ANCOVA — Bayesian Style
Following the very positive reception of the previous article seeking to understand if there is a proportional difference between school sectors and post-secondary outcomes, let’s follow up with a little more. We stated that the modelling was not intended to be causal, and is merely descriptive. This was prefaced by saying that there would be numerous factors that one might consider in a causal model. Well it so happens a proxy measure exists, ICSEA or Index of Community Socio-Educational Advantage.
Continuing on from the previous article, we will seek to explore if there is a causal relationship between ICSEA across proportional outcomes by sector, amounting to a Bayesian ANCOVA workflow.
Before jumping into the modelling, lets develop our causal model and understanding. ICSEA is a scale that identifies the socio-educational advantage of a school. This is a measure calculated by ACARA (Australian Curriculum Assessment Reporting Authority) that factors in parents educational background and occupation, Aboriginal status of students and the geographic location of the school. The average value of ICSEA is set to 1000 with a standard deviation of 100, and hence higher ICSEA values refer to schools with higher socio-educational advantage.
There are an enumerate number of factors that can affect student performance and outcomes. We’ve simplified to something more tangible below. Starting on the left hand side, we can reasonably expect a parents level of education to be an influence on their child’s personal ambitions, parental education will influence their salary, and hence what suburb they afford to live in, putting them proximal to schools within certain sectors. We are going to reasonably assume that affluent areas have a greater mix of Independent and Catholic schools ahead of Government schools. These are a lot of fields and data…