tttjjj/elt_bench huggingface dataset:
@Marcel you can also plot the Schoenfeld residuals generated by the cox.zph function to examine violations of the PH assumption.
@nicefella The proof is relatively easy: evaluating the MGF at imaginary values gives the characteristic function which can be inverted to produce the distribution. The inversion works provided the MGF is analytic in a neighborhood of the origin.
Inspecting a small example of $(A,B)$ pairs might help, such as $(10,1),(10,1),(x,1),(20,2),(20,2)$. If $10\\le x\\le 20$ then the median $A$ is $x$, the median $B$ is $1$, and the median of $A/B$ is $10$ (no matter what $x$ is). Thus if $x\\ne 10$ you have an obvious discrepancy.
Why check against a log odds ratio *z*-test? That's a Wald test, and Wald tests typically perform worse than score tests such as Pearson's chi-squared test. Is this known to be an exception?
However, you can look at how much each original variate contributes to the scores (= new variate values) for different cases. If your original data was standardized, the PC loadings will tell you that. If not, you need to multiply the loadings element-wise with the original data (i.e. stop before the summation of the matrix multiplication you need to obtain the scores).
I don't know about PASWStatistics18 but it seems like either the initialisation of the first k centers is different for each run, or a mean is immediately updated after each datapoint (or some datapoints) assignation (like for the online k-means) .
Perhaps, this question should be on superuser. There are web based software tools which would let your audience to see your desktop via a browser. Some of these tools also let you delegate control to your audience so that they can open docs/files at their end and it will show up on everyone's screen. Some commercial tools are gotomypc.com, webex etc
Great! Can you make it work with timeseries as a bonus? When using a zoo the border insists on appearing.
(...) The [FactoMineR](http://cran.r-project.org/web/packages/FactoMineR/index.html) includes a data set about wines, and many factor methods can be used to play with it (PCA, MFA), and even PLS or CCA as has been done by Michel Tenenhaus.
@Maddy, that isn't really correct. There is basically no case where you need to bin. What you could do is fit spline terms. The idea is discussed in the answer I link above.
> besides, the method is not very efficient (from a computationnal point of view)
This is not quite correct, if cross-validation performance is performed correctly, it is almost unbiased, so it should give the same performance estimate as a test set *in expectation*, whether the model is over-fit or not.  However, in this case CV has been used to make model choices, so it is no longer an (almost) unbiased estimator.
Why does each row have a male and female id?
Are you saying there's a strong *negative* autocorrelation, ie that if year t=1, year t+1 *must* equal 0? Is it possible to have two 0's in a row?
James, you are asking a very general question.  A full answer would require the resources of a small textbook, because there are dozens of ways to go about estimating $p$ and $n$.  To narrow it appropriately, could you state how much data you have (or contemplate obtaining), *why* you need to estimate these parameters, and how accurate you need the estimates to be?
Are you saying that you have 11 latent variables and 2 to 4 observed variables per latent variable?
@user1275515, see my revised answer.
So, you're saying at least start with what I described as Standardization (studentizing), then adjust the weights to best fit the data/scenario?  That makes sense.  I just don't understand why I would divide by the SD.  And in researching I found something called the Standardized Mean Difference.... and I've just been confusing myself.  It seems like it should be simple.  You either put them both on Scale-A, or one on the same scale as the other, then sum.  But no.  Instead I'm confused and all Wiki'd out for the moment.
That's very possible the two programs would match, since they had similar implementation approaches at that time (TOL = .001, M-step optimizer set to Newton-Raphson, etc). More recent package versions use the BFGS optimizer in the M-step instead of the Newton-Raphson since it is much more stable (and uses the log-likelihood directly), and the TOL criteria is set lower (1e-4). Other things have changed as well internally, but those are the big ones which probably caused the difference.
Welcome to the site, Matt. Regarding your opening sentence: *One very important thing to remember is that multiple testing correction assumes independent tests.* Note that this is true for *some* multiple-testing correction procedures, but certainly not all. For example, the *simplest of all* (Bonferroni) makes no independence assumption, and, indeed is quite inefficient if the tests actually are independent! :-) Also, in a continuous-distribution setting, the (marginal) distribution of a single $p$-value will be uniform under the null; you might consider editing to clarify your remarks.
+1 It's often even worse than this in practice, because people can use 2-sided hypothesis tests without thinking. So they can end up rejecting the null when the true/anticipated effect is in the opposite direction to their observed result.
Thank you for spending your time one this followup! It is definitely helpful and opened my eyes towards the problem from another perspective.
@Pardis I might be able to see a connection once the argument of $\\exp$ is clarified.  In its current form it does not appear to be related to a log probability.
I think the examples are most unfortunate, while maths and reading ability are stated as being assumed to be independent, this is probably not actually the case, which leads to some confusion with respect to the later use of the term "fact".
For more on the relationships among correlation coefficients and regression slopes please see the answer at http://stats.stackexchange.com/a/104577.
After a while my understanding is that each variables have to be split  in $\\phi$ parts independently from the others.
Done! The theory I have found until now tells me that I can obtain p-values using Quantile regression. I will give it a try. Thanks for the answer!
which version of KNN classification are you using? Are you using SPSS?
Perhaps you could give some more context here.  There is nothing wrong with having both binary and continuous variables in the explanatory variables of a linear regression model, but it isn't clear what you mean to do with this.  Are you fitting a range of explanatory variables to a response variable, and then using the predicted values from this model as a scale?  Also, by "convert binary data into a z score" do you mean scale it so it has zero mean and variance of one?  I'm not sure why you'd want to do this.
Why "should" the outcome be 0.610?
(...cont) That gave me the exact probabilities for $X_{final}$ being each order stat.  Then I used those weights to mix the 5th -8th order statistics for F(x), using a textbook formula to define the order distributions of F(x) (where the pdf of the 4kth order stat of n draws from cdf F(x) = $\\frac{n!}{(k-1)!(n-k)!}F(x)^{k-1}(1-F(x))^{n-k}f(x)$
Polynomials and splines are unlikely to be valid CDFs.
It should be noted that L1 and L2 regularizations are approaches to dimensionality reduction. But a user might not know it.  If any feature weight is reduced to 0, the dimension is effectively removed from the model. It's also fair to note that L2 regularization is pretty bad at this (i.e. setting a weight to exactly zero), compared to L1. (Hi Alexandre)
You could do Bonferroni or Holm.  Bonferroni is rather brutish.  If you like Holm's logic then us that.  And Tukey's HSD is a way of reporting that doesn't require an ANOVA first... thus it's probably conservative.  When I have a significant RM ANOVA I tend to use standard confidence intervals in a specific way (see edited answer).
They are different systems. Although they are similar they all differ significantly and I can't assume any parameters are the same between them.
Nevertheless the normal case has been well studied. Well, more has been written about the maximum, but that's just a matter of flipping about the mean (which for the standard normal is just taking the negative). There are tables, for example, and asymptotic approximations (which are a bit rough at n=10 but which I think do relatively well at higher n). The tables [here](http://faculty.washington.edu/heagerty/Books/Biostatistics/TABLES/NormalOrder.pdf) give an expected value for the maximum at n=10 of 1.53875.
In R, `ltm` and `mirt` both use MML, so checking out the source code for either package could be useful with your implementation.
Which alternative will you compute it under?
OK.  I'd still recommend doing some general reading about psychometrics so that you know what is often done in your situation and what is possible to do.  After all, doing some analyses will not be useful if you don't know the sorts of issues that are important in these situations!  Anyway, good luck with your project.
@ImAlsoGreg Strange question: did you go to Rutgers by any chance? If so, I think I might know you!  If not, thanks anyway for the answer, this has been very helpful!
That's too bad. We submitted a paper and our reviewer (whom the editor agreed with) insisted that we should use nested binary logistic regression. If in case we would want to find the final model, will it be ok to run all models and choose the final (one best model) model based on AIC values? About as.factor, we are interested in Odds ratios that determine differences in different categories for each independent variable. I'm not a statistician and i don't really know which is the best technique to use for our data. Thanks a lot for your help...
@Glen_b +1, sure. My comment was a reaction to the comment: "asymptotic approximation isn't accurate, but exact probability is accurate". I often see people being too impressed by any test carrying the label "exact".
If you just want to estimate a "similarity measure," you don't need the Mantel test: just compute (say) the Pearson correlation between the two matrices.
You might appreciate reading about the [Ecological Fallacy](http://en.wikipedia.org/wiki/Ecological_fallacy).
Did you want to write P(E|L,¬T)= 1.0 instead of the second P(E|L,T)= 1.0?
How can there be a dependence that is not due to causality?
Welcome to the site! Providing a bit more information about the approach you're imagining might help you get an answer that you can use! Maybe tell us a bit about the structure of your data and show a graph depicting the drop you describe?
(+1) Yes, I'm aware of that project too. But I know that those that are currently developing the `scikit.learn` are serious guys working in neuroimaging, and that the project will evolve and include ever growing features.
Analysis of correlation matrices may be misleading if the variances are different in different variables in different groups. Equality of "small" ($p << n$) covariance matrices can be tested using likelihood ratio tests (see e.g. [Rencher's book](http://www.amazon.com/Methods-Multivariate-Analysis-Probability-Statistics/dp/0470178965/)) or [the bootstrap](http://www.citeulike.org/user/ctacmo/article/3015345). With "huge" matrices (define "huge" please), you may not have enough eigenvalues to get a proper argument in place.
I agree that a well-argumented review might qualify as a ["valid, helpful and knowledgeable answer"](http://meta.stackexchange.com/questions/55888/when-to-mark-the-community-wiki-checkbox-on-a-new-question). (Incidentally, we both pointed to some of Good's textbooks on a [related question](http://stats.stackexchange.com/questions/5845/good-text-for-resampling).)
I can't recall anything for statistics as a single "infographic" (I am old enough still to think that's a horrible word). You've already indicated why that is unlikely: statistics can be sliced up by schools of thought, by application areas, by methods, by models, by kinds of data, and no doubt others that don't spring to mind right now. Any diagram that matched that diversity would be a confusing mess, I suspect.
Significance-hunting in this was is not a suitable way of finding things out and is not statistically justified.
Thank you for your answer. What do you think about GARCH(0,1), GARCH(1,1) AND GARCH(1,2) results I put abve?
A comforting thing to know.
See also: http://stats.stackexchange.com/questions/23391/how-does-a-support-vector-machine-svm-work
Do you mean that the response to the question must lie between $0$ and $1$? Also, how large is the sample? If it's big enough (practically speaking $>30$ with a reasonable range of answers), asymptotics should allow you calculate it on something approaching normal...
@jthetzel has listed some relevant questions on CV, but I would like to point your attention towards a couple more: [things-to-consider-about-masters-programs-in-statistics](http://stats.stackexchange.com/questions/25713/things-to-consider-about-masters-programs-in-statistics) is particularly relevant, & also [equivalent-knowledge-to-a-quality-stats-degre](http://stats.stackexchange.com/questions/6538/mathematician-wants-the-equivalent-knowledge-to-a-quality-stats-degree) may be of interest.
Use common sense, i.e. make an informed modeling choice. Bayesian statistics requires that you pick a likelihood and to pick a likelihood you need some familiarity with a few common probability distributions. You are probably looking for the binomial, but it could be the negative binomial, geometric, Bernoulli, or even Poisson. I don't know which one because you haven't framed your question very well.
The ASC and DAT files are plain text. ASC file tells you which columns match which variables so you could easily load DAT file into Excel. I agree that particular .ws file does not load.
In the the article you cited in your question, @Abdus
What you asking is a pretty well-studied problem in machine learning, I would suggest you to google "svm, text classification".
I have deleted my previous comments. The last line of your answer is the hard part. To the best of my knowledge, simulation or numerical integration is needed to compute $P(A > \\max(B,C))$.
1 note: the way I typically think of the Bonferroni correction, you *divide* your $\\alpha$-level (usually, $0.05$) by the number of comparisons & see if your p-value is below the adjusted threshold.
1. Is there a good overview about this topic for non-statisticians who want to apply these principles to data? Which robust regression can I use when both assumptions are not met?

2. What does "usually" mean? Googling "Ordered robust regression" literally finds nothing. Do you have a source for this topic? 

Thank you
I get a general sense of unease and doom when people talk about choosing a distribution simply because it "best fits the data."
Hello Anna, it would help to know a bit about your approach: do you normalize your data? what kind of architecture do you use? is it a standard package or your own implementation? What cost are you trying to minimize? for what problem (classification/regression)?
With n = 3 and n = 1, no nonparametric test is going to show significance, I think, no matter what the values are. You would have to make some strong assumptions about the group of 3.
Well, that's exactly the question, isn't it?  Precisely *how* should the algorithm be varied? (It isn't comforting that the Wikipedia article characterizes these problems as typically being NP hard!)
"Proportion of variance explained" equals the eigenvalue *divided by the total variance* (the trace of the covariance matrix). If all you know is this proportion, then you cannot recover the variances: you need the information about that trace. Think about what happens, for instance, when you simply change all units of measurement. If, say, all variables are lengths in meters, then when you change them to millimeters, all variances (whence all eigenvalues) are multiplied by one million. That shows why the absolute sizes of the eigenvalues mean little (and small values shouldn't bother you).
Picture Is Worth 1,000 Words Dept.:  could you post a table showing how your data are structured?
Please double-check your equation for the joint PDF: what are you doing subtracting $\\theta$ from it?
Great answer, thanks. As I now used the solution or ars I will accept his as the accepted answer.
That's the simplest one I know of.
Aha! I see the reason in the edit log: "[made Community Wiki by user27915816 editing at least 10 times]".
Can you add some details?
@Wayne: I am trying to keep a legend on top of the graph using auto.key with space="top", pch=c(1,2), lty=c(2,4) arguments, but the pch values and lty values are not working. Moreover, I would like to keep the X and Y as horizontal in the legend. Could you please help me for this.
Confidence intervals are not really used to determine the whether two separate estimates are statistically different or not. However, a statistical hypothesis test such as a z-test, can tell you within a certain probability whether or not two NPSs are different.

I don't mean to "correct" you, so please don't take offense. I just wanted to make sure people who stumble on this thread are aware of all the considerations.
This is more ore less textbook stuff. The key word here is t-statistic. Central limit theorem is certainly useful, if your latency has finite variance. If it does not, then it becomes trickier.
The overall ANOVA asks a question about the whole independent variable and its relation (or lack thereof) with the dependent variable. The pairwise comparisons ask about differences among pairs. Then the p-value looks at the statistical sig. of each of these, with the pairwise adjusted for multiple comparisons (in this case, using Tukey's HSD methods).
Thank you for such detailed answer!
Hi! Take a look at http://en.wikipedia.org/wiki/Structural_break
Duplicate of http://stats.stackexchange.com/questions/10544/difference-in-means-in-multiple-choice-poll perchance?
I don't need code , I need more of a paper of someone who went through the process and is explaining his or her methods and the subsequent explanations.
You ask "*how the computer software controls for all variables at the same time* ***mathematically***". You also say "I need an answer that does not involve formulas". I don't see how it's possible to really do both at the same time. At least not without serious risk of leaving you with flawed intuition.
I could be wrong, but I don't think this is the same thing.  From SEM graphs that I've seen, it looks like SEM uses multiple regression equations to determine the values of latent factors, and then another regression is run on the value of those latent factors to determine a higher-order factor.  Maybe this is wrong, but I've never seen an SEM graph that links several IVs to multiple DVs-- everything is hierarchical.
If this is for some subject could you tag it as `self study` please?
Thanks for the helpful reference!
Thankyou very much, a fantastic answer.
@Figaro, I have updated with an example of making the colors semi-transparent.
Arpit could you include the output that concerns you, and perhaps even the table of counts, and explain why you think something is wrong?
+2 Thanks for answering. There are some interesting points in your answer. Your guess is correct: they come from stochastic processes. I need to read your answer thoroughly, so.
That is too bad, I am having trouble with completing step (3) in the procedure that I outlined above. Even though I can easily complete the first two steps I continue to receive "error: unexpected symbol in lm" - even though none of the appearing symbols have caused any troubles before.
I've always splines, but fractional polynomials were popular at one stage and I think there is an R package for them. But....you don't have a lot of data, nothing is going to solve that or fit the data well as a result
My table has the following row headings: Demography (i.e. Gender), Pearson's 'r', r squared, p value, sample (n) and Equality of 'r'. The last label 'Equality of r' is what this question is about. Thanks a lot. (Am I missing any other vital information in this summary table?)
removed comment duplicating what KC_CAL said
You just may do singular-value or eigen-value decomposition of the matrix, to get eigenvalues and eigenvectors (and then compute loadings out of the two). But without casewise data you won't get component scores, of course.
@whuber I mean a case where the limit of the integral doesn't exist; I presume that's what you intend by 'fails to converge'.
Angles have no magnitude, if you transform it in something like sine, cosine or something similar, you introduce magnitude..
BNT has good demos and is easy to use. PMTK is developed by the same person so it probably has considerable overlap.
@MarcClaesen I have replicated the answer below.
You could try and use a Bayesian network for predicting some values, given a few other values.
censoring occurs even when you know for certain the event will eventually happen. What matters is whether all your observations have the event time recorded (e.g. if some are still alive when your study ends, or are lost to the study by other means)
@TOM is suggesting a procedure called double-prewhitening which can be useful to suggest which variable is "causing" the other. Ultimately one prefers the single pre-whitening, generating Impulse response weights as it doesn't distort the identification of the Transfer Function Model. Care has to be taken to deal with Pulses, level Shifts, Seasonal Pulses and/or Local time trends in forming a useful model Addditionally one needs to be concewrned with time changing parameters and time-varying error variance. Pursue (automatic) Transfer Function identification
How about doing what you did, and using an l1 regularizer while doing estimation to enforce sparsity?
Your formula seems to have $y$'s (observations) where I think it needs $\\hat{y}$'s. In this particular formulation, $p$ is the rank of $X$ in the regression - the number of predictors including the constant. Some books and papers will make $p$ the number in addition to the constant, and adjust the formula for $D_i$ to have $p+1$
I believe that the question is asking you to prove the [convergence in probability version of the continuous mapping theorem](http://en.wikipedia.org/wiki/Continuous_mapping_theorem#Convergence_in_probability).
Additionally, $h^{-1}(z_t) \\not= x(t) + w_t'$ (unless $h^{-1}()$ is linear or you make $w_t'$ depend on $x_t$).
So you would assume two of the series track the true price and look for the lag that best matches the series that lags with the other two assuming that they don't lag.
Correlation isn't necessarily much use for accuracy, because things can be correlated without being close. Consider if my forecast of y is y/100 -- perfectly correlated, but a terrible forecast. On the other hand t-tests really answer the wrong question. Why can't RMSE be used with one model? Its values are perfectly easy to interpret, being on the same scale as the data -- it's no trickier to comprehend than a standard deviation.
@Matt It is *practicable* (it can be done) but its meaningfulness is doubtful.  However, *ratios* of densities do make sense, as @ProbabilityIsLogic has suggested in a reply.  For instance, you might re-express all the results as ratios relative to the largest one.  They won't sum to unity--that is the part that is meaningless--but they will all lie between 0 and 1.
See Steyerberg et al (2001), "Internal validation of predictive models: Efficiency of some procedures for logistic regression analysis", *Journal of Clinical Epidemiology*, **54**, pp 774–781 for a comparative study.
A value of $0$ occurs when all the data in one group are strictly less than all those in the other group, that's all.  That suggests the normal approximation (to compute the P-value from Z) might be inaccurate.  Indeed, in the example shown, the exact two-tailed p-value is $2/\\binom{24}{12}$, about 7.4E-7, while the normal approximation gives 3.2E-5, which is 44 times too large--but that's unlikely to change the conclusion that the medians are different.
@gung. Thanks for your advice, I will take it seriously.
$(\\mu-\\frac{\\delta^2}{2})t$ correct? (I added the $t$)