Cover Page

Table of Contents

Title Page

Copyright

Preface

Acknowledgments

Chapter 1: Introduction

Reference

Chapter 2: Processing the Information and Getting to Know Your Data

2.1 Example 1: 2006 Birth Data

2.2 Example 2: Alumni Donations

2.3 Example 3: Orange Juice

References

Chapter 3: Standard Linear Regression

3.1 Estimation in R

3.2 Example 1: Fuel Efficiency of Automobiles

3.3 Example 2: Toyota Used-Car Prices

Appendix 3.A T1he Effects of Model Overfitting on the Average Mean Square Error of the Regression Prediction

References

Chapter 4: Local Polynomial Regression: a Nonparametric Regression Approach

4.1 Model Selection

4.2 Application to Density Estimation and the Smoothing of Histograms

4.3 Extension to the Multiple Regression Model

4.4 Examples and Software

References

Chapter 5: Importance of Parsimony in Statistical Modeling

5.1 How Do We Guard Against False Discovery

References

chapter 6 : Penalty-Based Variable Selection in Regression Models with Many Parameters (LASSO)

6.1 Example 1: Prostate Cancer

6.2 Example 2: Orange Juice

References

Chapter 7: Logistic Regression

7.1 Building a Linear Model for Binary Response Data

7.2 Interpretation of the Regression Coefficients in a Logistic Regression Model

7.3 Statistical Inference

7.4 Classification Of New Cases

7.5 Estimation in R

7.6 Example 1: Death Penalty Data

7.7 Example 2: Delayed Airplanes

7.8 Example 3: Loan Acceptance

7.9 Example 4: German Credit Data

References

Chapter 8: Chapter 8

8.1 Binary Classification

8.2 Using Probabilities to Make Decisions

8.3 Sensitivity and Specificity

8.4 Example: German Credit Data

Chapter 9: Classification Using a Nearest Neighbor Analysis

9.1 THE k-Nearest Neighbor Algorithm

9.2 Example 1: Forensic Glass

9.3 Example 2: German Credit Data

Reference

Chapter 10: The Naïve Bayesian Analysis: a Model for Predicting a Categorical Response from Mostly Categorical Predictor Variables

10.1 Example: Delayed Airplanes

Reference

Chapter 11: Multinomial Logistic Regression

11.1 Computer Software

11.2 Example 1: Forensic Glass

11.3 Example 2: Forensic Glass Revisited

Appendix 11.A Specification of a Simple Triplet Matrix

References

Chapter 12: More on Classification and a Discussion on Discriminant Analysis

12.1 Fisher's Linear Discriminant Function

12.2 Example 1: German Credit Data

12.3 Example 2: Fisher Iris Data

12.4 Example 3: Forensic Glass Data

12.5 Example 4: MBA Admission Data

Reference

Chapter 13: Decision Trees

13.1 Example 1: Prostate Cancer

13.2 Example 2: Motorcycle Acceleration

13.3 Example 3: Fisher Iris Data Revisited

Chapter 14: Further Discussion on Regression and Classification Trees, Computer Software, and Other Useful Classification Methods

14.1 R Packages for Tree Construction

14.2 Chi-Square Automatic Interaction Detection (CHAID)

14.3 Ensemble Methods: Bagging, Boosting, And Random Forests

14.4 Support Vector Machines (SVM)

14.5 Neural Networks

14.6 The R Package Rattle: A Useful Graphical User Interface For Data Mining

References

Chapter 15: Clustering

15.1 -Means Clustering

15.2 Another Way to Look at Clustering: Applying The Expectation-Maximization (EM) Algorithm to Mixtures of Normal Distributions

15.3 Hierarchical Clustering Procedures

References

Chapter 16: Market Basket Analysis: Association Rules and Lift

16.1 Example 1: Online Radio

16.2 Example 2: Predicting Income

References

Chapter 17: Dimension Reduction: Factor Models and Principal Components

17.1 Example 1: European Protein Consumption

17.2 Example 2: Monthly Us Unemployment Rates

Chapter 18: Reducing the Dimension in Regressions with Multicollinear Inputs: Principal Components Regression and Partial Least Squares

18.1 Three Examples

References

Chapter 19: Text as Data: Text Mining and Sentiment Analysis1

19.1 Inverse Multinomial Logistic Regression

19.2 Example 1: Restaurant Reviews

19.3 Example 2: Political Sentiment

References

Chapter 20: Network Data

20.1 Example 1: Marriage And Power In Fifteenth Century Florence

20.2 Example 2: Connections In A Friendship Network

References

Appendix A Exercises

Appendix B: References

Index

Title Page

Preface

This book is about useful methods for data mining and business analytics. It is written for readers who want to apply these methods so that they can learn about their processes and solve their problems. My objective is to provide a thorough discussion of the most useful data-mining tools that goes beyond the typical “black box” description, and to show why these tools work.

Powerful, accurate, and flexible computing software is needed for data mining, and Excel is of little use. Although excellent data-mining software is offered by various commercial vendors, proprietary products are usually expensive. In this text, I use the R Statistical Software, which is powerful and free. But the use of R comes with start-up costs. R requires the user to write out instructions, and the writing of program instructions will be unfamiliar to most spreadsheet users. This is why I provide R sample programs in the text and on the webpage that is associated with this book. These sample programs should smooth the transition to this very general and powerful computer environment and help keep the start-up costs to using R small.

The text combines explanations of the statistical foundation of data mining with useful software so that the tools can be readily applied and put to use. There are certainly better books that give a deeper description of the methods, and there are also numerous texts that give a more complete guide to computing with R. This book tries to strike a compromise that does justice to both theory and practice, at a level that can be understood by the MBA student interested in quantitative methods. This book can be used in courses on data mining in quantitative MBA programs and in upper-level undergraduate and graduate programs that deal with the analysis and interpretation of large data sets. Students in business, the social and natural sciences, medicine, and engineering should benefit from this book. The majority of the topics can be covered in a one semester course. But not every covered topic will be useful for all audiences, and for some audiences, the coverage of certain topics will be either too advanced or too basic. By omitting some topics and by expanding on others, one can make this book work for many different audiences.

Certain data-mining applications require an enormous amount of effort to just collect the relevant information, and in such cases, the data preparation takes a lot more time than the eventual modeling. In other applications, the data collection effort is minimal, but often one has to worry about the efficient storage and retrieval of high volume information (i.e., the “data warehousing”). Although it is very important to know how to acquire, store, merge, and best arrange the information, this text does not cover these aspects very deeply. This book concentrates on the modeling aspects of data mining.

The data sets and the R-code for all examples can be found on the webpage that accompanies this book (http://www.biz.uiowa.edu/faculty/jledolter/DataMining). Supplementary material for this book can also be found by entering ISBN 9781118447147 at http://booksupport.wiley.com. You can copy and paste the code into your own R session and rerun all analyses. You can experiment with the software by making changes and additions, and you can adapt the R templates to the analysis of your own data sets. Exercises and several large practice data sets are given at the end of this book. The exercises will help instructors when assigning homework problems, and they will give the reader the opportunity to practice the techniques that are discussed in this book. Instructions on how to best use these data sets are given in Appendix A.

This is a first edition. Although I have tried to be very careful in my writing and in the analyses of the illustrative data sets, I am certain that much can be improved. I would very much appreciate any feedback you may have, and I encourage you to write to me at johannes-ledolter@uiowa.edu. Corrections and comments will be posted on the book's webpage.

Acknowledgments

I got interested in developing materials for an MBA-level text on Data Mining when I visited the University of Chicago Booth School of Business in 2011. The outstanding University of Chicago lecture materials for the course on Data Mining (BUS41201) taught by Professor Matt Taddy provided the spark to put this text together, and several examples and R-templates from Professor Taddy's notes have influenced my presentation. Chapter 19 on the analysis of text data draws heavily on his recent research. Professor Taddy's contributions are most gratefully acknowledged.

Writing a text is a time-consuming task. I could not have done this without the support and constant encouragement of my wife, Lea Vandervelde. Lea, a law professor at the University of Iowa, conducts historical research on the freedom suits of Missouri slaves. She knows first-hand how important and difficult it is to construct data sets for the mining of text data.

Chapter 1: Introduction

Today's statistics applications involve enormous data sets: many cases (rows of a data spreadsheet, with a row representing the information on a studied case) and many variables (columns of the spreadsheet, with a column representing the outcomes on a certain characteristic across the studied cases). A case may be a certain item such as a purchase transaction, or a subject such as a customer or a country, or an object such as a car or a manufactured product. The information that we collect varies across the cases, and the explanation of this variability is central to the tools that we study in this book. Many variables are typically collected on each case, but usually only a few of them turn out to be useful. The majority of the collected variables may be irrelevant and represent just noise. It is important to find those variables that matter and those that do not.

Here are a few types of data sets that one encounters in data mining. In marketing applications, we observe the purchase decisions, made over many time periods, of thousands of individuals who select among several products under a variety of price and advertising conditions. Social network data contains information on the presence of links among thousands or millions of subjects; in addition, such data includes demographic characteristics of the subjects (such as gender, age, income, race, and education) that may have an effect on whether subjects are “linked” or not. Google has extensive information on 100 million users, and Facebook has data on even more. The recommender systems developed by firms such as Netflix and Amazon use available demographic information and the detailed purchase/rental histories from millions of customers. Medical data sets contain the outcomes of thousands of performed procedures, and include information on their characteristics such as the type of procedure and its outcome, and the location where and the time when the procedure has been performed.

While traditional statistics applications focus on relatively small data sets, data mining involves very large and sometimes enormous quantities of information. One talks about megabytes and terabytes of information. A megabyte represents a million bytes, with a byte being the number of bits needed to encode a single character of text. A typical English book in plain text format (500 pages with 2000 characters per page) amounts to about 1 MB. A terabyte is a million megabytes, and an exabyte is a million terabytes.

Data mining attempts to extract useful information from such large data sets. Data mining explores and analyzes large quantities of data in order to discover meaningful patterns. The scale of a typical data mining application, with its large number of cases and many variables, exceeds that of a standard statistical investigation. The analysis of millions of cases and thousands of variables also puts pressure on the speed that is needed to accomplish the search and modeling steps of the typical data mining application. This is why researchers refer to data mining as statistics at scale and speed. The large scale (lots of available data) and the requirements on speed (solutions are needed quickly) create a large demand for automation. Data mining uses a combination of pattern-recognition rules, statistical rules, as well as rules drawn from machine learning (an area of computer science).

Data mining has wide applicability, with applications in intelligence and security analysis, genetics, the social and natural sciences, and business. Studying which buyers are more likely to buy, respond to an advertisement, declare bankruptcy, commit fraud, or abandon subscription services are of vital importance to business.

Many data mining problems deal with categorical outcome data (e.g., no/yes outcomes), and this is what makes machine learning methods, which have their origins in the analysis of categorical data, so useful. Statistics, on the other hand, has its origins in the analysis of continuous data. This makes statistics especially useful for correlation-type analyses where one sifts through a large number of correlations to find the largest ones.

The analysis of large data sets requires an efficient way of storing the data so that it can be accessed easily for calculations. Issues of data warehousing and how to best organize the data are certainly very important, but they are not emphasized in this book. The book focuses on the analysis tools and targets their statistical foundation.

Because of the often enormous quantities of data (number of cases/replicates), the role of traditional statistical concepts such as confidence intervals and statistical significance tests is greatly reduced. With large data sets, almost any small difference becomes significant. It is the problem of overfitting models (i.e., using more explanatory variables than are actually needed to predict a certain phenomenon) that becomes of central importance. Parsimonious representations are important as simpler models tend to give more insight into a problem. Large models overfitted on training data sets usually turn out to be extremely poor predictors in new situations as unneeded predictor variables increase the prediction error variance. Furthermore, overparameterized models are of little use if it is difficult to collect data on predictor variables in the future. Methods that help avoid such overfitting are needed, and they are covered in this book. The partitioning of the data into training and evaluation (test) data sets is central to most data mining methods. One must always check whether the relationships found in the training data set will hold up in the future.

Many data mining tools deal with problems for which there is no designated response that one wants to predict. It is common to refer to such analysis as unsupervised learning. Cluster analysis is one example where one uses feature (variable) data on numerous objects to group the objects (i.e., the cases) into a smaller number of groups (also called clusters). Dimension reduction applications are other examples for such type of problems; here one tries to reduce the many features on an object to a manageable few. Association rules also fall into this category of problems; here one studies whether the occurrence of one feature is related to the occurrence of others. Who would not want to know whether the sales of chips are being “lifted” to a higher level by the concurrent sales of beer?

Other data mining tools deal with problems for which there is a designated response, such as the volume of sales (a quantitative response) or whether someone buys a product (a categorical response). One refers to such analysis as supervised learning. The predictor variables that help explain (predict) the response can be quantitative (such as the income of the buyer or the price of a product) or categorical (such as the gender and profession of the buyer or the qualitative characteristics of the product such as new or old). Regression methods, regression trees, and nearest neighbor methods are well suited for problems that involve a continuous response. Logistic regression, classification trees, nearest neighbor methods, discriminant analysis (for continuous predictor variables) and naïve Bayes methods (mostly for categorical predictor variables) are well suited for problems that involve a categorical response.

Data mining should be viewed as a process. As with all good statistical analyses, one needs to be clear about the purpose of the analysis. Just to “mine data” without a clear purpose, without an appreciation of the subject area, and without a modeling strategy will usually not be successful. The data mining process involves several interrelated steps:

1. Efficient data storage and data preprocessing steps are very critical to the success of the analysis.
2. One needs to select appropriate response variables and decide on the number of variables that should be investigated.
3. The data needs to be screened for outliers, and missing values need to be addressed (with missing values either omitted or appropriately imputed through one of several available methods).
4. Data sets need to be partitioned into training and evaluation data sets. In very large data sets, which cannot be analyzed easily as a whole, data must be sampled for analysis.
5. Before applying sophisticated models and methods, the data need to be visualized and summarized. It is often said that a picture is worth a 1000 words. Basic graphs such as line graphs for time series, bar charts for categorical variables, scatter plots and matrix plots for continuous variables, box plots and histograms (often after stratification on useful covariates), maps for displaying correlation matrices, multidimensional graphs using color, trellis graphs, overlay plots, tree maps for visualizing network data, and geo maps for spatial data are just a few examples of the more useful graphical displays. In constructing good graphs, one needs to be careful about the right scaling, the correct labeling, and issues of stratification and aggregation.
6. Summary of the data involves the typical summary statistics such as mean, percentiles and median, standard deviation, and correlation, as well as more advanced summaries such as principal components.
7. Appropriate methods from the data mining tool bag need to be applied. Depending on the problem, this may involve regression, logistic regression, regression/classification trees, nearest neighbor methods, images-means clustering, and so on.
8. The findings from these models need to be confirmed, typically on an evaluation (test or holdout) data set.
9. Finally, the insights one gains from the analysis need to be implemented. One must act on the findings and spring to action. This is what W.E. Deming had in mind when he talked about process improvement and his Deming (Shewhart) wheel of “plan, do, check, and act” (Ledolter and Burrill, (1999)).

Some data mining applications require an enormous amount of effort to just collect the relevant information. For example, an investigation of Pre-Civil War court cases of Missouri slaves seeking their freedom involves tedious study of handwritten court proceedings and Census records, electronic scanning of the records, and the use of character-recognition software to extract the relevant characteristics of the cases and the people involved. The process involves double and triple checking unclear information (such as different spellings, illegible entries, and missing information), selecting the appropriate number of variables, categorizing text information, and deciding on the most appropriate coding of the information. At the end, one will have created a fairly good master list of all available cases and their relevant characteristics. Despite all the diligent work, there will be plenty of missing information, information that is in error, and way too many variables and categories than are ultimately needed to tell the story behind the judicial process of gaining freedom.

Data preparation often takes a lot more time than the eventual modeling. The subsequent modeling is usually only a small component of the overall effort; quite often, relatively simple methods and a few well-constructed graphs can tell the whole story. It is the creation of the master list that is the most challenging task. The steps that are involved in the construction of the master list in such problems depend heavily on the subject area, and one can only give rough guidelines on how to proceed. It is also difficult to make this process automatic. Furthermore, even if some of the “data cleaning” steps can be made automatic, the investigator must constantly check and question any adjustments that are being made. Great care, lots of double and triple checking, and much common sense are needed to create a reliable master list. But without a reliable master list, the findings will be suspect, as we know that wrong data usually lead to wrong conclusions. The old saying “garbage in–garbage out” also applies to data mining.

Fortunately many large business data sets can be created almost automatically. Much of today's business data is collected for transactional purposes, that is, for payment and for shipping. Examples of such data sets are transactions that originate from scanner sales in super markets, telephone records that are collected by mobile telephone providers, and sales and rental histories that are collected by companies such as Amazon and Netflix. In all these cases, the data collection effort is minimal, even though companies have to worry about the efficient storage and retrieval of the information (i.e., the “data warehousing”).

Credit card companies collect information on purchases; telecom companies collect information on phone calls such as their timing, length, origin, and destination; retail stores have developed automated ways of collecting information on their sales such as the volume purchased and the price at which products are bought. Supermarkets are now the source of much excellent data on the purchasing behavior of individuals. Electronic scanners keep track of purchases, prices, and the presence of promotions. Loyalty programs of retail chains and frequent-flyer programs make it possible to link the purchases to the individual shopper and his/her demographic characteristics and preferences. Innovative marketing firms combine the customer's purchase decisions with the customer's exposure to different marketing messages. As early as the 1980s, Chicago's IRI (Information Resources Incorporated, now Symphony IRI) contracted with television cable companies to vary the advertisements that were sent to members of their household panels. They knew exactly who was getting which ad and they could track the panel members' purchases at the store. This allowed for a direct way of assessing the effectiveness of marketing interventions; certainly much more direct than the diary-type information that had been collected previously. At present, companies such as Google and Facebook run experiments all the time. They present their members with different ads and they keep track who is clicking on the advertised products and whether the products are actually being bought.

Internet companies have vast information on customer preferences and they use this for targeted advertising; they use recommender systems to direct their ads to areas that are most profitable. Advertising related products that have a good chance of being bought and “cross-selling” of products become more and more important. Data from loyalty programs, from e-Bay auction histories, and from digital footprints of users clicking on Internet webpages are now readily available. Google's “Flu tracker” makes use of the webpage clicks to develop a tool for the early detection of influenza outbreaks; Amazon and Netflix use the information from their shoppers' previous order histories without ever meeting them in person, and they use the information from previous order histories of their users to develop automatic recommender systems. Credit risk calculations, business sentiment analysis, and brand image analysis are becoming more and more important.

Sports teams use data mining techniques to assemble winning teams; see the success stories of the Boston Red Sox and the Oakland Athletics. Moneyball, a 2011 biographical sports drama film based on Michael Lewis's 2003 book of the same name, is an account of the Oakland Athletics baseball team's 2002 season and their general manager Billy Beane's attempts to assemble a competitive team through data mining and business analytics.

It is not only business applications of data mining that are important; data mining is also important for applications in the sciences. We have enormous data bases on drugs and their side effects, and on medical procedures and their complication rates. This information can be mined to learn which drugs work and under which conditions they work best; and which medical procedures lead to complications and for which patients.

Business analytics and data mining deal with collecting and analyzing data for better decision making in business. Managers and business students can gain a competitive advantage through business analytics and data mining. Most tools and methods for data mining discussed in this book have been around for a very long time. But several developments have come together over the past few years, making the present period a perfect time to use these methods for solving business problems.

1. More and more data relevant for data mining applications are now being collected.
2. Data is being warehoused and is now readily available for analysis. Much data from numerous sources has already been integrated, and the data is stored in a format that makes the analysis convenient.
3. Computer storage and computer power are getting cheaper every day, and good software is available to carry out the analysis.
4. Companies are interested in “listening” to their customers and they now believe strongly in customer relationship management. They are interested in holding on to good customers and getting rid of bad ones. They embrace tools and methods that give them this information.

This book discusses the modeling tools and the methods of data mining. We assume that one has constructed the relevant master list of cases and that the data is readily available. Our discussion covers the last 10–20% of effort that is needed to extract and model meaningful information from the raw data. A model is a simplified description of the process that may have generated the data. A model may be a mathematical formula, or a computer program. One must remember, however, that no model is perfect, and that all models are merely approximations. But some of these approximations will turn out to be useful and lead to insights. One needs to become a critical user of models. If a model looks too good to be true, then it generally is. Models need to be checked, and we emphasized earlier that models should not be evaluated on the data that had been used to build them. Models are “fine-tuned” to the data of the training set, and it is not obvious whether this good performance carries over to other data sets.

In this book, we use the R Statistical Software (Version 15 as of June 2012). It is powerful and free. One may search for the software on the web and download the system. R is similar to Matlab and requires the user to write out simple instructions. The writing of (program) instructions will be unfamiliar to a spreadsheet user, and there will be startup costs to using R. However, the R sample programs in this book and their listing on the book's webpage should help with the transition to this very general and powerful computer environment.

Reference

Ledolter, J. and Burrill, C.: Statistical Quality Control: Strategies and Tools for Continual Improvement. New York: John Wiley & Sons, Inc., 1999.

Chapter 2: Processing the Information and Getting to Know Your Data

In this chapter we analyze three data sets and illustrate the steps that are needed for preprocessing the data. We consider (i) the 2006 birth data that is used in the book R in a Nutshell: A Desktop Quick Reference (Adler, (2009)), (ii) data on the contributions to a Midwestern private college (Ledolter and Swersey, (2007)), and (iii) the orange juice data set taken from P. Rossi's bayesm package for R that was used earlier in Montgomery ((1987)). The three data sets are of suitable size (427,323 records and 13 variables in the 2006 birth data set; 1230 records and 11 variables in the contribution data set; and 28,947 records and 17 variables in the orange juice data set). The data sets include both continuous and categorical variables, have missing observations, and require preprocessing steps before they can be subjected to the appropriate statistical analysis and modeling. We use these data sets to illustrate how to summarize the available information and how to obtain useful graphical displays. The initial arrangement of the data is often not very convenient for the analysis, and the information has to be rearranged and preprocessed. We show how to do this within R.

All data sets and the R programs for all examples in this book are listed on the webpage that accompanies this book (http://www.biz.uiowa.edu/faculty/jledolter/DataMining). I encourage readers to copy and paste the R programs into their own R sessions and check the results. Having such templates available for the analysis helps speed up the learning curve for R. It is much easier to learn from a sample program than to piece together the R code from first principles. It is the author's experience that even novices catch on quite fast. It may happen that at some time in the future certain R functions and packages become obsolete and are no longer available. Readers should then look for adequate replacements. The R function “help” can be used to get information on new functions and packages.

2.1 Example 1: 2006 Birth Data

We consider the 2006 birth data set that is used in the book R In a Nutshell: A Desktop Quick Reference (Adler, (2009)). The data set births2006.smpl consists of 427,323 records and 13 variables, including the day of birth according to the month and the day of week (DOB_MM, DOB_WK), the birth weight of the baby (DBWT) and the weight gain of the mother during pregnancy (WTGAIN), the sex of the baby and its APGAR score at birth (SEX and APGAR5), whether it was a single or multiple birth (DPLURAL), and the estimated gestation age in weeks (ESTGEST). We list below the information for the first five births.

## Install packages from CRAN; use any USA mirror
library(lattice)
library(nutshell)
data(births2006.smpl)
births2006.smpl[1:5,]
        DOB_MM DOB_WK MAGER TBO_REC WTGAIN SEX APGAR5                 DMEDUC
591430       9      1    25       2     NA   F     NA                   NULL
1827276      2      6    28       2     26   M      9     2 years of college
1705673      2      2    18       2     25   F      9                   NULL
3368269     10      5    21       2      6   M      9                   NULL
2990253      7      7    25       1     36   M     10 2 years of high school
        UPREVIS ESTGEST DMETH_REC  DPLURAL DBWT
591430       10      99   Vaginal 1 Single 3800
1827276      10      37   Vaginal 1 Single 3625
1705673      14      38   Vaginal 1 Single 3650
3368269      22      38   Vaginal 1 Single 3045
2990253      15      40   Vaginal 1 Single 3827
dim(births2006.smpl)
[1] 427323     13

The following bar chart of the frequencies of births according to the day of week of the birth shows that fewer births take place during the weekend (days 1 = Sunday, 2 = Monday, …, 7 = Saturday of DOB_WK). This may have to do with the fact that many babies are delivered by cesarean section, and that those deliveries are typically scheduled during the week and not on weekends. To follow up on this hypothesis, we obtain the frequencies in the two-way classification of births according to the day of week and the method of delivery. Excluding births of unknown delivery method, we separate the bar charts of the frequencies for the day of week of delivery according to the method of delivery. While it is also true that vaginal births are less frequent on weekends than on weekdays (doctors prefer to work on weekdays), the reduction in the frequencies of scheduled C-section deliveries from weekdays to weekends (about 50%) exceeds the weekday–weekend reduction of vaginal deliveries (about 25–30%).

births.dow=table(births2006.smpl$DOB_WK)
births.dow
    1     2     3     4     5     6     7
40274 62757 69775 70290 70164 68380 45683
barchart(births.dow,ylab="Day of Week",col="black")
c02uf001
dob.dm.tbl=table(WK=births2006.smpl$DOB_WK,
+   MM=births2006.smpl$DMETH_REC)
dob.dm.tbl
   MM
WK  C-section Unknown Vaginal
  1      8836      90   31348
  2     20454     272   42031
  3     22921     247   46607
  4     23103     252   46935
  5     22825     258   47081
  6     23233     289   44858
  7     10696     109   34878
dob.dm.tbl=dob.dm.tbl[,-2]
dob.dm.tbl
   MM
WK  C-section Vaginal
  1      8836   31348
  2     20454   42031
  3     22921   46607
  4     23103   46935
  5     22825   47081
  6     23233   44858
  7     10696   34878
trellis.device()
barchart(dob.dm.tbl,ylab="Day of Week")
barchart(dob.dm.tbl,horizontal=FALSE,groups=FALSE,
+  xlab="Day of Week",col="black")
c02uf002

We use lattice (trellis) graphics (and the R package lattice) to condition density histograms on the values of a third variable. The variable for multiple births (single births to births with five offsprings (quintuplets) or more) and the method of delivery are our conditioning variables, and we separate histograms of birth weight according to these variables. As expected, birth weight decreases with multiple births, whereas the birth weight is largely unaffected by the method of delivery. Smoothed versions of the histograms, using the lattice command density plot, are also shown. Because of the very small sample sizes for quintuplet and even more births, the density of birth weight for this small group is quite noisy. The dot plot, also part of the lattice package, shows quite clearly that there are only few observations in that last group, while most other groups have many observations (which makes the dots on the dot plot “run into each other”); for groups with many observations a histogram would be the preferred graphical method.

histogram(∼DBWT|DPLURAL,data=births2006.smpl,layout=c(1,5),
+   col="black")
histogram(∼DBWT|DMETH_REC,data=births2006.smpl,layout=c(1,3),
+   col="black")
c02uf003
densityplot(∼DBWT|DPLURAL,data=births2006.smpl,layout=c(1,5),
+   plot.points=FALSE,col="black")
densityplot(∼DBWT,groups=DPLURAL,data=births2006.smpl,
+   plot.points=FALSE)
c02uf004
dotplot(∼DBWT|DPLURAL,data=births2006.smpl,layout=c(1,5),
+   plot.points=FALSE,col="black")
c02uf005

Scatter plots (xyplots in the package lattice) are shown for birth weight against weight gain, and the scatter plots are stratified further by multiple births. The last smoothed scatter plot indicates that there is little association between birth weight and weight gain during the course of the pregnancy.

xyplot(DBWT∼DOB_WK,data=births2006.smpl,col="black")
xyplot(DBWT∼DOB_WK|DPLURAL,data=births2006.smpl,layout=c(1,5),
+   col="black")
xyplot(DBWT∼WTGAIN,data=births2006.smpl,col="black")
xyplot(DBWT∼WTGAIN|DPLURAL,data=births2006.smpl,layout=c(1,5),
+   col="black")
c02uf006
smoothScatter(births2006.smpl$WTGAIN,births2006.smpl$DBWT)
c02uf007

We also illustrate box plots of birth weight against the APGAR score and box plots of birth weight against the day of week of delivery. We would not expect much relationship between the birth weight and the day of week of delivery; there is no reason why babies born on weekends should be heavier or lighter than those born during the week. The APGAR score is an indication of the health status of a newborn, with low scores indicating that the newborn experiences difficulties. The box plot of birth weight against the APGAR score shows a strong relationship. Babies of low birth weight often have low APGAR scores as their health is compromised by the low birth weight and its associated complications.

## boxplot is the command for a box plot in the standard graphics
## package
boxplot(DBWT∼APGAR5,data=births2006.smpl,ylab="DBWT",
+  xlab="AGPAR5")
boxplot(DBWT∼DOB_WK,data=births2006.smpl,ylab="DBWT",
+  xlab="Day of Week")
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## bwplot is the command for a box plot in the lattice graphics
## package. There you need to declare the conditioning variables
## as factors
bwplot(DBWT∼factor(APGAR5)|factor(SEX),data=births2006.smpl,
+   xlab="AGPAR5")
bwplot(DBWT∼factor(DOB_WK),data=births2006.smpl,
+   xlab="Day of Week")
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We also calculate the average birth weight as function of multiple births, and we do this for males and females separately. For that we use the tapply function. Note that there are missing observations in the data set and the option na.rm=TRUE (remove missing observations from the calculation) is needed to omit the missing observations from the calculation of the mean. The bar plot illustrates graphically how the average birth weight decreases with multiple deliveries. It also illustrates that the average birth weight for males is slightly higher than that for females.

fac=factor(births2006.smpl$DPLURAL)
res=births2006.smpl$DBWT
t4=tapply(res,fac,mean,na.rm=TRUE)
t4
            1 Single                 2 Twin              3 Triplet
              3298.263               2327.478               1677.017
          4 Quadruplet 5 Quintuplet or higher
              1196.105               1142.800
t5=tapply(births2006.smpl$DBWT,INDEX=list(births2006.smpl$DPLURAL,
+   births2006.smpl$SEX),FUN=mean,na.rm=TRUE)
t5
                                    F        M
      1 Single               3242.302 3351.637
      2 Twin                 2279.508 2373.819
      3 Triplet              1697.822 1655.348
      4 Quadruplet           1319.556 1085.000
      5 Quintuplet or higher 1007.667 1345.500
barplot(t4,ylab="DBWT")
barplot(t5,beside=TRUE,ylab="DBWT")
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Finally, we illustrate the levelplot and the contourplot of the R package lattice. For these plots we first create a cross-classification of weight gain and estimated gestation period by dividing the two continuous variables into 11 nonoverlapping groups. For each of the resulting groups, we compute the average birth weight. An earlier frequency distribution table of estimated gestation period indicates that “99” is used as the code for “unknown”. For the subsequent calculations, we omit all records with unknown gestation period (i.e., value 99). The graphs show that the birth weight increases with the estimated gestation period, but that birth weight is little affected by the weight gain. Note that the contour lines are essentially horizontal and that their associated values increase with the estimated gestation period.

t5=table(births2006.smpl$ESTGEST)
t5
    12     15     17     18     19     20     21     22     23     24     25
     1      2     18     43     69    116    162    209    288    401    445
    26     27     28     29     30     31     32     33     34     35     36
   461    566    670    703   1000   1243   1975   2652   4840   7954  15874
    37     38     39     40     41     42     43     44     45     46     47
 33310  76794 109046  84890  23794   1931    133     32      6      5      5
    48     51     99
     2      1  57682
new=births2006.smpl[births2006.smpl$ESTGEST != 99,]
t51=table(new$ESTGEST)
t51
    12     15     17     18     19     20     21     22     23     24     25
     1      2     18     43     69    116    162    209    288    401    445
    26     27     28     29     30     31     32     33     34     35     36
   461    566    670    703   1000   1243   1975   2652   4840   7954  15874
    37     38     39     40     41     42     43     44     45     46     47
 33310  76794 109046  84890  23794   1931    133     32      6      5      5
    48     51
     2      1
t6=tapply(new$DBWT,INDEX=list(cut(new$WTGAIN,breaks=10),cut(new$ESTGEST,breaks=10)),FUN=mean,na.rm=TRUE)
t6
levelplot(t6,scales = list(x = list(rot = 90)))
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contourplot(t6,scales = list(x = list(rot = 90)))
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2.1.1 Modeling Issues Investigated in Subsequent Chapters

This discussion, with its many summaries and graphs, has given us a pretty good idea about the data. But what questions would we want to have answered with these data? One may wish to predict the birth weight from characteristics such as the estimated gestation period and the weight gain of the mother; for that, one could use regression and regression trees. Or, one may want to identify births that lead to very low APGAR scores, for which purpose, one could use classification methods.

2.2 Example 2: Alumni Donations

The file contribution.csv (available on our data Web site) summarizes the contributions received by a selective private liberal arts college in the Midwest. The college has a large endowment and, as all private colleges do, keeps detailed records on alumni donations. Here we analyze the contributions of five graduating classes (the cohorts who have graduated in 1957, 1967, 1977, 1987, and 1997). The data set consists of images living alumni and contains their contributions for the years 2000–2004. In addition, the data set includes several other variables such as gender, marital status, college major, subsequent graduate work, and attendance at fund-raising events, all variables that may play an important role in assessing the success of future capital campaigns. This is a carefully constructed and well-maintained data set; it contains only alumni who graduated from the institution, and not former students who spent time at the institution without graduating. The data set contains no missing observations. The first five records of the file are shown below. Alumni not contributing have the entry “0” in the related column. The 1957 cohort is the smallest group. This is because of smaller class sizes in the past and deaths of older alumni.

## Install packages from CRAN; use any USA mirror
library(lattice)
don <− read.csv("C:/DataMining/Data/contribution.csv")
don[1:5,]
  Gender Class.Year Marital.Status   Major Next.Degree FY04Giving FY03Giving
1      M       1957              M History         LLB       2500       2500
2      M       1957              M Physics          MS       5000       5000
3      F       1957              M   Music        NONE       5000       5000
4      M       1957              M History        NONE          0       5100
5      M       1957              M Biology          MD       1000       1000
FY02Giving FY01Giving FY00Giving AttendenceEvent
1       1400      12060      12000               1
2       5000       5000      10000               1
3       5000       5000      10000               1
4        200        200          0               1
5       1000       1005       1000               1
table(don$Class.Year)
1957 1967 1977 1987 1997
127  222  243  277  361
barchart(table(don$Class.Year),horizontal=FALSE,
+   xlab="Class Year",col="black")
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Total contributions for 2000–2004 are calculated for each graduate. Summary statistics (mean, standard deviation, and percentiles) are shown below. More than 30% of the alumni gave nothing; 90% gave $1050 or less; and only 3% gave more than $5000. The largest contribution was $172,000.

The first histogram of total contributions shown below is not very informative as it is influenced by both a sizable number of the alumni who have not contributed at all and a few alumni who have given very large contributions. Omitting contributions that are zero or larger than $1000 provides a more detailed view of contributions in the $1–$1000 range; this histogram is shown to the right of the first one. Box plots of total contributions are also shown. The second box plot omits the information from outliers and shows the three quartiles of the distribution of total contributions (0, 75, and 400).

don$TGiving=don$FY00Giving+don$FY01Giving+don$FY02Giving
+    +don$FY03Giving+don$FY04Giving
mean(don$TGiving)
[1] 980.0436
sd(don$TGiving)
[1] 6670.773
quantile(don$TGiving,probs=seq(0,1,0.05))
     0%       5%      10%      15%      20%      25%      30%      35%
     0.0      0.0      0.0      0.0      0.0      0.0      0.0     10.0
     40%      45%      50%      55%      60%      65%      70%      75%
    25.0     50.0     75.0    100.0    150.8    200.0    275.0    400.0
     80%      85%      90%      95%     100%
   554.2    781.0   1050.0   2277.5 171870.1
quantile(don$TGiving,probs=seq(0.95,1,0.01))
      95%       96%       97%       98%       99%      100%
  2277.50   3133.56   5000.00   7000.00  16442.14 171870.06
hist(don$TGiving)
hist(don$TGiving[don$TGiving!=0][don$TGiving[don$TGiving!=0]<=1000])
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boxplot(don$TGiving,horizontal=TRUE,xlab="Total Contribution")
boxplot(don$TGiving,outline=FALSE,horizontal=TRUE,xlab="Total Contribution")
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We identify below the donors who gave at least $30,000 during 2000–2004. We also list their major and their next degree. The top donor has a mathematics–physics double major with no advanced degree. Four of the top donors have law degrees.

ddd=don[don$TGiving>=30000,]
ddd
ddd1=ddd[,c(1:5,12)]
ddd1
ddd1[order(ddd1$TGiving,decreasing=TRUE),]
    Gender Class.Year Marital.Status                Major Next.Degree   TGiving
99       M       1957              M  Mathematics-Physics        NONE 171870.06
123      M       1957              W   Economics-Business         MBA  90825.88
132      M       1967              M Speech (Drama, etc.)          JD  72045.31
105      M       1957              M              History         PHD  51505.84
135      M       1967              M              History          JD  42500.00
486      M       1977              M            Economics         MBA  36360.90
471      F       1977              D            Economics          JD  31500.00
1        M       1957              M              History         LLB  30460.00
2        M       1957              M              Physics          MS  30000.00
3        F       1957              M                Music        NONE  30000.00