tttjjj/elt_bench huggingface dataset:
I've never found these terms (eg, ANOVA, ANCOVA, General Linear Model, etc) to be very helpful. Ultimately, these are all the same thing. Traditionally, an ANCOVA was when you were primarily interested in the effects of categorical IVs, but also wanted to adjust for some continuous covariates that weren't of substantive interest. In realiality, these are all forms of multiple regression. Part of your confusion is that SPSS makes you ask for analyses using this terminology. I would probably call your situation *multiple regression*. You should be able to do what you want via that in SPSS.
What do you mean by "normal variables"? Are you trying to say you have 2 variables which are continuously measured?
You may be able to get some information from my answer here: [Determining similar users from hierarchical clustering](http://stats.stackexchange.com/a/91025/7290).
@Aniko The point that I do not understand is that "you could certainly argue that the rejection is appropriate because the values on the right tend to be higher" when the median is 3. Could you please elaborate more upon that?
@AsymLabs, how separate are Breiman's Two cultures (roughly predictors and modellers) ? Cf. [Two cultures](http://stats.stackexchange.com/questions/6/the-two-cultures-statistics-vs-machine-learning) -- contentious.
No, but two studies is enough.
Thank you. Makes sense. Good explanation.
@user34790 Δxi= xi-xi-1 They are the independent increments and they are summed to get the total walk.
Welcome to CV! I would double-check your text for the question and answer. If the two are [mutually exclusive](http://en.wikipedia.org/wiki/Mutually_exclusive_events), the answers are straight-forward: 0.8, 0.3, and 0. Is there anything more to the question?
Just a thought, but this reads like you're saying the probability of rolling a 12 (1/36) is the same as a 7 (1/6).
(+1) The question is interesting and challenging. I feel that it needs some refinement in order to have a good chance at a good answer. As currently stated it borders on being ill-posed. For a practical solution, you would need to provide some more details on the range of environments in which you wish to be able to perform this classification. What color backgrounds are possible? Always the same number of coins? Will you always have a color image? Good ambient lighting? Knowing these sorts of characteristics can provide guidance toward a solution.
(+1) It's interesting to note that if the ratio $s/n$ is very small then essentially no information about $n$ can be present and so one can't expect to do very well estimating $n$. If $s/n$ is very large then $U$ is a good estimator. So, we need something that works in a mid-range.
First a notational clarification: μ is a hypothesis about the true mean and n is the sample size. These are not the same thing.  X is *an* observation, but X with a bar on top (what I called X-bar above) is the *average* of all the observations.  If the estimated standard deviation is S, then the *standard error* is S divided by the square root of n (that is: the denominator in your original question).
Both books seem to have good reviews on amazon, can anyone add any opinions (perhaps in a bit more detail) on these? btw; by casella & berger do you mean "Statistical Inference"?
Hi Peter.  I'm unfamiliar with some of these aspects of reg. diagnostics.  Could you say just briefly why such output is more useful than, say, the combination of the tolerance statistic and a correlation matrix?
Poisson regression is not relevant here because the dependent variable is not a count. The independent variables are the ones with 0s.
What have you tried and why hasn't it satisfied you?
Given that all these inequalities are applicable, why not do the question both ways and see which result is better (that is, smaller)? There's a certain ambiguity to this question in any event: what does this "probability" mean? Although you seem to interpret it as a *proportion* of actual test scores (and there's nothing wrong with that), in similar circumstances it could be interpreted as an estimate of a property of some underlying distribution assumed to describe the test outcomes.
It depends on how many times you do it and how many dichotomies there are.
Concentrations are almost never exactly zero: if you name almost any molecule, you will likely find it in almost any living thing. Thus, your zeros probably represent *positive* values that are too small to be detectable. They are therefore *left censored.* Consider looking for solutions that accommodate censoring.  Such solutions typically allow for the variable to be re-expressed: usually, the logarithm is a good choice for environmental concentrations.
Thank you! Come to think of it, I think I have seen this before but not applied it. It doesn't seem incredibly easy, but perhaps I could manage after looking at it for a few minutes.
If you're suggesting finding the mean of correlations, you should probably mention the [Fisher transformation](https://en.wikipedia.org/wiki/Fisher_transformation). This step is too easy to forget otherwise.
Thanks for the great explanation .In a similar way I was able to show that $Y_{(n)}$ is also a consistent estimator for $\\beta$.There $\\alpha - \\beta <= Y_{(n)}-\\beta<=0$ and thus $0<=|Y_{(n)}-\\beta|<=1$.Thus $sup |Y_{(n)}-\\beta|=1$.And for $0<\\epsilon<1 $ case $P[|Y_{(n)}-\\beta|<\\epsilon]$ since  $Y_{(n)}-\\beta$<=0 this probability becomes $P[-(Y_{(n)}-\\beta)<\\epsilon]$
You are correct.  Could you explain the "logic of...how to approach this problem" requested in the question?
"*the Cauchy term itself could take on values of infinity too*" -- no, even though it's an unbounded random variable (i.e. defined on $(-\\infty,\\infty)$), every value taken by a Cauchy random variable is finite. You likely mean something a bit different from what you said there.
Can you be more specific? EG, are you asking about [Chebyshev's inequality](http://en.wikipedia.org/wiki/Chebyshev%27s_inequality)?
I do not know it "ad hoc test" has a special statistical meaning, but reading that sentence I would just understand that it refers to the fact that the test is usable only in certain specific conditions. *Ad hoc* is Latin for "to the purpose". Something made *ad hoc* is made for the specific purpose at hand.
Clearly the data this graph is based on are not derived from tossing a coin and appear to be continuous, not binary. Could you tell us what the substantive question is you're trying to answer? Putting it in terms of an stereotypical example isn't helping here.
If the data were exponential, *keeping* the zeros is a source of bias in estimation of the exponential mean, while tossing them out doesn't lead to bias.
Thank you ! Still one thing which is unclear to me. Why is the p.value lower and the R squared higher when forcing the regression to pass through the point (0,0) ?
What makes you think a flat forecast function is incorrect? The forecasts are the conditional means of the future demand, and when demand is intermittent, the future demand often has constant mean.
What about Nate Silver then?
I have already tell my opinion: I can't say more about this...
@TheCloudlessSky For the complete function and full simulation with the expected results in terms of coverage frequencies, see http://pastebin.com/qKpNKK0D
?! Should I report whichever I prefer, or always the lowest W (even if 0), as this is the value that is compared to the critical one in the Wilcoxon Rank Sum Table?
Thanks, this is helpful, I'm looking into using a mixed multinomial model and `gllamm' as mentioned in your link. (Computational time is probably not an issue here.)

(Incidentally, redoing the tests properly suggests that the model _doesn't_ violate IIA. However, I don't find this plausible given my strong priors about school types, so want to try different models anyway.)
I think I do not grasp how "clustering" and the logistic regression model would interact or affect one another.  Could you explain the difference between "clustering" in this context and including a group identifier as an explanatory variable in the regression?
Could you give some specific references we could check?
Can you provide more details about your situation? What kind of data do you have? What does it mean to have over-dispersion if your response distribution is Gaussian? In general, I would not use the term "generalized linear model" to describe a model w/ an identity link & a Gaussian response (although it isn't wrong), I'd just say 'regression'.
@Glen_b Thanks for the edit, it looks much cleaner now.
Some people find that `SmoothKernelDistribution` goes quite quickly; I have found it will take a few seconds with $10^4$ points.  See the response and comments at http://mathematica.stackexchange.com/a/2967.
Have you tried lasso or elastic net? packages: lasso, glmnet. Those methods can "select" some varibles on-the-go.
... right.  I wasn't suggesting he leave it to the reader *if it was a part of his message*.  I was saying that if the threshold weren't a part of the plot, he could either leave it out entirely or incorporate a subtle visual cue to make the threshold easier to find if the reader wanted to look for it.
It's using Google Maps, so works however Google would. (Only get a limited number of geocodes per day.)
Useful references on the "10 events per variable" rule: Harrell's *Regression Modeling Strategies*; Peduzzi et al., [A simulation study of the number of events per variable in logistic regression analysis](http://facmed.univ-rennes1.fr/wkf//stock/RENNES20100407100014blaviolllogistic1.pdf), J Clin Epidemiol (1996) 49(12):1373; Vittinghoff and McCulloch, [Relaxing the Rule of Ten Events per Variable in Logistic and Cox Regression](http://aje.oxfordjournals.org/content/165/6/710.short), Am J Epidemiol (2007) 165(6):710.
Yes you can have 1 portion of time.
+1 Nice interpretation!
@whuber I added an explanation.
I think this needs both (a) one paragraph summarizing your question (b) details of what you did (your discussion in various places seems to hint that cell frequencies are normally distributed or at least symmetrically distributed, neither of which is even possible, let alone assumed by the theory here.
Also, I think I would need something to normalize the values of weeks I get. Because the number of emails posted in not constant for each platform.
Please be *very specific* about what objective standards should be applied to determine "comparable," "good," and "best," for without such clear standards this question is off-topic here.  Consult our [help] for more information.
"I have seen articles, which uses strong learners in boosting" - any references?
To be sure to understand, the three datasets refer to different cross-classifications of two attributes? It may help if you could describe what's available in terms of number and type of variables (or attributes), number of statistical units, etc.
Thanks for the answer!   Why does   completeness ["ensures that the parameters of the probability distribution representing the model can all be estimated on the basis of the statistic: it ensures that the distributions corresponding to different values of the parameters are distinct"](http://en.wikipedia.org/wiki/Completeness_(statistics))? please also see my question here http://stats.stackexchange.com/q/53107/1005.
This is the third version of the same question. Please: modify a previous question, rather than ask the same thing again in different form. Now that you have asked: Please delete the two previous versions; otherwise they will be closed for you. Bombarding the list won't help you; in fact it makes you more likely to attract comment, even downvotes.
Each $b_i$ is a binary bit -- that is, $b_i \\in \\{0,1\\}$. But we don't assume anything about how the $b_i$s correlate to the costs $c_i$.
Most of the top-ranked rules you report are trivial ones (`subdivision X.y => division X`), discard all of these. In fact, you probably don't care about `division` since that information is already implicitly defined via `subdivision`.
Thank you, I revised the question.
in my data I have NO zeros. Maybe there is a recommended model with / without zero inflation and also one for low and one for high n...
Please read the *Mathematica* help page for `ProductDistribution`--which states it creates a distribution with *independent* components.
+1 for the web site VideoLecture, I did not know, did you mention it in the question about video lectures ?
Thanks for this suggestion. There must be multivariate machine learning methods though. Simliar to how you might have 2 dependent variables in an "easier" regression model.. and you just do lm(y+z~...) .. I think..
At first, I give the general formulae converting pattern loadings and structure loadings into each other. (It's what about question is.) **C** is a cosine matrix (like the one in the eq. 5.27). I then proceed to explain where that matrix comes from in a factor analysis: it is the product of the rotation matrix **Q**. FA first extracts orthogonal factors and then rotates them; the rotation is the multiplication by **Q**. **Q** is computed by a rotation algorithm (e.g. oblimin, varimax).
@user3557985: The proof for discrete random variables is very accessible and is outlined on page 43, exercise 5, of this excellent book chapter https://web.cse.msu.edu/~cse842/Papers/CoverThomas-Ch2.pdf
+1 Agree with whuber.  Very nice, and I appreciate the links to other answers.
@user46740 if not co-integration then what do I need to identify pairs for this kind of trading? Anyways I would appreciate if you could still help me in figuring out this doubt specific to the ADF test.
May I refer you to an earlier answer to this question: http://stats.stackexchange.com/questions/55316/is-the-mundlak-fixed-effects-procedure-applicable-for-logistic-regression-with-d/68577#68577
@Conjugate In some cases a probability may *equal* a proportion but it *is not* a proportion.  What relates a proportion to a probability is the specific procedure of sampling uniformly at random with replacement from a well-defined population (which are rare, by the way: 20 Ukrainians have been born since you wrote your comment!).  This clearly is a special case of other sampling methods, including without replacement, with stratification, etc.  In those other cases the proportions no longer even equal the probabilities.  Doesn't this suffice to show the two concepts are distinct?
That agrees with my subjective prior belief that there's no such thing as a non-informative prior.
+1 for the 'forecast' package.  Even if you have your own exponential smoothing model or arima model, it includes prediction functions for both classes of models that include confidence intervals.
How will factor analysis help here? Isn't k-modes clustering more meaningful here? I am very new to clustering. Would be really helpful if you throw some light on this.
@Moderator, thank you for migrating this question as a duplicate to CrossValidated. There are many smart people here, hopefully one or more will offer a reply to this question as I still don't have answers to this.
I think this is the right way to go about running the Poisson analog of ANOVA. You fit your full model w/ all levels of the factor & a nested model w/o the factor. Then you just need to perform a nested model test. In `R`, this can be done via `anova(model1, model2)`.
@MichaelMayer - Thanks very much for your comment- I've edited the model in my post to reflect your feedback. I'm still unsure if the two random effects (ID & Group) are sufficient to capture the nested structure of the data.  As to your question, are you asking why I didn't use the difference between Time 1 and Time 2 scores as my DV and Time 1 as a covariate as opposed to including both in an RM model?
@Fan Applicable techniques would include quadratic forms in random variables (http://stats.stackexchange.com/questions/9220), the "delta method" for estimating moments of functions of random variables; distributions of order statistics for uniform variables; the relationship between gaps between uniform variables and the exponential distribution, and possibly even saddlepoint methods, normal approximations, Central Limit Theorem, etc.
Great thorough answer! It was helpful to also run through these diagnostics with Poisson-simulated data to train my eye with what the plots should look like.
Thanks you, Nick
Hint: pay attention to the information in the problem, which involves the numbers two and *eight* (not two and six).
Julien, please visit our [Help Center](http://stats.stackexchange.com/help/merging-accounts) to merge your two unregistered accounts.
Should this be tagged survival analysis instead of time-series?
(+1) Welcome to our site!  It isn't just you: this is a deep question that goes to the foundations of statistics.
@user4581  Oh, notice that post.cov = solve(). Will edit my answer accordingly.
Have you thought of other options, such as referring those questions to a statistician?
Thanks for the elaborate answer, this backward reasoning approach I didn't see before, unfortunately I don't entirely get it. Isn't the part between the '=' and the integral sign, on the fourth formula line a bit artificial? (isn't moving 1/B(x+a,n-x+n) behind the integral sign already like moving the constant A behind the integral sign?)
This is a clear and correct post, but the OP seems to already understand this (I think). Rather, his/her question is asking $why$ this is correct.
All three of the current answers are very good. I would add only that Wagenmakers is making a strawman argument in the sense that no frequentist statistician would ever recommend this confidence interval -- it exists in the literature *only* as an example of a pathological confidence interval. From a frequentist point of view, it demonstrates that confidence coverage alone is not sufficient for good inference. (I'm a Bayesian.)
[oops-nevermind]
@Irish I think you're right about the textbooks (although the revenue typically is so paltry it's of no consequence: people usually write textbooks for other reasons).  One difference is that the textbook always reveals its authors' names, whereas a lot of software does not explicitly acknowledge its developers by name.  Yes, if you've been involved with the SW that you mention, you should say so.
Do test A and B test different competencies or the same ones? If the same ones, then the test with the small variance probably ought to contribute less.
Perhaps `gnormal` will work in English!
Also, DK could have real meaning, ie those individuals are not health conscious and could be at-risk.
You will need those 4 values at a variety of thresholds.
Is the sliding window uniform? i.e. are the weights on the deviations equal for all observations in the window?
How is that different from mbq comment? Multiplying by one or adding zero is just shorthand for using `as.integer`. One could argue `as.integer` is slightly more efficient, but for such application it is pointless to argue.
I am not sure whether my comment helps but once I had to write something about statistical comparison of credit default forecasts. And I also used ROC curves and calculated the AUC. I remember from the theory I read, when the two groups are independent and totally random, such that one cannot predict (whether a person belongs to 0 or 1) anything with a model,the distributions of the predicted values are almost equal. Hence, one cannot improve the model - no matter what threshold is chosen - because your ROC curve is then a straight line from 0 to 1. That is the same as saying AUC = 0.5
+1 The last paragraph is very well put.
I wonder if the non-central $\\chi^2$ distribution is a special case of some useful multivariate distribution. The generalizations I've seen (Wishart, etc...) don't seem appropriate.
Thanks.  These are life insurance claims, so the amount of each claim is fixed.  The only variable is the number of claims.
It would help us if you wrote your regression model in your question. What is the dependent variable? Which are the regressors?
@caracal Yep, that was supposed to point to the same post (but from Rbloggers). Thx for providing a working link.
Do you know the definition of a p-value?
Sorry for migrating it; it is on-topic here.
Is this a homework? Anyway, it needs clarification.
I also thought of running two pair-wise t-tests, and will try it out soon, plus mixed-effects modeling. Really appreciate the great help!
The min and max will be more useful if you have the *count* of your data as well. Is that available?  Is `Xs` the sample standard deviation?
No, I mean to improve the accuracy for any sample size. Bootstrap can be an alternative in certain circumstances, but it's not feasible when the ML estimation is computationally expensive. E.g., if it takes 30 secs to estimate the model, 10000 repetitions would take over 80 hours!
But I cant decide which elments I should use from y in the range [0,0.2]?
Are you sure that the peak you see in figure 2 an error? It looks like what would happen if you had a peak twice as fast as in figure 1, but your sample rate was too slow to capture the full shape of the curve.
Nice! Thanks for the suggestion; this is what I was looking for ;-).
Very useful comments, thanks. The theory predicts that $\\beta>0$ and $\\alpha>0$. So, I was expecting to get these results before the analysis. $Y$ is determined after $X$, and $Z$ after $Y$, which rules out the possibility of a feedback onto $X$. I guess what I'm really trying to understand is the following: 

Can a regression model have on the right hand side two variables one of which causes the other? Or would that be econometrically problematic?
Maybe look at factor analysis or principal components analysis?
I've written simulations in R for random effects meta-analysis. Would it be possible to do that? (I don't know anything about GWAS though.)
How would this work if you many random effects?
If there's anything in the video that answers the question, you should succinctly summarize/paraphrase the relevant information. We try to avoid link-only answers.
@gung yes, you are right. I'm talking about regressing A on B vs regressing B on A. The results are different. Can I solve this problem by introducing an artificial variable X as a response variable and regressing X on A and B?     X = Wa A + Wb B + W0.
(I'm posting still here, as most of this is again more related to the chemistry of the initial question).
@whuber: For me steric hindrance doesn't seem the same kind of bound as the limits that concentrations cannot be positive or that a probability must be in [0, 1]. The angle in an actual reaction may never take certain values, but those values are still part of the concept of an angle. Just like the height of a person may never take the value of 10 m, yet I wouldn't say modeling the height of persons needs a bound on the outcome.
Thanks for the article link. Very helpful. Gave me a good procedure for configuring my SVM. Have switched over to LibSVM and have noticed it is much faster too. It also allows me to get probabilistic results too which is helpful for later on.
Fixed the capitalisation - I was tired when I wrote the answer, and the OP had capitalised Gamma, so I ran with it. You are of course right that not every use of these distributions is a waiting time, but I think this provides the best intuition. If there's another good way of thinking about it, I'd love to hear it.
I'm not an expert on logistic regression, so I don't know typical goodness-of-fit methods. Just saying that when you say "70% accuracy" and "83% accuracy", there may be more to the story than that. But of course, it depends on the purpose of your regression.
I was going to write a separate answer, but I like yours. I'd expand #6 to say to bring ALL data into R and don't be in a hurry to aggregate, bin, etc. I think one error us non-experts make is to force data into a form that we think we'll need, or that we've seen others do. Let the actual data and the real-world factors behind that data guide you instead of naive assumptions related to processing the data.
Are you familiar with [control charts](http://en.wikipedia.org/wiki/Control_chart)?