CoolData blog

22 September 2014

What predictor variables should you avoid? Depends on who you ask

People who build predictive models will tell you that there are certain variables you should avoid using as predictors. I am one of those people. However, we disagree on WHICH variables one should avoid, and increasingly this conflicting advice is confusing those trying to learn predictive modeling.

The differences involve two points in particular. Assuming charitable giving is the behaviour we’re modelling for, those two things are:

  1. Whether we should use past giving to predict future giving, and
  2. Whether attributes such as marital status are really predictors of giving.

I will offer my opinions on both points. Note that they are opinions, not definitive answers.

1. Past giving as a predictor

I have always stressed that if you are trying to predict “giving” using a multiple linear regression model, you must avoid using “giving” as a predictor among your independent variables. That includes anything that is a proxy for “giving,” such as attendance at a donor-thanking event. This is how I’ve been taught and that is what I’ve adhered to in practice.

Examples that violate this practice keep popping up, however. I have an email from Atsuko Umeki, IT Coordinator in the Development Office of the University of Victoria in Victoria, British Columbia*. She poses this question about a post I wrote in July 2013:

“In this post you said, ‘In predictive models, giving and variables related to the activity of giving are usually excluded as variables (if ‘giving’ is what we are trying to predict). Using any aspect of the target variable as an input is bad practice in predictive modelling and is carefully avoided.’  However, in many articles and classes I read and took I was advised or instructed to include past giving history such as RFA*, Average gift, Past 3 or 5 year total giving, last gift etc. Theoretically I understand what you say because past giving is related to the target variable (giving likelihood); therefore, it will be biased. But in practice most practitioners include past giving as variables and especially RFA seems to be a good variable to include.”

(* RFA is a variation of the more familiar RFM score, based on giving history — Recency, Frequency, and Monetary value.)

So modellers-in-training are being told to go ahead and use ‘giving’ to predict ‘giving’, but that’s not all: Certain analytics vendors also routinely include variables based on past giving as predictors of future giving. Not long ago I sat in on a webinar hosted by a consultant, which referenced the work of one well-known analytics vendor (no need to name the vendor here) in which it seemed that giving behaviour was present on both sides of the regression equation. Not surprisingly, this vendor “achieved” a fantastic R-squared value of 86%. (Fantastic as in “like a fantasy,” perhaps?)

This is not as arcane or technical as it sounds. When you use giving to predict giving, you are essentially saying, “The people who will make big gifts in the future are the ones who have made big gifts in the past.” This is actually true! The thing is, you don’t need a predictive model to produce such a prospect list; all you need is a list of your top donors.

Now, this might be reassuring to whomever is paying a vendor big bucks to create the model. That person sees names they recognize, and they think, ah, good — we are not too far off the mark. And if you’re trying to convince your boss of the value of predictive modelling, he or she might like to see the upper ranks filled with familiar names.

I don’t find any of that “reassuring.” I find it a waste of time and effort — a fancy and expensive way to produce a list of the usual suspects.

If you want to know who has given you a lot of money, you make a list of everyone in your database and sort it in descending order by total amount given. If you want to predict who in your database is most likely to give you a lot of money in the future, build a predictive model using predictors that are associated with having given large amounts of money. Here is the key point … if you include “predictors” that mean the same thing as “has given a lot of money,” then the result of your model is not going to look like a list of future givers — it’s going to look more like your historical list of past givers.

Does that mean you should ignore giving history? No! Ideally you’d like to identify the donors who have made four-figure gifts who really have the capacity and affinity to make six-figure gifts. You won’t find them using past giving as a predictor, because your model will be blinded by the stars. The variables that represent giving history will cause all other affinity-related variables to pale in comparison. Many will be rejected from the model for being not significant or for adding nothing additional to the model’s ability to explain the variance in the outcome variable.

To sum up, here are the two big problems with using past giving to predict future giving:

  1. The resulting insights are sensible but not very interesting: People who gave before tend to give again. Or, stated another way: “Donors will be donors.” Fundraisers don’t need data scientists to tell them that.
  2. Giving-related independent variables will be so highly correlated with giving-related dependent variables that they will eclipse more subtle affinity-related variables. Weaker predictors will end up getting kicked out of our regression analysis because they can’t move the needle on R-squared, or because they don’t register as significant. Yet, it’s these weaker variables that we need in order to identify new prospects.

Let’s try a thought experiment. What if I told you that I had a secret predictor that, once introduced into a regression analysis, could explain 100% of the variance in the dependent variable ‘Lifetime Giving’? That’s right — the highest value for R-squared possible, all with a single predictor. Would you pay me a lot of money for that? What is this magic variable that perfectly models the variance in ‘Lifetime Giving’? Why, it is none other than ‘Lifetime Giving’ itself! Any variable is perfectly correlated with itself, so why look any farther?

This is an extreme example. In a real predictive model, a predictor based on giving history would be restricted to giving from the past, while the outcome variable would be calculated from a more recent period — the last year or whatever. There should be no overlap. R-squared would not be 100%, but it would be very high.

The R-squared statistic is useful for guiding you as you add variables to a regression analysis, or for comparing similar models in terms of fit with the data. It is not terribly useful for deciding whether any one model is good or bad. A model with an R-squared of 15% may be highly valuable, while one with R-squared of 75% may be garbage. If a vendor is trying to sell you on a model they built based on a high R-squared alone, they are misleading you.

The goal of predictive modeling for major gifts is not to maximize R-squared. It’s to identify new prospects.

2. Using “attributes” as predictors

Another thing about that webinar bugged me. The same vendor advised us to “select variables with caution, avoiding ‘descriptors’ and focusing on potential predictors.” Specifically, we were warned that a marital status of ‘married’ will emerge as correlated with giving. Don’t be fooled! That’s not a predictor, they said.

So let me get this straight. We carry out an analysis that reveals that married people are more likely to give large gifts, that donors with more than one degree are more likely to give large gifts, that donors who have email addresses and business phone numbers in the database are more likely to give large gifts … but we are supposed to ignore all that?

The problem might not be the use of “descriptors,” the problem might be with the terminology. Maybe we need to stop using the word “predictor”. One experienced practitioner, Alexander Oftelie, briefly touched on this nuance in a recent blog post. I quote, (emphasis added by me):

“Data that on its own may seem unimportant — the channel someone donates, declining to receive the mug or calendar, preferring email to direct mail, or making ‘white mail’ or unsolicited gifts beyond their sustaining-gift donation — can be very powerful when they are brought together to paint a picture of engagement and interaction. Knowing who someone is isn’t by itself predictive (at best it may be correlated). Knowing how constituents choose to engage or not engage with your organization are the most powerful ingredients we have, and its already in our own garden.”

I don’t intend to critique Alexander’s post, which isn’t even on this particular topic. (It’s a good one – please read it.) But since he’s written this, permit me scratch my head about it a bit.

In fact, I think I agree with him that there is a distinction between a behaviour and a descriptor/attribute. A behaviour, an action taken at a specific point in time (eg., attending an event), can be classified as a predictor. An attribute (“who someone is,” eg., whether they are married or single) is better described as a correlate. I would also be willing to bet that if we carefully compared behavioural variables to attribute variables, the behaviours would outperform, as Alexander says.

In practice, however, we don’t need to make that distinction. If we are using regression to build our models, we are concerned solely and completely with correlation. To say “at best it may be correlated” suggests that predictive modellers have something better at their disposal that they should be using instead of correlation. What is it? I don’t know, and Alexander doesn’t say.

If in a given data set, we can demonstrate that being married is associated with likelihood to make a donation, then it only makes sense to use that variable in our model. Choosing to exclude it based on our assumption that it’s an attribute and not a behaviour doesn’t make business sense. We are looking for practical results, after all, not chasing some notion of purity. And let’s not fool ourselves, or clients, that we are getting down to causation. We aren’t.

Consider that at least some “attributes” can be stated in terms of a behaviour. People get married — that’s a behaviour, although not related to our institution. People get married and also tell us about it (or allow it to be public knowledge so that we can record it) — that’s also a behaviour, and potentially an interaction with us. And on the other side of the coin, behaviours or interactions can be stated as attributes — a person can be an event attendee, a donor, a taker of surveys.

If my analysis informs me that widowed female alumni over the age of 60 are extremely good candidates for a conversation about Planned Giving, then are you really going to tell me I’m wrong to act on that information, just because sex, age and being widowed are not “behaviours” that a person voluntarily carries out? Mmmm — sorry!

Call it quibbling over semantics if you like, but don’t assume it’s so easy to draw a circle around true predictors. There is only one way to surface predictors, which is to take a snapshot of all potentially relevant variables at a point in time, then gather data on the outcome you wish to predict (eg., giving) after that point in time, and then assess each variable in terms of the strength of association with that outcome. The tools we use to make that assessment are nothing other than correlation and significance. Again, if there are other tools in common usage, then I don’t know about them.

Caveats and concessions

I don’t maintain that this or that practice is “wrong” in all cases, nor do I insist on rules that apply universally. There’s a lot of art in this science, after all.

Using giving history as a predictor:

  • One may use some aspects of giving to predict outcomes that are not precisely the same as ‘Giving’, for example, likelihood to enter into a Planned Giving arrangement. The required degree of difference between predictors and outcome is a matter of judgement. I usually err on the side of scrupulously avoiding ANY leakage of the outcome side of the equation into the predictor side — but sure, rules can be bent.
  • I’ve explored the use of very early giving (the existence and size of gifts made by donors before age 30) to predict significant giving late in life. (See Mine your donor data with this baseball-inspired analysis.) But even then, I don’t use that as a variable in a model; it’s more of a flag used to help select prospects, in addition to modeling.

Using descriptors/attributes as predictors:

  • Some variables of this sort will appear to have subtly predictive effects in-model, effects that disappear when the model is deployed and new data starts coming in. That’s regrettable, but it’s something you can learn from — not a reason to toss all such variables into the trash, untested. The association between marital status and giving might be just a spurious correlation — or it might not be.
  • Business knowledge mixed with common sense will help keep you out of trouble. A bit of reflection should lead you to consider using ‘Married’ or ‘Number of Degrees’, while ignoring ‘Birth Month’ or ‘Eye Colour’. (Or astrological sign!)

There are many approaches one can take with predictive modeling, and naturally one may feel that one’s chosen method is “best”. The only sure way to proceed is to take the time to define exactly what you want to predict, try more than one approach, and then evaluate the performance of the scores when you have actual results available — which could be a year after deployment. We can listen to what experts are telling us, but it’s more important to listen to what the data is telling us.

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Note: When I originally posted this, I referred to Atsuko Umeki as “he”. I apologize for this careless error and for whatever erroneous assumption that must have prompted it.

15 January 2013

The cautionary tale of Mr. S. John Doe

A few years ago I met with an experienced Planned Giving professional who had done very well over the years without any help from predictive modeling, and was doing me the courtesy of hearing my ideas. I showed this person a series of charts. Each chart showed a variable and its association with the condition of being a current Planned Giving expectancy. The ultimate goal would have been to consolidate these predictors together as a score, in order to discover new expectancies in that school’s alumni database. The conventional factors of giving history and donor loyalty are important, I conceded, but other engagement-related factors are also very predictive: student activities, alumni involvement, number of degrees, event attendance, and so on.

This person listened politely and was genuinely interested. And then I went too far.

One of my charts showed that there was a strong association between being a Planned Giving expectancy and having a single initial in the First Name field. I noted that, for some unexplained reason, having a preference for a name like “S. John Doe” seemed to be associated with a higher propensity to make a bequest. I thought that was cool.

The response was a laugh. A good-natured laugh, but still — a laugh. “That sounds like astrology!”

I had mistaken polite interest for a slam-dunk, and in my enthusiasm went too far out on a limb. I may have inadvertently caused the minting of a new data-mining skeptic. (Eventually, the professional retired after completing a successful career in Planned Giving, and having managed to avoid hearing much more about predictive modeling.)

At the time, I had hastened to explain that what we were looking at were correlations — loose, non-causal relationships among various characteristics, some of them non-intuitive or, as in this case, seemingly nonsensical. I also explained that the linkage was probably due to other variables (age and sex being prime candidates). Just because it’s without explanation doesn’t mean it’s not useful. But I suppose the damage was done. You win some, you lose some.

Although some of the power (and fun) of predictive modeling rests on the sometimes non-intuitive and unexplained nature of predictor variables, I now think it’s best to frame any presentation to a general audience in terms of what they think of as “common sense”. Limiting, yes. But safer. Unless you think your listener is really picking up what you’re laying down, keep it simple, keep it intuitive, and keep it grounded.

So much for sell jobs. Let’s get back to the data … What ABOUT that “first-initial” variable? Does it really mean anything, or is it just noise? Is it astrology?

I’ve got this data set in front of me — all alumni with at least some giving in the past ten years. I see that 1.2% percent of all donors have a first initial at the front of their name. When I look at the subset of the records that are current Planned Giving expectancies, I see that 4.6% have a single-initial first name. In other words, Planned Giving expectancies are almost four times as likely as all other donors to have a name that starts with a single initial. The data file is fairly large — more than 17,000 records — and the difference is statistically significant.

What can explain this? When I think of a person whose first name is an initial and who tends to go by their middle name, the image that comes to mind is that of an elderly male with a higher than average income — like a retired judge, say. For each of the variables Age and Male, there is in fact a small positive association with having a one-character first name. Yet, when I account for both ‘Age’ and ‘Male’ in a regression analysis, the condition of having a leading initial is still significant and still has explanatory power for being a Planned Giving expectancy.

I can’t think of any other underlying reasons for the connection with Planned Giving. Even when I continue to add more and more independent variables to the regression, this strange predictor hangs in there, as sturdy as ever. So, it’s certainly interesting, and I usually at least look at it while building models.

On the other hand … perhaps there is some justification for the verdict of “astrology” (that is, “nonsense”). The data set I have here may be large, but the number of Planned Giving expectancies is less than 500 — and 4.6% of 500 is not very many records. Regardless of whether p ≤ 0.0001, it could still be just one of those things. I’ve also learned that complex models are not better than simple ones, particularly when trying to predict something hard like Planned Giving propensity. A quirky variable that suggests no potential causal pathway makes me wary of the possibility of overfitting the noise in my data and missing the signal.

Maybe it’s useful, maybe it’s not. Either way, whether I call it “cool” or not will depend on who I’m talking to.

13 November 2012

Making a case for modeling

Guest post by Peter Wylie and John Sammis

(Click here to download post as a print-friendly PDF: Making a Case for Modeling – Wylie Sammis)

Before you wade too far into this piece, let’s be sure we’re talking to the right person. Here are some assumptions we’re making about you:

  • You work in higher education advancement and are interested in analytics. However, you’re not a sophisticated stats person who throws around terms like regression and cluster analysis and neural networks.
  • You’re convinced that your alumni database (we’ll leave “parents” and “friends” for a future paper) holds a great deal of information that can be used to pick out the best folks to appeal to — whether by mail, email, phone, or face-to-face visits.
  • Your boss and your boss’s bosses are, at best, less convinced than you are about this notion. At worst, they have no real grasp of what analytics (data mining and predictive modeling) are. And they may seem particularly susceptible to sales pitches from vendors offering expensive products and services for using your data – products and services you feel might cause more problems than they will solve.
  • You’d like to find a way to bring these “boss” folks around to your way of thinking, or at least move them in the “right” direction.

If we’ve made some accurate assumptions here, great. If we haven’t, we’d still like you to keep reading. But if you want to slip out the back of the seminar room, not to worry. We’ve done it ourselves more times than you can count.

Okay, here’s something you can try:

1. Divide the alums at your school into ten roughly equal size groups (deciles) by class year. Table 1 is an example from a medium sized four year college.

Table 1: Class Years and Counts for Ten Roughly Equal Size Groups (Deciles) of Alumni at School A

2. Create a very simple score:

EMAIL LISTED(1/0) + HOME PHONE LISTED(1/0)

This score can assume three values: “0, “1”, or “2.” A “0” means the alum has neither an email nor a home phone listed in the database. A “1” means the alum has either an email listed in the database or a home phone listed in the database, but not both. A “2” means the alum has both an email and a home phone listed in the database.

3. Create a table that contains the percentage of alums who have contributed at least $1,000 lifetime to your school for each score level for each class year decile. Table 1 is an example of such a table for School A.

Table 2: Percentage of Alumni at Each Simple Score Level at Each Class Year Decile Who Have Contributed at Least $1,000 Lifetime to School A

 

4. Create a three dimensional chart that conveys the same information contained in the table. Figure 1 is an example of such a chart for School A.

In the rest of this piece we’ll be showing tables and charts from seven other very diverse schools that look quite similar to the ones you’ve just seen. At the end, we’ll step back and talk about the importance of what emerges from these charts. We’ll also offer advice on how to explain your own tables and charts to colleagues and bosses.

If you think the above table and chart are clear, go ahead and start browsing through what we’ve laid out for the other seven schools. However, if you’re not completely sure you understand the table and the chart, see if the following hypothetical questions and answers help:

Question: “Okay, I’m looking at Table 2 where it shows 53% for alums in Decile 1 who have a score of 2. Could you just clarify what that means?”

Answer. “That means that 53% of the oldest alums at the school who have both a home phone and an email listed in the database have given at least $1,000 lifetime to the school.”

Question. “Then … that means if I look to the far left in that same row where it shows 29% … that means that 29% of the oldest alums at the school who have neither a home phone nor an email listed in the database have given at least $1,000 lifetime to the school?”

Answer. “Exactly.”

Question. “So those older alums who have a score of 2 are way better givers than those older alums who have a score of 0?”

Answer. “That’s how we see it.”

Question. “I notice that in the younger deciles, regardless of the score, there are a lot of 0 percentages or very low percentages. What’s going on there?”

Answer. “Two things. One, most younger alums don’t have the wherewithal to make big gifts. They need years, sometimes many years, to get their financial legs under them. The second thing? Over the last seven years or so, we’ve looked at the lifetime giving rates of hundreds and hundreds of four-year higher education institutions. The news is not good. In many of them, well over half of the solicitable alums have never given their alma maters a penny.”

Question. “So, maybe for my school, it might be good to lower that giving amount to something like ‘has given at least $500 lifetime’ rather than $1,000 lifetime?”

Answer. Absolutely. There’s nothing sacrosanct about the thousand dollar level that we chose for this piece. You can certainly lower the amount, but you can also raise the amount. In fact, if you told us you were going to try several different amounts, we’d say, “Fantastic!”

Okay, let’s go ahead and have you browse through the rest of the tables and charts for the seven schools we mentioned earlier. Then you can compare your thoughts on what you’ve seen with what we think is going on here.

(Note: After looking at a few of the tables and charts, you may find yourself saying, “Okay, guys. Think I got the idea here.” If so, go ahead and fast forward to our comments.)

Table 3: Percentage of Alumni at Each Simple Score Level at Each Class Year Decile Who Have Contributed at Least $1,000 Lifetime to School B

 

Table 4: Percentage of Alumni at Each Simple Score Level at Each Class Year Decile Who Have Contributed at Least $1,000 Lifetime to School C

Table 5: Percentage of Alumni at Each Simple Score Level at Each Class Year Decile Who Have Contributed at Least $1,000 Lifetime to School D

Table 6: Percentage of Alumni at Each Simple Score Level at Each Class Year Decile Who Have Contributed at Least $1,000 Lifetime to School E

Table 7: Percentage of Alumni at Each Simple Score Level at Each Class Year Decile Who Have Contributed at Least $1,000 Lifetime to School F

Table 8: Percentage of Alumni at Each Simple Score Level at Each Class Year Decile Who Have Contributed at Least $1,000 Lifetime to School G

Table 9: Percentage of Alumni at Each Simple Score Level at Each Class Year Decile Who Have Contributed at Least $1,000 Lifetime to School H

Definitely a lot of tables and charts. Here’s what we see in them:

  • We’ve gone through the material you’ve just seen many times. Our eyes have always been drawn to the charts; we use the tables for back-up. Even though we’re data geeks, we almost always find charts more compelling than tables. That is most certainly the case here.
  • We find the patterns in the charts across the seven schools remarkably similar. (We could have included examples from scores of other schools. The patterns would have looked the same.)
  • The schools differ markedly in terms of giving levels. For example, the alums in School C are clearly quite generous in contrast to the alums in School F. (Compare Figure 3 with Figure 6.)
  • We’ve never seen an exception to one of the obvious patterns we see in these data: The longer alums have been out of school, the more money they have given to their school.
  • The “time out of school” pattern notwithstanding, we continue to be taken by the huge differences in giving levels (especially among older alums) across the levels of a very simple score. School G is a prime example. Look at Figure 7 and look at Table 8. Any way you look at these data, it’s obvious that alums who have even a score of “1” (either a home phone listed or an email listed, but not both) are far better givers than alums who have neither listed.

Now we’d like to deal with an often advanced argument against what you see here. It’s not at all uncommon for us to hear skeptics say: “Well, of course alumni on whom we have more personal information are going to be better givers. In fact we often get that information when they make a gift. You could even say that amount of giving and amount of personal information are pretty much the same thing.”

We disagree for at least two reasons:

Amount of personal information and giving in any alumni database are never the same thing. If you have doubts about our assertion, the best way to dispel those doubts is to look in your own alumni database. Create the same simple score we have for this piece. Then look at the percentage of alums for each of the three levels of the score. You will find plenty of alums who have a score of 0 who have given you something, and you will find plenty of alums with a score of 2 who have given you nothing at all.

We have yet to encounter a school where the IT folks can definitively say how an email address or a home phone number got into the database for every alum. Why is that the case? Because email addresses and home phone numbers find their way into alumni database in a variety of ways. Yes, sometimes they are provided by the alum when he or she makes a gift. But there are other ways. To name a few:

  • Alums (givers or not) can provide that information when they respond to surveys or requests for information to update directories.
  • There are forms that alums fill out when they attend a school sponsored event that ask for this kind of information.
  • There are vendors who supply this kind of information.

Now here’s the kicker. Your reactions to everything you’ve seen in this piece are critical. If you’re going to go to a skeptical boss to try to make a case for scouring your alumni database for new candidates for major giving, we think you need to have several reactions to what we’ve laid out here:

1. “WOW!” Not, “Oh, that’s interesting.” It’s gotta be, “WOW!” Trust us on this one.

2. You have to be champing at the bit to create the same kinds of tables and charts that you’ve seen here for your own data.

3. You have to look at Table 2 (that we’ve recreated below) and imagine it represents your own data.

Table 2: Percentage of Alumni at Each Simple Score Level at Each Class Year Decile Who Have Contributed at Least $1,000 Lifetime to School A

Then you have to start saying things like:

“Okay, I’m looking at the third class year decile. These are alums who graduated between 1977 and 1983. Twenty-five percent of them with a score of 2 have given us at least $1,000 lifetime. But what about the 75% who haven’t yet reached that level? Aren’t they going to be much better bets for bigger giving than the 94% of those with a score of 0 who haven’t yet reached the $1,000 level?”

“A score that goes from 0 to 2? Really? What about a much more sophisticated score that’s based on lots more information than just email listed and home phone listed? Wouldn’t it make sense to build a score like that and look at the giving levels for that more sophisticated score across the class year deciles?”

If your reactions have been similar to the ones we’ve just presented, you’re probably getting very close to trying to making your case to the higher-ups. Of course, how you make that case will depend on who you’ll be talking to, who you are, and situational factors that you’re aware of and we’re not. But here are a few general suggestions:

Your first step should be making up the charts and figures for your own data. Maybe you have the skills to do this on your own. If not, find a technical person to do it for you. In addition to having the right skills, this person should think doing it would be cool and won’t take forever to finish it.

Choose the right person to show our stuff and your stuff to. More and more we’re hearing people in advancement say, “We just got a new VP who really believes in analytics. We think she may be really receptive to this kind of approach.” Obviously, that’s the kind of person you want to approach. If you have a stodgy boss in between you and that VP, find a way around your boss. There’s lots of ways to do that.

Do what mystery writers do; use the weapon of surprise. Whoever the boss you go to is, we’d recommend that you show them this piece first. After you know they’ve read it, ask them what they thought of it. If they say anything remotely similar to: “I wonder what our data looks like,” you say, “Funny you should ask.”

Whatever your reactions to this piece have been, we’d love to hear them.

13 June 2012

Finding predictors of future major givers

Guest post by Peter B. Wylie and John Sammis

(Download a print-friendly .pdf version here: Finding Predictors of Future Major Givers)

For years a bunch of  committed data miners (we’re just a couple of them) have been pushing, cajoling, exhorting, and nudging  folks in higher education advancement to do one thing: Look as hard at their internal predictors of major giving as they look at outside predictors (like social media and wealth screenings). It seems all that drum beating has been having an effect. If you want some evidence of that, take a gander at the preconference presentations that will be given this August in Minneapolis at the APRA 25th Annual International Conference. It’s an impressive list.

So…what if you count yourself among the converted? That is, you’re convinced that looking at internal predictors of major giving is a good idea. How do you do that? How do you do that, especially if you’re not a member of that small group of folks who:

  • have a solid knowledge of applied statistics as used in both the behavioral sciences and “business intelligence?”
  • know a good bit about topics like multiple regression, logistic regression, factor analysis, and cluster analysis?
  • are practiced in the use of at least one stats application whether it’s SPSS, SAS, Data Desk, or R or some other open source option?
  • are actively doing data mining and predictive modeling on a weekly, if not daily basis?

The answer, of course, is that there is no single, right and easy way to look for predictors of major giving. What you’ll see in the rest of this piece is just one way we’ve come up with – one we hope you’ll find helpful.

Specifically, we’ll be covering two topics:

  • The fact that the big giving in most schools does not begin until people are well into their fifties, if not their sixties
  • A method for looking at variables in an alumni database that may point to younger alums who will eventually become very generous senior alums

 

Where The Big Money Starts

Here we’ll take you through the steps we followed to show that the big giving in most schools does not begin until alums are well into their middle years.

Step 1: The Schools We Used

We chose six very different schools (public and private, large and small) spread out across North America. For five of the schools, we had the entire alumni database to work with. With one school we had a random sample of more than 20,000 records.

Step 2: Assigning An Age to Every Alumni Record

Using Preferred class year, we computed an estimate of each alum’s age with this formula:

Age = 2012 – preferred class year + 22

Given the fact that many students graduate after the age of 22, it’s safe to assume that the ages we assigned to these alums are  slight to moderate underestimates of their true ages.

Step 3: Computing The Percentage of  The Sum of Lifetime Dollars Contributed by Each Alum

For all the records in each database, we computed each alum’s percentage of the sum of lifetime dollars contributed by all solicitable alums (those who are living and reachable). To do this computation, we divided each alum’s lifetime giving by the sum of lifetime giving for the entire database and converted that value to a percentage.

For example, let’s assume that the sum of lifetime giving for the solicitable alums in a hypothetical database is $50 million. Table 1 shows both the lifetime giving and the percent of the sum of lifetime giving for three different records:

Table 1: Lifetime Giving and Pecentage of The Sum of All Lifetime Giving for Three Hypothetical Alums

Just to be clear:

  • Record A has given no money at all to the school. That alum’s percentage is obviously 0.
  • Record B has given $39,500 to the school. That alum’s percentage is 0.079% of $50 million.
  • Record C has given $140,500 to the school. That alum’s percentage is 0.280% of $50 million.

Step 4: Computing The Percentage and The Cumulative Percentage of The Sum of Lifetime Dollars Contributed by Each of 15 Equal-Sized Age Groups of  Alums

For each of the six schools, we divided all alums into 15 roughly equal-sized age goups. These groups ranged from alums in their early twenties to those who had achieved or passed the century mark.

To make this all clear we have used School A (whose alums have given a sum of $164,215,000) as an example. Table 2 shows the:

  • total amount of lifetime dollars contributed by each of these age groups in School A
  • the percentage of the $164,215,000 contributed by these groups
  • the cumulative percentage of the $164,215,000 contributed by alums up to and including a certain age group

Table 2: Lifetime Giving, Percent of Sum of Lifetime Giving, and Cumulative Percent of Sum of Lifetime Giving for Fifteen Equal-Size Age Groups In School A

Here are some things that stand out for us in this table:

  • All alums 36 and younger have contributed less than 1% of the sum of lifetime givng.
  • For all alums under age 50 the cumulative amount given is just over 7% of the sum of lifetime givng.
  • For all alums under age 62 the cumulative amount given is less than 30% of the sum of lifetime givng.
  • For all alums under age 69 the cumulative amount given is slightly more than 40% of the sum of lifetime givng.
  • Well over 55% of the sum of lifetime givng has come in from alums who are 69 and older.

The big news in this table, of course, is that the lion’s share of  money in School A has come in from alums who have long since passed the age of eligibility for collecting Social Security. Not a scintilla of doubt about that.

But what about all the schools we’ve looked at? Do they show a similar pattern of giving by age? To help you decide, we’ve constructed Figues 1 – 6 that provide the same information as you see in the rightmost column of Table 2: The cumulative percentage of all lifetime giving contributed by alums up to and including a certain age group.

Since Figure 1 below captures the same information you see in the rightmost column of Table 2, you don’t need to spend a lot of time looking at it.

But we’d recommend taking your time looking at Figures 2-6. Once you’ve done that, we’ll tell you what we see.

These are the details of what we see for Schools B-F:

  • School B: Alums 48 and younger have contributed less than 5% of the sum of lifetime giving. Alums 70 and older have contributed almost 40% of the sum.
  • School C: Alums 52 and younger have contributed less than 5% of the sum. Alums 70 and older have contributed more than 40% of the sum.
  • School D: Alums 55 and younger have contributed less than 30% of the sum. Alums 70 and older have contributed almost 45% of the sum.
  • School E: Alums 50 and younger have contributed less than 30% of the sum. Alums 61 and older have contributed more than 40% of the sum.
  • School F: Alums 50 and younger have contributed less than 20% of the sum. Alums 68 and older have contributed well over 50% of the sum.

The big picture? It’s the same phenomenon we saw with School A: The big money has come in from alums who are in the “third third” of their lives.

One Simple Way To Find Possible Predictors of The Big Givers on The Horizon

Up to this point we’ve either made our case or not that the big bucks don’t start coming in from alumni until they reach their late fifties or sixties. Great, but how do we go about identifying those alums in their forties and early fifties who are likely to turn into those very generous older alums?

It’s a tough question. In our opinion, the most rigorous scientific way to answer the question is to set up a longitudinal study that would involve:

  1. Identifying all the alums in a number of different schools who are in the forties and early fifties category.
  2. Collecting all kinds of data on these folks including giving history, wealth screening and other gift capacity information, biographic information, as well as a host of fields that are included in the databases of these schools like contact information, undergraduate activities, and on and on the list would go.
  3. Waiting about ten or fifteen years until these “youngsters” become “oldsters” and see which of all that data collected on them ends up predicting the big givers from everybody else.

Well, you’re probably saying something like, “Gentlemen, surely you jest. Who the heck is gonna wait ten or fifteen years to get the answers? Answers that may be woefully outdated given how fast society has been changing in the last twenty-five years?”

Yes, of course. So what’s a reasonable alternative? The idea we’ve come up with goes something like this: If we can find variables that differentiate current, very generous older alums from less generous alums, then we can use those same variables to find younger alums who “look like” the older generous alums in terms of those variables.

To bring this idea alive, we chose one school of the six that has particularly good data on their alums. Then we took these steps:

We divided alums 57 and older into ten roughly equal size groups (deciles) by their amount of lifetime giving. Figure 7 shows the median lifetime giving for these deciles.

Table 3 gives a bit more detailed information about the giving levels of these deciles, especially the total amount of lifetime giving.

Table 3: Sum of Lifetime Dollars and Median Lifetime Dollars for 10 Equal Sized Groups of Alums 57 and Older

We picked these eight variables to compare across the deciles:

  • number of alums who have a business phone listed in the database
  • number of alums who participated in varsity athletics
  • number of alums who were a member of a greek organization as an undergraduate
  • number of alums who have an email address listed in the database
  • number of logins
  • number of reunions attended
  • number of  years of volunteering
  • number of events attended

Before we take you through Figures 8-14, we should say that the method we’ve chosen to compare the deciles on these variables is not the way a stats professor nor an experinced data miner/modeler would recommend you do the comparisons. That’s okay. We were aiming for clarity here.

Let’s go through the figures. We’ve laid them out in order from “not so hot” variables to “pretty darn good” variables.

It’s pretty obvious when you look at Fig. 8 that bigger givers, for the most part, are no more likely to have a business phone listed in the database than are poorer givers.

Varsity athletics? Yes, there’s a little bit of a trend here, but it’s not a very consistent trend. We’re not impressed.

This trend is somewhat encouraging. Good givers are more likely to have been a member of a Greek organization as an undergraduate than not so good givers. But we would not rate this one as a real good predictor.

Now we’re getting somewhere. Better givers are clearly more likely to have an e-mail address listed in the database than are poorer givers.

This one gets our attention. We’re particularly impressed with the difference in the number of logins for Decile 10 (really big givers) versus the number of logins for the lowest two deciles. At this school they should be paying attention to this variable (and they are).

This figure is pretty consistent with what we’ve found across many, many schools. It’s a good example of why we are always encouraging higher ed institutions to store reunion data and pay attention to it.

This one’s a no-brainer.

And this one’s a super no-brainer.

Where to Go from Here

After you read something like this piece, it’s natural to raise the question: “What should I do with this information?”  Some thoughts:

  • Remember, we’re not assuming that you’re a sophisticated data miner/modeler. But we are assuming that you’re interested in looking at your data to help make better decisions about raising money.
  • Without using any fancy stats software and with a little help from your advancement services folks, you can do the same kind of analysis with your own alumni data as we’ve done here. You’ll run into a few roadblocks, but you can do it. We’re convinced of that.
  • Once you’ve done this kind of an analysis you can start looking at some of your alums who are in their forties and early fifiteies who haven’t yet jumped up to a high level of giving. The ones who look like their older counterparts with respect to logins, or reunion attendance, or volunteering (or whatever good variables you’ve found)? They’re the ones worth taking a closer look at.
  • You can take your analysis and show it to someone at a higher decision-making level than your own. You can say, “Right now, I don’t know how to turn all this stuff into a predictive model. But I’d like to learn how to do that.” Or you can say, “We need to get someone in here who has the skills to turn this kind of information into a tool for finding these people who are getting ready to pop up to a much higher level of giving.”
  • And after you have become comfortable with these initial explorations of your data we encourage you to consider the next step – predictive modeling based on those statistics terms we mentioned earlier. It is not that hard. Find someone to help you – your school has lots of smart people – and give it a try. The resulting scores will go a long way toward identifying your future big givers.

As always: We’d love to get your thoughts and reactions to all this.

21 February 2012

Putting an age-guessing trick to the test

Filed under: Alumni, Predictor variables — Tags: , , , , — kevinmacdonell @ 5:53 am

This question came to me recently via email: What’s a good way to estimate the age of database constituents, when a birth date is missing? The person who asked me wanted to use ‘age’ in some predictive models for giving, but was missing a lot of birth date data.

This is an interesting problem, and finding an answer to it has practical implications. Age is probably the most significant predictor in most giving models. It might be negative in a donor-acquisition model, but positive in almost any other type (renewal, upgrade, major giving). For those of us in higher ed, ‘year of graduation’ is a good proxy for age just as it is. But if you want to include non-degreed alumni (without an ‘expected year of graduation’), friends of the university who are not spouses (you can guess spouse ages somewhat accurately), or other non-graduates, or if you work for a nonprofit or business that has only partial age data, then you might need to get creative.

Here’s a cool idea: A person’s first name can be indicative of his or her probable age. Most first names have varied widely in popularity over the years, and you can take advantage of that fact. Someone named Eldred is probably not a 20-something, while someone named Britney is probably not a retiree. Finding out what they probably ARE is something I’ve written about here: How to infer age when all you have is a name.

It’s simple. If you have age data for at least a portion of your database:

  1. Pull all first names of living individuals from your database, with their ages.
  2. Calculate the average (or median) age for each first name. (Example: The median age of the 371 Kevins in our database is 43.) This is a job for stats software.
  3. For any individual who is missing an age, assign them the average (or median) age of people with the same first name.

When I wrote my first post on this topic, I put the idea out there but didn’t actually test it. It sounds approximate and unreliable, but I didn’t test it because I have no personal need for guessing ages: I’ve got birth dates for nearly every living alum.

Today I will address that omission.

I pulled a data file of about 104,000 living alumni, excluding any for whom we don’t have a birth date. All I requested was ID, First Name, and Age. (I also requested the sum of lifetime giving for each record, but I’ll get to that later.) I pasted these variables into a stats package (Data Desk), and then split the file into random halves of about 52,000 records each. I used only the first half to calculate the average age for each unique first name, rounding the average to the nearest whole number.

I then turned my attention to the ‘test’ half of the file. I tagged each ID with a ‘guessed age’, based on first name, as calculated using the first half of the file.

How did the guessed ages compare with peoples’ real ages?

I guessed the correct age for 3.5% of people in the test sample. That’s may not sound great, but I didn’t expect to be exactly right very often: I expected to be in the ballpark. In 17.5% of cases, I was correct to within plus or minus two years. In 37.6% of cases, I was correct to within plus or minus five years. And in 63.5% of cases, I was correct to within plus or minus 10 years. That’s the limit of what I would consider a reasonable guess. For what it’s worth, in order to reach 80% of cases, I would need to expand the acceptable margin of error to plus or minus 15 years — a span of 30 years is a bit too broad to consider “close”.

I also calculated median age, just in case the median would be a better guess than the average. This time, I guessed the correct age in 3.7% of cases — just a little better than when I used the average, which was also true as I widened the margin of error. In 18.5% of cases, I was correct to within plus or minus two years. In 38.8% of cases, I was correct to within plus or minus five years. And in 64.1% of cases, I was correct to within plus or minus 10 years. So not much of a difference in accuracy between the two types of guesses.

Here’s a chart showing the distribution of errors for the test half of the alumni sample (Actual Age minus Guessed Age), based on the median calculation:

The distribution seems slightly right-skewed, but in general a guess is about as likely to be “too old” as “too young.” Some errors are extreme, but they are relatively few in number. That has more to do with the fact that people live only so long, which sets a natural limit on how wrong I can be.

Accuracy would be nice, but a variable doesn’t need to be very accurate to be usable in a predictive model. Many inputs are not measured accurately, but we would never toss them out for that reason, if they were independent and had predictive power. Let’s see how a guessed-age variable compares to a true-age variable in a regression analysis. Here is the half of the sample for whom I used “true age”:

The dependent variable is ‘lifetime giving’ (log-transformed), and the sole predictor is ‘age’, which accounts for almost 15% of the variability in LTG (as we interpret the R squared statistic). It’s normal for age to play a huge part in any model trained on lifetime giving.

Now we want to see the “test” half, for whom we only guessed at constituents’ ages. Here is a regression using guessed ages (based on the average age). The variable is named “avg age new”:

This tells me that a guessed age isn’t nearly as reliable as the real thing, which is not a big surprise. The model fit has dropped to an R squared of only .05 (5%). Still, that’s not bad. As well, the p-value is very small, which suggests the variable is significant, and not some random effect. It’s a lot better than having nothing at all.

Finally, for good measure, here’s another regression, this time using median age as the predictor. The result is practically the same.

If I had to use this trick, I probably would. But will it help you? That depends. What is significant in my model might not be in yours, and to be honest, with the large sample I have here, achieving “significance” isn’t that hard. If three-quarters of the records in your database are missing age data, this technique will give only a very fuzzy approximation of age and probably won’t be all that useful. If only one-quarter are missing, then I’d say go for it: This trick will perform much better than simply plugging in a constant value for all missing ages (which would be one lazy approach to missing data needed for a regression analysis).

Give it a try, and have fun with it.

P.S.: A late-coming additional thought. What if you compare these results with simply plugging in the average or median age for the sample? Using the sample average (46 years old):

  • Exact age: correct 2.2% of the time (compared to 3.5% for the first-name trick)
  • Within +/- 2 years: correct 11.1% of the time (compared to 17.5%)
  • Within +/- 5 years: correct 24.4% of the time (compared to 37.6%)
  • Within +/- 10 years: correct 46.5% of the time (compared to 63.5%)

Plugging in the median instead hardly makes a difference in age-guessing accuracy. So, the first-name trick would seem to be an improvement.

16 January 2012

Address updates and affinity: Consider the source

Filed under: Correlation, Predictor variables, skeptics — Tags: , , , , — kevinmacdonell @ 1:03 pm

Some of the best predictors in my models are related to the presence or absence of phone numbers and addresses. For example, the presence of a business phone is usually a highly significant predictor of giving. As well, a count of either phone or address updates present in the database is also highly correlated with giving.

Some people have difficulty accepting this as useful information. The most common objection I hear is that such updates can easily come from research and data appends, and are therefore not signals of affinity at all. And that would be true: Any data that exists solely because you bought it or looked it up doesn’t tell you how someone feels about your institution. (Aside from the fact that you had to go looking for them in the first place — which I’ve observed is negatively correlated with giving.)

Sometimes this objection comes from someone who is just learning data mining. Then I know I’m dealing with someone who’s perceptive. They obviously get it, to some degree — they understand there’s potentially a problem.

I’m less impressed when I hear it from knowledgeable people, who say they avoid contact information in their variable selection altogether. I think that’s a shame, and a signal that they aren’t willing to put in the work to a) understand the data they’re working with, or b) take steps to counteract the perceived taint in the data.

If you took the trouble to understand your data (and why wouldn’t you), you’d find out soon enough if the variables are useable:

  • If the majority of phone numbers or business addresses or what-have-you are present in the database only because they came off donors’ cheques, then you’re right in not using it to predict giving. It’s not independent of giving and will harm your model. The telltale sign might be a correlation with the target variable that exceeds correlations for all your other variables.
  • If the information could have come to you any number of ways (with gift transactions being only one of them), then use with caution. That is, be alert if the correlation looks too good to be true. This is the most likely scenario, which I will discuss in detail shortly.
  • If the information could only have come from data appends or research, then you’ve got nothing much to worry about: The correlation with giving will be so weak that the variable probably won’t make it into your model at all. Or it may be a negative predictor, highlighting the people who allowed themselves to become lost in the first place. An exception to the “don’t worry” policy would be if research is conducted mainly to find past donors who have become lost — then there might be a strong correlation that will lead you astray.

An in-house predictive modeler will simply know what the case is, or will take the trouble to find out. A vendor hired to do the work may or may not bother — I don’t know. As far as my own models are concerned, I know that addresses and phone numbers come to us via a mix of voluntary and involuntary means: Via Phonathon, forms on the website, records research, and so on.

I’ve found that a simple count of all historical address updates for each alum is positively correlated with giving. But a line plot of the relationship between number of address updates and average lifetime giving suggests there’s more going on under the surface. Average lifetime giving goes up sharply for the first half-dozen or so updates, and then falls away just as sharply. This might indicate a couple of opposing forces: Alumni who keep us informed of their locations are more likely to be donors, but alumni who are perpetually lost and need to be found via research are less likely to be donors.

If you’re lucky, your database not only has a field in which to record the source of updates, but your records office is making good use of it. Our database happens to have almost 40 different codes for the source, applied to some 300,000 changes of address and/or phone number. Not surprisingly, some of these are not in regular use — some account for fewer than one-tenth of one percent of updates, and will have no significance in a model on their own.

For the most common source types, though, an analysis of their association with giving is very interesting. Some codes are positively correlated with giving, some negatively. In most cases, a variable is positive or negative depending on whether the update was triggered by the alum (positive), or by the institution (negative). On the other hand, address updates that come to us via Phonathon are negatively correlated with giving, possibly because by-mail donors tend not to need a phone call — if ‘giving’ were restricted to phone solicitation only, perhaps the association might flip toward the positive. Other variables that I thought should be positive were actually flat. But it’s all interesting stuff.

For every source code, a line plot of average LT giving and number of updates is useful, because the relationship is rarely linear. The relationship might be positive up to a point, then drop off sharply, or maybe the reverse will be true. Knowing this will suggest ways to re-express the variable. I’ve found that alumni who have a single update based on the National Change of Address database have given more than alumni who have no NCOA updates. However, average giving plummets for every additional NCOA update. If we have to keep going out there to find you, it probably means you don’t want to be found!

Classifying contact updates by source is more work, of course, and it won’t always pay off. But it’s worth exploring if your goal is to produce better, more accurate models.

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