Since I purchased some web space, I have been thinking how to get most out of this decision. I contacted Dr. Shiming Fang about the possibility of mirroring his “New Thread” website, as I have been a frequent visitor for more than four years (maybe too frequently and for too long).

Anyway, Dr. Fang generously allowed me to mirror his site and gave me some instructions (written by Slashdot and Squirrel. I think Fang may not know much about those technical details either). Following the suggestions, I downloaded almost all webpages from the New Thread using teleport pro (suggested by Squirrel). The New Thread is surprisingly big with more than 400MB materials. Not without pain, I uploaded materials to my website. That’s a full day’s job.

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Economics can be fun, rewarding, and surprising. Steven Levitt has strived to tell us this in the book “Freakonomics,” coauthored with Stephen J. Dubner from New York Time. The book is indeed fascinating, full of interesting anecdotes and detective stories. How can you catch cheating among teachers? Where have all the criminals gone? What makes a perfect parent? Steven has answered all these questions in a vivid, scientific, and empirical way.

The structure of the book is unconventional. Topics and ideas are jumping all around. Stories are not internally correlated. Furthermore, some chapters (e.g., the last chapter on naming kids) are too loose and some tables are redundant. Consequently, the authors claimed that the book had no theme. Actually, it does promote one central dogma throughout the text. That is, theories and conventional wisdom should be subjected to empirical test. Let data speak themselves. We social scientists all know it. Now you morons should know it too.

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“Pluralitas non est ponenda sine neccesitate” — “plurality should not be posited without necessity.”

When the medieval philosopher William of Ockham first stated his minimalism principle, he probably never thought that the principle could be applied everywhere and last forever. In causal inference, it is one of the most often cited tenets to justify parsimonious explanations.One argues that unnecessary factors may not only complicate matters, but also hide truth. In particular, parsimony is one hallmark of statistical modeling. The simpler models are always more favorable than complicated ones.

The real world is complicated and interconnected (Karl Marx).In social science, data at hand are often massive in both the number of observations and characteristics in each observation.One wishes to reduce the complexity to a few parameters with which he can predict the reality. Statistical modeling is essentially a technique of dimension reduction.Through modeling, one can answer questions such as “can condom usage reduce the risk of STD and/or HIV infection” or “does it increase the risk of excessive sex instead?” These are important questions, as 70% high school girls are sexually active.

Unfortunately, statistical models are for prediction, not for inference. It becomes obvious when one recalls that all model fitting checkups are derived from prediction purpose. With a large number of variables in the model, one can fit data as well as treating each observation as a covariate.However, a model with hundreds of covariates only proves that analyst is not sophisticated and intelligent.

Therefore, all analysts will select some models, exclude some covariates, and check-recheck model fitting until it looks good enough. The “principle of parsimony” derived from “Occam’s Razor” is applied when assessing models.Given the same model fitting, the fewer number of covariates, the better model is.

However, the above process is a wrong practice. Parsimony is not an appropriate goal for statistical modeling. Instead, to reveal reality is the ultimate and only goal of analysis. If the reality is complex, only a complex model can reflect it.

Take linear regression analysis as an example, many people have traumatic experience of whether an insignificant covariate should be included in the model or not.Often the insignificant covariates are eventually excluded to favor the “Occam’s razor.”However, although one covariate may be insignificant in the model (given all others in the model), a collection of several covariates together can be significant. The insignificant variable may also have large influences on the effects of other covariates. Omitting a relevant covariate may bias the effects of other covariates (beta coefficients).This won’t be resolved by large sample size.Furthermore, an insignificant covariate may be due to inappropriate function form. Changing modeling settings to incorporate nonlinearity may improve the model significantly.

Here is another catch. Including an irrelevant covariate will increase standard errors of the beta coefficients of other covariates, although it may decrease model residual error. The conundrum can not be resolved without a prior knowledge of problems. The only way to perform any analyses is based on social or biological theories. One should always include all important and relevant covariates in the model, no matter what significance they have.

However, causal inference is more than including or excluding some covariates. In a sense, statistical models in causal inference are for testing theories, not for fitting data. The truth is hidden in the data, but the truth is by no means simple, despite the existence of possible simple relationships.

Facing the complex and the demand of causal inference, more complex models may be preferred over simple models.If a simple model fits data better than complex model, one possibility is that the complex model is misspecified, and another complex model should be assessed to capture more information in the data.

Certainly, the complex models are not restricted to simple linear regressions. Structural equation model can directly model the interrelationships between covariates and responses. Dynamic model and mixed model can capture changes in longitudinal data.Multivariate analysis should be used more often than the current practice. People should also be familiar with nonlinear model, as nonlinear relationships are far more common than linear relationship.Bayesian theories may be appealing in some situations.Nonparametic and statistical learning methods are indispensable in statistical analysis.

“Modeling in science remains, partly at least, an art.” (McCullagh & Nelder, 1989)As an art, we have to admit that imprecision is inevitable. On the other hand, it is the imprecision that makes modeling an art. Therefore, Box claimed “all models are wrong, but some are useful.” (GP Box, 1980) We are seeking those useful ones, but we must acknowledge that “eternal truth is not within our grasp.”

It is not uncommon that people take liberty to interpret their data as if they indeed hold truth. The practice in econometrics, unfortunately, suggests that overconfidence is pervasive, as it is evident in the Steven Levitt’s “Freaknomics.”Because that book targets the general population, some of the strong conclusions may have unwanted effects on people’s beliefs.

More to come…

Mount Everest, or Mount Himalaya which I prefer, is more than 29,000 feet (8848 m) in height.With its formidable statue and intriguing myths, she is a sheer beauty of nature.Topping the Mount is a dream of human beings, and to some extent, national prides.

The first organized serial assaults on the Mount Himalaya were carried out by Britons from 1922 to1924.The first expedition was the reconnaissance phase to examine the Mount closely and to set up a feasible route to the top.The second expedition was the first attempt to climb the Mount.It failed due to severe weather and inadequate preparations.The third expedition was the last attempt before Tibet closed the Mount area.The mountaineers brought oxygen tubes, established more camps, and tried three times.They failed again.Two adventurous people: George L. Mallory, and Andrew S. Irvine, lost their lives. The epic of these earlier climbers was told in the free online book “the Epic of Mount Everest” by Sir Francis Younghusband.

The book is fascinating in that it not only vividly recounted how they organized the three expeditions, but also evaluated what decisions they made during the process. It showed that the expeditions were indeed tantamount tasks and everybody involved was responsible, invincible, and creditable. I will not repeat all those events as you can read them for free.But the last expedition during which the tragedy happened deserved comments.

In the beginning of May 1924, eight climbers, together with a couple supporters and almost a hundred porters reached the foot of Mount Himalaya.Unfortunately, the weather was terrible compared with that of the previous two expeditions.Nevertheless, nothing could deter these brave gentlemen.They struggled and finally established six camps up to almost 27000 feet.It was even more amazing that untrained porters successfully carried heavy loads to the farthest camp VI.There was no doubt that they could top the mountain if they wanted.They were also heroes in these expeditions.

The route to the Mount summit was sketched by Mallory based on the first two expeditions. It started from the camp VI, climbed over the North East Ridge, and then reached the summit.There were several hurdles along this route.The first is the Yellow Band which comprises layers of fragile rocks.The second is the First Step, a big rock cliff which needs careful maneuver to circumvent.The third is the Second Step which is an almost vertical 15 feet high rock cliff.It was impossible to climb without some tools. The Third Step and the summit pyramid were also difficult but nonetheless negotiable.

Eight climbers, two in each group, assaulted the Mount.The first two groups crossed 28000 ft line, overcome the Yellow Band, and even climbed over the First Step.However, they were extremely tired after climbing the First Step.Time and energy didn’t allow them to go any further.In a sense, they were also courageous to admit their limit and abandon the plan.However, they didn’t use oxygen which was thought to be the only way to reach the top.

The use of oxygen was debatable even within the team.People were skeptical about the apparatus.The oxygen tubes were unreliable, unwieldy, and most disastrously, heavy.Carrying 30 pounds on the back and climbing Himalaya was not much different from suicide. Nevertheless, after the first two attempts, Mallory and Irvine decided to give oxygen a try.

At the age of 38, Mallory was the ablest mountain climber in his time. He was the core of the three expeditions.He was the one who determined to set his feet on the top of Mount Himalaya. Irvine, on the other hand, was only 22 years of old and inexperienced.He never climbed above 20000 feet high.Because Irvine could manage the oxygen tubes, Mallory took him as a partner.With some determinations and little hope, they pressed on.The last time people talked to them was June 7^th, 1924.Only Odell, the supporting climber, saw two black dots moving on the ridge at 12:50pm the next day.Then they disappeared.

Did Mallory reach the summit?Odell thought he did but most people were not convinced.There were several reasons against Odell’s belief.Firstly, the Second Step on the Mallory’s route was impossible to climb with their primitive tools.In fact, when a Chinese team first climbed that stage, they had to step on each other’s shoulder to climb over the rock.It took them a long time to overcome this Step.Now people can climb it without difficulty due to a ladder left by a Chinese team. Secondly, even if Mallory overcome the Second Step miraculously, the next 800 feet was still out of his time limit.It might take him several hours to cover that distance, let alone there were still two more hurdles before them.Thirdly, as Odell had proved by himself, oxygen was not very useful.He could climb back and force twice to above 27000 feet in four days without using oxygen tubes.On the contrary, the heavy tubes might be too burdensome, thus hindering the climbing.Finally, later climbers never found any trace suggesting that Mallory reached the summit.Now people believed that they might reach the Second Step.After a few fruitless tries, they decided to go back.During the descending, tragically, they slid on the surface and died.

In 1975, a Chinese climber, Wang Hongbao found an “English dead” around the Chinese camp VI.Unfortunately, Wang died in an avalanche the next day after he told his findings to a Japanese climber in 1979. Thus in 1999, PBS organized an expedition to solve the mysteries associated with the 1924’s expedition.They set out to determine who the body was: Irvine or Mallory.

It turned out, he was Mallory.He obviously fell from around the Yellow Band. There was no note in his pocket indicating that he reached the summit. Irvine’s body was never spotted.

There were still many myths surrounding Mallory and Irvine. On the other hand, their failure may be masked by many later successes, despite that many climbers also died in assaulting the Mount. In these days, the climbing is more like personal excursions rather than national or mankind exertions.

Why would human beings want to go up there?There is nothing on the summit of Mount Himalaya except for a grand view of Tibet plateau.Himalayans worship the mountain.They never think of climbing it even though they are capable of doing it.

To the least extent, however, human beings were born with courage and curiosity.The original humans colonized almost all lands long before any civilizations.On the other hand, we human naturally tend to avoid hash environment, thanking for the evolution.It was the renaissance that rekindled human spirit.The confidence of human beings grew rapidly.They crossed oceans and found America. Furthermore, the industry revolution made westerners believe that they could do anything.They climbed Alps, reached the North and South poles, and at the beginning of twentieth century, targeted the third pole of the earth—the Mount Himalaya.

In a sense, the existence of the Mount posed a challenge to the arrogance of human beings.We want to conquer it, not only out of scientific curiosity, but also of inner desire and ambition, as Sir Francis Younghusband put it: “the mount may be high.But he will show that his spirit is higher.And he will not be content until he has it in subjection under his feet.”

To me, climbing the Mount Himalaya is, not the “I came, I conquered,” but “I tried, I succeeded.”

I posted below paragraphs somewhere else but thought this was a pretty good summary for the Psychopath inspite of its rush writing.

Keith Ablow is a forensic psychiatrist. Pyschopath is his second best-seller book. It is about the psychopathological characteristics of a serial highway killer.

The novel is not for thrilling (although inexperienced readers may find the killing scary), instead it seems a teaching material to me. There are many good examples on how to interpret other people’s minds.

Ablow is not good at plot, unfortunately. Nevertheless, this weakness is compensated by his professional handling of psychopathological analysis. There are myriads of examples about child abuse, as the murderer is a child psychiatrist. It is a good reading about child development and how abuse may lead to violence.

Admittedly, the novel belongs to psychoanalysis, but in a modern way. In fact, this is probably the way current FBI and other psychoanalysts are using to crack down criminals, as Ablow himself had served as chief psychiatrist in justice department.

The following blog is lengthy (1700 words). Anyone interested may keep reading on for a detailed recount of the plot, and some of my reflections on our own dealing with kids. I also unearthed my childhood memory and glad to discover that there are not much traumas severe enough to trigger my dark side. Obviously, they still had profound influences on my personality development, and to some extent, on my life till now.

The more I read psychology, the more I know myself, the more I appreciate my life, and the more I love my son.

Several months ago, the BTK, a serial murderer in Wichita, Kansas, had been captured. As we all know, all serial murderers are psychopath. But in what way?

Keith R. Ablow, who himself is a well-known forensic psychiatrist, gave us one example of psychologically damaged serial murderer in his book “Psychopath”. This is a book that will chill your bone, unease your nerve, and end up assessing yourself critically.

Not surprisingly, the murderer was also a gifted psychiatrist, so do the hunters.It was a war between an evil psychiatrist and good psychiatrists.

There was no mystery who the serial high way killer was. In fact, the first chapter detailed the cruel killing and mental distortion the murderer experienced and enjoyed.Readers could give their own psychoanalysis on the murderer.The book was more likely for teaching purpose—how a highly intelligent man turned into a serial murderer.

As a traveling doctor, Dr. Jonah Wrens cruised across country, filling short-term vacancies from one hospital to another.He enjoyed working with new people in different places every several weeks.However, driving in the middle of night, the physical isolation and emotional loneliness made him overwhelmingly angry and thirsty for blood.On the other hand, he never killed persons selectively.He would approach a stranger gracefully and deceitfully.He wanted to know every bit of his/her life. If satisfied, he would not kill him/her.There was one occasion during which he made sex with his victim instead of killing her because she was nice and opened her heart to him completely. Unfortunately, most people would shun him away when approached too aggressively. He would be agitated and then kill them.The random killing relieved his tension, and most importantly, integrated his victims into himself.

As a dedicated child psychiatrist, Jonah showed his exceptional sympathy to his patients.His charismatic appearance and hypnotic voice always encouraged them to open their mind.For example, when he counseled the daughter of his last victim, he cried with her and convinced her that although her mother was dead physically, she would live inside her heart forever because they loved each other.Indeed, he thought all his patients were related to himself in blood. He loved his patients and literally lived in their pains.

After Jonah noticed that the forensic psychiatrist, Dr. Frank Clevenger, was hired to trace him, he wrote a public letter to the New York Times to challenge Frank.He knew Frank recently adopted a boy who was a victim of childhood abuse.He surmised, correctly, that Frank also had traumatic experience during his childhood.He further inferred, correctly again, that Frank’s love of forensic psychiatry and the adoption of the boy reflected his desire to dark side.He concluded that Frank was not much different from himself.

Frank was a brave man.He fought back by revealing his own childhood and by acknowledging his dark side.However, he pointed out that the vital difference between he and Jonah was that he himself turned his dark desire for good purpose, while Jonah turned his to Satan.

Interestingly, Jonah believed that God had a purpose for him.The Lord would save him by sending him an angel.He pleaded Frank to heal him.He described that he was abused by his father. For instance, he was beaten up severely by his father after his fourth birthday party.His Hot Wheels were crushed and he felt helpless.His beloved mother was also crying in the other side of room.Although this seemed reasonable, Frank and his son, Billy, discovered that Jonah was lying.It was not his father but his mother who abused Jonah.Frank believed that Jonah’s mother had psychological problems.She behaved like half angel and half devil.The conflicting characteristics of his mother confused Jonah and made him wish he had only the angel side of his mother.Frank encouraged Jonah to be strong and face the reality.

Jonah was ferocious and hurt.He started to make mistakes.He decapitated an old woman near the hospital he stayed, which confirmed Frank’s hypothesis that he was troubling with his mother.Jonah made another mistake to let a patient’s family took him back home ignoring the possibility that the patient would be beaten up again by his mother, a psychotic mother whom Jonah insightfully discovered.The FBI psychiatrist, Dr. McCormick, later pointed out to Jonah that he was projecting his patient to himself, and wishing the patient’s father would stand up for the boy.He would not be forgiven for the patient’s death.

Dr. McCormick’s revelation finally pushed Jonah into a psychotic state.He fled home to confront his mother, with an intention to kill her, only to find that she was a pure angel now. She regretted her mistreatment to him and pleaded for his forgiveness.Meanwhile, his home was surrounded by FBI agents.Jonah felt desperate but also relieved.He believed that God finally saved him.He committed suicide in front of Frank.There goes the whole story.

Although many of Freud’s ideas have been dismissed by contemporary psychologists, in particular by behaviorists, one idea survives and is even accoladed.That is, one’s childhood experience will have life-long effects on his/her mental development including personality and emotion. Most criminals suffered childhood abuse or had no parents to love them.The lack of love turned to the hatred to innocent people.Many, like Jonah Wrens, found their internal tension relieved from violence.The weakness in their personality leads them to offensive behaviors.

In reality, I believe that the results of psychological analysis for BTK are more complicated that that of Jonah.Nonetheless, in terms of religious beliefs, there were stark similarities between Jonah and BTK in Kansas.Both were religious people believing that God used the victims to teach him and the world lessons.Both internalized their thirsty for blood through religion.Jonah constantly sought for redemption, and BTK diligently served his church and treated himself as God Himself.

Fortunately, it seems that everybody has a good part in his/her heart, even among criminals.Frank Clevenger turned his dark desire for good use.In reality, an Atlanta woman, herself just reborn from misery, saved a rapist and murderer from going down to the hell by reading a religious book to him.The criminal admired her and believed that she was an angel sent from God to save him.He turned himself to authority, which testified that the mighty God is still living within us, hopefully.

Having written thus far, I felt this essay is not complete without some reflections on our own lives. Have we done anything wrong to our children?What if…?

Thank God, for most families do not abuse their children.However, no one is a saint.As a father myself, I know that there are occasions when parents are so despaired and irritated that they could not control their emotion.Sometimes my son refused to sleep while both my wife and I had too much things to do (e.g., final exams).We went mad at him and he cried hopelessly.It always ended up so miserably that we all completely exhausted in the middle of night, back studying for the whole night, resenting each other, and wishing we never married.Even though my son is big now, similar incidences still happen.This is the life, as I always told my wife and myself.

Children are very sensitive.They can sense something is happening and parents are ignoring them.The fear of being abandoned grasps their minds but they don’t know how to express it.Parents don’t know how to communicate with him either (and often children could not understand it).I don’t know how this kind of impulsiveness will affect child’s development.However, I believe that if the traumas are severe enough, they may have unwanted effects.

When I looked inside my heart, back as far as when I was four years old, I find there are only very few incidences I can remember, and some are indeed heartbreaking.I remember that I was always very sad and lonely because no kid wanted to play with me partly because there were not many kids around, partly because I behaved differently from others. I didn’t like physical activities such as fighting and running around.I didn’t play dirty mud and stones which were almost the only stuff you could do in a rural place.I recall that I overreacted when my older sister started her school.We had a fierce fight in her first school morning.I tore her books and kicked her like a mad boy.Surely, my father spanked me but luckily I didn’t remember how badly he hit me.Superficially, I might be jealous of my sister because she could go to school while I had to stay at home.Deeply, I might fear of losing her because she was the only companion during most of the day. Retrospectively, this, I believe, may cause my forever longing for friends but always failing to establish and maintain friendship (I found this is a characteristic of many giants too, e.g. Benjamin Franklin and our Chairman Mao).

Fortunately, all my bad memories, beside unreasonable hunger, are at this level, not traumatic enough to trigger my dark side.Furthermore, there seems to be more happy moments than miserable ones.

Nevertheless, childhood traumas are not easy to heal.In fact, even happy memory can have profound influences.All my childhood memory, good or bad, are associated with extraordinary events.Those happy incidences were mostly resulted from indirect deprivation.For example, I still remember the joy of eating meats and trying new cloths at every new year eve and my parents’ hearty laughter during that time.It was registered in my memory as happy events not only because it was happy but also because it was the compensation for the lasting deprivation.They constantly remind me to be frugal.This further leads my inclination to the over-compensation to my son.I am now too liberal to my son’s desire for toys and books.Meanwhile, I kept warning him not wasting my money. I am not sure how this will affect my son (I am implementing money management training for him now).

I wish there will be no major traumas inscribed in my son’s mind.I recently threw a lavish birthday party for him (admittedly, it cost me almost $1000, which also left a memory in my mind).He seemed very happy about that.I hope that happy feeling will stay in his memory forever.

Two days ago, an Ohio high school graduate shot his family members and friends to death in his graduation day. Two months ago, a Minnesota high school student killed several of his classmates.Why did these tragedies happen?We all want to know.

The May 27 Science Magazine published a report suggesting that earlier firearm violence exposure could cause later serious violent behavior. This is not much surprising, as other studies have already reached similar conclusion.However, the strong word—“cause” that authors from U of Michigan used in the title unnerves many people (and probably that is why it was accepted by the Science which seldom publishes social science reports).

Given recent lessons from hormone replacement therapy, all researchers are skeptical of any strong conclusions from observational studies. Then how could the authors claim the “causal effect” using an observational study?

The magic, as advertised in the paper, was the propensity score method.

Propensity score method was proposed by DB Rubin and his colleagues 20 years ago.It has been underused for a long time but it is getting popular these days. Here is an outline of this method in the context of firearm exposure study.

Over five years, three assessments were conducted every two years among adolescents from 78 Chicago neighborhoods.

At assessment 1, demographic, socioeconomic, behavior and psychological, and health related factors, together with neighborhood characteristics, were assessed. These covariates were used to develop the propensity score.

At assessment 2, firearm exposure status was obtained among these adolescents.Stepwise logistic regressions with the covariates from the first assessment were employed to predict the probability of exposure. The estimated probability is the propensity score. Thus, hundreds of covariates were reduced to one variable—the propensity score.Participants were then grouped into 12 strata based on the propensity score (It is too many.Usually one creates only five groups).

At assessment 3, the perpetrators, the outcome, were defined as those who experienced serious firearm violence during last 12 months.A stratified analysis by propensity score was then conducted to assess the magnitude of association (such as odds ratio). One can also use regression to adjust for residual confounding effects, e.g., small imbalance of covariates within propensity score strata.

The propensity score method is intuitively appealing and has several advantages over model based analysis such as adjustment for all covariates in one regression.

First, the propensity score summarizes many confounding factors (confounders) which are related to both exposure and outcomes.By explicitly exploring the relationship between exposure and confounders, one may discover imbalance among these variables and rectify it.

Second, by conducting stratified analysis for outcomes, one does not assume any association (e.g., linear) between outcome and confounders (in particular the joint distribution of confounders).

Third, one doesn’t have to worry too much about how to adjust hundreds of covariates in the outcome analysis. In the traditional regression analysis, too many covariates cause the dataset too sparse, and may require a large number of outcomes. Using propensity score, one essentially reduces the number of covariates. Note, in developing propensity score, we usually have enough exposed participants as “outcomes.”

Fourth and the most importantly, post-stratifying data based on propensity score is analogous to constructing a random experiment design within an observational study.By balancing propensity score between exposed and unexposed groups, one essentially creates comparable groups similar to those in random trials.As random trials are more valuable than observational studies in assessing causal inference, this feature is certainly desirable.

Now back to the firearm study.Did this study provide enough evidence to suggest a causal-effect link between firearm exposure and subsequent serious violence? There are many standards in assessing causal inference but let’s examine a couple essential criteria relevant to observational studies and to this study.

First, the risk factor must be associated with the outcome.In this study, the statistical significance of the results seems to support this. (Warning: no statistical significance doesn’t mean not causal).

Second, the factor must occur before the outcome.This seems obvious but has often been overlooked.In this study, the exposure did occur before the outcome assessment.However, the exposure is not static in nature.That is, those unexposed at the second assessment can be exposed to firearm during the following years, and vice versa.Nonetheless, because those having outcome were exposed to firearm by definition, exposure switches that occurred in the unexposed group were more likely to attenuate the association rather than strength it (if we believe there is a positive association).Therefore, there is no need to worry about this criterion either.

Third, is it consistent with other studies?Yes, the results from this study were consistent with conclusions from many previous studies.

Fourth, are there any experimental studies that can confirm the results?Well, there is no way to conduct experimental studies on this kind problem. The authors undertook indirect ways such as propensity score method to construct an “experimental” study.However, the propensity score only balances those known confounders.Unobservable factors are not accounted for in the method. Furthermore, although the paper includes more than one hundred candidate variables in the model for propensity score, they used stepwise logistic regression to select only 48 covariates (including quadratic terms) in the final model, which is questionable.Unfortunately, they didn’t provide the goodness-of-fit statistic for the final logistic regression.We didn’t know how well the estimated propensity score reflects the true probability of exposure.

In addition, the propensity score method is most useful in large dataset which can provide sufficient exposed and unexposed observations within each propensity stratum (i.e., overlapping observations within propensity score). However, because 20% participants dropped out of the study after the second assessment, there were only 210 exposed participants in the third assessment.In addition, because this study used too many propensity strata (12), the sample size in each stratum was too small and severely unbalanced on exposure status.

The outcome analysis in this report is also questionable.It is possible that some covariates are not significantly related to the exposure in the above stepwise regressions but may be significantly related to the outcome by themselves.Theoretically, those covariates unrelated to exposure (i.e., orthogonal) should not affect the relationship between exposure and outcome.However, reality is far more complicate than statistical theories. Different combinations of variable sets may yield different answers.

Fifth, are there any biological, psychological, or social theories for the association?Well, sort of.For example, social learning theory—learning by observing is a good candidate.However, given the complexity of the social phenomenon, the propensity score adjustment seems too parsimonious. In fact, because so many socioeconomic and psychological factors are related to violence, and because these relationships are naturally dynamic, regression methods used to form the propensity score and to assess the outcome are inevitably inadequate.

Overall, although asserting the “causal” relationship between violence exposure and subsequent serious violent behavior was somewhat overstretching the truth, the report had indeed advanced our knowledge on this arresting social phenomena. Its methodology was better than many previous reports. Nevertheless, for any causal factor whose effects are intertwined with myriads of others, it is never easy to reach a definite conclusion.