Saturday, June 23, 2018

38 g of sardines or 2 fish oil softgels? Let us look at the numbers

The bar chart below shows the fat content of 1 sardine (38 g) canned in tomato sauce, and 2 fish oil softgels of the Nature Made brand. (The sardine is about 1/3 of the content of a typical can, and the data is from Nutritiondata.com. The two softgels are listed as the “serving size” on the Nature Made bottle.) Both the sardine and softgels have some vegetable oil added; presumably to increase their vitamin E content and form a more stable oil mix. This chart is a good reminder that looking at actual numbers can be quite instructive sometimes. Even though the chart focuses on fat content, it is worth noting that the 38 g sardine also contains 8 g of high quality protein.


If your goal with the fish oil is to “neutralize” the omega-6 fat content of your diet, which is most people’s main goal, you should consider this. A rough measure of the omega-6 neutralization “power” of a food portion is, by definition, its omega-3 minus omega-6 content. For the 1 canned sardine, this difference is 596 mg; for the 2 fish oil softgels, 440 mg. The reason is that the two softgels have more omega-6 than the sardine.

In case you are wondering, the canning process does not seem to have much of an effect on the nutrient composition of the sardine. There is some research suggesting that adding vegetable oil (e.g., soy) helps preserve the omega-3 content during the canning process. There is also research suggesting that not much is lost even without any vegetable oil being added.

Fish oil softgels, when taken in moderation (e.g., two of the type discussed in this post, per day), are probably okay as “neutralizers” of omega-6 fats in the diet, and sources of a minimum amount of omega-3 fats for those who do not like seafood. For those who can consume 1 canned sardine per day, which is only 1/3 of a typical can of sardines, the sardine is not only a more effective source of omega-3, but also a good source of protein and many other nutrients.

As far as balancing dietary omega-6 fats is concerned, you are much better off reducing your consumption of foods rich in omega-6 fats in the first place. Apparently nothing beats avoiding industrial seed oils in that respect. It is also advisable to eat certain types of nuts with high omega-6 content, like walnuts, in moderation.

Both omega-6 and omega-3 fats are essential; they must be part of one’s diet. The actual minimum required amounts are fairly small, probably much lower than the officially recommended amounts. Chances are they would be met by anyone on a balanced diet of whole foods. Too much of either type of fat in synthetic or industrialized form can cause problems. A couple of instructive posts on this topic are this post by Chris Masterjohn, and this one by Chris Kresser.

Even if you don’t like canned sardines, it is not much harder to gulp down 38 g of sardines than it is to gulp down 2 fish oil softgels. You can get the fish oil for $12 per bottle with 300 softgels; or 8 cents per serving. You can get a can of sardines for 50 cents; which gives 16.6 cents per serving. The sardine is twice as expensive, but carries a lot more nutritional value.

You can also buy wild caught sardines, like I do. I also eat canned sardines. Wild caught sardines cost about $2 per lb, and are among the least expensive fish variety. They are not difficult to prepare; see this post for a recipe.

I don’t know how many sardines go into the industrial process of making 2 fish oil softgels, but I suspect that it is more than one. So it is also probably more ecologically sound to eat the sardine.

Monday, May 28, 2018

Moderate alcohol consumption’s benefits: Blood flow or hormesis?


Moderate alcohol consumption has been found again and again to be beneficial to health (, , ). Even somewhat pessimistic studies linking alcohol consumption with health suggest that 6 drinks per week is optimal (). One drink is generally defined as: a 4-ounce glass of wine, a 12-ounce bottle or can of beer, or a 1.5-ounce shot of hard liquor. The amounts of ethanol vary, with more in hard liquor: 4 ounces of wine = 10.8 g of ethanol, 12 ounces of beer = 13.2 g of ethanol, and 1.5 ounces of spirits = 15.1 g of ethanol.

Contrary to popular belief, the positive health effects of moderate alcohol consumption have little, if anything, to do with polyphenols such as resveratrol. It is in fact the ethanol content that leads to the positive effects, apparently reducing the incidence of coronary heart disease, diabetes, hypertension, congestive heart failure, stroke, dementia, Raynaud’s phenomenon, and all-cause mortality. Raynaud's phenomenon is associated with poor circulation in the extremities (e.g., toes, fingers), which in some cases can progress to gangrene.

Two main explanations for the positive health effects of moderate alcohol consumption are: (a) that it improves blood flow; and (b) that it improves liver function via hormesis. These two explanations are not mutually exclusive and may both be right. The latter explanation is based on the assumption that often a favorable biological response results from low exposures to toxins and other stressors. This is fundamentally a compensatory adaptation response ().

It is not very easy to find evidence in favor of the first explanation above – that moderate alcohol consumption improves blood flow. An old study by Fewings and colleagues is a welcome exception. The study was published in 1966 in the British Journal of Pharmacology. It is titled: “The effects of ethyl alcohol on the blood vessels of the hand and forearm in man” ().

The figure below, from the study, shows average measures for 5 people who consumed 100 ml of brandy. This is equivalent to about 2 drinks. Each set of points reflects measurements taken at 30-minute intervals. The top graph shows the variation in blood alcohol content over time in mg / 100 ml. The middle graph shows the variation in hand blood flow over time in what the authors reported to be ml / 100 ml / min. The bottom graph shows the variation in forearm blood flow over time in the same scale as hand blood flow.



Many other measures are reported by the authors of the study, including measures in response to direct intra-arterial injection of ethanol. When injected, ethanol appears to have a nonlinear effect, opposite to that of oral consumption at first. Injected ethanol seems to impair blood flow at first, and then improve it significantly after a while.

Oral ethanol intake, through drinking alcoholic beverages, is the main focus of this post.

The authors also show evidence that the improvement in blood flow maintains itself for more than 2 h, and that flow becomes impaired at very high levels of blood alcohol.

So, as we can see, moderate alcohol consumption seems to improve blood flow. Why would this enhance one’s health?

One reason is that many important chemicals flow through the blood, which is about 90 percent water. Among these chemicals are free fatty acids, glucose, vitamins, minerals and oxygen. Without these chemicals, organs cannot operate properly, and in fact their tissues may die rather quickly. For example, for normal function the brain requires 3.3 ml / min of oxygen per 100 g of brain mass.

Another reason is that impaired blood flow seems to be significantly associated with accelerated atherosclerotic plaque growth, via a phenomenon known as endothelial cell apoptosis ().

Wednesday, April 25, 2018

Alcohol consumption, mortality, and cardiovascular disease


The graphs below summarize key results from a study published in April of 2018 by the highly influential journal The Lancet (). The study reported having included at least 599,912 drinkers in the analysis and having recorded 40,310 deaths and 39,018 cardiovascular disease events. The authors of the study concluded that “For all-cause mortality, we recorded a positive and curvilinear association with the level of alcohol consumption, with the minimum mortality risk around or below 100 g per week.



The study was presented as being somewhat pessimistic: one cannot drink as much as previous data suggested. Let’s see. Two drinks of a spirit (e.g., whiskey) served “neat” (i.e., with nothing added to it) will typically add up to about 84 g; or 3 oz. If the alcohol content is 40 percent, such a double drink will contain about 33 g of alcohol. So, according to this study, you can still enjoy three double drinks of spirit per week, or six single drinks – which is almost one per day. That is not so little.

This study is consistent with most studies of the effect of alcohol consumption on health, which generally show results in terms of averages within fixed ranges of consumption. For example, they will show average mortality risks for people consuming 1, 2, 3 etc. drinks per day. These studies suggest that there is a J-curve relationship between alcohol consumption and health. That is, drinking a little is better than not drinking; and drinking a lot is worse than drinking a little.

Contrary to popular belief, the positive health effects of moderate alcohol consumption have little, if anything, to do with polyphenols such as resveratrol. Resveratrol, once believed to be the fountain of youth, is found in the skin of red grapes.

It is in fact the alcohol content that has positive effects, apparently reducing the incidence of coronary heart disease, diabetes, hypertension, congestive heart failure, stroke, dementia, Raynaud’s phenomenon, and all-cause mortality. Raynaud's phenomenon is associated with poor circulation in the extremities (e.g., toes, fingers), which in some cases can progress to gangrene.

In most studies of the effects of alcohol consumption on health, the J-curves emerge from visual inspection of the plots of averages across ranges of consumption. Rarely you find studies where nonlinear relationships are “discovered” by software tools such as WarpPLS (), with effects being adjusted accordingly.

Still, this study is indeed consistent with some past studies suggesting that the amount of alcohol intake that is optimal maybe less than most of us think ().

Sunday, February 25, 2018

Baked cod and lobster


Many years ago I lost 60 lbs (27 kg) over a period of about 2-3 years, and kept it off. Often people are surprised when I show them an old picture of myself, where I am visibly obese ().

I have always felt that one of the keys to losing a significant amount of body fat without triggering body starvation responses is to eat a diet that has a high nutrient-to-calorie ratio. The baked cod and lobster dish below, with photos before and after baking, is a good example of a meal in such a diet.





This is a fairly simple meal to prepare; simple and delicious. The cost of this dish goes down significantly if you do not include the lobster. Below is a recipe. I used it to prepare the baked cod and lobster shown on the photos above.

- Cut and spread on two sheet pans about 4 tomatoes, 1 cup of onion, 1 cup of spinach, 2 lbs of cod, and 4 lobster tails (approx. 4 oz each).

- Add some butter to the mix. I recommend more butter on the lobster than on the cod.

- Preheat the oven to 350 degrees Fahrenheit.

- Add seasoning to taste. I suggest using a small amount of salt, and some chili powder, garlic powder, cayenne pepper, and herbs.

- Bake for about 30 minutes, or until the lobster is soft.

Let us say you are hungry, so you eat about one-fourth of all of this. That is one lobster tail and about a quarter of the cod dish. The nutrition content of such a meal is shown below.



So you will be getting about 86 g of protein in this one single meal. The vitamins and mineral contents listed are mostly above 100 percent of the usually recommended intake. All of this while taking in only a little over 500 calories.

It is very difficult to get fat eating like this!

Tuesday, October 24, 2017

Could the low testosterone problem be a mirage?


Low testosterone (a.k.a. “low T”) is caused by worn out glands no longer able to secrete enough T, right? At least this seems to be the most prevalent theory today, a theory that reminds me a lot of the “tired pancreas” theory () of diabetes. I should note that this low T problem, as it is currently presented, is one that affects almost exclusively men, particularly middle-aged men, not women. This is so even though T plays an important role in women’s health.

There are many studies that show associations between T levels and all kinds of diseases in men. But here is a problem with hormones: often several hormones vary together and in a highly correlated fashion. If you rely on statistics to reach conclusions, you must use techniques that allow you to rule out confounders; otherwise you may easily reach wrong conclusions. Examples are multivariate techniques that are sensitive to Simpson’s paradox and nonlinear algorithms; both of which are employed, by the way, by modern software tools such as WarpPLS (). Unfortunately, these are rarely, if ever, used in health-related studies.

Many low T cases may actually be caused by something other than tired T-secretion glands, perhaps a hormone (or set of hormones) that suppress T production; a T “antagonist”. What would be a good candidate? The figure below shows two graphs. It is from a study by Starks and colleagues, published in the Journal of the International Society of Sports Nutrition in 2008 (). The study itself is not directly related to the main point that this post tries to make, but the figure is.



Look at the two graphs carefully. The one on the left is of blood cortisol levels. The one on the right is of blood testosterone levels. Ignore the variation within each graph. Just compare the two graphs and you will see one interesting thing – cortisol and testosterone levels are inversely related. This is a general pattern in connection with stress-induced cortisol elevations, repeating itself over and over again, whether the source of stress is mental (e.g., negative thoughts) or physical (e.g., intense exercise).

And the relationship between cortisol and testosterone is strong. Roughly speaking, an increase in cortisol levels, from about 20 to 40 μg/dl, appears to bring testosterone levels down from about 8 to 5 ηg/ml. A level of 8 ηg/ml (the same as 800 ηg/dl) is what is normally found in young men living in urban environments. A level of 5 ηg/ml is what is normally found in older men living in urban environments.

So, testosterone levels are practically brought down to almost half of what they were before by that variation in cortisol.

Chronic stress can easily bring your cortisol levels up to 40 μg/dl and keep them there. More serious pathological conditions, such as Cushing’s disease, can lead to sustained cortisol levels that are twice as high. There are many other things that can lead to chronically elevated cortisol levels. For instance, sustained calorie restriction raises cortisol levels, with a corresponding reduction in testosterone levels. As the authors of a study () of markers of semistarvation in healthy lean men note, grimly:

“…testosterone (T) approached castrate levels …”

The study highlights a few important phenomena that occur under stress conditions: (a) cortisol levels go up, and testosterone levels go down, in a highly correlated fashion (as mentioned earlier); and (b) it is very difficult to suppress cortisol levels without addressing the source of the stress. Even with testosterone administration, cortisol levels tend to be elevated.

Isn't possible that cortisol levels go up because testosterone levels go down - reverse causality? Possible, but unlikely. Evidence that testosterone administration may reduce cortisol levels, when it is found, tends to be rather weak or inconclusive. A good example is a study by Rubinow and colleagues (). Not only were their findings based on bivariate (or unadjusted) correlations, but also on a chance probability threshold that is twice the level usually employed in statistical analyses; the level usually employed is 5 percent.

Let us now briefly shift our attention to dieting. Dieting is the main source of calorie restriction in modern urban societies; an unnatural one, I should say, because it involves going hungry in the presence of food. Different people have different responses to dieting. Some responses are more extreme, others more mild. One main factor is how much body fat you want to lose (weight loss, as a main target, is a mistake); another is how low you expect body fat to get. Many men dream about six-pack abs, which usually require single-digit body fat percentages.

The type of transformation involving going from obese to lean is not “cost-free”, as your body doesn’t know that you are dieting. The body “sees” starvation, and responds accordingly.

Your body is a little bit like a computer. It does exactly what you “tell” it to do, but often not what you want it to do. In other words, it responds in relatively predictable ways to various diet and lifestyle changes, but not in the way that most of us want. This is what I call compensatory adaptation at work (). Our body often doesn’t respond in the way we expect either, because we don’t actually know how it adapts; this is especially true for long-term adaptations.

What initially feels like a burst of energy soon turns into something a bit more unpleasant. At first the unpleasantness takes the form of psychological phenomena, which were probably the “cheapest” for our bodies to employ in our evolutionary past. Feeling irritated is not as “expensive” a response as feeling physically weak, seriously distracted, nauseated etc. if you live in an environment where you don’t have the option of going to the grocery store to find fuel, and where there are many beings around that can easily kill you.

Soon the responses take the form of more nasty body sensations. Nearly all of those who go from obese to lean will experience some form of nasty response over time. The responses may be amplified by nutrient deficiencies. Obesity would have probably only been rarely, if ever, experienced by our Paleolithic ancestors. They would have never gotten obese in the first place. Going from obese to lean is as much a Neolithic novelty as becoming obese in the first place, although much less common.

And it seems that those who have a tendency toward mental disorders (e.g., generalized anxiety, manic-depression), even if at a subclinical level under non-dieting conditions, are the ones that suffer the most when calorie restriction is sustained over long periods of time. Most reports of serious starvation experiments (e.g., Roy Walford’s Biosphere 2 experiment) suggest the surfacing of mental disorders and even some cases of psychosis.

Emily Deans has a nice post () on starvation and mental health.

But you may ask: What if my low T problem is caused by aging; you just said that older males tend to have lower T? To which I would reply: Isn’t possible that the lower T levels normally associated with aging are in many cases a byproduct of higher stress hormone levels? Take a look at the figure below, from a study of age-related cortisol secretion by Zhao and colleagues ().



As you can see in the figure, cortisol levels tend to go up with age. And, interestingly, the range of variation seems very close to that in the earlier figure in this post, although I may be making a mistake in the conversion from nmol/l to ηg/ml. As cortisol levels go up, T levels should go down in response. There are outliers. Note the male outlier at the middle-bottom part, in his early seventies. He is represented by a filled circle, which refers to a disease-free male.

Dr. Arthur De Vany claims to have high T levels in his 70s. It is possible that he is like that outlier. If you check out De Vany’s writings, you’ll see his emphasis on leading a peaceful, stress-free, life (). If money, status, material things, health issues etc. are very important for you when you are young (most of us, a trend that seems to be increasing), chances are they are going to be a major source of stress as you age.

Think about individual property accumulation, as it is practiced in modern urban environments, and how unnatural and potentially stressful it is. Many people subconsciously view their property (e.g., a nice car, a bunch of shares in a publicly-traded company) as their extended phenotype. If that property is damaged or loses value, the subconscious mental state evoked is somewhat like that in response to a piece of their body being removed. This is potentially very stressful; a stress source that doesn’t go away easily. What we have here is very different from the types of stress that our Paleolithic ancestors faced.

So, what will happen if you take testosterone supplementation to solve your low T problem? If your problem is due to high levels of cortisol and other stress hormones (including some yet to be discovered), induced by stress, and your low T treatment is long-term, your body will adapt in a compensatory way. It will “sense” that T is now high, together with high levels of stress.

Whatever form long-term compensatory adaptation may take in this scenario, somehow the combination of high T and high stress doesn’t conjure up a very nice image. What comes to mind is a borderline insane person, possibly with good body composition, and with a lot of self-confidence – someone like the protagonist of the film American Psycho.

Again, will the high T levels, obtained through supplementation, suppress cortisol? It doesn’t seem to work that way, at least not in the long term. In fact, stress hormones seem to affect other hormones a lot more than other hormones affect them. The reason is probably that stress responses were very important in our evolutionary past, which would make any mechanism that could override them nonadaptive.

Today, stress hormones, while necessary for a number of metabolic processes (e.g., in intense exercise), often work against us. For example, serious conflict in our modern world is often solved via extensive writing (through legal avenues). Violence is regulated and/or institutionalized – e.g., military, law enforcement, some combat sports. Without these, society would break down, and many of us would join the afterlife sooner and more violently than we would like (see Pinker’s take on this topic: ).

Sir, the solution to your low T problem may actually be found elsewhere, namely in stress reduction. But careful, you run the risk of becoming a nice guy.

Friday, September 29, 2017

Gaining muscle and losing fat at the same time: Various issues and two key requirements

In a previous post (), I mentioned that the idea of gaining muscle and losing fat at the same time seems impossible to most people because of three widely held misconceptions: (a) to gain muscle you need a calorie surplus; (b) to lose fat you need a calorie deficit; and (c) you cannot achieve a calorie surplus and deficit at the same time.

The scenario used to illustrate what I see as a non-traumatic move from obese or seriously overweight to lean is one in which weight loss and fat loss go hand in hand until a relatively lean level is reached, beyond which weight is maintained constant (as illustrated in the schematic graph below). If you are departing from an obese or seriously overweight level, it may be advisable to lose weight until you reach a body fat level of around 21-24 percent for women or 14-17 percent for men. Once you reach that level, it may be best to stop losing weight, and instead slowly gain muscle and lose fat, in equal amounts. I will discuss the rationale for this in more detail in my next post; this post will focus on addressing the misconceptions above.


Before I address the misconceptions, let me first clarify that, when I say “gaining muscle” I do not mean only increasing the amount of protein stored in muscle tissue. Muscle tissue is mostly water, by far. An important component of muscle tissue is muscle glycogen, which increases dramatically with strength training, and also tends to increase the amount of water stored in muscle. So, when you gain muscle, you gain a significant amount of water.

Now let us take a look at the misconceptions. The first misconception, that to gain muscle you need a calorie surplus, was dispelled in a previous post featuring a study by Ballor and colleagues (). In that study, obese subjects combined strength training with a mild calorie deficit, and gained muscle. They also lost fat, but ended up a bit heavier than at the beginning of the intervention. Another study along the same lines was linked by Clint (thanks) in the comments section under the last post ().

The second misconception, that to lose fat you need a calorie deficit; is related to the third, that you cannot achieve a calorie surplus and deficit at the same time. In part these misconceptions are about semantics, as most people understand “calorie deficit” to mean “constant calorie deficit”. One can easily vary calorie intake every other day, generating various calorie deficits and surpluses over a week, but with no overall calorie deficit or surplus for the entire week. This is why I say that one can achieve a calorie surplus and deficit “at the same time”. But let us make a point very clear, most of the evidence that I have seen so far suggests that you do not need a calorie deficit to lose fat, but you do need a calorie deficit to lose structural weight (i.e., non-water weight). With a few exceptions, not many people will want to lose structural weight by shedding anything other than body fat. One exception would be professional athletes who are already very lean and yet are very big for the weight class in which they compete, being unable to "make weight" through dehydration.

Perhaps the most surprising to some people is that, based on my own experience and that of several HCE () users, you don’t even need to vary your calorie intake that much to gain muscle and lose fat at the same time. You can achieve that by eating enough to maintain your body weight. In fact, you can even slowly increase your calorie intake over time, as muscle growth progresses beyond the body fat lost. And here I mean increasing your calorie intake very slowly, proportionally to the amount of muscle you gain; which also means that the incremental increase in calorie intake will vary from person to person. If you are already relatively lean, at around 21-24 percent of body fat for women and 14-17 percent for men, gaining muscle and losing fat in equal amounts will lead to a visible change in body composition over time () ().

Two key requirements seem to be common denominators for most people. You must eat protein regularly; not because muscle tissue is mostly protein, but because protein seems to act as a hormone, signaling to muscle tissue that it should repair itself. (Many hormones are proteins, actually peptides, and also bind to receptor proteins.) And you also must conduct strength training to the point that you are regularly hitting the supercompensation window (). This takes a lot of individual customization (). You can achieve that with body weight exercises, although free weights and machines seem to be generally more effective. Keep in mind that individual customization will allow you to reach your "sweet spots", but that still results will vary across individuals, in some cases dramatically.

If you regularly hit the supercompensation window, you will be progressively spending slightly more energy in each exercise session, chiefly in the form of muscle glycogen, as you progress with your strength training program. You will also be creating a hormonal mix that will increase the body’s reliance on fat as a source of energy during recovery. As a compensatory adaptation (), your body will gradually increase the size of its glycogen stores, raising insulin sensitivity and making it progressively more difficult for glucose to become body fat.

Since you will be progressively spending slightly more energy over time due to regularly hitting the supercompensation window, that is another reason why you will need to increase your calorie intake. Again, very slowly, proportionally to your muscle gain. If you do not do that, you will provide a strong stimulus for autophagy () to occur, which I think is healthy and would even recommend from time to time. In fact, one of the most powerful stimuli to autophagy is doing strength training and fasting afterwards. If you do that only occasionally (e.g., once every few months), you will probably not experience muscle loss or gain, but you may experience health improvements as a result of autophagy.

The human body is very adaptable, so there are many variations of the general strategy above.

Thursday, September 7, 2017

PLS Applications Symposium; 11 - 13 April 2018; Laredo, Texas


PLS Applications Symposium; 11 - 13 April 2018; Laredo, Texas
(Abstract submissions accepted until 15 February 2018)

*** Health researchers ***

The research techniques discussed in this Symposium are finding growing use among health researchers. This is in part due to steady growth in the use of the software WarpPLS (visit: http://warppls.com) among those researchers. For those interested in learning more, a full-day workshop will be conducted (see below).

*** Only abstracts are needed for the submissions ***

The partial least squares (PLS) method has increasingly been used in a variety of fields of research and practice, particularly in the context of PLS-based structural equation modeling (SEM). The focus of this Symposium is on the application of PLS-based methods, from a multidisciplinary perspective. For types of submissions, deadlines, and other details, please visit the Symposium’s web site:

http://plsas.net

*** Workshop on PLS-SEM ***

On 11 April 2018 a full-day workshop on PLS-SEM will be conducted by Dr. Ned Kock and Dr. Geoffrey Hubona, using the software WarpPLS. Dr. Kock is the original developer of this software, which is one of the leading PLS-SEM tools today; used by thousands of researchers from a wide variety of disciplines, and from many different countries. Dr. Hubona has extensive experience conducting research and teaching topics related to PLS-SEM, using WarpPLS and a variety of other tools. This workshop will be hands-on and interactive, and will have two parts: (a) basic PLS-SEM issues, conducted in the morning (9 am - 12 noon) by Dr. Hubona; and (b) intermediate and advanced PLS-SEM issues, conducted in the afternoon (2 pm - 5 pm) by Dr. Kock. Participants may attend either one, or both of the two parts.

The following topics, among others, will be covered - Running a Full PLS-SEM Analysis - Conducting a Moderating Effects Analysis - Viewing Moderating Effects via 3D and 2D Graphs - Creating and Using Second Order Latent Variables - Viewing Indirect and Total Effects - Viewing Skewness and Kurtosis of Manifest and Latent Variables - Viewing Nonlinear Relationships - Solving Collinearity Problems - Conducting a Factor-Based PLS-SEM Analysis - Using Consistent PLS Factor-Based Algorithms - Exploring Statistical Power and Minimum Sample Sizes - Exploring Conditional Probabilistic Queries - Exploring Full Latent Growth - Conducting Multi-Group Analyses - Assessing Measurement Invariance - Creating Analytic Composites.

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Ned Kock
Symposium Chair
http://plsas.net