tttjjj/elt_bench huggingface dataset:
You can set the argument Hess=TRUE to get the Hessian back from multinom and then calculate the p-values manually. But I suggest you use the mlogit library (nnet can have convergence issues when the covariates are not scaled correctly). The vignettes for mlogit are pretty good, and should help you get your data set up correctly. The vignettes can be found at the usual place: http://cran.r-project.org/web/packages/mlogit/
You want to the know how good the "fit" is. But what are you fitting?
"monotony" is a standard English word but it does not, so far as I know, have the mathematical meaning you seem to think it has. Monotony changing is just a matter of not being monotonic, or of being non-monotonic. I don't think this question is getting clearer or more helpful to anyone else. If the point is that monotonic nonlinear relationships can be associated with high (Pearson) correlation, a short answer is Indeed; and a slightly longer answer is that your teachers or textbooks were at fault if they didn't emphasise that.
@JacobMick Why would p=0 rule out GARCH?
Another (ultimately equivalent) way to think about this is that you use 1 df for each parameter estimate (ie, $\\hat\\beta$), plus 1 df for the mean of the response (ie, $\\bar y$), since the intercept is determined once you have $({\\bf\\bar x}, \\bar y)$ and the slopes.
@user16096 Do we have to merge them?
@TomekTarczynski I summarized the relevant information from the paragraph, so you may not get any more info related to this question from looking at the book (although the book is great so you will get other good info).
Actually, I think one other factor that matters is sample size. I am not sure if you can expect identical values with a sample size of just 15 odd points. With only 15 points there is not enough information in the likelihood to outweigh the prior. In other words, the likelihood is not 'concentrated enough' which suggests that when you integrate out the parameters you may get a different mcmc marginal likelihood. Does that make any sense? You can do a small simulation to check the above.
Modified the answer regarding this point. I wasn't aware that computational simplicity is required.
I'm assuming that the two part model you refer is the Heckman correction sugested by Mermex, in this case, yeah, it will take into account the prob of enrolment. If it's not, than I don't know if it's ok to just estimate the probability of using health and then use this probability as a independent variable in the main regression. The heckman correction has this idea, but I think it's slightly different and has some assumptions to work.
It is rarely a good idea to reduce the number of categories. One case where it might be is if one level (or more than one) has almost no observations. 

Usually best to leave it as 5 points.
+1, this is good information, but it is also worth noting that because the OP looked at the data first & then decided to test this, & b/c this contrast is not orthogonal to the initial one, it would be best to use the Bonferroni correction for all pairwise comparisons, ie, divide $\\alpha_{crit}$ by 3-choose-2 (namely, 3).
Sure, but GE does not imply elliptical. For some skew elliptical variations check also here: http://www.stat.tamu.edu/~genton/STAT689/TAMU2009SE.pdf
40 clusters -> 145,6 wcss, but i 'dislike' a good wcss value with a subpar count of clusters. using em helps to compare the clustering results.
Quantile *vs.* percentile (it's merely a matter of terminology), http://j.mp/dsYz9z.
MI is often used in feature selection. Try to have a look at the minimum redundancy maximum relevancy method (mRMR). In case of continuous variables they go for discretization. You could also use an estimator of MI for continuous feature but in mRMR paper they say that dicretization led to better results. Another interesting method for feature selection is the one in Boruta package. As output you will get a set of potential predictor variables useful to predict the class. However, they might be correlated to each others.
Note: if your data is all numerical, convert each data.frame to matrix first, then do an rbind, and turn the result into a data.frame again.
I used matlab to reproduce your simulation. Conclusions: when all $z_i$ deviate consistently from 0, then Stouffer wins over Fisher with a small margin and "my" method looses hopelessly (as you showed). When only one of $z_i$ deviates a lot from 0, then Fisher wins over "my" method with a small margin and Stouffer loses hopelessly.
Here are train and test errors: http://i46.tinypic.com/rkvvag.png
The situation in developed countries is exactly the same.
@Michelle, AFAIK the distribution represents human impact, and is a composite metric which ranges from 1 to 100 (though this is arbitrary).
I see six local maxima.  To which three are you referring? :-).  (Of course it's obvious--the thrust of my remark is to encourage you to define a "peak" more precisely, because that's the key to creating a good algorithm.)
The hypotheses you mention aren't (conventional) null hypotheses. I think you may have missed the point of the OP.
Multiple logistic regression means you have more than one predictor. Simple logistic regression is when you only have one predictor. In both cases you can use both categorical and continuous predictors.
What are the questions you're trying to answer/what hypotheses are you trying to test?
Are these animated or taken from a still position? Are you measuring torsion?
Dear @user21240, many thanks for your answer. I am looking for your views about the specification for the unit root tests. should I include trend in the final specification?
I presume that this would need to be looped through to get combinations/sequences of longer lengths?
Chris, As you say this is quick and dirty. perhaps too quick and too dirty ! Consider a time series 1,9,1,9,1,9,1,9,5   ... the anomalous data point ( the "5"  ) would fall "safely" within your bands ... so much for quick 'n dirty . Inliers like outliers left untreated can lead to bad but quick conclusions. Additionally your bands are flawed by the assumption of normality of the residuals around the expectation AND bythe anomalous data points themselves as the inflate the bands thus potentially masking themselves.The whole idea of goods statistical process is to help the eye not hinder the eye
(+1) This is good to know. One question: do you know why the standard errors for the `x12` and `x13` different in the two models? It seems that the models, as you've described them, are mathematically equivalent so I'm not sure why the precision of the estimates of the mean of `y|x1=2` and `y|x1=3` would differ in the two models. Any ideas?
There is no need to do FA both on corr and cov matrices, because these are two different analyses (irrespective to whether they give similar results). You should decide apriori which matrix to analyse.
@Behacad: I'd go and ask in SEMNET :-) Well, in fact I've no experience with the coefficients for testing of latent structures. Possibly a good introduction is given by a book of James Steiger, to whom SEMNETters often refer. (Sorry I cannot be of more help here)
Welcome to our community and thanks for your contribution!
Ceck out wxMaxima.
Think you mean 'difference', not 'differentiate'.
Please consider the quality of your questions and the frequency of asking them. You can't possibly have done much background searching/research yourself on such disparate topics if you are posting 4 questions within 24hours (unless you save up the questions for us ;-) We really aren't here to do your work/research for you. The number of votes for Qs reflects the quality and amount of research effort demonstrated, and your Qs are somewhat lacking in that regard.
I work in lakes and lake sediments and putting depth on the y-axis (despite its being the independent variable) is actually the standard in papers in my field.  My guess is that for atmospheric scientists this wouldn't be that unconventional either. As you suggest, it makes it so the figure is spatially accurate and therefore easier to read.
Thanks for your answer. I'll try Mallet library. The MATLAB Topic Modelling toolkit doesn't allow setting asymmetric priors, although it should not be difficult to modify it's source code for that.
@Adam It is not the Gibbs sampler. The Gibbs generates a random draw from the conditional density at any given iteration whereas the proposed algorithm computes the expected value from the conditional at any given iteration.
I don't know if this has been done, but I see no reason why a model of this sort couldn't be derived (it would involve assuming that the underlying multinomial distribution is changing over time). However, it would introduce some tricky parameters. For example, how fast is the vocabulary growing? What is the functional form of this growth (linear, exponential, etc)? Are other words getting dropped from the vocabulary at the same rate? At different rates? How large a corpus is needed to estimate these parameters reliably? Also, when would the modified analysis beat the "naive" analysis?
I would suggest going through at least two articles 1] [Random Walks On Graphs: A Survey by Laszlo Lovasz](http://www.cs.elte.hu/~lovasz/erdos.pdf) and 2] [Sampling From Large Graphs by Jure Leskovec](http://www.stat.cmu.edu/~fienberg/Stat36-835/Leskovec-sampling-kdd06.pdf)
@user90275: To use Berry-Esseen you correct the mean to be 0, then need to calculate the third *absolute* moment and the variance of X so you can get the upper bound on the maximum deviation between the two CDFs for a given N (i.e, $\\Delta_N$). Now, for given N, you know that the maximum absolute deviation in the normalized distribution and the normal is less than the Berry-Esseen bound i.e, $\\\\max\\{\\Phi(x)-\\Delta_N,0\\}<P(\\frac{\\bar X_N-E[X]}{\\sigma\\sqrt{N}}\\leq x)<min\\{\\Phi(x)+\\Delta_N,1\\}$
"x per y" is a *frequency,* not a mean.  Could you therefore elaborate on the sense in which people might be referring to medians or means?
+1 I am interested too in an introduction to hypothesis testing. I have read "Introduction to Statistical Thought"
by Michael Lavine http://www.math.umass.edu/~lavine/Book/book.html and found it interesting but it does not cover a lot the subject.
The [Binomial Theorem](http://en.wikipedia.org/wiki/Binomial_theorem#Newton.27s_generalised_binomial_theorem) (Newton, c. 1665) says that $m(t)$ = $(1-2t)^{-k/2}$ = $1 + \\binom{-k/2}{1}(-2t) + \\binom{-k/2}{2}(-2t)^2 + O((-2t)^3)$ = $1 + kt + \\frac{k^2+2k}{2!}t^2 + O(t^3)$. Comparing coefficients with $\\mathbb{E}(\\exp(tX))$ shows the first two moments are $k$ and $k^2 + 2k$, whence the mean is $k$ and the variance is $(k^2 + 2k) - k^2$ = $2k$.
As bayer answered, I think you meant multi-class classification. The paper you cited talk about multi-label classification, i.e. every record has many different labels. For multi-class classification with kNN just have a look to classical Data Mining book as "Introduction to Data Mining" by Tan et al.
I agree.  And apparently "yes" isn't long enough to be a valid answer.
Are you defining "relatedness" by a correlation cut-off (e.g. 0.4 or 0.7) or using clustering algorithms or a pre-specified knowledge based linkage of like-industries?
Appreciate the answer, but I think if two predictors are uncorrelated, then the regression weight of a predictor in linear OLS regression do not change from a regression that includes only one or both of the uncorrelated predictors. This also follows from the formulas for regression weights in multiple regression which can be expressed as:
beta = (r_y1 - r_y2*r_12) / (1-r_12)
where r_y1 is the correlation of rv1 with outcome y
r_y2 is the correlation of rv2 with outcome y
and r_12 is the correlation among the predictors. 
In the case of uncorrelated predictors, r_12 is zero
Thanks Wolf, that link really helps. I'll take some time to slowly read and digest that. :)
I've got a feeling that it might not be possible. Can you impute instead?
I'm sorry, what distinction are you making between the large sample formula and the small sample formula?  Are you calculating the variances using a population formula in large samples rather than using a sample estimate of the population variance?
This implementation is mad. I have decided to just reject it rather than improve on it. Thanks anyway. I'd be inclinded to say if you want to see if if the column is "random" do a standard randomness test.
+1: Amazing reply. I don't suppose you have some references to some of the canonical literature you mentioned?
So $y_t$ is intended to be some kind of shifted lognormal?
Why not project the non-euclidian vectors into euclidian space?
Yes it can be the reason, because the skewer is the distribution of one of the two variables, the less is the power of the test. But it depends on what algorithm of computing p-value you use. If that's usual one based on normal approximation it's one story. If you use exact computation it's another story. You should use exact method for your small, skewed data.
@statskeptic Your argument is very similar to Taleb's skepticism/ bashing of statistics in his book the Black Swan.  I think many statisticians myself included have shot holes in his argument which basially says that statistics is useless because it cannot predict that rare and unthinkable event (9/11 in your example,the stock market crash in his).
There's elastic net regularisation, which combines LASSO with Ridge. As for penalising only some of the variables couldn't you just use a weighted L1/L2-norm when calculating the penalty? As far as I can see the this should affect the computation procedure very little (i.e. you could use the same ones as for "regular" lasso/ridge/elastic net). That being said, I'm not aware of this being implemented anywhere.
Ladislav, this an excellent answer to this question. It is extremely thorough and complete. The only issue I see is that Kruskal-Wallis ANOVA's also have an assumption of independence of observations, such that there are different subjects at each level of the independent variable, which in this case, we do not have as we are following the same 11 patients across 4 time points. Do you have any opinion on this or have any other methods in mind to address this issue? Thanks so much!
Have you tried logistic regression?
This looks like a duplicate of (this question)[http://stats.stackexchange.com/questions/3200/is-adjusting-p-values-in-a-multiple-regression-for-multiple-comparisons-a-good-i] if it isn't please say why not.
And it is quite strange that excel has a different degrees of freedom for covariance(). I wondered if they had an logic for that.  or its really just a mistake. Apparently, R works smoothly in the same case. cov(x,y)/(sd(x)*sd(y)). Thanks again!
So, if I need to use special methods to account for the autocorrelation, the time-series methods appear to be the way to go.  However, in the example I used a dataset with 24 points.  What happens when I only have 10 or 6 or even 3? The above method returns the mean for those values, but the data is obviously exponentially distributed so the mean would be highly inflated from the actual.
(+1) The typical definition of a stable law is more restrictive than you've given and requires that the form of the distribution be closed under *all* linear transformations, not just sums. In particular, the Poisson is *not* a stable law. (For the same reason that, e.g., the Gamma of fixed scale parameter is not either, even though it is "stable" under sums.) In fact, it is well-known that the **only** stable distribution with finite variance is the normal.
thanks for a great answer! +1
I think most researchers would entertain both OLS and quantile regression; differences between the methods would shine light on what you are trying to model.  With respect to OLS, if you toss in normality assumptions you do get a lot of fairly well documented and thorough testing methodology that is available in most statistical packages.
By the way the place for this question is stackoverflow
Within the context of each training session, you do indeed know the specific number of hidden states, as you are using that as an input to the training.  Also note that just because the  process hasn't been produced by an HMM doesn't mean that it's meaningless to think of what states might, conceptually, be an adequate basis for an HMM model, and use that to help come up with initial probabilities.  Furthermore, you can estimate the initial probabilities as part of the estimation process.
You want the Fisher-Irwin test. See Ian Campbell's [website](http://www.iancampbell.co.uk/twobytwo/twobytwo.htm) for the details and data to support the recommendation.
Thanks for the observation, John. I have changed it a little to make it a factor. All I did was remake the original vector from the table though, so if there's a way to skip that step, this will be faster.
Since this is a homework/self-study question, it should have the `self-study` tag. See http://stats.stackexchange.com/tags/self-study/info
you need EMINER to do the integration...you can either hook them up in a chain, or run the NNET and then group the predictions to make a logit class 2nd stage model
@whuber: unfortunately, the answer is fairly broad: "how busy, how used, is this system?" Some people felt that the system was hardly used at all, but I've been able to show that 25% of possible users have logged in during the last 3 months, and 50% during the last 9 months, which gives a feeling that it's more than "hardly used at all". But that answer's not that satisfying, really, and I feel like it's easy to misinterpret what it means (e.g. "25% of users log in on a quarterly basis").
+1 This example nicely shows how arbitrary the question actually is: when you measure floods in terms of peak discharge, they will be *positively* skewed, but measured in log discharge, they (apparently) are negatively skewed. Similarly, *any* positive variable can be re-expressed in a simple way that skews its distribution negatively (merely by taking a suitably negative Box-Cox parameter). It all comes down to what is meant by "easily grasped," I suppose--but that's a question about the students, not about statistics.
You are quite right. This approach does not generally work and often yields confidence intervals that do not include the population mean or even the sample mean. Here is some discussion on it: http://www.amstat.org/publications/jse/v13n1/olsson.html This is not an answer, since I did not look into the matter enough to actually comment on the link in detail.
One class of examples are called *curved exponential families*. I would be surprised if your book (or course notes) does not make any mention of them or  give at least one example. The classic example is a normal with mean $\\mu$ and variance $\\mu^2$.
It is. Analytic solutions are indeed rare and the existence of a solution is to be demonstrated but you are always able to simulate though...I will end-up recoding my R programs in C if nobody comes up with a ready made tool...most general analysis software generally have an all-purpose solver funny R seems to provide only specific simulators, or I may have overlooked the right package
Recall that the standard deviation of the proportion in a Binomial experiment involving $n$ independent results with success probability $p$ is $\\sqrt{p(1-p)/n}$. Plugging in the estimates of $p$ gives standard errors of $0.18$%, $0.15$%, and $0.09$%, respectively. (These values can easily be estimated just by looking at the data: no computer is needed.) Because the difference $5.53$% - $\\max(4.09, 3.82)$% = $1.44$% equals almost ten of *any* of those standard errors, the result is glaringly obvious that A has a greater return rate than B or C and no formal testing is needed.
Gesture recognition is rather a specific application; if you can't find such using a search engine, you'll have to get lucky to get some here.  Also, C++ code samples for HMM will be rather lengthy.  I'm sure this is what you'd like, ideally, but is there something less restrictive that would be useful to you?
Another issue is whether you want to optimize the overall solution (in some sense) or whether you want to proceed in a greedy manner to find the largest rectangle and then recursively obtain largest rectangles subject to fixing the rows and columns of all rectangles found so far. As far as "each cluster to be identified" goes, that's going to be a *huge* number in general.  It will include all individual nonzero cells, all pairs of cells that can be brought into proximity via permutations, etc.  Is that what you really need?
@Adhesh If each three scores are expressed on a common scale (say, 0-100 point), then $\\bar x = (x_A+ x_B+ x_C)/3$ is what you are after (each scale contributes equally to the total score). With individual data like $(22,15,10)$, the final score would be $1/3\\times(21/30+14/45+9/10)=0.637$ which you can conveniently express on any scale you want. (On a 0-45 point scale, it amounts to 28.7; on a 0-100 point, it is 63.7, etc.)
So is it correct to say that before seeing a confidence interval there is a 95% probability that it will contain the true parameter, but for any given confidence interval the probability that it covers the true parameter depends on the data (and our prior)? To be honest, what I'm really struggling with is how *useless* confidence intervals sounds (credible intervals I like on the other hand) and the fact that I never the less will have to teach them to our students next week... :/
To clarify - aside from whuber's comment and your inclusion of the tag, it doesn't look to me like you're asking about that kind of approach, which is why I wondered.
I don't think I was using a likelihood ratio test, although the concepts seem the same. I found this [link](http://www.weibull.com/DOEWeb/tests_on_subsets_of_regression_coefficients.htm) which explains the test I used. It seems to support your conclusion though: "...the test simultaneously checks the significance of including many **(or even one)** regression coefficients in the multiple linear regression model". Also, the T-test on the variable and the partial F-test gave consistent results, since they both argued for the inclusion of the variable.
Thanks John, that was a great help.
@user466441 I'm sorry to see that you did not receive a satisfactory answer to your question. The "possible duplicate" should have helped you to some extent, but I think what you want is a specific numerical example. I won't go through an example using regression to estimate partial autocorrelation coefficients, but I have written a short document to show you how they can be estimated using the Yule-Walker equations. You can access the .pdf file at my dropbox: https://www.dropbox.com/s/phbdr1k0twxcs47/yulewalker.pdf Maybe this will help you out.
How do you know what the cut off is for good/bad fit based on the deviance and number of predictor variables (without the pchisq)? Is it just if Residual Deviance > NULL Deviance or is there some range/ratio?
The CLT doesn't *allow* us to assume there are lots of individual effects in any given process - if we are *given* that there are lots of not-too-dependent individual factors contributing to a measurement (none of which have too much of the total variation), we may be justified in assuming normality by invoking the CLT. The assumption of many contributions precedes the application of the CLT, it's not in any sense a result of the CLT. Otherwise everything would be normal, when in fact that's only sometimes roughly true.
@user8434: if the answer suits you well enough, then you could consider adding (+1) to my score maybe...
I glanced thru the attached document and could not see obvious mistakes. Are you really checking that the _observed_ likelihood is increasing? LL is the _joint_ log-likelihood...
This is two questions: (1) Why does a double integral express an area? (2) How can an area be estimated by an average?  The second question is essentially the same as your immediately previous one at http://stats.stackexchange.com/questions/39128.  The first is a matter of mathematics, where you might hope for good explanations on the [math site](http://math.stackexchange.com/)--but it really comes down to that's the *definition* of area.