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The following excerpt from Data Mining and Predictive Analysis: Intelligence Gathering and Crime Analysis, written by Colleen McCue, is reprinted with permission from Butterworth-Heinemann, a division of Elsevier; copyright 2007. Download the complete chapter for free: "Law enforcement data mining, predictive analysis: Terms, errors of data mining for violent crime."
Basic data mining statistics
Some of my earliest work using data mining and predictive analytics on crime and criminals employed the use of relatively advanced statistical techniques that yielded very complex models. While the results were analytically sound, and even of interest to a very small group of similarly inclined criminal justice and forensic scientists, the outcomes were so complicated and arcane that they had very little utility to those who needed them most, particularly those on the job in the public safety arena. Ultimately, these results really contributed nothing in a larger sense because they could not be translated into the operational environment. My sworn colleagues in the law enforcement world would smile patiently, nodding their heads as if my information held some meaning for them, and then politely ask me what it really meant in terms of catching bad guys and getting the job done. I rarely had an answer. Clearly, advanced statistics was not the way to go.
Data mining, on the other hand, is a highly intuitive, visual process that builds on an accumulated knowledge of the subject matter, something also known as domain expertise. While training in statistics generally is not a prerequisite for data mining, understanding a few basic principles is important. To be sure, it is well beyond the scope of this book to cover statistics with anything more than a cursory overview; however, a few simple "rules of the road" are important to ensure methodologically sound analyses and the avoidance of costly errors in logic that could significantly confound or compromise analysis and interpretation of the results. Outlined below are some simple statistical terms and concepts that are relevant to data mining and analysis, as well as a few common pitfalls and errors in logic that a crime analyst might encounter. These are by no means all inclusive, but they should get analysts thinking and adjusting the way that they analyze and interpret data in their specific professional domain.
Inferential versus descriptive statistics and data mining
Descriptive statistics, as the name implies, is the process of categorizing and describing the information. Inferential statistics, on the other hand, includes the process of analyzing a sample of data and using it to draw inferences about the population from which it was drawn. With inferential statistics, we can test hypotheses and begin to explore causal relationships within data and information. In data mining, we are looking for useful relationships in the information or models, particularly those that can be used to anticipate or predict future events. Therefore, data mining more closely resembles descriptive statistics.
It was not that long ago that the process of exploring and describing data, descriptive statistics, was seen as the necessary though unglamorous prerequisite to the more important and exciting process of inferential statistics and hypothesis testing. In many ways, though, the creative exploration of data and information associated with descriptive statistical analysis is the essence of data mining, a process that, in skilled hands, can open new horizons in data and our understanding of the world.
Population versus samples
It would be wonderful if we could know everything about everything and everybody, and have complete access to all of the data that we might need to answer a particular question about crime and criminals. If we had access to every criminal, both apprehended and actively offending, we would have access to the entire population of criminals and be able to use population-based statistics. Similarly, if we had access to all of the information of interest, such as every crime in a particular series, this also would resemble a population because it would be all inclusive. Obviously, this is not possible, particularly given the nature of the subject and the questions. It is a common joke that everything that we know about crime and criminals is based on the unsuccessful ones, those that got caught. Most criminal justice research is based on correctional populations, or offenders that have some sort of relationship with the criminal justice system. Research on the so-called "hidden" populations can be extremely difficult, even dangerous in some cases, as these hidden populations frequently include criminals who are still criminally active. Moreover, any time that we extend beyond official documents and records, we step into a gray zone of potentially unreliable information.
Similarly, we have the disadvantage of relying almost exclusively on official records or self-report information from individuals who are not very reliable in the first place. Consequently, we frequently have access to a very limited amount of the total offense history of a particular offender, because generally only a relatively small fraction of criminal behavior is ever identified, documented, and adjudicated. Criminal justice researchers often are limited in this area because offender interviews regarding nonadjudicated criminal activity approach the "third rail" in criminal justice research. For example, criminal justice researchers must obey existing laws requiring the reporting of known or suspected child abuse. Similarly, researchers should consider the ethical issues associated with uncovering or gaining knowledge of unreported, ongoing, or planned criminal activity. Because this information can cause potential harm to the offender due to legal reporting requirements and ethical considerations, research involving the deliberate collection of unreported crime frequently is prohibited when reviewed by institutional review boards and others concerned about the rights of human research subjects. Similar to drug side effects, there are those crimes and behaviors that we know about and those that we do not. Also like drug side effects, it is generally true that the ones that we do not know about will come up and strike us eventually.
What we are left with, then, is a sample of information. In other words, almost everything that we know about crime and criminals is based on a relatively small amount of information gathered from only a fraction of all criminals—generally the unsuccessful ones. Similarly, almost everything that we work with in the operational environment also is a sample, because it is exceedingly rare that we can identify every single crime in a series or every piece of evidence. In many ways, it is like working with a less than perfect puzzle. We frequently are missing pieces, and it is not unusual to encounter a few additional pieces that do not even belong and try to incorporate them. Whether this is by chance, accident, or intentional misdirection on the part of the criminal, it can significantly skew our vision of the big picture.
We can think of samples as random or nonrandom in their composition. In a random sample, individuals or information are compiled in the sample based exclusively on chance. In other words, the likelihood that a particular individual or event will be included in the sample is similar to throwing the dice. In a nonrandom sample, some other factor plays a significant role in group composition. For example, in studies on correctional samples, even if every relevant inmate were included, it still would comprise only a sample of that particular type of criminal behavior because there would be a group of offenders still active in the community. It also would be a nonrandom sample because only those criminals who had been caught, generally the unsuccessful ones, would be included in the sample. Despite what incarcerated criminals might like to believe, it generally is not up to chance that they are in a confined setting. Frequently, it was some error on their part that allowed them to be caught and incarcerated. This can have significant implications for the analytical outcomes and generalizability of the findings.
In some cases, identification and analysis of a sample of behavior can help to illuminate a larger array of activity. For example, much of what we know about surveillance activity is based on suspicious situation reports. In many cases, however, those incidents that arouse suspicion and are reported comprise only a very small fraction of the entire pattern of surveillance activity, particularly with operators highly skilled in the tradecraft of covert surveillance. In some cases, nothing is noted until after some horrific incident, and only in retrospect are the behaviors identified and linked. Clearly, this retrospective identification, characterization, and analysis is a less than efficient way of doing business and underscores the importance of using information to determine and guide surveillance detection efforts. By characterizing and modeling suspicious behavior, common trends and patterns can be identified and used to guide future surveillance detection activities. Ultimately, this nonrandom sample of suspicious situation reports can open the door to inclusion of a greater array of behavior that more closely approximates the entire sample or population of surveillance activity.
These issues will be discussed in Chapters 5 and 14; however, it always is critical to be aware of the potential bias and shortcomings of a particular data set at every step of the analytical process to ensure that the findings and outcomes are evaluated with the appropriate level of caution and skepticism.
Throughout the data mining and modeling process, there is a fair amount of user discretion. There are some guidelines and suggestions; however, there are very few absolutes. As with data and information, some concepts in modeling are important to understand, particularly when making choices regarding accuracy, generalizability, and the nature of acceptable errors. The analyst's domain expertise, or knowledge of crime and criminals, however, is absolutely essential to making smart choices in this process.
Common data mining errors
No model is perfect. In fact, any model even advertised as approaching perfection should be viewed with significant skepticism. It really is true with predictive analytics and modeling that if it looks too good to be true it probably is; there is almost certainly something very wrong with the sample, the analysis, or both. Errors can come from many areas; however, the following are a few common pitfalls.
- Data mining error No.1: Infrequent Events When dealing with violent crime, the fact that it is a relatively infrequent event is a very good thing for almost everyone, except the analysts. The smaller the sample size, generally, the easier it is to make errors. These errors can occur for a variety of reasons, some of which will be discussed in greater detail in Chapter 5. In modeling, infrequent events can create problems, particularly when they are associated with grossly unequal sample distributions.
While analyzing robbery-related aggravated assaults, we found that very few armed robberies escalate into an aggravated assault. In fact, we found that less than 5% of all armed robberies escalated into an aggravated assault. Again, this is a very good thing from a public safety standpoint, although it presents a significant challenge for the development of predictive models if the analyst is not careful.
Exploring this in greater detail, it becomes apparent that a very simple model can be created that has an accuracy rate of greater than 95%. In other words, this simple model could correctly predict the escalation of an armed robbery into an aggravated assault 95% of the time. At first blush, this sounds phenomenal. With such a highly accurate model, it would seem a simple thing to proactively deploy and wipe out violent crime within a week. Examining the model further, however, we find a critical flaw: There is only one decision rule, and it is "no." By predicting that an armed robbery will never escalate into an aggravated assault, the model would be correct 95% of the time, but it would not be very useful. What we are really looking for are some decision rules regarding robbery-related aggravated assaults that will allow us to characterize and model them. Then we can develop proactive strategies that will allow us to prevent them from occurring in the future. As this somewhat extreme example demonstrates, evaluating the efficacy and value of a model is far more than just determining its overall accuracy. It is extremely important to identify the nature of the errors and then determine which types of errors are acceptable and which are not.
One way to evaluate the specific nature of the errors is to create something called a confusion or confidence matrix. Basically, what this does is break down and depict the specific nature of the errors and their contribution to the overall accuracy of the model. Once it has been determined where the errors are occurring, and whether they impact significantly the value of the overall error rate and model, an informed decision can be made regarding acceptance of the model. Confusion matrices will be addressed in greater detail in Chapter 8, which covers training and test samples.
The confusion matrix is an important example of a good practice in analysis. It can be extremely valuable to challenge the results, push them around a bit analytically and see what happens, or look at them in a different analytical light. Again, the confusion matrix allows analysts to drill down and examine what is contributing to the overall accuracy of the model. Then they can make an informed decision about whether to accept the model or to continue working on it until the errors are distributed in a fashion that makes sense in light of the overall public safety or intelligence objective. While this process might seem somewhat obscure at this point, it underscores the importance of choosing analysts with domain expertise. Individuals that know where the data came from and what it will be used for ultimately can distinguish between those errors that are acceptable and those that are not. Someone who knows a lot about statistical analysis might be able to create extremely elegant and highly predictive models, but if the model consistently predicts that an armed robbery will never escalate into an aggravated assault because the analyst did not know that these events are relatively infrequent, there can be serious consequences. Although this might seem like an extreme example that would be perfectly obvious to almost anyone, far more subtle issues occur regularly and can have similar harmful consequences. The ultimate consequence of this issue is that the folks within the public safety community are in the best position to analyze their own data. This is not to say that it is wrong to seek outside analytical assistance, but totally deferring this responsibility, as seems to be occurring with increasing frequency, can have serious consequences due to the subtle nature of many of these issues that permeate the analytical process. This point also highlights the importance of working with the operational personnel, the ultimate end users of most analytical products, throughout the analytical process. While they might be somewhat limited in terms of their knowledge and understanding of the particular software or algorithm, their insight and perception regarding the ultimate operational goals can significantly enhance the decision-making process when cost/benefit and error management issues need to be addressed.
Given the nature of crime and intelligence analysis, it is not unusual to encounter infrequent events and uneven distributions. Unfortunately, many default settings on data mining and statistical software automatically create decision trees or rules sets that are preprogrammed to distribute the cases evenly. This can be a huge problem when dealing with infrequent events or otherwise unequal distributions. Another way of stating this is that the program assumes that the prior probabilities or "priors" are 50:50, or some other evenly distributed ratio. Generally, there is a way to reset this, either automatically or manually. In automatic settings, the option generally is to set the predicted or expected probabilities to match the prior or observed frequencies in the sample. In this case, the software calculates the observed frequency of a particular event or occurrence in the sample data, and then uses this rate to generate a model that results in a similar predicted frequency. In some situations, however, it can be advantageous to set the priors manually. For example, when trying to manage risk or reduce the cost of a particularly serious error, it might be necessary to create a model that is either overly generous or very stringent, depending on the desired outcome and the nature of misclassification errors. Some software programs offer similar types of error management by allowing the user to specify the "cost" of particular errors in classification, in an effort to create models that maximize accuracy while ensuring an acceptable distribution of errors.
- Data mining error No. 2: Magnified or obscured effects
- Uneven distributions also can create errors in the interpretation of link analysis results, which is discussed in Chapter 3. Briefly, link analysis can be a great way to show relationships between individuals, entities, events, or almost any variable that could be considered in crime and intelligence analysis. Some of the new software tools are particularly valuable, in that actual photos of individuals or elements of interest can be inserted directly into the chart, which results in visually powerful depictions of organizational charts, associations, or events. Beyond just demonstrating an association, however, link analysis frequently is employed in an effort to highlight the relative strength of relationships. For example, if Bob calls Joe 15 times, but Joe calls Paul 52 times, we might assume that the relationship between Joe and Paul is stronger than the relationship between Joe and Bob based on the relative difference in the amount of contact between and among these individuals (Figure 1-1).
These programs often allow the user to establish thresholds for link strength; however, this can provide a false sense of security. For example, in Figure 1-2, it appears that Paul has a stronger relationship with Pete, as compared to his relationship with Joe, based on the relative levels of contact. Bob, on the other hand, appears to have relatively similar relationships with both Joe and Pete, based on relatively equal levels of contact, as depicted in the link chart. Reviewing the related association matrix, however, indicates that this might not be true (Figure 1-3). The actual numbers of contacts indicates that both Paul and Bob had contact with Pete almost twice as much as they did with Joe. The relationship is skewed somewhat in the link analysis chart (Figure 1-1) because the relative levels of activity associated with Bob were much higher than those associated with Paul. As a result, the settings used in the link analysis skewed the visual representation of the relative strength of the relationships noted. For example, in this particular situation, it might be that weak links include 10 associations or less, while strong links require 20 associations or more. Unfortunately, unequal distributions can skew the relative importance of certain associations. In this example, both Paul and Bob had similar ratios of contact with Pete and Joe, a 2:1 relationship, but this difference was magnified in Paul because he was associated with a lower overall frequency of contact. This allowed the difference in his contact with Pete and Joe to be revealed. On the other hand, the same relative difference in the number of contacts Pete and Joe had with Bob was obscured due to the larger number of contacts overall.-
Figure 1.1 Link charts can not only depict relationships between individuals or events, but also relative strength of the relationship based on relative differences in the amount of contact.
Figure 1.2 Examination of this link chart suggests that Paul has a stronger relationship with Pete compared to his relationship with Joe, while Bob appears to have relatively similar relationships with both Joe and Pete, based on relatively equal levels of contact. These apparent differences in the relationships are based on differences in the strength of the association illustrated by relative differences in the lines in the link chart.
Figure 1.3 This simple association matrix depicts the number of contacts between a group of individuals, and highlights the errors in the associated link chart depicted in Figure 1-2.
Signal-to-noise issues like this can be particularly tricky for at least two reasons. First, they can magnify differences in less-frequent events. Because it takes less to show a difference, it is relatively easy to cross the arbitrary thresholds established either by the user or preset in the software. Second, they can obscure differences in the events associated with greater frequencies. This is particularly true when simultaneously comparing relationships that are associated with very different levels of activity. Again, if the thresholds are not set thoughtfully with an understanding of relative frequencies, some associations can be magnified while other relationships can be obscured. There are a variety of mechanisms available to address this potential confound, including the use of percentages or ratios, which are discussed in Chapter 5; however, the key to addressing this issue generally is awareness and caution when interpreting these types of results.
- Data mining error No. 3: Outliers
- "Outliers," unusual subjects or events, can skew dramatically an analysis, model, or outcome with a small sample, as is found with relatively infrequent events. For example, if we analyze a sample of three armed robbers, one of whom likes fruitcake, we might assume erroneously that a preference for fruitcake is a good indicator of criminal behavior; after all, in our current sample, one-third of the subjects likes fruitcake. Perhaps we further expand our sample, though, to include a total of 100 armed robbers. Again, this one subject has a preference for fruitcake, but he remains the only one. In this case, a preference for fruitcake is associated with only 1% of the sample, which is not nearly as exciting. While this is a simple example, similar errors in judgment, analysis, and interpretation of results based on small, nonrandom samples have been made throughout history, sometimes with tragic consequences. All too frequently, public safety programs and policies are based on relatively small samples with unusual characteristics.
There is a saying in medicine that there are the side effects that you know about, and those that you do not. It is the side effects that you do not know about that will get you every time. Similarly, when doing data mining and constructing models, it is absolutely imperative to remember that you are only working with a sample of the total information. Even if you believe that you have gathered the total universe of information related to a particular organization, investigation, or case, it is unlikely that you have. There is always that one little tidbit of missing information that will get you in the end. Be prepared for it. Maintaining a healthy degree of realism or skepticism regarding the information analyzed can be extremely important, particularly when new information emerges that must be integrated. So keep in mind as you deal with potentially nonrandom samples that "outliers" need to be considered seriously when analyzing these types of data.
- Data mining error No. 4: Remember the baseline
- It is important to consider baseline data when analyzing and interpreting crime and intelligence information and what might skew or otherwise impact that information. Failure to consider baseline data is an error that occurs frequently, and relates back to the incorrect assumptions that samples are representative of the larger population and that variables tend to be distributed evenly. During the sniper investigation in October 2002, when 10 people were killed around the Washington, D.C. metropolitan area, one of the first assumptions made was that the suspect would be a white male because almost all serial killers are white males. When it turned out that the snipers were black, there was great surprise, particularly among the media. As one stops to consider the likely racial distribution among serial killers, it is important to note the relative distribution of race in the population of interest, in this case the United States, which is approximately 12% black according to the 2000 census data. Taking this information into consideration, we would not expect a 50:50 split along race lines when examining serial killers. Population statistics would indicate fewer black serial killers, if the distribution mirrored the overall population.
Moreover, serial killers are relatively rare, which further confounds our calculations for reasons similar to those addressed earlier regarding small sample sizes and infrequent events. Further confounding the "conventional wisdom" regarding this subject is the highly skewed racial distribution of homicide offenders, which are 51.5% black and 46.4% white. When adjusted to per-capita rates, the FBI Uniform Crime Reports indicate that blacks are eight times more likely to commit homicides than whites. These numbers are based on cleared cases and arrests, though, which have their own unique limitations. Therefore, when viewed in light of these apparently contradictory statistics, possible reasons for the apparent bias in the initial demographic predictions of the D.C. sniper case start to make sense. Clearly, baseline information should be used to filter data and outcomes; however, this simple exercise demonstrates that even determining the appropriate baseline can be a challenge in many cases.
This example also highlights the importance of keeping an open mind. Seasoned investigators understand that establishing a mindset early in an investigation can significantly affect interpretation of subsequent leads and clues, allowing important evidence to be overlooked, such as the "white van" emphasized by the media in the sniper investigation, which artificially filtered many leads from concerned citizens and cooperating public safety agencies alike. Similarly, analysts can fall prey to these same challenges if they are not careful and consider appropriate comparative information with a clear mind that is open to alternative explanations for the data. Again, knowledge of the potential pitfalls is almost as important as the analysis, because ignorance can have a significant impact on the analysis and interpretation of the data.
Arrest data is another area in which considering variances in population distribution can be essential to thoroughly understanding trends and patterns. When we think logically about where and when many arrests occur, particularly vice offenses, we find that officer deployment often directly affects those rates. Like the proverbial tree falling in the woods, it follows that if an officer is there to see a crime, it is more likely that an arrest will be made. This goes back to the earlier discussion regarding the crime that we know about and the crime that we do not know about. Locations associated with higher levels of crime also tend to be associated with heavier police deployment, which concomitantly increases the likelihood that an officer will either be present or nearby when a crime occurs, ultimately increasing the arrest rate in these locations. Unfortunately, the demographics represented among those arrested might be representative of the residents of that specific area but differ greatly from the locality as a whole. This can greatly skew our interpretation of the analysis and findings. What does this mean to data mining and predictive analytics? Simply, that it can be an error to use population statistics to describe, compare, or evaluate a relatively small, nonuniform sample, and vice versa. Remember the baseline, and give some thought to how it was constructed, because it might differ significantly from reality.
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