Beware Phantom Data

One of the perennial challenges facing the data analyst is missing values. A great deal has been written about the importance of identifying the source of missing values, the danger of overly simplistic solutions and, of course, the many and varied mechanisms for "filling them in" with synthetic data ("imputation").

Of the tremendous volume of material written on this subject, nearly all assumes that the analyst knows precisely which items are missing from the data. In reality, this is sometimes not the case. Relational databases and statistical software files, as a rule, have a special value to indicate "missing", though that does not mean that it is always used. Some file formats offer only indirect provision for missings, if any at all, and how software reacts to such missings varies.

Consider, too, the popular practice of using special values (such as -9999) to represent missing values. What could possibly go wrong? For one thing, the person writing the data may not consider whether the flag value might represent a legitimate value. Is it possible, for instance, to have an account balance of -9999 dollars (euros, etc.)? In my career, I have seen databases which used different flag values for each field (-99, -9999, -99999, etc.), making the writing of code against such data extremely tedious (and error-prone). I have also seen -9999 used to indicate one type of missing value, and -9998 to indicate another type of missing. When the hand-off of information from one person (system, process, etc.) to another is confused or incomplete, interpretation of the data becomes incorrect.

Another aspect of this problem is the precise definition given to fields, and their possible misinterpretation by data consumers (such as data miners). Imagine that a particular integer field is being used to record the number of times each customer has made a payment on their loan, within the past 6 months. As customers begin their tenure, this variable starts with a value of zero. Suppose our model included this field as an independent variable. Presumably low risk customers have higher values, while higher risk customers have lower values. Without missing any payments, early lifecycle customer are penalized arbitrarily by the model. One could make the argument that this variable should be undefined (recorded as a database missing value flag) until a customer has a full 6-month track record, but this is exactly the sort of conversation which very often fails to materialize in real organizations.

These are all instances of "phantom data": Items in the database which are missing values, but mistaken for real data. It shouldn't take much imagination on the reader's part to conjure similar problematic situations in his or her own field. The lesson is to look beyond the known missings for more subtle gaps in the data. Time spent investigating the nature of database systems, company procedures and so forth which generate data is insurance against being burned by serious misunderstanding of the data.

Missing Values and Special Values: The Plague of Data Analysis

Every so often, an article is published on data mining which includes a statistic like "Amount of data mining time spent preparing the data: 70%", or something similar , expressed as a pie chart. It is certainly worth the investment of time and effort at the beginning of a data mining project, to get the data cleaned up, to maximize model performance and avoid problems later on.

Two related issues is data preparation are missing values and special values. Note that some "missing values" are truly "missing values" (items for which there is a true value which is not present in the data), while others are actually special values or undefined (or at least poorly defined) values. Much has already been written about truly missing values, especially in the statistical literature. See, for instance:

Dealing with Missing Data, by Judi Scheffer

Missing data, by Thomas Lumley

Working With Missing Values, by Alan C. Acock

How can I deal with missing data in my study?, by Derrick A. Bennett

Advanced Quantitative Research Methodology, G2001, Lecture Notes: Missing Data, by Gary King

Important topics to understand and keywords to search on, if one wishes to study missing data and its treatment are: MAR ("missing at random"), MCAR ("missing completely at random"), NMAR ("not missing at random"), non-response and imputation (single and multiple).

Special values, which are not quite the same as missing values, also require careful treatment. An example I encountered recently in my work with bank account data was a collection of variables which were defined over lagged time windows, such as "maximum balance over the last 6 months" or "worst delinquency in the last 12 months".

The first issue was that the special values were not database nulls ("missing values"), but were recorded as flag values, such as -999.

The second issue was that the flag values, while consistent within individual variables, varied across this set of variables. Some variables used -999 as the flag value, others used -999.99. Still others used -99999.

The first and second issues, taken together, meant that actually detecting the special values was, ultimately, a tedious process. Even though this was eventually semi-automated, the results needed to be carefully checked by the analyst.

The third issue was the phenomenon driving the creation of special values in the first place: many accounts had not been on the system long enough to have complete lagged windows. For instance, an account which is only 4 months old has not been around long enough to accumulate 12 months worth of delinquency data. In this particular system, such accounts received the flag value. Such cases are not quite the same as data which has an actual value which is simply unrecorded, and methods for "filling-in" such holes probably would provide spurious results.

A similar issue surrounds a collection of variables which relies on some benchmark event- which may or may not have happened, such as "days since purchase" or "months since delinquency". Some accounts had never purchased anything, and others had never been delinquent. One supposes that, theoretically, such situations should have infinity recorded. In the actual data, though, they had flag values, like -999.

Simply leaving the flag values makes no sense. There are a variety of ways of dealing with such circumstances, and solutions need to be carefully chosen given the context of the problem. One possibility is to convert the original variable to one which represents, for instance, the probability of the target class (in a classification problem). A simple binning or curve-fitting procedure would act as a single-variable model of the target, and the special value would be assigned whatever probability was observed in the training data for those cases.

Many important, real circumstances will give rise to these special values. Be vigilant, and treat them with care to extract the most information from them and avoid data mining pitfalls.