FMSN30/MASM22

Examine the precipitation data, weather.rda, again. We now want to look at the extreme amounts of precipitation, both low and high. This can be done in several different ways.

Choose any of the following problems. You should be able to talk for 10-15 minutes about what you have done.

Discussion forum: Project 3B low-medium-high rain help

1. Ordinal logistic regression

Divide the amount of precipitation into three categories: low, medium, high where the low category is defined as less than 25mm (same as in Project 2). The high category is defined as more than 60mm. The medium category is then 25-60mm.

Model the probabiliy for low-medium-high amount of precipitation as a function of temperature, air pressure and location as before, using an ordinal logistic regression.

Some things you could chose to focus on:

(a) Additional variables

Use the seasons as well, in order to get a better model.

(b) Performance

Check the performance of the model by comparing its predictions to the true outcome. The confusion matrix is now a 3x3-table but you can still calculate sensitivity and specificity (except that you get 3 of them). You can also divide the probabilities into groups and compare the number of observed and expected observations of each type in each group.

(c) Multinomial logistic regression

Ignore that there is a logical ordering between the precipitation categories and model the probabilities using a multinomial logistic regression instead. Compare the results with the ones from the ordinal logistic model.

2. Quantile regression

Model the 25% and 75% quantiles of the precipitation as a function of temperature, air pressure and location.

Feel free to add other quantiles as well.

You might want to transform the precipition first and add the seasons in order to improve the model.