Which kind of general linear model?

#1
Hello statisticians,

Let me introduce myself. I am a 19 year old student Applied Economic Sciences at the University of Antwerp (Belgium). We are given a task for the course 'regression and anova' consisting of 5 questions. The first four questions were no problem but I'm stuck at the last one. Let me share it with you:

"In this example, the number of maintenance repairs on a complex system are modeled as realizations of Poisson random variables. The system under investigation has a large number of components, which occasionally break down and are replaced or repaired. During a four-year period, the system was observed to be in a state of steady operation, meaning that the rate of operation remained approximately constant. A monthly maintenance record is available for that period, which tracks the number of components removed for maintenance each month.
The data are listed in the following statements that create a SAS data set.

data equip;
input year month removals @@;
datalines;
1987 1 2 1987 2 4 1987 3 3
1987 4 3 1987 5 3 1987 6 8
1987 7 2 1987 8 6 1987 9 3
1987 10 9 1987 11 4 1987 12 10
1988 1 4 1988 2 6 1988 3 4

(only part of the dataset)

For planning purposes, it is of interest to understand the long- and short-term trends in the maintenance needs of the system. Over the long term, it is suspected that the quality of new components and repair work improves over time, so the number of component removals would tend to decrease from year to year. Can you confirm this with an appropriate Generalized linear model ? "


Now, there is no information about generalized linear models in our course, so we have to find out the appropriate model ourselves. I've done some research and so far the most appropriate GLM seems to be either a loglinear model or a poisson regression because these have (obviously) a poisson distributed random component. But is is still not clear how the decreasing trend from year to year can be showed with this model.

So my question to you, oh dear statisticians, is which model is the one to be used here and how the demanded trend can be shown (Is it just a mather of parameter interpretation?). The needed SAS procedure would be very helpful too.

I've been thinking about this question all day and this forum seems to be the last resort. Hopefully some genius can help me in some way :tup:

Many thanks in advance! :wave: