tttjjj/elt_bench huggingface dataset:
My fear was the (weak) dependency. I noticed a detailed answer here: http://stats.stackexchange.com/questions/4517/regression-with-multiple-dependent-variables so, I guess my question is a duplicate.
@PeterFlom: This is correct if you base the PCA on the VC-matrix (and not on the correlation matrix)
Was your question answered ?If you need help let me know.
@user3671 I modified the answer to allow including additional school variables.  I don't see how you could add additional student variables unless you include students who passed as well.  If you had that data as well, the school data could be bound to the individual students and their respective pass/fail would be the dependent variable.  Also, I agree with the comment above that this looks like a binary problem as a student can only pass or fail.  Finally, in hind-sight this is not a Bayesian solution as you had specified.
@deinst: I posted below what I understood from your explanation.
@SimonHayward, I've updated with a few more examples. It appears the Parallel sets application has the behavior you want as opposed to the Fineo application.
That's a good observation about the constant injury rate. I was thinking, though, that this question could be answered (in the negative) even without looking at the numbers. Suppose (hypothetically) the injury rates did vary.  What would justify the conclusion that *job function* is the cause?  Maybe the departments are housed in different areas and location is the cause, for instance.  Thus, although department could be *associated* with injury rates, we still could not justify any causal--"due to"--conclusions based on such data.
By "... and *it* is also a (nonlinear) function of age and gender...", I assume you mean that the best estimate of the estimated baseline value is a function of age & gender, not that X is a function of age & gender. Is that right?
With only 8 cases you cannot even estimate the intercept in a model with no predictors.  The only thing you could possibly estimate would be the proportion of $Y=1$ along with a 0.95 Wilson confidence interval.
This question appears to be off-topic because it is about searching for an R package.
+1, however "automatically get taken care of" isn't quite true (at least in the immediate situation, which is what you primarily care about). It is true in the long run, but you still can very much have type I & type II errors due to sampling error (ie, patients in 1 treatment condition tended to have more severe diseases by chance alone).
@Dougal thankyou, I originally had 2/9 for the probability and then had to go through the whole post correcting it and missed one!
Sometimes people do this, but it's problematic.  The issue is that the quality of *any* spatial interpolation relies on spatial correlation, which tends to decrease with distance ("Tobler's First Law of Geography").  If you split randomly, you tend to increase average distances (by about $\\sqrt{2}$ on average), degrading the quality.  If you split spatially (e.g., east versus west), you introduce a confounder (because the correlation of terrain in one half could differ from that in the other half).  That's why *jackknifing* (leave-one-out cross-validation) is usually recommended here.
If the outcome is binary, you don't want Cox -  Cox is for cases where the outcome is time and is censored. But do you have one observation per person or multiple observation? If the latter (which I think it is) you need to account for that, perhaps with a nonlinear mixed model.

But I think you need to clarify what data you have and what you want to find out.
I am still not entirely sure how it is different. Isn't it also possible to have the independence assumption in $P(T|W)$?  $P(T_1|W_1) * P(T_1|W_2)$... etc.
"_If you have a lot of variables that you are profiling over, then if the number of data points per dimension is low, the profile likelihood can be very biased and optimistic_" Optimistic compared to what?
Just a programming note: it is useless (and will slow down your script) to create a function that just calls another function. There is no real advantage in calling `find_domain` if the only thing it does it's calling `grep`. You are just adding the overhead of another function call.
+1 Very interesting comments.  As far as the borderline becoming "blurred," I take that as a correct statement about *perception,* but there is no blurriness in the definitions themselves: the distinction between parametric and non-parametric is as clear and sharp as that between, say, finite and infinite.
+1 Welcome to our site, htr!
You are right. I'm using Matlab to do the computation and the covariance function `cov` computes covariance by row, while I thought it was by column. Then mistakenly, without checking the covariance matrix size, I assumed that the `svd` function did some "magic" (taking into account that $p>n$), instead of checking that the dimensions make sense. If I could, I would downvote my own question! Thanks for your time.
Zen, your answer is _way_ too complicated. My idea was to note that $x+y=z$ is at distance $z/\\sqrt{2}$ from the origin, and so after rotation we have that $$F_Z(z) = P\\{Z \\leq z\\} = P\\{X \\leq z/\\sqrt{2}\\} = F_X(z/\\sqrt{2}).$$  Thus, $$f_Z(z) = \\frac{1}{\\sqrt{2}}f_X\\left(\\frac{z}{\\sqrt{2}}\\right)$$ where $f_X(x)$ is easy to determine by inspection: it is the cross-sectional area of the joint pdf solid at $x$, which area (being that of a rectangle of height $\\frac{1}{\\pi}$ and width  $2\\sqrt{1-x^2}$) is easily calculated. So I say, "Look, Ma! It's easy! No integration needed!"
Hmm...b0 and b1 will likely be in the millions and tau is likely less than 0.01.  That would place your truncation interval [0,10] a gazillion standard deviations away from the mean, making its total probability equal to about exponential(-gazillion^2), which is guaranteed to underflow.  This suggests that rethinking some of the prior parameters might help.  But why use a truncated normal?  It's not very flexible anyway.  Why not a (scaled) beta or even a mixture of betas?
I don't think it's particularly insensitive; I'd say it's more sensitive there than the Lilliefors test, for example, and I'm having trouble thinking of another comparable goodness of fit test in wide use that I think will be much more sensitive to the tails. Do they say how this sensitivity was measured or what it was compared to? Does the paper give any justification or context for the claim at all?
I don't know what "analogy" you have in mind. The point is that there is no such analogy. If you are guessing that the Cox-Wermuth limit applies to linear regression with a continuous response and binary predictors, then that's not so. I've already given a counter-example.
You (almost) always will do a good deal better on the training data than the test data, since you optimize the fit on the training data.
+1 This is relatively simple to do and very handy!
I did remove some predictors that the lrm told me were not significant, and I did not pass the original model to validate, but the latter one without those predictors. Am I doing it wrong? Should I pass the model with all predictors? Also I should note that what I'm trying to do is to determine which grammatical factors have a significant correlation with construction A or B, and if this correlation could be extended beyond the data I have. I don't really need to go beyond that. Thanks again for your answers.
Using more hidden layers will increase complexity in the network architecture which in turns increase the training time
Hi Gary. A fellow post doc in this behavior field has suggested that if re-fitting the transformed data does not give normality in residuals, we can then to a simple non-parametric such as Kruskal Wallis and compare results to a Mixed/Glimmix ( SAS mixed models). WPlease see my above comments on the purpose of my data just in case you are wondering. Thanks
I cannot see how $\\sim$ could be equated with $\\in$: the former names a *random variable* whose distribution is determined by a *particular* tuple of parameters $(u,\\sigma^2)$ whereas the latter is a *generic* element of a set of *distributions*. I suppose you could (rigorously) write "$Y\\in\\{X|X\\sim \\mathcal{N}(u,\\sigma^2)\\}$"--but that even more clearly shows the distinction between $\\sim$ ("has a distribution given by") and $\\in$ ("is an element of").
There are non-parametric tests, but they have a very different null hypothesis.
I'm doing basic descriptive analysis on a data set which is pretty complex too. I'm just plotting the dependent measures against the factors now though, trying to see if there are any interesting patterns... Would be great if there are more ways to describe the data!
See [this](http://en.wikipedia.org/wiki/Likelihood_function#Continuous_probability_distribution) for more details regarding my answer, and [this](http://en.wikipedia.org/wiki/Likelihood_function#Likelihoods_for_continuous_distributions) for (I think) more details regarding @procrastinator's.
Entirely possible and indeed very common. Significance of predictors will depend on what else is in the model. Should be discussed in any decent regression text or course. Similar issues discussed at http://stats.stackexchange.com/questions/14500/how-can-a-regression-be-significant-yet-all-predictors-be-non-significant
What is the model that you are considering? A linear regression model? In structural equation modeling, you'd want to drop a variable if it is uncorrelated with other variables, and keep only the highly correlated one. Please clarify, edit your question, and make a more generous use of tags.
Got `table` to work using `cut2`. Couldn't get `xtabs` to work. Thanks for the ideas.
check that those boolean values do not sum to the constant. Or easier do `qr(cbind(1,xreg))$rank` and look at the result. If it is less than 100 (99+1), you have multicolinearity issues, which can be solved by removing columns from xreg.
@TooTone, perhaps I didn't express myself clearly... Some of the answers I was expecting were things like: Linear regression, neural networks, SVM...
@user1912925: yes.
Could you create an "attendance" variable that's either the percentage of a "full class" or the percentage of the department that attended? Also, is "(1|pair)" sufficient? I wish I knew enough to make an answer, but I'll bump the question up.
I may have misunderstood your data in my response. I now think I was led astray by the word "initial". Do these numbers represent final outcomes? That is, is 121 the number of people who merely browsed the product page and then dropped off, or does it also include those who clicked, stepped, and completed?
Another characteristic of the Poisson distribution is that its mean and variance are the same.
If you have just one tuning parameter or if, in case of multiple tuning parameters, they are not correlated to each other (which is rarely the case) then your order of averaging is reasonable. If you really want to find out which tuning approach is better for your dataset/model, I would run both tuning approaches and then compare the resulting models on a holdout data set (a "validation" data set not used in training/tuning). This makes sure that you are not "over-tuning" the parameters such that the resulting model may not generalize well on other datasets.
How exactly does plotting the ratios answer the question that the OP speculated (which is in essence that the two series are correlated)?
@Jonathan: Especially in the population (but probably also in the survey) we have data entry errors for age. In the population age was collected from various sources including an overlay from various data vendors, and using seed records, I have confirmed an error rate of about 10%. In the population we have lots of missing values for age (about 40%), and we have a house holding problem: one constituent (donor) is multiple people (example: husband, wife, and kids), some with significantly different ages.  Also we don't know the "primary" for the household, so I'd have to guess which age to use.
@Stas Understanding the question is usually rewarded by getting your answer accepted :-).  The points and badges naturally ensue.  I personally don't think much of answers that are right because the respondent guessed correctly.  A respondent following that strategy is often going to give the right answer to the wrong question, and that's usually worse than not answering at all due to the confusion it causes.  Much of the art of creating a great answer lies in eliciting a clear question.  In fact, the question as first stated often is not the question the OP really wanted to ask.
"At any level of hierarchy" is the key piece of this answer. It's important to realize that models for panel data are a very particular kind of hierarchical model.
THanks for your time. That's a good suggestion to have a look at both versions. I'll definitely do that.
@Randel:  It does in Spanish editions of Excel and I suspect many others.  See [this](http://www.mrexcel.com/forum/excel-questions/385317-semicolon-comma-regional.html) for a discussion
Excel is an awful recommendation for this (Access is defensible). I've never seen a form for excel that was more than a few items, and I have no idea what you are talking about with "excel will automatically generate forms", perhaps you should elaborate and point to some examples.
Because the errors are assumed normal, then the parameter estimates--being linear functions of the data, whence of the errors too--must themselves be normal, implying a normal distribution for $\\hat{v}$.
nlme is mixed effects models - correct? I read that these can be used somewhere else and the R code makes understanding it easier - I will look into it and give feedback.
+1 In an effort to make this argument clearer, I have posted a reply that contains a similar analysis.
There are some inconsistencies in the notation--for instance, what is "c2"?--but overall it seems to me that if by "P(w1)" you mean a single *number* giving the prior chance of "w1", that "w1" and "w2" are the only two possible prior values, and the "action" is tantamount to guessing whether "w1" or "w2" holds--then the Bayes error is a *linear* function of the P(wi).  Because that is trivially concave down (*and* concave up!), I wonder whether I might be misinterpreting this question. Could you set me straight?
If this was an answer and not a comment I would/could accept it.
The coefficient of the covariance term should be $-2$ not $+2$.  Your formula gives the variance of the sum, not the difference.
This question is for Mathoverflow: http://mathoverflow.net/. Seems to be a good question anyway. I remember I saw a generalization of the results in Baraud's paper done by Rozenholc an other collaborators but I can't find the paper anymore...
Where did you read that "glmm's won't perform well like that"? What was the argument? On a different note, be aware that questions that are *only* about how to use software are generally considered off-topic here. This Q strikes me as on-topic, but near the borderline; I don't know if others will disagree.
I edited my post. Note, that I assumed the error to be proportional to the observations as you stated in your first post. You seem to mix it up with the predictions, which can also be used.
Could you please expand the question to show *how* variable A does not meet the assumption of proportionality? I'm guessing you're basing this on residuals, but would be helpful for readers unfamiliar with this difficulty... also [this question](http://stackoverflow.com/questions/14347004/can-i-perform-all-subsets-variable-selection-for-a-cox-proportional-hazards-mode/14667311#14667311) may be helpful.
That is exactly the goal...to find mathematical way to separate two goat horns according to sex because both sexes have them and I don`t know in advance which one is it. Fourier series is commonly used for shape approximation of the complex outlines. LDA do sepatate them, but I can envision only extremes and not the intermediate shapes.
How many dimensions do you have? What classification algorithm do you intend to use?
I wonder whether there is a good way to quantify variability among 3 scores on the individual level.  If you had more variables, individuals' standard deviations among their scores might be a possible candidate to compare between the two schools. With 3 (if all on the same likert scale), sums of absolute differences might be possible. Others might have better suggestions and I'm curious too.
I already have a graphical representation of the data and can see that the usage is concentrated in between 8 and 17 for one case but I have many other cases, I am trying to find if there is any method to accomplish this without me having to manually idenditfy the pattern for every case.
I think what you are looking for is referred to as a stochastic volatility model. I am not terribly familiar with them though. I added some more explanation to my answer.
(1) What is the distinction between "test" and "test task"? (2) Many authors have characterized the t test as *nonparametric* because it only assumes the *sampling distribution* is *approximately* normal *when the null is true.* (3) By definition, "hypotheses" are subsets of all possibilities (the "states"). If the set of states is non-parametric, then the test is non-parametric, period. (4) In your second question you appear to confuse the distribution of the *data* with the distribution of a *test statistic.* Almost all non-parametric tests have parametric statistical distributions!
The text clearly states what $g(y|\\phi)$ is: a "$\\text{family of sampling densities}$", though depending on how you view $\\phi$, you could think of it as a conditional density or a family indexed by $\\phi$. Why would it be a probability? In 4, $\\pi$ is just a parameter there, on which the 4 population probabilities depend.
To get a useful answer, you'll need to provide more information. What does your experiment consist of?
I completely agree. When observing the current craze about Machine Learning (practitioners and programmers mostly), Big Data and "data science", I find it ridiculously common for people to completely ignore sampling, inference, statistical reasoning understanding  and meaning and to sacrifice it for blindly applying whatever algorithm is hip on it. You can even see that with questions and some answers here on cross validated. That's why I also believe it to be a hype that will soon be obsolete or borrow statistical epistemology and thus become a branch of stats (I view it as such anyway).
1. Can you please give us a representative dataset? 2. The `NA`'s is signify you have some singularities in your model. Find out why the `NA`'s occur. 3. Have you checked `garchFit` from `fGarch` package? I just read that some people think it is more robust in some cases than `garch` (this is *not* a statement I have tested).
I added tags marking the question as chemometrics and QSAR.
Minor quibble: You cannot say anything about normality or non-normality based on those 5 quantiles alone. All you can say based on that summary is whether the estimated residuals are approximately symmetric around zero.  You could divide the reported quantiles by the estimated residual standard error and compare these values to the respective quantiles of the N(0,1), but looking at a QQ-plot probably makes more sense.
The answer to http://stats.stackexchange.com/questions/21875/delta-method-and-correlated-variables/21888#21888 will get you started; your problem has four variables and will therefore be more complicated, but the core approach is the same.
Significance is often found with highly colinear variables. The problem is that a small change in the input data can make a large change in the model.
Not exactly -- I think a saturated model used up all its degrees of freedom. It depends on the model what this means exactly. In a log-linear model, for example including all interactions in the model makes it saturated, as df=0, then, but it is not overfitted.
(+1) I (and everyone who gave me an upvote) stand corrected. Well done ! I have worked through your numbers, but I was not able to reproduce (0.481,0.504,0.488), since e.g. $\\frac{1}{2} \\alpha + \\frac{1}{2}\\beta$ for $(\\alpha,\\beta)=(-1,0.85)$ results in -0.075. Your "proof by example" remains of course still correct.
+1 for emphasizing the point that the answer *has* to depend the relationship between the categorical covariate and all the other columns of the design matrix $X$.
+1 Well done!  I appreciate the explanation why this solution is faster.
As a quick comment, adding irrelevant predictors can worsen performance on new data - increased variance of the prediction (over fitting). This is because you end up fitting to noise and dilute the "true signal".
(+1) A little bit hard to read, though (especially for someone seeking R applications).
You should really say something more about how this data was obtained, specifically how the response variable --- use of alcohole --- was defined.
@whuber: I add an example to my answer. About the difficult questions, I suppose that they arise even if you answer refers to the normal distribution (as other answers to this question do), or some other concept. Could be simpler to explain a 50%-trimmed mean? If it is so, then say that the IQR is the length of the range of its observations
Did you find a good solution for multiclass svm?
Such rules will only really be feasible if you fairly precisely define 'reasonably stable' - and even so it will depend on the distributions.
@Corone, thanks that makes sense but what about creating a probability distribution?
Race is categorical. Why would you not use [dummies](http://en.wikipedia.org/wiki/Dummy_variable_%28statistics%29) for Race?
It may be easier for people to help you if you provide a reproducible example that others can run themselves that illustrates this behavior.
Let us assume you are doing classification. You can think of neurons as feature detectors, were the output represents the conditional probability of having that feature. When averaging the weights of different networks, you combine weights that might represent detectors for different features.
Make sure that you do not use an improper accuracy scoring rule such as proportion classified correct, as this rewards inappropriate prediction/models.  And compare with L2 norm.  I'll bet it will be better then the 3 approaches you tried.
It takes a large textbook just to cover special subsets of this problem, such as the recent *Statistics for Spatio-Temporal Data* by Cressie & Wikle. You will need to characterize your data more precisely and provide more context in order to narrow down this question into something that can be answered with less than an entire text.
And you might explain what is it about the problem that made you think that an ROC curve was helpful.
@whuber - valid point. I wasn't trying to suggest density curves were the be all end all method to use, simply offering other alternatives. It is clear from this post that there are pros and cons to any approach, so was offering this up as another viable alternative to throw into the mix.
The M3 data are also available as part of the Mcomp package for R: http://cran.r-project.org/web/packages/Mcomp/
Just adding 0.5 strikes me as a fudge at best; do you have literature or theoretical support for that?
@Scortchi: yes.
Thanks for your input.  I've been doing a bit of research about this today, and I was drifting towards PCR as well.  I'm not sure that I quite understand PLS and PCR yet enough to be confident about executing them, but it does sound like it might make more sense considering my goals.
Nice question. I was going to suggest a Jeffreys prior, but it turns out that's just [a special case of the beta distribution for binomial models](http://www.cs.berkeley.edu/~jordan/courses/260-spring10/lectures/lecture7.pdf).  I'll keep thinking and see if I can come up with any others.  I have some vague sense that there are transformations of Gaussians that work, but Google isn't helping me pin that down.
Hmm.. I'm assuming that when you ask me to create a square matrix for protein interactions, the values in matrix represent number of interactions between proteins. But, I don't see where we are using features here. Can you elaborate on that?