tttjjj/elt_bench huggingface dataset:
Did you read the accompagnying vignette, [Estimation of multinomial logit models in R : The mlogit Packages](http://cran.r-project.org/web/packages/mlogit/vignettes/mlogit.pdf)? It seems to me you just have to apply the fitted coefficients on new data, isn't it?
I think you might want to read about type I error rates and hypothesis testing in general. Non-significant p-values are inconclusive and have anyway do not lead to a type I error. Also, what is "a better result"? Both tests fail to reject the zero hypothesis, meaning that you cannot conclude that the variances you are comparing are different.
Note that the variance of the mean of several variables with equal variance will indeed be smaller than the variance of the original variables. That's the whole point of multi-item scales and the basis for much of classical psychometrics. The underlying idea is that the item-specific variance that gets “lost” in the process is error variance that isn't related to the characteristic you are trying to measure and should be averaged out. Therefore, adding appropriate items gives you a more precise measurement, more powerful comparisons between groups, etc.
I gave my 2 cents to the answer, but I'm not sure if your answer is a typical answer for that site. Let's see what the others think.
This question appears to be off-topic because it is about numerical integration in STATA, not statistics at all.
I slightly edited my post... I am aware that you can use a prediction interval to get general bounds on a set of data, but I'm wondering if you have a non-normal distribution of data, if you can determine the bounds at different regions of the data.
If $C$ was the *reciprocal* of the covariance the result would simply be the squared [Mahalanobis distance](http://en.wikipedia.org/wiki/Mahalanobis_distance). It's probably a typo.
See http://stats.stackexchange.com/questions/8000/proper-way-of-using-recurrent-neural-network-for-time-series-analysis and http://stats.stackexchange.com/questions/9842/getting-started-with-neural-networks-for-forecasting
I don't have an analytic method of solution, but I can verify your simulation using explicit enumeration:  the exact probability is $\\frac{257}{792}$ for your example.  I used *Mathematica*:  `Select[(Sign /@ BinCounts[#, {{1, 6, 9, 11, 13}}]) & /@ Subsets[Range[12], {7}], Total[#] == 3 &] // Length` returns $257$, the desired number of outcomes out of $\\binom{12}{7} = 792$.  I suspect that your question does not have a straightforward closed-form solution for the general case.
$\\propto$ means "proportional to" here: You found out the markup for that, which is a strong clue: see also http://en.wikipedia.org/wiki/Mathematical_symbols. Angle brackets can indicate means; that's dubious here. In any case, giving a source for your quotation never hurts and is often useful.
Do you understand me in the previous comment?any suggestion?
Thanks, that's great. I'm also comparing another set of measurements, so given the average variance I can then ask questions like "How confident am I that the two means are different?"
In this case, why not email Andrew? He might like to redress the omission.
Thank you for your answer. I realize that this would be the most appropriate way to go. Since I already have the data I had 2 options: 1) Think about questions that this data can help answer. 2) Think about answers that particular methods of analysis give you and decide whether they make sense with my current data. The reason I chose to go with the second option was my lack of experience in asking the right questions. Sometimes reverse engineering works wonders.
Given that "$f$" clearly stands for at three very different things in its three appearances in equation (3), and both are conditional probability distributions, it would seem that this letter has been reserved by the authors generically to refer to any probability density function.  $H$ is defined in equation (2) *et seq.*
In the context of this post, 'rescore' means computing the predicted dependent values using new readings of the predictor variables.
@StéphaneLaurent I am not saying that.  I am just saying that for multivariate normal distributions it is easy to calulate ingegrals for elliptical regions but difficult for rectangular ones.
@user603 Here is a simple demo: http://nbviewer.ipython.org/4383682/ ; this relies on fairly recent iPython, I believe.
To add to @iliasfl's good answer, clustering, unlike, e.g., OLS regression, has no single "right" solution, so some variation in cluster membership is to be expected on different trials.
Is your question related to topic models?
Thanks. I'll need some time to digest this, but your help is much appreciated.
You should consider up voting the accepted answer. After all you found that answer useful.
@mbaitoff: You could use Python with `scipy`, especially if you already use Python. If you use/like Clojure (lisp based on JVM, http://clojure.org/), there's the `Incanter` (http://incanter.org/) statistical environment built on that. You could also try gnu Octave.
Just to be clear, this is not an "incorrect" method. It is a simulation-based alternative to the analytic method of `multcomp`. They are both based on the same underlying math. To address your concerns, though, I posted an answer that focuses on `multcomp` more specifically.
I fixed the grammar; I also changed "too" to "so", but perhaps you actually meant "too".
Indeed, one can show via [Schur convexity](http://en.wikipedia.org/wiki/Schur-convex_function), that for *any* nonuniform distribution of birthdays, the probability of a match is at least as great as in the uniform case. This is **Exercise 13.7** of J. Michael Steele, *[The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities](http://www.amazon.com/Cauchy-Schwarz-Master-Class-Introduction-Mathematical/dp/052154677X)*, Cambridge University Press, 2004, **pg. 206**.
@Bruder: 2 thoughts: 1. You could look at a simple naive forecast, rather than a seasonal forecast.  A simple naive forecast just uses the previous value of the time series, and will pick up a strong trend (with a 1-period lag).  2. STL decomposition is a good idea.  If the residuals are very small compared to the seasonal and trend components, then you can probably easily forecast the series.
You raise some interesting questions. I've posted a separate question quoting you: http://stats.stackexchange.com/questions/4466/how-to-increase-longer-term-reproducibility-of-research-particularly-using-r-and
I cannot recommend using "dummy variable adjustment" (aka "a dummy variable can be used just to control for the missing values."). It is known that "this method generally produces biased estimates of the coefficients" ([Allison, Missing Data, p. 10](http://bit.ly/lEyBj8)).
I think what wasn't clear is that my data is discrete. Basically my algorithm (let's forget about the word estimator which has a specific meaning in statistics) spits out a number of $V(t_n)$ values which should be approximately aligned. I'm looking for a measure of this linearity.
Typically, significance is assessed with p-values and normal probability plots are used only to help interpret those p-values (by assessing whether the distributional assumptions needed to compute them are plausibly consistent with the data). I am therefore curious how you would use the normal probability plot directly to "see which effects are significant."  How exactly would that work?
Nothing in the question is indicative of a GOF test because it would require the OP to supply theoretical proportions rather than observed counts (and we couldn't get such a table of expected counts this way).
I found Strang's Linear Algebra and its applications to be extremely useful in understanding the matrix manipulations which form a large part of the elements.
First, I was making a stats joke. But there is a serious point. If you believe the student then the probability is 1.0 because the data have already been observed.
A few weeks ago I was given a paper to review and found that 85% of it had been published in another journal...by the same authors.  That, too, is still considered plagiarism.  For the last several years I have routinely submitted chunks of papers--especially abstracts, introductions, and conclusions--to Web search engines *before* doing any review.  I want to be sure the work is original before I invest any time in reading it.
When it comes to GLMM noone asking questions is considered pejoratively as "a noob". For what its worth, I think this applies to this site generally.
If `*` means include the interaction, I am not sure if you need them all. Deciding on the right model is complex (and discussed here a lot). But I do think including the characteristics in your model building is appropriate.
What does "TAQ" mean?  Trade-and-quote?  DNA polymerase?  The Twitter tag?
Exactly, 2901 new values is nothing for a computer.
Does anyone help me?
It seems you already have an [unregistered account](http://stats.stackexchange.com/users/7910/michelle) on this site, michelle. Can you confirm this? We will merge them but you will need to [register](http://stats.stackexchange.com/faq#login) to take full advantage of SE facilities.
Thanks DaemonMaker. This should help me get started!
I see now. Your link is also informative. I've tried OLS regression and indeed that sheer amount of parameters is difficult to understand. I think I'll just do the very basic using multiple regression (path analysis) and Cronbach's alpha. Thanks anyways!
As far as I can see, my particular problem of TRIVIAL identical distributions is not solved by Shannen-Jensen / Kullback-Leibler. Look!! Sum_i[ ln(Pi/Qi) * Pi]   means that all precisely similar ps and qs make it ln(1) * whatever = 0. It measures closeness only too good, because it assumes that information in itself has no variance-properties. Very weird since Shannon was an information theorist. Or am I missing something big? Stats appears to be too tough for me..
practically you are thinking correct !
OK, you definitely have a problem because these data are about as far from Normal as they can be! What exactly do these data measure and what do you need to deduce from them? Could you supply a reference that explains why you are "supposed" to use Normally distributed data? (Motion data often are not Normal: see the examples at http://mathematica.stackexchange.com/questions/2711 for instance.)
@Jens : It's a classic. I've been looking at it, and the problem is that the equation as it stands can cause non-identifiable cases. This will lead the more sophisticated methods like nls() to fail. There are other options, but for that I suggest you read the other question. The solution there is definitely what you're looking for, as your case is just a special case of the more general problem presented there. I will add a few other options for piecewise later on, but I'm too busy right now to write it up. Cheers
I don't know how you coded mobility. It's for wherever that variable = 1. A second interaction does not affect the meaning of the first.
Ah, I see what you mean. I wasn't aware of this problem. Well, maybe you can put in constraints - such as a minimum standard deviation - to avoid the solutions to degenerate to this kind of minima.
Apologies, just some arbitrary transformation of the data. The permutation is used incorrectly in the original problem domain, but I'll change that now.
Yes, but that's not non-parametric. With 7 categories, you're going to need some big samples too.
@Hellski: You could simply use [TDistribution.cumulativeProbability](https://commons.apache.org/math/api-3.1.1/org/apache/commons/math3/distribution/TDistribution.html) here.
Thanks. So if x or w or both do not improve the model but x*w does, it is OK to keep just x*w
@gung It takes a little reputation to be able to post a comment ;-).
Check out the [UCI repository](http://archive.ics.uci.edu/ml/) for public benchmark data sets.
+1 Really wonderful job of seeing into the practical heart of the matter and explaining it clearly.
No sources given here. Conservative relative to what precisely, in what circumstances? Less scuttlebut, more scholarship please!
Hi Brian, I don't see how this answers my question. The gradient is just the first derivative. When we assume a discretization, the smallest epsilon we get is 1. The first derivative, which is $lim_{e\\rightarrow0}\\frac{f(x+e) - f(x)}{e}$, takes the form of: x(i+1) - x(i) because epsilon is 1. If my interpretation is wrong, please, feel free to correct me.
I assumed `D=svd(A)$d` in R returns the square roots of the non-zero eigen values, hence I used $UD$. I do not have a problem with the dimensionality reduction aspect, and I do understand a lower rank approximation of A can be formed as they describe. I found the answer on [this link](http://math.stackexchange.com/questions/89924/clustering-algorithm-to-cluster-objects-based-on-their-relation-weight/89931#89931) partially answers my question.
How do you know who is in the neighborhood? Do you have a social network of a person and that person's (potential) influencers (e.g. friends)?
(If anyone would like to elaborate even further on the vectorization part, that'd be great.)
I try different parameter values to get best results but I was unsuccessful, and always naive bayes outperforms the SVM, I also tried different kernels
BUGS can read data in almost the same format as you present it, see for example the data in the Jama.odc example on the WinBUGS website. http://www.mrc-bsu.cam.ac.uk/software/bugs/the-bugs-project-new-winbugs-examples/
Do you have data or just this question of interest? If you have data then you can try fitting it to probability distributions. I am familiar with what this package is in R ("fitdistrplus") although I don't know what you use, either. It's probably not terribly sexy or exciting but wikipedia usually has the PDFs for probability distributions, and it's a simple matter to find lists of common probability distributions (like Vose's Compendium of Distributions pdf online)
+1 great solution and thanks for the reference.
There's no point trying to assess the distribution of the errors when more basic assumptions are not satisfied -- the variance isn't constant, so the error distribution will be a mixture. (However, conditionally on the fitted values, the distribution appears right skew.)
There are a large variety of methods for drawing random samples from different distributions. In many cases, several methods may be used, as different ones may be more suitable in different regions of the parameter space. For example, if the parameters of a beta distribution are small, different approaches may be better than when they are not small. Stats packages usually implement pretty efficient methods for sampling from the common distributions
I still think that this question is nearly impossible to answer without understanding what "different" means...
How many questions are you asking here? How long do you expect a reply to be? On any forum, it's a good idea to try role reversal, namely, if you knew all the answers here, would you write a reply? Wait a while to see if you get a good answer, but if not try to trim this down, and ask first what you want to know first.
Is such a dataset publicly available somewhere? I am interested in taking a look.
I'm not sure I can give effective comments on that @uncoolbob. Do you maybe only want to restrict the test to very nearby "nodes"? You might consider Ripley's K for that but only evaluate very small bin distances. The global tests for non-randomness tend not to be very informative about the nature of the distribution. That suggested solution reminds me somewhat of [this question on the GIS site](http://gis.stackexchange.com/q/42427/751).
Thanks, that helped me! (I have no strong requirement for accuracy.)
+1 It may be worth noticing that all three examples are really the same: #2 can be rewritten as $((X_1+X_4)^2 + (X_2+X_3)^2 - [(X_1-X_4)^2 +  (X_2-X_3)^2])/4$, a scaled difference of two scaled $\\chi^2(2)$ (Exponential) distributions, and #3 is the difference of two Exponential distributions because the $\\log(X_i)$ are Exponential.
It is important to point out that this solution implicitly assumes the independent variable is not random; only the dependent variable is.
Any automation that ignores the possibilities of Level Shifts, Local Time Trends, Seasonal Pules and/or One-Time Pulses should be reviewed very carefully as these kinds of structures in the error process "blind-side" identification strategies.
I also think the slides is wrong.
@chase thanks. I had thought about `polr`, but I wanted to use `clm` and polr is slow with my data size (and so is `clm`)
"Who 'chooses' a test result" is a part of what I'm trying to test -- the guess is that all are equally likely if there is a measurement failure.  The hypothesis is that the model itself is a reasonable fit for the data, for any p (which I would then want to estimate); if for k = (1, 2, 3) I had (100, 100, 300) then the model would be a very bad match, regardless of what p value I chose and the number of discarded measurements.
Actually @Chase was faster by a factor of ~9 over data.table, so I changed my accepted answer. Thanks again everyone - learned a bunch of new tools.
"Clustering based on **correlational** similarity" - which is very different from distance measures -  sounds as if it's Principal Components Analysis (PCA) you're really looking for. I believe Cluster Analysis is rarely used for clustering variables since PCA is thought to be the better approach for this.
Create a simulation in which the true mean is a tiny fraction of the standard deviation and the sample size is small: that will cause the sample means typically to vary much further from the true mean than $0$ differs from the true mean.
thank you.This is very useful.
6-In the women who use nicotine replacement therapy do their babies do better than ones who refuse nicotine replacement therapy? (subgroup analysis), thanks
This might be a good solution. But to appreciate it, one would like to see the graph (the matrix) itself and the solution as graph. Not just the code and and the output.
I am absolutely sure that skewness and kurtosis *do not* cover all deviations from normality. A thought experiment: symmetric distribution (0 skew), bimodal. Now imagine such a distribution with heavy tails (negative kurtosis); you can also imagine it in peaky form with thin tails (high positive kurtosis). There are zero kurtosis zero skewness bimodal distributions, and therefore kurtosis and skewness tests are not definitive for normality. As a bonus there are an infinite number of symmetric >2-modal distributions with zero skew and zero kurtosis also.
I've added a link describing DIF so that people get a better idea of what you are really testing. In your case, as you do not consider any interaction between trait level and group, an LRT of M1 vs. M2 will assess *uniform DIF*. And +1, this is a good question.
1) `significantly` you shouldn't rely on p-value in such problems as yours; the very size of the correlation matters more. 2) You have to define your understanding of "combination" before you can post a question (when you do it, please post a new, another question. Let this old one be as is).
cuz you need to start somewhere :)
Typically, when you integrate over a known function, you can do much better than Monte Carlo integration.  Monte Carlo converges to the true value at a rate of $1/\\sqrt{N}$, where $N$ is the number of evaluation points.  Other algorithms, e.g., quadrature-based, will converge at a rate $1/N$ or even faster (e.g., for a function that's periodic over the region of integration), assuming some level of smoothness of the function.  Still others, based on quasi-random sequences (e.g., Sobol' sequences), will converge at intermediate rates, e.g., $(\\ln N)^n/N$ for an $n$-dimensional integration.
@Seb I think it is ok for this question to stay on CV as the second (sub)question asks specifically what to do with the result from a statistical standpoint, if I understand it correctly. Otherwise, if this purely R-related programming, tom, please tell us and we will migrate it to SO.
I got the SE(d') formula from Macmillan's Signal Detection book.  It's from the 60s and is an approximation which holds when the sample size is large enough for observed the hit & FA rate to converge on normality.  The formula is as you suggest, but the summed N in each denominator is multiplied by "ord^2(z)", or the square of the height of the normal density function at the z-score of the response rate (hit rate and false alarm rate for respective denominators).  So...yes, I've just been using it without understanding it- but since you asked :)
I'm confused: $N$ is a random variable, not a population parameter you might want to estimate. Do you want to find its expected value (the average)?
(i) The problem is that the distribution for $\\hat{\\theta}$ depends on $\\theta$. If you look at the distribution of $Q = \\hat{\\theta}/\\theta$, it doesn't depend on $\\theta$ (you can construct an interval for it that doesn't depend on $\\theta$). From that interval you can back out an interval for $\\theta$. $Q$ is called a [*pivotal quantity*](http://en.wikipedia.org/wiki/Pivotal_quantity).  (ii) You don't know how to graph an exponential distribution? I'm not even sure what the difficulty is here - it's a function of $x$, which you have already given (I didn't check your work though).
+1 **Objective**, **well-supported** replies are welcome.  This includes information based on experience, provided the nature of that experience is documented.  Because it's possible there is a demonstrably best solution, I believe this question does not necessarily need to be made CW, although it could be converted later if the replies appear to warrant that.
I sense the user is looking for a statistical test to determine the fit. PCA falls a bit short on that. I think LDA as suggested by @chl is the way to go here.
I mean log(5/3)
But "what affects what we're interested in" is THE research question, at least in my field (epidemiology). While it is clear that we don't either know or don't know, but rather have some quantity of knowledge we can build on, it is unrealistic to be certain two populations are comparable. Or  is it? As to the data splitting (also @Peter Flom): This is a surprise. I thought that the answer was "no", for if there is an artifact in my current population, caused by some phenomenon unknown to me, it will likely exist in any two partitions regardless of how I split.
Have you considered using Gibbs sampling for each variable?
My suggestion would be to put whatever is necessary to understand the question directly in your question, instead of linking to a post elsewhere. In other words, it'd be best if your question was standalone.
I can't see that this is a Stata question; conversely, if it is, it is off-topic here. If the doubt is what to do, then much of any time series text or course includes material on (e.g.) removing trends and/or building models that include trends. As formulated, this question is too broad to be answered, as it is too close to what should I do with nonstationary data?
It's unclear how one could use distance to induce an ordering on vectors.  Also unclear is what would be accomplished by the mapping when $\\mathbb{R}^N$ already has a "nice distance."
@Chris Yes you have the correct Fox and Levin. The Haan is: An Introduction to Statistics. I struggle with writing the formula for the standard deviation on a website. I don't know how to use the correct symbols so I had to write it in words. Hope it is still clear. I am looking forward to your response.
I'd vouch for those materials as well. They also have intro tutorials and not just multi level modelling resources.
Do you have SAS/ETS installed?
In your last paragraph are you implicitly comparing two models where you have a sample of 16 million and a population of (how many?): A), where an event occurs one in a million and B) where an event is unique in the population?  And you want to decide whether A or B is more plausible, given an observation of one event out of 16 million?