tttjjj/elt_bench huggingface dataset:
Why do you want to subtract the fitted amplitude from the original data? This seems like subtracting apples from oranges. Essentially, you have two-dimensional original data, fit a model to the absolute values and then want to subtract the fitted one-dimensional values from the original two-dimensional values. (You could *scale* the original data by dividing by the fits.)
If you have seen this multiple times, can you post a full output? Just knowing there is no F value and no p-value is likely not enough. Also, what function in Stata were you using? There is a Q&A on [Stata forum](http://www.stata.com/statalist/archive/2011-06/msg01303.html) about -svy- having this kind of behaviors.
Thanks @Peter. I read the Wikipedia entry, along with some other sources, but I found it hard to believe the reliability of one's results doesn't increase with the number of judges agreeing: three people agreeing on something seems stronger than two people doing the same, don't you think?
The title of your question is asking a totally different question from what you really ask­. I, for one, was curious about the real differences between the Linear SVM (let's take the hard margin SVM) and other linear discriminants.
@mbq Good point.  My first fear was that the median might be some outlier in between real modes, so I'll need some technique to detect that.  Also, given one mode, I wonder how best to identify the points that really are "nearby" that one, assuming a nice normal distribution.  Finally I could subtract that set out and iterate by going back to look for the median again.
Does the model have a constant term?
Do you have more than one assessment per worker?
@Nick Thanks on the title thing. That was a typo resulting from moving words around in edit. Sorry about not spotting I had duplicated that other one.
Well, these are very related problems. Consider the linear regression of type $y_j=\\sum_i^N \\varphi(x_i, x_j)\\alpha_i$ where $\\alpha_i$ are your parameters (weights in terms of ANN). In the case of ANN, you have the problem above multiple times, which leads to "deep learning".
Good question.  I stand corrected.
@Macro, please see this official link: http://blog.stackoverflow.com/2011/07/its-ok-to-ask-and-answer-your-own-questions/ (it's linked on the Ask a Question page in the checkbox label at the bottom: "Answer your own question – share your knowledge, Q&A-style"). I had this question while I was doing homework (having chosen to use R instead of Minitab, though Minitab was demonstrated in class), but I didn't have enough time to type up the question and wait for a response. I figured out this workaround, and decided to share it with the community.
The standard approach would be Box-Jenkins: http://en.wikipedia.org/wiki/Box-Jenkins For weather data, you should definitely check for seasonality before proceeding. I don't know how to do this in Matlab, though, but I'm sure something exists there. You may want to search for "Box-Jenkins Matlab" or some such.
@steffen I think it's fine.  One assumption of regression is that the residuals are normally distributed.  How would you check that before running the regression?
Could you say a little more about what you mean by "valid" results? BTW, when covariances and correlations are computed the data are automatically centered, so there's no need to do any centering at all.
A positive coefficient means that the variables tend to move in the same direction and this is always called a "positive effect", irrespective of whether the values of the variables involved are negative or positive, in any combination. Analogously for a negative coefficient. The effect does not change character or name  when you move to the real scale of the variables, although it may be "swamped" by the trend, season, drift, and persistence components. Given that you have taken out all these features of your variables, try to describe verbally what exactly is left that you are measuring.
I know Max Kuhn (author of "caret") at Pfizer has done work along these lines
U know what I think ur right
@AlefSin remember that p-values are just a monotonic transformation of the test statistic.  The advantage of p-values are that they are uniformly distributed between 0 and 1 if the null (and other assumptions) are true and they are on the 0 to 1 scale.  If you are interested in comparing effect sizes, why not just compare the effect sizes (or the normalized test statistic)?  I see no advantage of converting to p-values 1st.
Your log likelihood formula is assuming the mean of the *returns* is zero.  The more general formula would replace y_i with y_i - \\mu.
Here's the article with a working link. http://www.ncbi.nlm.nih.gov/pubmed/20528863
This is a good answer in my opinion. It might be worth adding that the reason that the posterior distribution and the likelihood are proportional is that the posterior distribution is itself proportional to the product of the likelihood and the prior. When the prior takes the same value everywhere, as in the uniform distribution, then the posterior distribution is simply proportional to the likelihood.
Could be some insight here: http://stats.stackexchange.com/questions/35276/svm-overfitting-curse-of-dimensionality?rq=1
@MarkRansom, it was not exactly clear either. To someone familiar with how it works it might have served as an enforcer of knowledge but hard to learn anything new from it.
We moved to chat. I saw his later comments. He will not see mine until tomorrow as he said he is in the UK. If you have to delete the comments before tomorrow then I will just repeat and resume in chat. I don't think it is necessary to move the latter comments. @whuber Thanks for letting me know.
There are definitely problems with some of the topics you raise (for me, that delta function is the worst).  One thing that isn't clear though is this: what is your question?  Your post contains more of a "thinking out loud" process rather than a specific question.  You are kind of right about $ p (h) $ and the answer is "it depends" - sometimes it matters, sometimes not.  If you think in terms of "logic" then the prior is important when it is " informative" (meaning it tells you something that the data/likelihood does not).
Uh?! You assume independence between the components of $X$ so $\\Sigma$ is a diagonal matrix with elements $\\sigma_1^2$ and $\\sigma_2^2$.
The difference is obvious: in the one case you have just one (log-normal) random variable, in the second case, many identically distributed random variables, that may or may be not independent. The issue is what holds in your case.
Despite the quip, it helps to know enough measure theory that you won't be afraid to read articles in JASA (or wherever) that could be useful or instructive.  If you're going to work in stochastic processes and mess about with Ito integrals and the like, and if you care to understand the tools you'll be using, then you actually do need a serious dose of measure theory.
@Henrik, you can imaging that for each window $w$ we have $N$ numeric verctor of length $L_w$ and we want to test if some vectors have a significant hight value than the rest
many thanks for getting back to me, help much appreciated and makes sense. Thanks for speaking 'plain english' back!
Hi @marco, welcome to the site! [Miguel Hernan](http://www.hsph.harvard.edu/miguel-hernan/) has a free PDF of his book "Causal Inference". [Part 1](http://www.hsph.harvard.edu/miguel-hernan/files/2013/05/hernanrobins_v1.10.21.pdf) (chapter 7 on page 83) discusses the structure of confounding. That could be an interesting read. Specifically he writes: "Confounding is the bias that arises when the treatment and the outcome share
a common cause."
If the first quartile (the lower quartile) is 1, then at least 75% of the distribution is at 1. In that case, no transformation will separate those values at 1, since they all have the same value - they'll always be transformed to the same thing. One thing you can do is look at the ecdf, perhaps.
the obvious answer is to aggregate your subject-level covariates up to the cluster-level, and pursue a cluster-level analysis
Instead of logistic regression, just use the appropriate form of regression for whatever the response is.  For example, ordinal logistic regression.
Some related Q/A:  http://stats.stackexchange.com/questions/8344/influence-functions-and-ols       http://stats.stackexchange.com/questions/82717/how-to-find-influence-function
Maximize $\\log(L),$ just as the answer in the other question recommends.  You will discover the MLE and that will tell you whether an order stat works and if so, which one.
@Mark, I did some simulations with R, everything holds pretty good for correlation 0.75
In fact, higher kurtosis is associated with both increased peakedness and *heavier* extreme tails, but there's no necessary relationship in either case (you can find counterexamples to higher peak or heavier extreme tails, even though both are typical with higher kurtosis). A variety of shapes is possible in either case.
E(ln(CDF(Z))) is equivalent to E(ln(U)) where U is uniformly distributed on (0, 1]. That can be found by integrating ln(), which is x(ln(x))-x + C, which is -1 if C is 0 x is 1.
I wonder if it is so because there's no correlation between x1 and x2, or there are some linearity assumptions in the optimization mechanism (I use Python's sklearn.linear_model) that fail in my case?
+1, nice, didn't know about this.  So, am I correct to interpret this as Blinder Ozxaca vs. dummy variables is just apples and oranges?
So for CTR I can use a test of proportions, for CPI I can look at the distribution of all of the costs of individual bids, but what I'm not sure about is CPC - it's an average of CTR times CPI for a given (arbitrary) time period. So I'm not sure what the "distribution" is that I can look at.
(1) What is your cluster variable? (2) How many levels does it have? How many would you really need? (2) Can a cluster variable be an IV in a mixed model?
Have you considered Bayes' Theorem?
The description of your "models" make no sense. Please edit to make this more clear.
It does not really change the answer.  First what are you hypothesizing to be equal or not equal to 0?  it is not the hypothesis, but rather parameters such as the difference of 2 means or proportions.  And still the power is calculated assuming a given value (suspected difference, minimally interesting difference, etc.).  If you have high power to reject at a given effect size and don't reject then that is suggestive that the effect size is smaller, but a confidence interval still conveys this better when possible.
How much data have you got? Estimating measure-dependent main effects and interactions may be possible (using e.g. Seemingly Unrelated Regression or some GEE analog) but the wisdom of trying this approach depends on k, and your sample size.
Hi Greg, thank you for the answer. It sounds like what you are saying is I found somewhat of a special case where the test does not work properly under the equal distributions null. And furthermore, the null hypotheses I stated are not equal. Is that correct?
Agree 100%. And we don't have access to the paper. But perhpas worth noting that as a result, when the words equivalence or non-inferiority are used in medical research there is an explicit or implicit equivalence or non-inferiority margin. Without these margins (and the justification for them) statements regarding equivalence are meaningless.
Thank you so much for this - it makes sense :). I get ~0.92 as my answer.
If it is $\\eta^2$ (and it may well be) then it is indeed a typo, since the question listed it as $\\mu^2$
I have gone ahead and made the edits. I hope you don't mind. Cheers. :)
Well I do not understand the question, do you want to simplify the informal description of stationarity concept you quoted here? If you ask is this explanation correct, yes it is. Though non-stationarity has much more forms, any time-dependence in up-to second order moments will be the source for such in weak case (structural changes could be added, for example). Are you looking for some other quotes?
mms and rss are both results of z, which is the name of the lm object inside of summary.lm.  So, an answer probably does require an explanation of QR decomposition, its use in linear regression, and specifically some details QR decomposition as instantiated in the code underlying R in order to explain why the QR decomposition ends up with approximations of 0 rather than 0 itself.
[This document](http://www.upassoc.org/upa_publications/jus/2006_may/lewis_small_sample_estimates.pdf) might be of interest. There is an [online calculator](http://www.measuringusability.com/wald.htm) that calculates point estimates and confidence intervals based on the different methods discussed in the paper.
+1 well illustrated
@DmitrijCelov, those are excellent questions and I must admit I haven't done a good job exploring them before posting. I'd say that as a start I won't include any exogenous variable. The reason I asked this question is that coming from a stats world I'd have some ideas if there were only 2 or 3 variables; with so many variables I naturally thought of more "ML" techniques that deals with tons of features. But my little knowledge of those techniques doesn't include anything specific to time series.
@Benjamin-very interesting, but I don't think it will do stepwise regression.
+1, with @onestop's caveat in comment above that robust se's could very well be bigger or smaller, though typically we expect them to be bigger and thus "conservative" wrt type I error. And yes, I always use either heteroskedastic robust or cluster robust se's in my work, as does everyone I know.
Draw a graph with $\\theta $ on horizontal and $ L_x (\\theta)\\pi (\\theta) $ on the vertical.  Now what happens when you plot $\\pi (\\theta|x) $ on the vertical instead?  The scale of the vertical axis changes - and nothing else.
@ Jim M. Does it make sense to include the grouping variable (`choicenum`) as a random and a fixed effect?
+1 clear explanation of the central problem
does the stable distribution still hold if you apply the "maximum" function to portions of the time series?
I was thinking that there had to be some kind of limit and that after checking 27 times that you would stop. But thats a presumption that I probably should not have made.. What would you suggest?
@KarlOveHufthammer That is it! Thank you. If you want to change your comment to an answer, I'd be happy to award you the correct answer and bounty.
It might help to post a plot of your data as well.
I will definitely take a look at the course, but his course also requires some programming. NeuroXL is only $99 once it expires, so if I can understand some basics with the tool, it will work for me.
@chl This popularity of the sphericity assumption is exactly what I am frightened about. I know some statisticians who use this model whereas it is far to be appropriate (e.g. there are 3 repeated measures at 3 different timepoints and the correlation between measure 3 and measure 1 is clearly lower than the one between measure 2 and mesure 1). Because they do not understand what they are doing.
I don't see any obvious reason why you couldn't.
Psst... you might want to ask a question in your question.
@cxr Thank for your response. I has a look at `surveillance` and `DCluster `, but could you please be a bit more specific? They are both relatively large packages and their aim seems quite specific. I'm not sure where to begin.
Survey one must have been weighted to population and it sounds like there are at least instructions on creating confidence intervals from it so perhaps we can assume that was done correctly.  You need to do the same for survey two.  Then you have two estimates which are just independent random variables and you can take a weighted average of the two as your combined estimate.  But this will only work as Michelle says if the sampling method for two was random and in a known fashion that can be taken into account in weighting; and the weights for survey one are appropriately constructed.
Thank you very much for this thorough response! I'm wondering if there's any technique for choosing the $\\lambda$ so that the mixing time can be minimized. I was thinking trying out different random values and pick the best one, but is there a more systematic approach to this?
user27008 Just a caveat - you can't choose *which* of Fisher or chi-square to use based on which one is most significant. Pick one kind of analysis both for the whole table and any partitions (where the choice is based on considerations other than the values within the table -- though basing that choice on the margins shouldn't matter).
Can you put the rather crucial information that it's not monotonic in your question? Can you plot the data?
Could you provide more details on exactly what you want? What you achieve using `bs` as above essentially amounts to evaluations of B-splines at the data points to form a design matrix, which is used for the estimation of the coefficients for the B-spline basis expansion. Using the `predict` function it is pretty easy to get the resulting fitted curve at the data points as well as at new points if desired, but it does not give you any equations.
If you only want to test the three-way interaction, the two-way interactions should be in your null model. That means `(sex + vowel3 + Language)^2`.
Perhaps write out the exact operations you are considering. It's not quite clear what you mean as of now.
See [here](http://stats.stackexchange.com/questions/68834/what-is-the-benefit-of-breaking-up-a-continuous-predictor-variable/68839#68839). And I don't think using a neural net makes any difference.
I do not want to twist this answer, but it seems that the demonstration could be misconstrued as showing that *asymptotically,* a sufficiently large experiment will produce a p-value that is *approximately* the same as the "probability of $H_0$."  In other words, this (nice) demonstration might not accomplish the learning objectives you believe it does, because it does not appear directly to attack the fundamental misconception (in the frequentist paradigm, of course) that it even makes sense to assign a probability to the null.
It follows directly from basic properties of [expectation](http://en.wikipedia.org/wiki/Expected_value#Linearity) and [variance](http://en.wikipedia.org/wiki/Variance#Basic_properties). Hint: write the mean as a constant times a sum. I really can't teach you a whole subject in comments. Where's your textbook? Notes? ... and so on? In fact if you really can't get started at all, I don't think this is the right forum for you.
@ChenghaoLiu Formulas were designed for small yet complex liner model frames, and thus they are inefficient when copying the set becomes expensive.
Actually I ended up not using it at all, it was indeed very difficult. But, I do think it's very useful and worth poring over because there's not really another formula I know of that can do what this one does -- ie estimate probabilities for Weibulls like how we do it for normal curves.
Likely there is an existing, published literature on weight change over time.  Your definition of a large (suspect) change could be based on that literature.
I don't understand what you mean by 'Ymod' and 'the results that come from the linear fit, when i use it on the original samples.' Can you actually write down how 'Ymod' is computed?
Another issue to consider when choosing the "best" algorithm is whether to choose supervised or unsupervised learning. Do you have any training examples (whose class are known)?
Oh okay, my apologies. I gather ICC might not be the best measure in this case - there are other measures of inter-rater agreement that are better for ordinal data, e.g. Kappa. People with more knowledge than me have answered similar questions elsewhere on here: e.g. http://stats.stackexchange.com/questions/3539/inter-rater-reliability-for-ordinal-or-interval-data
This is either more appropriate as a CW or it should be closed as too broad. If you've run into some specific questions based on practice, a more suitable question for this community would be based on specific context and motivation.
Please post your data as we have seen this kind of problem resolved with causal input series and empirically identified level shifts and/or local time trends. A cost accountanting firm had retained us to analyze such data in order to estimate "fixed costs" and "variable costs". I will try and help.
Thank you for your reply.
I would also know how does the regressor work.
Does the regressor regress on the remainder to find out the effect (coefficient)?
Is regression performed at the decomposition stage or forecast stage?

Thanks again in advance
Jonathan
Do you still have access to the original data?  I would recommend including all of the data (you can either control for across-season differences by adding season as a parameter, or ignore it -- which will have the effect as averaging, but be statistically correct).  Correcting for slope should be done as part of the model, and the correction for study area should be done with an offset as in @user13317's answer below.
Thanks! This question was actually prompted by that post, I saw the horizontal red line representing CI coverage and wondered if this line is always horizontal, or if the (normal + known variance) case is a special case. I guess what I was interested in is not so much about the definition of CI, but more like, in general, are there cases where it is impossible for the coverage to be $1-\\alpha$ for all parameter values, and so you have to choose your CI to make the coverage $1 - \\alpha$ for some parameters and greater for others? (I'm guessing yes, but confirmation would be nice).
@user1493368: I think the book is still very useful, especially if you are interested in (teaching) typical econometric estimators / methods because it contains different issues which are important in econometrics (such as SUR) but less frequent in other applied fields and vice versa. Still many topics are only briefly mentioned or missing (such as IV or propensity score matching). I do not whether other books such as Hands-On Intermediate Econometrics Using R (mentioned by vinux) discuss these topics.
Thank you for your answer! The data has a very high amount of random noise at the daily level. So much so that it completely obscures any trends, even when accounting for day of week, weekends, etc usual tactics. Going to Monthly, or even weekly seems to greatly improve the signa-to-noise ratio...or am I reading too much into the structure that appears when the daily noise is smoothed out? Could the aggregated data make trends appear more obvious or stronger than they really are?
Power will necessarily depend on what distributional assumptions you make for the processes.  Could you please give us some indication of what assumptions you can make in your application?
Can you write the model?
Hi @Marc.  No need for "sir"! :-)

Unfortunately, days and months do not fully account for the dependence of the data - the value of the DV on (say) Jan 2 is going to be related to that on Jan 1, beyond the fact that both are January and whatever day of the week each is.

You can get the probability of each outcome directly in SAS and R, and probably in Stata as well, but since I don't use Stata, I don't know how in that program
Sorry, I corrected the error in my answer - thanks for keeping me honest! Of course the logit can reach zero. The problem is that its *inverse*, the logistic function, from which we calculate fitted values, will not reach zero. Hope it is clearer now?
Also, in ridge regression a factor of 10 increase or decrease in the ridge parameter often can have relatively little effect on the fitted model- this isn't necessarily a very large change in the ridge parameter.  Another point here is that with your original parameter you may be overfitting the test data.  Multiplying the ridge parameter by 10 will tend to stabilize the fit.
Just use the definition of expectation: $E[(X+Y)\\cdot(|X-Y|)]=\\sum_{y=0}^{1}\\sum_{x=0}^{1}(x+y)\\cdot|x-y|P(X=x)P(Y=y)$
Which probabilities are given to start with?
I thought then synonymous:http://mathworld.wolfram.com/Analytic.html