Wednesday, December 30, 2009

Tuesday, December 29, 2009

Top Ten Must-Have R Packages for Social Scientists

The political scientist Drew Conway has come up with a useful list of his ten "must-have" R packages for social scientists. I agree with him for the most part, and his list highlights the usefulness of R (vis-a-vis Stata) for social network analysis (see statnet/igraph) and graphics (see ggplot2). In some respects, his list also underscores the fact that R is arguably more suited for sociological data analysis than Stata, given the former's unique packages not only for social network analysis but also multilevel modeling and  a variety of non-parametric methods (including more recent forms of matching and classification techniques), which were especially popular in sociology before the "path analysis" revolution of the 1960s.

Tuesday, December 22, 2009

Multilevel and Longitudinal Modeling in Stata

For my "off-task" reading I recent perused an excellent book on multilevel and longitudinal modeling in Stata by Sophia Rabe-Hesketh and Anders Skrondal. The second edition (which I read) has been updated by including several chapters providing an overview of regression modeling and ANOVA (analysis of variance) as well as additional background information on models with nonlinear outcomes (e.g., logistic regression). The authors even include a self-test near the beginning of the book to ensure that readers can confidently progress through the rest of the material. The book has many great features, including ease of data accessibility (simply go to this website and you instantly have all the datasets used in the book), clarity of presentation, and numerous applied examples with accompanying Stata code. The only problem, which is not a problem with the book, is that multilevel modeling in Stata (as the authors note) can be rather slow, especially for nonlinear outcomes with many levels. (For this reason, when using nonlinear outcomes other statistical packages may be more desirable than Stata, such as R.) Yet overall the book is an excellent overview of an important class of statistical models, and can even be viewed as a way of take advantage of Stata beyond the realm of "econometric" approaches (which seems to be Stata's strength) and toward the realm of putatively more "sociologic" methods of data analysis, in which clustered data are viewed as something important in their own right rather than as statistical nuisances.

Thursday, December 17, 2009

Sociology = Hedge Fund?

Some people have blamed hedge funds (whose managers can earn extraordinarily high returns) for contributing to the high level of economic inequality in the USA. And who invented the hedge fund? We can thank the sociologist Alfred Winslow Jones, Ph.D.

Monday, December 14, 2009

A Quantitative Tour of the Social Sciences

I just read "A Quantitative Tour of the Social Sciences," edited by Andrew Gelman and Jeronimo Cortina. I highly recommend the book for anyone who does quantitative research, including part-time quantitative analysts and ambitious undergraduates. The aim of the book is to expose the reader to the similarities and differences in quantitative thinking across five core social science disciplines: history (a welcome but oft neglected member of the social sciences), economics, sociology, political science, and psychology. The editors are unabashedly in favor of methodological pluralism, and present as diverse set of views as possible. What is notable about this volume is that for each discipline the authors have included exercises ranging from conceptual questions to hands-on data analyses. From my perspective, especially illuminating chapters include Andrew Gelman's thoroughly informative discussion of the application of game theory to trench warfare (in part because he discusses the criticisms of his paper as it went through peer review) and Jeronimo Cortina's overview of the potential outcomes model of causality (which, while familiar to more advanced readers, is presented with enviable clarity).

The chapters capture most of the differences among the disciplines in quantitative thinking. However, a few differences in mathematical modeling may be missed. In particular, likely reflecting an enduring interest in social context and interconnections among individuals, sociologists tend to use multilevel models and social network methods more frequently than other social scientists. As well, economists are much more likely to focus on trying to interpret observational data causally through the use of instrumental variables and, to a lesser extent, regression discontinuity design. Notwithstanding, overall this book is a welcome addition to the bookshelf of any scholar who does quantitative work.

Creating Summated Scales

The sociologist Paul Millar has created a very useful tool in Stata called optifact for creating summated scales. Often social scientists simply throw together some variables, report a Cronbach's alpha as a measure of reliability, and then move on to other analyses. But there are some well-known problems with Cronbach's alpha; in particular, the value of alpha will increase if you add more items in the scale. Millar's program is useful because for those items which load on one dimension, it sorts candidate scales by increasing number of items in descending order of Cronbach's alpha. For instance, the program will first list all scales with, say, two items that load on one factor, starting with the scale with the highest Cronbach's alpha. This way the analyst can easily create summated scales that are parsimonious (i.e., consist of few items), unidimensional (i.e., load on one factor), and have a high level of reliability (i.e., have a high Cronbach's alpha).

Simpson's Paradox Strikes Again

The Wall Street Journal published a recent article on Simpson's paradox and the jobless rate in the USA. When aggregated, the jobless rate is lower today than in the 1980s; however, when broken down by educational levels, the jobless rate for each educational group is higher. How can this be? The reason the overall rate is higher today is because college graduates, who tend to have a lower unemployment rate than other groups even in good economic times, are a larger proportion of the population today than in the past. Thus, the weighted average across all educational groups is weighted much more by college graduates today than in the 1980s, lifting the overall unemployment rate higher even though all educational groups are faring worse.

Sunday, December 13, 2009

The Relative Size of Things

Sociologists are often focused on different levels of phenomena; hence the attention paid by sociologists to the micro-macro problem (see James S. Coleman's "boat" showing linkages at various levels), Anthony Giddens' structuration theory (orienting social theory toward micro-macro concerns), and hierarchical linear models, otherwise known as multilevel models (in which the analyst models two or more levels of given social phenomena). Although dealing with biology and physics rather than sociology, both of the following hyperlinks help us to visualize the importance of how reality differs by various levels: cell size and scale (developed by scientists at the University of Utah) and Powers of Ten (created by IBM in the 1970s for the Museum of Science and Industry in Chicago). Cool stuff.

Multiple Imputation with Deletion

The sociologist Paul T. von Hippel has written a great article outlining how to deal with missing values when the Y's are also missing. Typically the gold standard for dealing with missing data has been multiple imputation, but he advocates multiple imputation with deletion (MID): that is, you use all cases for multiple imputation, but after imputing you delete those cases with imputed Y values. Somewhat surprisingly (because of the reduced sample size after excluding those cases with imputed Y values), MID usually leads to smaller standard errors; moreover, since the Y's are excluded from the analysis, MID is robust to problems with the imputation model. Check out von Hippel's informative paper here.

The Paradox of Choice

Last week I read Barry Schwartz's (a professor of social theory and social action at Swarthmore) book The Paradox of Choice. I highly recommend reading his book, especially chapters 4 and 11, which summarize his main ideas. In a nutshell, he contends that the plethora of choices before us in modern capitalist economies often leads to chronic indecision, anxiety, unhappiness. (Sociologists may glean some elements of Durkheim from Schwartz's arguments.) In the final chapter Schwartz outlines several recommendations for how to decrease choice in your life and thus increase your overall life satisfaction. Here are some points I found particularly useful:

(1) Choose when to choose: In other words, make rules so you have fewer decisions to make. We often make rules for mundane tasks (such as "I always brush my teeth before going to bed") but not for other tasks, such as what hobbies to pursue, what clothes to purchase, and so forth. By reducing the number of decisions, you can increase your focus on those decisions you do decide to make (e.g., "Where should I move to?") and decrease your overall anxiety.

(2) Satisfice more and maximize less: That is, do not try to do the best and expect the best; rather, expect to do "good enough" while trying to do your best. Expecting to be the best will lead to anxiety and depression; after all, the "best" is almost always an illusion because there is never one metric for what constitutes the best. (Do this little experiment: compare the number of citations in google scholar for Albert Einstein's versus Anthony Giddens'. Who comes out on top? Who is the "best"?)

(3) Think about the opportunity cost of opportunity costs: Do not think about the attractive features of choices you do not make. For example, if you move decide to Florida, avoid thinking how much better the public transportation is in New York City, or how much better the universities are in Boston. Instead, focus on the warm weather, beautiful beaches, and fascinating American-Cuban culture.

(4) Cultivate non-reversible decisions: By making your decisions non-reversible, you can sink your efforts deep into what you're doing rather than thinking about what else you "should" be doing. A useful analogy is skiing: when you go skiing down hills, you decrease your chances of falling by leaning forward a bit rather than leaning back (i.e, you must commit to you decision!).

(5) Curtail social comparison: It's a good idea to obliterate social comparisons, especially upward social comparisons (which seems natural to many of us). It's always possible to find someone more successful by some standard, so it's always possible to be unhappy.

Of course, none of this easy (as Schwartz himself emphasizes)!

Abandoned Sociology

Today I re-read an article from 1994 in the Sociological Forum by James A Davis, who for many years taught at the Harvard sociology department. What intrigued me most about this article is that Davis thinks that sociologists are often very good at coming up with original ideas and then dropping them. Some of his examples of abandoned sociology:

(1) Occupational prestige: According to Davis, occupational prestige ratings are "remarkably robust" and constitute "the only sociological finding one can try on a class knowing it will work and knowing they will not say they knew it already" (180). More studies could examine the causes and consequences of occupational prestige, as well as investigate prestige scales for other categories (e.g., schools, countries, parties, and so on).

(2) Union Democracy: Lipset, Trow, and Coleman's (1956) classic study of the International Typographical Union showed that, contra Robert Michels' "iron law of oligarchy," the large union governed itself through democratic means. Davis wonders why more sociological studies haven't developed basic principles for the factors underlying democratic forms of governance in various types of organizations.

(3) Authoritarianism: The idea of the "authoritarian personality" dominated research in public opinion and sociology, but then disappeared (according to Davis), despite the fact that measures capturing authoritarianism were highly predictive of views on free speech and other attitudinal variables. Davis concludes: "Does personality have a big influence on social attitudes? We'll probably never know since we lost interest in the question (181)."

Are these ideas uncovered by sociology still abandoned 15 years after Davis' article was first published? While not as dominant as before in sociology, many researchers are still exploring these ideas. For example, regarding prestige, in the past several years scholars have examined various topics, including diseases (myocardial infarction is the most prestigious, anxiety neurosis the least so),  women in occupations (occupations with a balanced proportion of men and women are the most prestigious), and prestige in firms (young firms benefit from prestigious affiliations). Similarly, researchers have resurrected work on authoritarian personality (see, for instance, research by the social psychologist John T. Jost) as well as democratic forms of organization (see, for example, research by Archon Fung and Erik Olin Wright on "Real Utopias"). Thus, although sociologists have shared these recent extensions of sociological findings with other researchers, it is fair to say they have not been entirely abandoned.

LaTeX or MS Word?

Many, many people have rave reviews about LaTeX, a document preparation system. Take the political scientist Jeff Gill, who writes that LaTeX is a "wonderful and addicting tool," noting that he hasn't used a word processor in over a decade. So should sociologists use LaTeX? Certainly mathematicians, computer scientists, and physicists should use LaTeX, given the LaTeX format is often the default for journal articles, which are frequently short, highly structured, and filled with mathematical expressions. (Almost the opposite of sociology articles!) However, I have difficulty discerning the advantages of learning LaTeX compared to MS Word, for several reasons:

(1) Time management: LaTeX undeniably has a much steeper learning curve than MS Word. This is time that could be spent on other activities, such as learning more advanced statistical methodologies, perusing historical monographs, or even writing more papers! Of course some LaTeX users would probably claim that LaTeX saves time over the long run, but this is of course an empirical question (and likely varies by the skills, goals, and mindset of the individual).

(2) Interdisciplinary work: Sociologists tend to be quite interdisciplinary, often working with scholars who are less likely to be statisticians and more likely to be historians, anthropologists, or humanists. It doesn't make much sense to learn LaTeX if your co-authors don't use LaTeX, and never will learn LaTeX. The advantage of MS Word is that it is widely used by people from many different disciplines, applied fields, and methodological orientations, from cultural anthropologists to business consultants to computational neuroscientists.

(3) MS equation editor: One of the putative advantages of LaTeX is that it is useful for mathematical typesetting (hence the widespread use by mathematicians, economists, and physicists); however, for most sociologists MS equation editor is likely to be sufficiently useful for inserting a wide variety of equations into word documents. In fact, from my experience I've tended to put in too many equations rather than not enough! This likely reflects that sociologists need to write papers so that intelligent people from a variety of different backgrounds can understand the arguments.

(4) Other minor issues: There are some some minor but nonetheless possibly problematic features of LaTeX: the text in LaTeX is not very good at "flowing" around graphs and pictures; LaTeX encourages a type of structured writing and form of document organization that is extremely rare in the humanities and many subfields of sociology, anthropology, and psychology; finally, font selection is much more difficult in LaTeX than in MS Word and other word processors.

(5) LaTeX-based word processors: Even if you want to create documents in LaTeX but are not inclined to learn the details of type setting, Scientific WorkPlace offers a very useful WYSIWYG LaTeX-based word processor. It's not currently available for the Mac OS, but I called the manufacturer and they plan on shipping out a version for Macs sometime in late 2010. However, there is also Lyx, a WYSIWYG word document processor, which is currently available for Macs.

Why You Have No Friends

One of my favorite sociology articles is Scott Feld's article "Why Your Friends Have More Friends Than You Do ," published in the American Journal of Sociology in 1991. As the title of his paper promises, using logical deduction and ample data Feld shows that your friends are indeed more likely to have friends than you do (i.e., that the average number of friends of friends is always greater than the average number of friends of individuals). Why is this, though? To put it as simply as possible, the reason is that you are more likely to be friends with popular people than unpopular people. To confirm this for myself, I quasi-randomly selected ten of my friends on Facebook. Here is the sum of the friends of my friends in my sample:

358 + 271 + 694 + 104 + 403 + 315 + 302 + 891 + 83 + 1,986 = 5,389.

Dividing this total by ten (the size of my sample) equals 538.9, well above my 400 or so friends on Facebook. Even with this small quasi-random sample, the phenomenon holds!

An unexplored (as far as I can tell) corollary of Feld's finding is that any characteristic correlated with the number of friends a person has would also appear greater among your friends. For instance, if having more friends means being more extroverted, then on average your friends are going to be more extroverted than you. Similarly, if having more friends means being taller or better looking, than your friends will also be taller or better looking than you.

A related issue is the so-called class size paradox: you are more likely to be in a classroom that has more students than the average classroom. Likewise, you are more likely to be on a beach more crowded than average, or in a movie theatre more crowded than average.

Saturday, December 12, 2009

The Language of Economists

For the past few days I've been brushing up on econometrics (i.e., statistical methods used and developed by economists) and I've run across a number of curious terms used by economists (at least in the examples mentioned in the particular textbook). What I find fascinating is how economists and sociologists can examine similar phenomenon yet use different terminology, reflecting differences in training, theories, and political opinions. Here is an abbreviated dictionary of my favorite terms from economics, with my (cheeky?) translations into sociology:

Equilibrium:  A condition in which (economic) forces are balanced and, in the absence of an external force, the values of variables do not change; according to many sociologists, an outdated concept from either the 19th Century (see, for example, Charles Tilly's view on equilibrium as conceptual baggage) or mid-20th century structural functionalism (see, for instance, the work by Talcott Parsons and his followers) that is either (a) generally not useful for understanding actually existing social conditions or (b) somehow used to justify the status quo.

Utility function: A mathematical equation showing people's total satisfaction equivalent to a set of variables, often reflecting a combination of consumption of goods and work performance. According to sociologists, a radical abstraction, obscuring the fact that people's preferences (on which utility is usually based) are often incoherent, ill-formed, and even non-existent until they are asked about them.

Revealed preference: The idea that what you truly want is revealed by what you do rather than what you say; according to many sociologists, patterns of behavior independent of what you really want, influenced by social structures, norms, and governments, and even ideology. Regarding the latter, see Steven Lukes' classic work on power, in which he contends that what you think what you want may not be what you really want if you were in a society free of ideology.

Flexibility: A condition in the labor market in which workers shift from one economic activity to another very quickly; according to many sociologists, pervasive job insecurity (see, for example, the recent work by the sociologist Arne Kalleberg). Among sociologists and public health researchers, research has generally demonstrated the negative effects of job insecurity, which leads to lower levels of physical health, higher rates of depression, and disruptions over the life course.

Free market: A system of transactions based on supply and demand with extremely little government involvement; according to many sociologists, an impossible fiction. As the late sociologist Charles Tilly put it, the market is run not by an "invisible hand" (which is capable and in control) but by an "invisible elbow" (which clumsily knocks things over without realizing it). Or to refer to another sociologist, Karl Polyani, the free market is at most a temporary phase of systemic social disruptions pushed through by the heavy hand of the state, which if left unchecked leads to mass unemployment, financial chaos, and violent social movements.

Ever wonder why economists and sociologists have trouble agreeing?

Friday, December 11, 2009

A Neat Mathematical Trick

What is 1 minus 0.99 (repeating)? The answer is rather surprising: it's zero. A colleague of mine revealed to me how this can be the case. When you subtract 0.99 (repeating) from 1, you are left with 0.00 (repeating). You will never "reach" that final "1" at the end of the string of zeros because you can always add another zero since the number of zeros repeats indefinitely. Ergo, 1 minus 0.99 (repeating) is always zero. Cool, huh?

Do Social Networks Affect Health?

In a recent series of ground-breaking articles over the past several years, Nicholas Christakis (a sociologist here at Harvard) and James Fowler (a political scientist at UC Davis) have shown that health behaviors seem to flow through social networks. Using new data from the Framingham Heart Study, they've shown apparent contagion effects for obesity, smoking, depression, and even isolation. Recently, however, Ethan Cohen-Cole and Jason M. Fletcher (two economists) have used data from Add Health to show apparent "implausible social network effects" for acne, height, and headaches. The economists also demonstrate that after controlling for "environmental confounders" the effects disappear, suggesting that contagion through networks are really just capturing similar structural conditions (e.g., the fact that I get obese after you are obese is really because we both live in a neighborhood with another fast food restaurant).

Although Cohen-Cole's and Fletcher's criticisms might seem relatively damning, there are a number of very serious problems with concluding that social network effects do not exist:

(1) Different data: Cohen-Cole and Fletcher use a different dataset than Christakis and Fowler. The studies differ in location (high schools versus homes), population (teenagers versus the general population), time (less than one decade versus three), and so forth. It's entirely possible that contagion effects do not exist for teenagers in high schools, but do exist for members of Framingham, Massachusetts. This would make sense if, for example, social imprinting effects were weaker among teenagers with possibly ephemeral relations in high schools rather than adults with more durable relationships.

(2) Presence vs. absence: The presence of putatively implausible contagion effects for variables such as height and acne does not demonstrate the absence of plausible contagion effects for variables such as obesity and happiness. Another way to think about it: studies showing that smoking causes cancer are just as valid even if, say, frequent use of a fireplace in a house does not cause cancer. Although the mechanisms are broadly similar (inhaling smoke), there may be important differences (the substance that is smoked).

(3) Definition of "implausible": Cohen-Cole and Fletcher assert that network effects for acne, headaches, and height are "implausible." Is this really the case, however? All the data from AddHealth on acne, headaches, and height are self-reported; thus, if I have a friend who complains of headaches then I may very well find it easier to complain of headaches due to changing norms or a driving desire to be more like my friends. Or perhaps my friend has found an effective way to prevent headaches (such as a daily dose of aspirin), and I've adopted my friend's behaviors. Or it's even possible that headaches are associated with stress, and that what is actually spreading through social networks is stress along with headaches. These same points can also be said about acne. What about height, though? Self-reported height could also spread through networks; if my friends are tall, then I'm likely to nudge up or down my actual height. We've all known short guys who have added a few inches and tall women who've subtracted a few. In addition, even assuming that height in AddHealth is accurately measured, there is substantial evidence that height during adolescence is greatly influenced by diet, exercise, and smoking habits. To the extent that any of these flow through networks, then so will height.

(4) Flaws with fixed effects: Cohen-Cole and Fletcher used fixed effects to "control" for time-invariant unobserved differences between schools. Although superficially a good way to adjust for all stable differences between schools, it is well-known that the fixed effects estimator reduces the size of the standard errors (intuitively, because less information is used to estimate the coefficients). This is especially the case if the number of waves is small (as is the case with AddHealth, which consists of only three waves of data, although each school has numerous individuals). More importantly, however, is that with a lot of inefficiency not only are the standard errors larger, but the point estimates may also become small and fragile, resulting in erroneous inferences (in the same way that a biased coefficient would). For this reason I'd recommend Cohen-Cole and Fletcher re-do their analyses using fixed effects vector decomposition, which can improve the efficiency of estimates yet retain some of the advantages of the traditional fixed effects estimator.

(5) Neglected information: Another problem is that Cohen-Cole and Fletcher neglect important ancillary evidence that supports the interpretation of the Framingham data given by Christakis and Fowler; to wit, there is substantial evidence from social psychology that people automatically mimic each other in myriad ways (e.g., emotions and behavior, including other people's tone of voice and body posture). Social mimicry is a highly plausible mechanism that buttresses the network diffusion interpretation of the data.

(6) Relevance of networks: Even if network effects are not causal, such descriptive information is still highly relevant. Most importantly, knowing the social patterning of behaviors and attitudes is extraordinarily useful for maximizing the impact of social interventions. For example, regarding obesity, clinicians could provide information on the benefits of dietary changes to people and then offer incentives to overweight people to recruit others in their social network. In this way, the population in most need of a particular intervention would be efficiently affected.

Understanding social causes is complex, and necessarily requires an accumulation of different kinds of knowledge. This is how epidemiologists discovered that smoking causes cancer: a few observational studies combined with information on the substances in cigarette smoke, not to mention a dash of qualitative evidence from clinicians. There was no single "smoking gun" (pun intended). In the same way, understanding social network effects will not be ruled out by a single study using a fixed effects estimator on a handful of variables gathered from a few thousand teenagers living in late 20th century America. Rather, understanding the degree to which social network effects can be understood as causal will require results from various sources, including both nationally-representative datasets (e.g., AddHealth and Framingham) as well as additional studies on contagion mechanisms (such as the findings on social mimicry from social psychology).

Thursday, December 10, 2009

Economists > Political Scientists > Sociologists?

I recently encountered a blog entry by the eminent (and often wrong) economist Greg Mankiw . In his blog he notes that the ex-president of Harvard, the economist Larry Summers, asked a dean at Harvard if it isn't true that "in general, economists are smarter than political scientists, and political scientists are smarter than sociologists?" Mankiw then links to these 2002 data of GRE scores by field of Ph.D. study (with the obligatory "joke" that public administration is at the bottom of the hierarchy):


There are two big problems with Mankiw's claim that Larry Summers is "vindicated." First, does the GRE measure what it means to be "smart"? As much as I'd like to think so (since I scored in the 99th percentile on the GRE), the answer is a resounding no. The GRE is not recognized by Mensa, the high IQ society, as a legitimate IQ test. The lack of validity of the GRE as an IQ test is echoed by Educational Testing Service (ETS), the company that created the GRE, which has since removed the analytical section of the GRE listed above and replaced it with a writing section. And of course we should not forget that the GRE does not even attempt to measure the multitude of intelligences discussed by Robert J. Sternberg and Howard Gardner: social, emotional, visual, and so forth. Intelligence has likely evolved into a system of modules in the brain embodying different capabilities rather than a single, unitary construct that can be organized on one dimension (or a small number of dimensions).

Second, even if the GRE does measure what it means to be "smart," is there any reason to think these differences will persist after entry into graduate school? Again, there are serious problems with such a claim. Sociologists (especially vis-a-vis economists) are an especially diverse group of people: we are more likely to be female, non-white, and come from poorer backgrounds. These disadvantages can lead to stereotype threat (as discussed by the late John Ogbu) or other forms of test anxiety, resulting in lower test scores even when such tests measure raw intelligence. Moreover, the GRE scores listed above are only those for Doctoral students who enter programs, not those who exit them; given the difficulty of academic work, it is likely the differences between fields become flattened when you compare students who graduate with degrees. Finally, the GRE scores above ignore possible cohort effects: it is possible current sociology faculty score just as highly as current faculty in economics.

In short, pace Mankiw, Summers has not been "vindicated."

Wednesday, December 09, 2009

An Extraordinarily Useful Command

What is the most useful Stata command that "nobody" uses? A particular favorite of mine is "plotbeta" written by Adrian Mander, a public health researcher at the University of Cambridge in the UK. His program enables you to plot regression coefficients graphically in one simple, easy-to-use command. Too often  social scientists (especially economists) present results in tables when they could be displaying their results in pie charts, bars charts, and scatterplots. The end result is that we create tables that are difficult to interpret, obscure patterns in the data, and foster an undue obsession on focusing on only those coefficients with an adequate number of "stars" next to them! Graphs are undoubtedly superior to tables in several respects: first, they present results in a way are easier everyone, including people who do not read academic journal articles, to interpret and understand; second, they encourage the researcher to examine patterns in the data that might otherwise be missed (for example, increasing returns to education on income); and finally, they help shift focus away from evaluating coefficients on whether or not they are statistically "significant" (an inherently arbitrary cutoff) and toward whether or not coefficients are large or small, positive or negative, and accompanied with a confidence interval that is wide, narrow, or in-between. Kudos to Adrian Mander for creating "plotbeta," the most useful Stata .ado file that "nobody" uses. Let's hope more people take advantage of it.