable upon another. For the purposes of this model we are modelling the effect of income on health rather than the reverse. That is to say we are assuming that it is income that affects health rather than the other way around. What is the size of the effect of income on health? We can estimate this from the difference in proportions of high and low income people reporting very good health. From the table or the diagram we have drawn above we can see that this difference is 0.128.

The figure of .239 represents the proportion of low income respondents (our base category) who nevertheless reported very good health (the non-base category of the dependent variable). We can also think of this figure as representing the effect of all the variables that are not in our model. If income was the only determinant of health, then all low income people would have poor health and all high income people would have good health, and this figure would be zero, while the difference in proportions in the arrow going from high income to very good health would be one. However, since many other variables will be relevant, a proportion of low income people still report very good health.