# Monotonic and non-monotonic patterns of missing values: how do they look like?

I was reading the user's guide of SPSS on missing value analysis and I found the terms monotonic and non-monotonic pattern of missing values. The terms are not quite clear to me. They used telco_missing.sav data file to show a graph from which they comment:

If the data are monotone, then all missing cells and nonmissing cells in the chart will be contiguous; that is, there will be no “islands” of nonmissing cells in the lower right portion of the chart and no “islands” of missing cells in the upper left portion of the chart.

I didn't either understand that. I hope someone will be kind enough to show me how a monotone and non-monotone patterns does look like and tell me how do I understand it a little more clearly.

## 2 Answers

The definition of monotonic missing is that, once the subject dropped out he will drop out forever, while for non-monotonic missing the subject may come back or be missing again.

For example, if we follow one subject for five years and he dropped out in the third year, monotonic missing is like o o m m m, and one kind of non-monotonic missing can be o o m o m, where o indicates observed, m indicates missing.

So the third o in the non-monotonic missing is like an island. This is just to classify the pattern of missing, and generally the monotonic missing is easier to handle.

Actually the accepted answer is not completely correct. According to the Statistical Analysis with Missing Data book a monotone pattern is:

monotone missing data: where the variables can be arranged so that all Y(j+1) ... Y(K) are missing for cases where Y(j) is missing, for all J = 1 ... K-1.

So for ANY order of Y. This means that also o o m o m can be a monotone pattern as long as the rest of the data has either a subset of a superset of the parameters missing.