Question

Econometrics Question

The ordered multinominal logit model (OLM) is also referred to as the proportional odds model, explain the underlying assumption. How would you test this assumption?

Answer 1

The proportional odds model is a class of generalized linear model used for modelling the dependence of an ordinal response on discrete or continuous covariates. For example, if we conduct a survey after presentation, say on predictive machine learning, audience can respond like; very satisfied, satisfied, ok, dissatisfied and very dissatisfied. If we look at here, there is no equal clear cut difference between the options. Here there is order in dependent variable. A logic regression model trying to use independent variables to predict, what is the likely response of each individual in the survey is ordinal logic regression. Examples of proportional odds models are (1) state spending on health programmes (2) level of insurance coverage (3) employment status etc.

Now we are going to explain the proportional odd assumption. If the probabilities of below events are like this: (a) very dissatisfied (P1), (b) Dissatisfied (P2), (c) OK (P3), (d) Satisfied (P4), and (e) Very satisfied (P5). Here the logarithms of odds form an arithmetic sequence.

Very dissatisfied :

Dissatisfied :  

Neutral or worse :

Satisfied, neutral or worse :

Here the sequences are in arithmetic order.

If we test the assumption of this proportional odd model, where this models allow the assumption of proportional odds to be relaxed for one or small subset of explanatory variables, but retained for majority of explanatory variables. For current analysis, inspection of the separate ordinal regressions for a series of binary logistic regression suggests it is reasonable to conclude the ordinal proportional odds model is a fair summary of the pattern in data in relation to tier of entry. On the other hand, a ordinal model was built hierarchically over a series of steps looking first at prior attainment then progressively adding further explanatory variables.