tttjjj/elt_bench huggingface dataset:
This question [has already been answered](http://stats.stackexchange.com/questions/45820/pca-and-small-number-of-observations/45827#45827). In short: 30 is very small, traditional guidelines would certainly be that you need more, at least around 100-200 but it is really difficult to know exactly as the stability of the results will also depend on the number of factors and the communalities.
It seems the two methods are closely related, both are trying to find the inverse of the covariance in order to make the covariance diagonal. In GLS you modify the response as well as the predictor, so it might be a good idea to do so here as well.
This is your 6th attempt to post a question on an SE site. Could you now take some time to read some of the recommendations that were provided to you and try to add some details to your question? As it stands, it is difficult to tell what is being asked so I'm closing it in the hope you'll be able to add more context.
I was absent this lecture, and I dont have any idea about GLOM. I have checked some online books but they didnt help me.
Also, you say you have a uniform prior but what parameter is that prior for?  The Normal distribution has two parameters so which parameter are you referring to (the mean or the standard deviation)?
Android's is based on deep learning methods. http://www.wired.com/wiredenterprise/2013/02/android-neural-network/
@Glen_b Your edits always improve things, thanks!
I thought(maybe erroneusly or unnacurately) that normal data would be better described by a PCA by correlation because a line could better represent the variance carried on a normal distribution than on another one(e.g. exponential). Thus the representation in a line of correlated variables would make sense. However, i saw here: http://stats.stackexchange.com/questions/32105/pca-of-non-gaussian-data. that the real problem with data reduction is not normality but the representation of the variance of the variables contained by each one of the PCs.
@Simon - Sorry - I don't have any straight-up answer for you then. I guess I would follow guidelines for Path Analysis, and see what you can do - perhaps there are variables that you could condense into a compound variable or something...
Quite a few. See [PCA, randomness of component?](http://stats.stackexchange.com/q/87198/32036) This may even be a duplicate, but your title is much clearer (hence probably easier to find by searching), so please don't delete it even if it gets closed as such.
While this answer demonstrates the reason why we can't use one variable (i.e. that we do indeed need 'some sort of coding'), it doesn't (yet) explain why we can't do it with say *two* variables, as the OP suggests in the question.
(+1) Such a confidence interval would be useful and sensible. If a P value was wanted then, rather than using anything parametric, I would suggest a permutations test to give an exact value. (In fact I _did_ suggest it!)
I would probably do it in a two-step approach, using the PROC REG (or PROC GENMOD or PROC LOGISTIC etc.) to produce the original regression, get the residuals, and then use that as a weighting variable in a repeat of the analysis. This may, admittedly, be my own internal oddness, but I'd consider the weights to be a separate data-generating step, and I like to keep those separate from my final analysis.
FYI I used this great post as an inspiration: http://stats.stackexchange.com/questions/15664/how-to-test-for-differences-between-two-group-means-when-the-data-is-not-normall
It sounds like the program is providing solid advice :-).  Have you established--by exploring the data--whether there is any chance at all these data could yield reliable results of any kind? They would need to exhibit very strong, consistent relationships indeed.
Is this for some subject?
Now you subtracted the [trace](http://en.wikipedia.org/wiki/Trace_%28linear_algebra%29), which is the norm, normalized by the variance of each term. Can you show us the source? It is incumbent on the writer to explain the notation, not the reader to guess it.
Try [Wikipedia page about MDS](http://en.wikipedia.org/wiki/Multidimensional_scaling), especially the "External links" section.
As many already know, the current ez package (version 3) has updated ezANOVA, which has arguments for SS Type and return aov model.
On the latter see e.g. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2064100/ and other papers with the same first author; http://www.tandfonline.com/doi/abs/10.1198/000313001317097960
I believe you mean $\\hat\\beta_{\\hat{Y}Y} = \\hat\\beta_{Y\\hat{Y}}$ in your second enumeration point?
If $t$ is uniform, then $p(v|r)=p(\\varepsilon)$ is Gaussian, but $p(r)$ is definitely not. Maybe that is your problem.
I really like this type of question, I think this type of precise real worl problem will increase the interest of the site. It would be even better if you had the possibility to add a link to the data, or to tell us (as a complement to the post) what you finally did, what was the conclusions .... however I understand that this can be confidential ...
I'd bet on anything but... the die has already proven itself unfair.
I don't know pybrain but did you test your method first on smaller example, like XOR that should be not far from what you are looking for.
Second, increase your number of epoch, I don't think 5 iterations is enough to go anywhere.
If you add reproducible example (or raw data) it would be helpfull.
To have sufficient precision you may need 100 repeats of 10-fold cross-validation.  Or just use the bootstrap.
+1, I like the insight that "architecture selection... is a discrete, rather than continuous, control of the complexity of the model".
The last two numbers just look like numerical approximations of zero. My guess is you're dealing with nothing more than accumulated numerical error. I would have called those the same answer!
Visualizing it? The two distributions will be indistinguishable on any graph you care to use. Histograms, distribution functions, quantiles: it is immaterial which. In practice, your data are samples and samples will differ, but in principle, the graphs are just identical copies of each other.
@Macro Find maximum is pretty simple task it's just a maximum value of data sets or extremum of given function right? On my plots you can see different types of curves. Somewhere it looks like: 1,1,1,1,1,4,5,6,5,4,1,1,1,1 and here i want to detect that part "4,5,6,5,4". Somewhere it slowly decreases 10,9,9,7,6,7,5,4... I want to understand what is it type of the plot and found features parts.
Perhaps you want to give this question a shot yourself and people can chime in with additional insight?  I also recommend avoiding using the letter B as a variable name because it usually represents a coefficient, for consistency stick with x1, x2, x3, etc. Finally, you should be default include both terms in the interaction independently as well, which would give you 3 coefficients.
It's hard to say based on what is listed here, but one possibility is that you have insufficient statistical power.
Very nice! I wonder off-hand if given the summary statistics you could actually calculate the maximum or minimum possible D statistic for the KS test. For example, you can draw the CDFs based on the summary statistics, and then there will by [p-box](http://stats.stackexchange.com/a/86120/1036) windows for each sample CDF. Based on those two p-box windows you could calculate the maximum or minimum possible D statistic - and then look up the test statistic in usual tables.
They are both sufficient and we can say the same thing in a more general context: If $T$ is a sufficient statistic for some parameter $\\theta$ than any almost-surely invertible transformation $U = h(T)$ is also sufficient for $\\theta$.
I am not sure, but from what you are saying this sounds like a time-series problem; with such a lot of observations and such a small N, approaches from that field may work better. If you agree, you should add the time-series tag so that the time series experts (not me!) will see it.

if you don't agree, then in `SAS` look into PROC GLIMMIX and in `R` look into `nlme`.
It may not be limited to those subjects, but it would be nice to have them.
What kind of "information" do you wish to extract? How are the many papers that return when you google "Extract Information from Traded volumes" insufficient to answer your question?
@AndyW: Thanks Andy. Is there any formal way to connect the cross-post questions or should I simply link to the question?
Say, eroeijr, is [this post](http://stats.stackexchange.com/questions/51718/assessing-approximate-distribution-of-data-based-on-a-histogram) yours? (Aside from the 'guest' at the start there's a distinct similarity in the names.) If it is yours you should ask to merge the two accounts and take that big bonus in points you'd have.
Stepwise refers to the model incorporating impacts on mortality factor by factor (step by step). For example, Factor 2 is impacted by Factor 1, and Factor 3 is impacted by Factor 2.
Do you mean one only has 20 cases and the other one has 40 cases?
@loganecolss, [This](https://engineering.purdue.edu/kak/Trinity.pdf) is a good summary of the MLE, MAP and Bayesian inference. And this [link](http://stats.stackexchange.com/questions/47771/what-is-the-intuition-behind-beta-distribution) give s a good summary of how to incorporate a prior to Bayesian inference for a binomial distribution.
"it" referred to the inappropriateness of doing a One-way Independent ANOVA under the conditions described.
By definition you don't have an ascent algorithm. Let's see some code.
Hi @JupiterM104! thanks for recomendation, what the difference between my data and data from [here](http://www.theanalysisfactor.com/ancova-assumptions-when-slopes-are-unequal/)? Could you specify more precisely what of the statistical assumptions for an ANCOVA are not suitable here?
A minor point: The Cauchy distribution does *not* have infinite variance; in fact, it does not have a variance *at all* !!
@Macro, that's not correct. See, for example, the abstract of Roeder 1994 (JASA) for the well-known result that "the density of two mixed normals is not bimodal unless the means are separated by at least 2 standard deviations". If they are separated by less than this, the mixture is unimodal.
@Archer, you split the data into `train` set (75%) and `test` set or called hold-out/back set (25%) as topepo said exactly. Finally, you should be able to optimize the model by using the `train` set only but that should be done via 10k-cv may be. so suppose you have 1000 whole data, 750 `train`, 250 `test`, tuning/optimization of model via e.g., 10-cv (very common approach) then you end up with 90% = 675 for fitting, the 10% = 75 for evaluation of the tuning parameters (specific to the model you choose). The best model finally evaluated on `test` = 250. Last thing fit model on data (10000).
@Stat That's correct.  A zero-dimensional vector subspace would be the origin; a zero-dimensional affine subspace would be any single point in $\\mathbb{R}^1$. In either case the distribution of the distances is easy to obtain and so is the desired limiting ratio mentioned in the question.
@Samuel: I see nothing wrong with omitting rows with missing data. So the problem is solved?
@mpiktas: thanks for the suggestion. I hope this is clearer now.
I'm fairly new to statistics (been studying for a couple of months), so I don't have a good notion of how things are -- or should be -- done in the real world.
I don't see it on p30, can you you give the number of the equation?
Thanks. I think I side with the latter group as there is a little theorem that states that if an expectation for $X_k$ exists then the expectation for all values of $n\\leq k$ exist as well.
@Irish Let $x$ be the mean (among color) for one day and $y$ the mean for another.  I assume homoscedasticity; that is, $Var(x)=Var(y)=\\sigma^2$ ($\\sigma$ unknown).  The desired comparison ("usage ... going up or down") tests whether $x-y=0$.  Without correlation, $Var(x-y)=2\\sigma^2$.  With correlation $\\rho$ between $x$ and $y$, $Var(x-y)=2(1-\\rho)\\sigma^2$.  When $\\rho \\gt 0$, the variance actually is *less* than assumed in the ANOVA model.  Consequently t-statistics, F-statistics, and the Tukey HSD all should be *more* significant than they appear.
+1 Thank you for the detailed explanation. I was just wondering if the methodology to determine the optimal number of clusters changes if I use a different distance metric, say, cosine similarity. Would you have any thoughts on this?
But is the meet-and-greet participation itself endogenous? That is might the percentages have affected whether someone entered that area? If so, you would need to model that part of the process, too.
As a first step calculate the ($T \\land L \\land E$, $T \\land L \\land \\lnot E$, $T \\land \\lnot L \\land E$, $T \\land \\lnot L \\land \\lnot E$, $\\lnot T \\land L \\land E$, $\\lnot T \\land L \\land \\lnot E$, $\\lnot T \\land \\lnot L \\land E$, $\\lnot T \\land \\lnot L \\land \\lnot E$) probabilities (I suggest using a spreadsheet), their sum must be 1. Then write zeros into the cells containing $? \\land ? \\land \\lnot E$ as $Pr(\\lnot E) = 0$. Then multiply each value with the same number to make the sum of the posterior probabilities 1.
Links: [Friedman's test and post-hoc analysis](http://stats.stackexchange.com/questions/10309/friedmans-test-and-post-hoc-analysis), [Nonparametric statistical methods](http://books.google.ru/books?ei=zMOfTquxFKPP4QT-quDEBA&ct=result&id=RJAQAQAAIAAJ&dq=Hollander+%26+Wolfe+%281999%29,+page+244&q=Nemenyi#search_anchor), [Evaluating learning algorithms](http://books.google.ru/books?id=VoWIIOKVzR4C&lpg=PA256&dq=nemenyi%20post&pg=PA256#v=onepage&q=nemenyi%20post&f=true), [R](http://finzi.psych.upenn.edu/R/library/coin/html/LocationTests.html)
"It is said" ... *by whom*, and *where*? Your post is very unclear. More context - especially if we can actually see what was said - may help.
Maybe I'm being too idealistic, but I think the effect size is apparent in the scatterplot in a way that it can be actually understood, while the coefficient of determination values on their own would have no real meaning to non-statisticians.
Hi Andre,This work has sprung up again, I am wondering Central Limit Theorem is possible to experiment by using Microsoft Excel 2007? I use Excel extensively but confess not used for statistical modelling, any guidance possible?
+1, this is good info & well put. However, one small question / quibble: regarding the 1st question, even if $y$ conditional on $x$ is not normally distributed, w/ sufficient $N$ the sampling distribution should be. Are we on different pages here? I wonder if I'm misinterpreting this.
Welcome user1261558, maybe you could be a bit more specific about the context in which you've encountered both type of analysis, it would make it easier to answer your question. You can also have a look at the [faq](http://stats.stackexchange.com/faq) on what to put in a question to maximize the chances of getting an answer. Conditional logistic regression is usually used to model choice between several alternatives (e.g. brand A or B at different prices), or in the context of a case/control situation assess characteristics found in the cases but not in the controls.
Not clear what you are asking. Are you asking on DIC, Dhat or both?
I find the solution a little confusing (at least for me); what do you mean by "a meaningful set of parameters" for the candidate distribution? You initially don't know the parameters of the candidate distribution, how would you know what a "meaningful set of parameters" is?
It's Beautiful.
Also, if its not too much trouble, might someone be able to recommend me a p-value to use for the test?
A proper soring rul an a loss function are two distinct concepts!  The loss function should only measure the economic consequences, and a proper scoring rule has nothing to do with that.
It's important to distinguish the event space for a single observation vs. the event space for an experiment. At n=1000, for iid data the event space is a 1000 dimensional Cartesian product of the event space for that 1 observation. They need to be denoted differently. When you can define a sufficient statistic $S_n$ then you can speak of $f_S$ and $\\Omega_S$ (note, these change depending on $n$!). For instance if you flip 1000 coins, $S_n = \\Sigma X$. The distribution of $S$ depends on $n$ even though $S$  and its support are unidimensional.
Consider providing the full reference and a description of their moderator analysis method.
As Peter indicated, you are still not understanding earlier comments.  Quantile regression has nothing to do with computing probabilities of falling above or below a certain quantile (note that the probability of falling "in" the 0.6 quantile is zero by definition).  You find out if you are interested in predicting the median or other quantiles then do that.  A conditional quantile is a single number not a range.
+1 Wow python spreadsheets!  Hadn't heard of those yet.  I always wished OpenOffice/LibreOffice would really embrace and integrate python scripting in their spreadsheet software
As said in the book, it assumes $\\sigma^2$ is known indeed for simplicity, but the prior will be different when assume $\\sigma^2$ is know or not, so I don't see the point why should it make such assumption.
@whuber Another logically valid answer is to use a reliable source that states the full set of conditions, which is what I did. Then, if these conditions are more numerous than the conditions stated in the question, it follows that the latter are not sufficient. Moreover my answer, by providing the full set of conditions, could help future users that may wonder "what are the sufficient conditions for asymptotic normality to hold", and may come to CV looking for an answer. Certainly, adding counter examples would make for a fuller and more educational answer... so I added one such example.
Welcome to the site. There is not enough information here to be able to answer. You may find a post I wrote on my blog helpful: [How to ask a statistics question](http://www.statisticalanalysisconsulting.com/how-to-ask-a-statistics-question/)
Thanks @MikeP, I'll try this. I'm more looking for an absolute score between 0 and 1, but the placing technique is intuitive and seems to fulfill what's i'm looking for. If I knew the distribution though, would I be able to device an absolute measure?
@JeremyMiles: Good point. Basically it is a full analogy to the paired t-test (which is actually a simplest case of repeated measures ANOVA).
There is a *large* literature addressing this question. It offers methods depending on (a) the type of response $z$ (whether it represents a continuously varying function, a Census of results, a  sample of results, some kind of statistical summary aggregated by spatial unit, etc.); (b) the spatial units represented by the function values: true points, tiny point-like regions, linear features or arcs, natural regions (like watersheds), artificial regions (like Census blocks), etc.; (c) the uniformity of size and location of the data; etc. Can you provide some of those details?
@Andreas Statistical tests are done on averages/expectations. Your rule of thumb is a little bit too loose and can easily be tightened up by Michael Chernick's commentary and Gung's reflections. It is time that statistical rigor be incorporated rather than ignored.
@GraemeWalsh Maybe you misunderstood. What I meant by the "full spectrum Of Creativity" is all from the minimum value to the maximum value. So on the high end of Intelligence, we have observations from the lowest level of Creativity to the highest level. I think that makes us in agreement that there are cases of "being highly intelligent and having zero creativity".
But in case what I imagined is still wrong, would you know how to test any necessary/sufficient relationship?
Hi, Juan. Take a look at this book by Peter Lee http://www.amazon.com/Bayesian-Statistics-Introduction-Peter-Lee/dp/1118332571/ref=dp_ob_title_bk
One way is dummy variables for your segments. More advanced is regime switching model or hidden Markov chain
Extensive googling had it wrong: these are the OLS estimates and its SE
I will also check the variance in $R^2$ for different days. If the variance is high, I would expect cross validation to be helpful. If not, I would expect it to give similar results to just having a validation set like I already have. Thanks again!
I must admit I get a bit confused myself. Typically with an exponential smoothing model you would not re-estimate alpha (in fact, with a short time series you might not estimate it in the first place, just "borrow" an alpha from a similar series).   Yet with ARIMA models "there are no easy ways to update the parameters of an ARIMA model as new data become available, as there are in some smoothing methods."  (Hanke and Wichern, Business Forecasting, 9th ed. p. 444)  QUESTION: What about ARIMA models that map to smoothing models, e.g. (0,1,1) without constant and single exponential smoothing?
@Elpezmuerto If each row represents a region and they are not ordered, then how are you doing a Kruskall-Wallis test? That test only applies to ordered outcomes. Please, please, please add a compelete description of your problem by editing your original question.
There's an answer here, but it might be unsatisfying: https://stat.ethz.ch/pipermail/r-help/2008-July/168947.html
Thanks Peter, your answer is helpful :)
I can see no reason why using age as a continuous predictor should cause this problem as compared with categorizing it. A dataset of this size is not really large by modern standards. Your problem is really a problem with your use of R and should be asked directly by describing the data and the R command used: it is not clear why the program needs several Gb to do its work! The problem may well have a statistical misunderstanding at its heart, so you could try posting it separately here, but I doubt there is enough information in your comment to diagnose the mistake.
**"There is NO reason to do stepwise selection. It's just wrong."** - Almost never are incredibly sweeping statements like that, devoid of context, good statistical practice. If anything here is "just wrong", it's the bolded statement above. If your analysis is not emphasizing $p$-values or parameter estimates (e.g. predictive models) then stepwise variable selection may be a sensible thing to do and can ::gasp:: outperform LASSO in some cases. (Peter, I know we've had this convo before - this comment is more directed at a future reader who may only come across this post and not the other).
In what context does this question arise (does this fall under [self-study](http://stats.stackexchange.com/tags/self-study/info), for example)? ... The lack of random sampling makes it impossible to generalize from the sample, so I agree with your "2". With good sampling practices, even such sample sizes as those might be adequate. However, note that there's nothing to indicate the samples are for people over 30; that might be another problem.
Are these ordered classes or not? Is your issue with developing a prediction from probabilistic classifications? Or do you want to maintain the probabilistic structure of the NB model and calculate a weighted sensitivity/specificity for your model?
Thank you for answering. For numerical variables I mean for example student grades, and ordinal if they are Likert sacale
Sorry my question was unclear, thank you for following up!  Yes, the multivariate version of what you linked is what I'm after.  Would also appreciate a nudge on how to derive it for myself, not just the formula (that I just can't seem to find).  Thank you!
Welcome to our site, Jen.  You would open your question up to many more (knowledgeable) people by explaining what these parameters 'lambda' and 'lambda2' mean: many of us don't want to go to the trouble of looking up the documentation for your package in order to find out (and that's something that surely you have already done).
See also these other options for analysis of [2 by 2 pre-post designs](http://stats.stackexchange.com/questions/3466/best-practice-when-analysing-pre-post-treatment-control-designs)