tttjjj/elt_bench huggingface dataset:
I don't get this question. To me, discrete and categorical mean the same thing: you have labeled categories, that's all. There's a subset of categorical/discrete variables called "ordinal" variables, where the categories have a well-defined ordering. For any two numbers on the pain scale, and for each individual, the greater number means greater pain (although one could argue that a pain of 3 for one person may be another person's 5). Likewise, with tumor progression, the greater number means the more serious condition. Is this question about terminology, really?
@MichaelMayer Thanks. multivariate input for different groups.
Thank you for the thoughts. I realize now that I wanted 2 tests (whether the distributions are the same and whether the means are different) and then an estimation of the difference should they prove to be different.
OK, you're right: once alpha+beta exceeds 10^30 or so, you will have difficulties with doubles :-).  (But if you represent l and r as differences from the mean of alpha/(alpha+beta), you'll be fine until alpha or beta exceed about 10^303.)
under certain regularity conditions MLEs are asymptotically normal.
While I agree that that would more reasonable, I'm explicitly asked to use a Gaussian. Technically, we haven't even learnt about the Poisson distribution yet. It is supposedly somehow possible to find an approximate variance for a gaussian, based on just the data I'm given.
Ah I *think* I see... this may be more of a variable definition and coding problem, than a missing data problem *per se*. For example:$$\\text{Test score} = \\beta_0+\\beta_1\\text{Mother's employed*MotherAbsent}+\\beta_2\\text{Mother's education*MotherAbsent}$$ where **Mother's education** is now simply unemployed/35+ hours. Will have to think on it.
Given that the IVs are grouped, I would suggest that you use principal component analysis to get one variable for each of the six groups, and then use those 6 variables in a regression. You would not then need NNLASSO, you could easily include all 6 variables (you could still use lasso if you wanted, but it wouldn't really be needed).
This was asked (and answered) in greater generality at http://math.stackexchange.com/questions/148353, where "2" was replaced by any $k \\ge 1$ and the coin was assumed to have probability $p$ of heads instead of just $1/2$.
Common sense might not be correct, Eduardo.  Often, equipment exhibits a U-shaped hazard function: its downtime *decreases* during its early life, settles to a low level, and then eventually starts increasing.  This can have important implications for proposed solutions, such as regression (which, if applied naively, simply would not be appropriate in such cases).  It is often called the "bathtub curve."  About it, [Wikipedia](http://en.wikipedia.org/wiki/Bathtub_curve) writes, "Many consumer products strongly reflect the bathtub curve, such as computer processors."
Is this a statistical or a software question?
I can't speak to what the package you refer to does or assumes; my response about being able to use empirical distributions was a general one: it is possible to base inference on empirical distributions, since that's the basis of resampling methods - the ecdf is how such as permutation/randomization tests and bootstrap intervals work. In any case your initial question relates simply to smoothing the empirical distribution. An advantage of using parametric distributions for risk assessment (assuming they're reasonable approximations) is they give you some tail - empirical distributions can't
@daja: Yes, typically there'd be six coefficients for the interaction of a seven-level categorical predictor with a linear continuous predictor - it would be unusual to want to allow only certain levels to have slopes for the effect of the continuous predictor different from the reference level.
Hi, and welcome to CrossValidated! When we're presented with requests for homework assistance (which are often, but not always, tagged as "self-study") we generally try to help people get to the solutions on their own without taking them all the way there. In the future, please resist the urge to actually do someone's homework for them, and instead consider asking questions or illustrating examples that will nudge them toward the correct solution or highlight flaws in their current thought process.
No, it's not obvious at all. If I toss a coin ten times and only get 4 heads, should I conclude that my coin is biased toward tails?
Do you think that by "those" he means "everyone" ? what was the context of this citation ? it seems a bit strong like this :)
@mariana soffer Click the 'Star' icon under the up/down arrows.
Sorry, M. Tibbits updated the answer later, but my comments are still valid for David's question.
Have you seen the August issue of The American Statistician?  The article "Two Pitfalls in Survival Analyses of Time-Dependent Exposure" covers exactly this issue.  Abstract at  http://pubs.amstat.org/doi/abs/10.1198/tast.2010.08259
I have added the weight discussion to the answer.
Simple arithemtic combinations of the two predictions, or you could try training another classifier to combine their outputs.
You seem to have mixed up "dependent" and "independent" in this answer, which causes it to contradict the older (and correct one).
That second line is mysterious: what do three ordered pairs have to do with "time series" or curves? If we ignore that line, we are still led to wonder *how* your "curve" is given. Is it provided as a set of regularly spaced discrete data?  Irregularly spaced data? Terms in an orthogonal expansion (such as Fourier series)? Something else? And are these data considered mathematically accurate or are they measurements whose variation has to be considered? To what do the data correspond: points in time, averages over time intervals, something else? All these dictate the possible answers.
The question needs to be restricted. The covariate is determined with a view to indicate the extent of relationship between two variables that interact on account of some third factor. Further, there is ambiguity in the questions (3 in number). please clarify the variables.
@denis I have added a link to the data in my last question edit (second last paragraph). x and y are both in mm but corresponding to objects of a rather different size so the 10-fold difference. Thanks for pointing that out! perhaps I need to scale the data into roughly the same size before fitting?
@ProbabilityIsLogic derived this integral for all order statistics in the first half of his reply.
I've taken the liberty of removing some of the capitalization of whole words and phrases, which is often interpreted as "shouting". Please check that I have not altered the intended content. I won't make further edits if you choose to rollback or edit my changes. Cheers.
The p-value for the regression F is the same as the p-value for the R^2 in regression. Yes, the critical value can be calculated by hand from the connection between F and R^2.
If you are interested in the effect of your stimuli on the ordinal response levels as you've stated, then this is a standard "full factorial" design. For an example of a different approach, look at latin squares. Both are examples of repeated measures analyses and you're correct in assuming you need to take the correlated nature of the data into account. Repeated measures ANOVA would be the knee jerk reflex analysis for this type of data. No need for a Wilcoxon since there's no censored data.
+1, nice example and good explanation. Thank you.
@Procrastinator: When I use NIntegrate, I get: NIntegrate::inumr: The integrand E^(n x-a x^b) has evaluated to non-numerical values for all sampling points in the region with boundaries {{\\[Infinity],0.}}. >> How did you integrate? Yves: Thank you, I am working on it.
If you are willing to make Gaussian assumption you may want to look at the MARSS package which would allow you model multivariate responses.
This sounds like a job for [Bayesian PCA](http://www.che.eng.ohio-state.edu/~bakshi/research/HLBPCA.html)
Yes, that should work fine
Great pointer and advice. Thanks. Can you please elaborate what you mean by "start with only a few and work your way up"?
"*I can't get a confidence interval for the population mean, because I can't calculate the standard deviation of a single sample mean.*"-- you can't? I could understand saying you can't form a confidence interval unless the sample size is sufficiently large, but standard deviations of sample means (assuming independence) can be estimated from single samples.
I hope that the text explains why this is an invalid statistical procedure.
Although it is mathematically natural to try a regression of this form, behind it lurks a statistical mistake: the error term will now be strongly correlated with the predicted value.  That's a pretty strong violation of OLS assumptions.  Instead, use a count-based technique as suggested by Greg Snow's reply.  (I gladly upvoted this question, though, because it reflects some real thought and cleverness.  Thank you for asking it here!)
Why not just think of it as a sample of size 12 and take the sample standard deviation?
I provided an answer below, but this question might have been more on topic on StackOverflow.
To give you a start, for any fixed bucket, the number of balls in that bucket has a [binomial distribution](http://en.wikipedia.org/wiki/Binomial_distribution). This is *only* a start though; for this particular problem, you may be interested in how long to fill all of the buckets with at least one ball (the *coupon collector* problem), the size of the bucket with the most balls, etc., which are all more interesting both from probability and computer-science perspectives. :)
+1 for ggplot2 - by far best graphs you can get
The references are indeed comprehensive, thank you.  I have read them and some by Dimov.  I added a clearer explanation of my model.. What do you think?  Also in a development of this model an input parameter may be correlated to another making it non-linear, do you suggest anything there? Regards,
It is probably the repeated cross-validation used for model selection that reduces the bias.  The higher the variance of the model selection criterion, the larger the bias you will be likely to get in the second cross-validation.  Repeated cross-validation in the second part should be expected to reduce the variance of the estimate, but I can't see why it should have a big effect on the bias.  I find nested cross-validation is the best protocol for most experiments.  Hope this helps.
First hit when Googling "negative binomial confidence interval": http://www.bepress.com/ucbbiostat/paper242/ (abstract only).  The seventh hit gets you a full paper along with its references to the literature: http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0000180 .
Are you reasonably certain that everyone's scoring the measure the same way? The unweighted mean of all items, I assume?
Did you check http://www.stanford.edu/group/SOL/software/lsqr/matlab?
@topepo: Hi. I have updated my question with the `sessionInfo()` results.
And I wish you luck making 10-fold cross validation on set with 9 objects.
The problem is that one doesn't know a priori howto construct the null hypothesis.You created a simulated example where you knew the state of nature.In practice one needs to form a model based upon the data to empirically detect the unspecified effect via model diagnostics.Intervention Detection would suggest the slope change and intercept change in your data.Alternative data might suggest "parameter changes" and/or error variance changes. This is why I asked the OP to actually post his data so that objective analytics could be used to construct the hypothesis which was most rejectable.
I thought that's what I explained in my answer. You are only looking at relative ranking output by whatever method ( RF, PLS etc...) for each variable in question. You should study the 1st image in my answer.
This sounds like an odd thing to do... can you give more details about the circumstances that lead you to try to do this?
Thanks for the input, Glen. I will look into your pointers and get back to the question.
Are there any other cleansing methods?
Hmm... [biglars](http://cran.r-project.org/web/packages/biglars/index.html) uses the transparent-flat-file-storage package [ff](http://cran.r-project.org/web/packages/ff/index.html) to get around that difficulty. Maybe we need a bigglmnet package. I don't know your R hacking skill level; it's within my capabilities, but I have other things on my to-do list right now...
Can you write this question clearly enough for us to understand what you are asking? Maybe a data example would help.  Otherwise the question should be closed as not a real question.
Hello Whuber.
After sleeping on this a bit, I think that the issue is that the example I gave is one where the NP procedure does not provide a test for every given alpha. And in such case, I guess my question is if there is an alternative procedure to find an optimal solution for some given alpha. In the above case, the easiest solution is to go through all of the possible tests, but I wonder if a smarter algorithm exists.
Thanks for your suggestion, I will look into the pointers and get back later.
"To determine if results are statistically significant" is too vague to be meaningful. What are your hypotheses and research questions? Is there a dependent variable?
The thread at http://stats.stackexchange.com/q/18215/ may shed some light on this question.
@Andrej I edited the answer. The quote is from section 13.1, page 339.
The problem for an F test won't be normality, it will likely be independence. These are time series.
I placed a question at local Meta: http://meta.stats.stackexchange.com/questions/1010/is-this-the-correct-place-for-some-questions-that-confused-nearly-everyone-on-mo
I cannot see any $N$ above!  Yes, this seems to be somewhat mystical.  To find out what is the idea behind $J$ above I think you must look in the references of the paper you have given. $\\beta$ seems to be the true value of the regression parameter, so $J$ seems to be a random variable. Seems to be some sort of randomized estimator? If you are interested in this you must go to the references in your cited paper.
Regression is not about causation necessarily.
Although depending on your graphical interface to R there could be an easier way, and while you can always take a screenshot and prune it, the standard way is to create a device (e.g. `png(filename)`, then `plot()` your graphics, then call `dev.off()` and you should have a nice image suited for uploading here).
That is good general advice (+1). I was moved to post the first comment because these data are getting near that gray area on the border between "significant" and not, which is where a little more effort to select a more powerful test can pay off. I also had in mind the idea that even if no appropriate test finds significant evidence, the next step might be to plan to collect additional data, in which case a more powerful test will reduce the subsequent data-collection budget.
+1 Thank you for sharing the Python translation.  Welcome to our site!
Thanks. In fact, $\\bar{S} = S/n$ and $\\bar{C} = C/n$ are commonly useful, as they provide the coordinates to the centroid as you calculated it. However, here, it is irrelevant whether we sum or average, because $\\text{atan2}(x, y) = \\text{atan2}(cx, cy)$, for each constant $c \\neq 0$.}
@BondedDust I added some code and a figure to explain my query. Hope this meet your requirements!
I would suggest reviewing the wiki link: http://en.wikipedia.org/wiki/Akaike_information_criterion and then edit the question so that you can highlight the aspect of AIC that you do not understand.
HAIR et al is good if you don't like math and you want a step by step process. It's popular in management and business schools. If you can handle math, Hair et al can seem verbose.

Tabachnick and Fidell is popular in psychology. It's clearly written and does contain some mathematics. However, if you want a rigorous mathematical treatment, I'd look for an additional book to complement it.
@whuber I interpreted "divided in four groups..." as 'the data are sampled at 4 levels of estimated_completion_time', rather than 'these are the centers of 4 intervals', but I could be wrong.  If the info is of no value to giorgio_v, I can delete it.
Better still, the authors have announced that a free online pdf of this book will be available from January 2013 (it is being used in a MOOC which they are running.)
It might depend on what you have in mind by "general analytic formula." At a minimum we should expect that any formula would depend essentially on the mixture weights and will therefore not reduce nicely to a closed form whose length remains independent of the number of weights. Because (raw) moments of mixtures are just weighted linear combinations of the moments of the components and kurtosis depends on the first through fourth raw moments, it is clear a formula exists for the kurtosis of the mixture--and, I hope, equally clear how to obtain it, even though it's a bit messy.
"11% of a field" is a continuous proportion, not a count proportion.
How much lag are you talking about? Just one week, or multiple weeks? Are you expecting that $y_{week\\ n}$ is a function of the $x$s from just one previous week, or many previous weeks? Although your example is well laid out, providing a set of real-world variables will likely get you better answers, as answerers will be able to see what you're trying to do.
Thank you very much for your help. This really helped me out.
(1) What is your sample size? (2) Is the scale designed to be unidimensional? (3) Is the scale well established with standard scoring procedures?
@Pedro.Alonso $\\text{d-sep}(A,\\emptyset,E)$ appears to be more important. After all $D,B$ are not given in the query.
What is PROCESS Hayes? Can you show more of your output? Is that the output for the interaction or the factor? What software are you using?
+1 Nice question.
For the global null hypothesis, that should be up to $beta_{12}$. Also, in this case you need to omit the intercept otherwise you will fall into dummy variable trap.
This look like a duplicate of http://stats.stackexchange.com/questions/61173/rmse-vs-correlation-coefficient In general, it doesn't surprise me that real data are more problematic than synthetic data.
Yes, there is information in the placement, for example centrality. Perhaps it is possible for you to add a link to the data or show a picture of the graph?
Is it a quotation? I'm just wondering how trying alternative testing procedures (not analysis strategies!) may not somewhat break control of Type I error or initial Power calculation. I know SAS systematically returns results from parametric and non-parametric tests (at least in two-sample comparison of means and ANOVA), but I always find this intriguing: Shouldn't we decide before seeing the results what test ought to be applied?
Geyer's slides are really helpful. Thanks.
**Crosspost**: http://math.stackexchange.com/q/583186/7003
@JeffreyEvans Why not use party for regression? I thought party was supposed to help with correlated predictors – I may have missed an important detail in my recent scanning of the literature.
I was exactly like you ! Solid background in probability theory, but ignorant in statistics. And I was charmed by Bayesian statistics (especially Christian Robert's book). I learned frequentist statistics in Fourdrinier's book http://www.amazon.fr/Statistique-inf%C3%A9rentielle-Cours-exercices-corrig%C3%A9s/dp/2100044451 but I'm not sure you read French. Please let me note you're wrong about "secret priors".
The problem is that almost all such measures for GLMs are *ad-hoc*. In my experience, the best goodness of fit measure for Poisson distributed data is $\\frac{O-E}{E}$ which has a known distribution for Poisson distributed data (and also can be interpreted as % error).
Is this for some course?
Could you explain how GWR (presumably geographically weighted regression) could be applied to spatial point patterns and marked point patterns?
Given that you only want a crude fast measure, why not just pad out the shorter strings with empty characters?  In effect, define the Hamming distance to be the number of places in which the two strings differ plus the difference in their lengths.
Many thanks for your comments.
I disagree with your claim; FS is interesting on its own for some explanatory information that it delivers (marker/SNPs selection is an example when it is a main aim of analysis). The feature selection overfit is of course a problem, but there are methods to omit it.
Can you provide a simple example w/ data for time-series A & B that would demonstrate what you mean?
If it's possible to quote the passage in question that might help: sometimes nuances get lost in the retelling.
It's a good idea, but

    "mtcars$dummy <- 1; lrm(am ~ dummy, data=mtcars);" 

gives back:

    singular information matrix in lrm.fit (rank= 1 ) Offending variable(s):
    dummy 
    Error in lrm(am ~ dummy, data = mtcars) : 
    Unable to fit model using “lrm.fit”
I'm not a Bayesian expert. But after looking for such a package, I found WinBUGS, OpenBUGS, JAGS and STAN.
JAGS is a very good one: easier than WinBugs and openbugs and very important it's faster for my model. I try to compute with Stan which seems very powerful, but without succes till now. Jag is very easy to call from R. There are plenty of examples. I found the following blog very powerful:
http://www.johnmyleswhite.com/notebook/2010/08/20/using-jags-in-r-with-the-rjags-package/ As I'm new on Bayesian modelling, I'll be happy to hear what you found on your own.
Great answer.  Thanks whuber.
Found a good page that quickly explains how to read the chart.
http://www.skymark.com/resources/tools/normal_test_plot.asp
@StéphaneLaurent He/she appears to be asking for the name of the code provided in my answer here: https://stats.stackexchange.com/questions/91575/random-walk-under-changing-conditions/91584#91584 I am also interested.
Hi Aaron.  Thanks, I'll do both.  We have about 500 sites, so I'll take a look at some high and low sample sites to see how the model is performing.
@BGreene Very clever. Why not post that as an answer? You're also making me wonder whether the ensemble learning literature holds something relevant.
From your description and example it sounds like you might be looking for something like [Association rule learning](http://en.wikipedia.org/wiki/Association_rule_learning). Does this seem right?
I think what Glen_b means is that testing a difference will likely only tell you that there is a difference. But, it doesn't make sense to even do the test because this particular test strictly needs the same dependent variable.
I agree with this. My answer focuses on comparing means, but with the way the question is stated, and the fact that you definitely have enough data to do this, this would be a more appropriate way to go. And you could decide _a priori_ how large a difference between CDFs is enough to be relevant to you (suggestion: $\\delta_F=\\max_x\\{\\Phi((x-\\delta)/\\sigma) - \\Phi(x/\\sigma)\\}$ where $\\delta$ is a minimally important shift in means (like in my answer) and $\\Phi$ is the normal CDF (or some other standardized CDF).
Let _x_ be counts per minute and _y_ is price (for example).  When predictor is original, then it is easy to say: increasing "counts per minute" on 1 makes "price" to increase on _b_. But this relation is more difficult after normalization, since _x-normalized_ is measured in some derived scale, but not "counts per minute". And you are right, normalization is nice for predictors' importance comparison.
Note: a unique generator may or may not exist for X1; I am only interested in obtaining a transition probability matrix P2 for X2.
A few suggestions:
1. Replace acronyms with complete words,
2. Elaborate a little more on what you are trying to achieve statistically.
Are you simply trying to determine which regression coefficients are larger or smaller?
Could you please tell us what exactly you mean by "expected tables from randomization"?