tttjjj/elt_bench huggingface dataset:
I can't remember the best reference on this.  I think it's a paper by John Whitehead.  The best way to see it is to derive the score test for comparing two groups from the PO model.  The numerator of the score test is exactly the Wilcoxon test, and Kruskal-Wallis with two groups is the Wilcoxon test.
Ah, ok, I was confused -- linear means it only needs to be "linear in" the coefficients.
Although explicitly not asked for, this question on when Likert scales should be treated as ordinal or interval scales may be of interest: http://stats.stackexchange.com/q/10/442
Can you tell me where the data is from?
@mp re Note 2: Ah, Taylor's Theorem!  But real data aren't even continuous, much less differentiable.  The *model* might enjoy these mathematical properties.  Especially in explanations for the uninitiated, it may be worthwhile to distinguish the model's behavior from the behavior we expect of the data.  Also, Taylor's Theorem says little about the range of $X$ values over which near-linearity holds.  The regression model says this range is infinite!
I believe we have $\\psi_{\\kappa} = \\sum_i \\frac{\\lambda_i}{1 + \\kappa\\lambda_i}$, where $\\lambda_i$ are the eigenvalues of $HE^{-1}$. But that doesn't seem to get me anywhere. I guess I don't know enough about the distribution of sums of the eigenvalues ...
For the fair and unfair coins this is a helpful read:
http://www.stat.columbia.edu/~gelman/research/published/diceRev2.pdf
You might want to go to a more specific help site. Hayes runs a moderation and mediation group on Facebook, and often answers stuff like this.
As I've already said, you have the wrong signs for the MA coefficients. Look at the help file for arima().
I wouldn't say the uniform was unimodal. It doesn't satisfy your definition.
@gung, I see, no problem. There are more than 15 different post hoc adjustments in GLM, but once we introduced a covariate, the Post Hoc button becomes inactive (as seen in the screenshot of step 4 above). I guess in SPSS those post hoc cna only work if we don't specify any continuous independent predictors. If we do, the three only choices are LSD, Bonferroni, and Sidak. I did try your method to replace LSD with TUKEY but SPSS showed an error and refused to proceed.
The former is concerned with the accumulation of entropy over time and how it compares to the true entropy of the system. The SLLN and CLT tell one a lot about how it behaves. The second is concerned with *estimating* the entropy from data and some of its properties can also be obtained via the same two tools just mentioned. But, whereas the first is unbiased, the second is not under any $p$. I can fill in some details if it would be helpful.
1) Rows are independent. Each row is a study. We had replicates within studies, but removed those so we didn't have to worry about non-independence due to study. 2) Weights are based on sample sizes from within a study. We are using an unusual effect size, so we went with sample size instead of variance (which we do have). So we would use the weight column as is in the model as studies with larger sample size should be weighted more.
You could apply any ranked preference voting system, e.g., Condorcet method. Or for simplicity you could record each survey as a row of ranks and then sum down the columns, whichever has lowest sum is probably most important (equivalent to Borda count).
But perhaps also see @Benjamin's answer here (http://stats.stackexchange.com/questions/96739/what-is-the-632-rule-in-bootsrapping) as a case where a jackknife is still useful.  Jackknifes are also still used (it seems) in estimating $a$ when calculating BCa confidence intervals.
But what does that *mean* for your analysis?  Are you asking about how to write a macro to remove columns based on values in certain cells in Excel?  If not, what is the intended interpretation of removing a column (and why should it depend on a t test, which was never intended for such purposes)?
Now that I see this laid out in an example, it is clear I should have used the transpose of $A$ rather than $A$ itself: this would provide a better visual relationship with $X$, whose columns are in one-to-one correspondence with the columns of $A^{'}$.
What is the statistical question here? Why do you (think you) need to use kernel density estimation to calculate a cumulative distribution function any way? Author and title alone are an incomplete reference by most standards.
I must be misunderstanding your setup, then. As far as I can tell, for any given values of $N,n_A,n_B,$ the value of $S$ is a *number.* Therefore, accepting that $N, p_A,$ and $p_B$ are fixed for the moment (as they are in your code), $S$ is a function of $(n_A,n_B)$. But the latter, being realizations of two Binomial distributions, can attain only a discrete set of values. When I reproduce your code in `R`, I get decidedly non-uniform histograms for small $N$.
My bad. Yes, they are count variables.
Tobits are used when the outcome is censored above or below some threshold. For example, we don't observe any wages below the minimum wage or incomes above some top coded value. This application is for an independent variable.
It looks like the opening three lines and the title (and the tags) misrepresent the actual question here, which doesn't seem to be about error-propagation at all, but dealing with the problem with $C$. *Once* you have a way of dealing with that, it might lead to a question about how that impacts error propagation, but this doesn't look like that question.
@Chris, You have a quadratic objective function and an $\\ell_2$ norm equality constraint. Alternatively, under the formulation in @NRH's answer, you have a matrix rank constraint. That's not going to beat itself down to a linear-programming problem. @NRH gives some good intuition, and, in fact, there is a very close connection between the two perspectives on PCA that have been given. Perhaps in collaboration with @NRH, we can add that to his/her post to make the full set of answers more complete.
@Mustafa  That would be yes.
Since it's the difference in log-likelihood that matters, the terms that are in common are irrelevant, while any that different will matter.
Your samples are the different queries and your different treatments are the two search engines (both treatments are applied to each query). Clearly you have to use a paired t test!
That is the point of factor analysis, it empirically tells you whether they measure the same construct. Those might be the same construct (e.g., anxiety), or they might not. For example, children anxiety and underwater body anxiety may well best be conceptualized as distinct construct (despite both being anxiety-related).
I would also like to suggest adding "openmx" as a tag.
I guess to make it more convenient for a large range, you could type in the range in the [name box in the formula bar](http://excelsemipro.com/2010/09/use-the-name-box-to-select-a-range-in-excel/) and then choose "Fill right/down" from the menu.
As I reread it it seems that you are asking for a way to estimate variance without cross-validation or bootstrap.  The problem I have with your remarks though is that you seem to be assuming that there is a "relevant" answer out there.  I am saying that there probably isn't and that if you are interested in variability due to the procedure then you have to see how the procedure varies as the data gets slightly perturbed.  This could be done using simulated sensitivity analysis or by bootstrapping.
+1 for the `table` test. Is there really no shortcut for this assignment in R? I was thinking about a dedicated model class for which `predict` could be applied.
Arg - I am sorry! Actually I missed the `self-study` tag. Gladly, my function is only practical and does not solve all the partial questions...
(+1) To help the OP with additional searching on this model, here are a few additional points. (1) This model is often called the Bradley-Terry model (though it goes back to at least some work of Zermelo). (2) Letting $s_A = \\exp(\\lambda_A)$, the predicted probability of $A$ beating $B$ is $s_A/(s_A + s_B)$. (3) If a full round-robin tournament is played (which isn't the case here), the rankings of the strengths will coincide exactly with the winning percentage of each player. (4) The goodness-of-fit is related to flows over the graph with players as nodes and games as edges.
No. The procedure is the same but the value isn't. The standard error of the slope of the first segment is in your regression table (0.1788). The standard error of the second segment's slope is 0.1160. If we had a third segment, it would involve more variance-covariance terms in its sum (before the square root is taken).
@Glen_b I'm new here. Rookie mistake. Sorry!
I've made some significant edits to this question since smillig's comments.
There is a lot of literature on this topic (while I don't fully understand the question). Please formulate your question so that it is answerable within a reasonable timeframe. What problem are you facing? What steps have you done to solve it and what particular issue you don't understand? As it stands now, his question is not answerable.
Forget regression; just do a t-test for a difference in means. I'm tempted to say that there's no relationship and so should you. Your eyes are smarter than your model. However you should always jitter your points (just add uniform-distributed noise to your y variable) when you're making this kind of plot, because overplotting makes it impossible to get a sense of relative densities.
Hi there, could you please explain how you wish to incorporate costs into your model, as your problem statement in your first paragraph only talks about quality?
@user1956609 (1) that is correct, but often you require fairly large (or several) hidden layers in computer vision applications and (2) this depends on the hyperparameters but in practice this is quite common, particularly for low dimensional problems.
Thanks. Yeah, this plot is what I would like to do from the arimax model - look at with and without the intervention (and subtract). I think the filter function in R can be used to generate the transfer function value for each month (and then just plot it to visualize) but I cant figure out how to do it for an arbitrary pulse intervention function.
Many thanks. I'll go through this ASAP, and put up the means and a covariance matrix of my observed data as well.
The model you've written there is not the model you fit with your call to `glmer()`.
Ranabir - thanks for editing and tex-ifying the post. For me, in my browser, this just shows up as $y_1$ - is there something I should be doing to get it properly formatted?
@dfrankow *About the 1.06 value*: It seems Wikipedia is referring to Fieller et al.'s [Biometrika paper](http://solarmuri.ssl.berkeley.edu/~schuck/public/manuscripts/Fieller1.pdf) where the estimate of the population variance of $\\hat\\zeta=\\text{tanh}^{-1}\\hat\\theta$ ($\\hat\\theta$ is the correlation estimate) is defined as $\\sigma^2_{\\hat\\zeta}\\approx 1.06/(n-3)$, but see Bonnett and Wright, [Sample size requirements for estimating pearson, kendall and spearman correlations](http://biostat.georgiahealth.edu/Journal%20Club/bonett_wright_2000.pdf), Psychometrika 65(1):23, 2000.
I understand it is frustrating not get an answer on the sites you mentioned, but this still doesn't make it fit for this site. This is clearly a CS algorithmic question. Try putting a bounty on it in StackOverflow or CS.stackexhange.
This is a nice read. Thus far I have not yet considered Dante but perhaps renaming the cheat sheet to "The Statistics Purgatorio" comes to mind ;-).
The $Y$ values I am using are time series % changes from the previous period.
There might be a futures market in both of these things.  If there is, I doubt any statistical model you could develop would give a better answer than that (and if it does, you can make some money).
@JeanV.Adams, post an answer and i'll accept it.  I just got it working with lme.
@Casebash It is the partial regression on X1, given X2 and X3 are in the model
If your data are (e.g.) grades 1 to 5 or something similar, your frequency distribution is a set of spikes and no transformation will change that. Moreover, your variable is defined as a discrete ordered or ordinal variable, and no such variable can be normally distributed. Nor is it important that your data are normally distributed for any fair statistical purpose.
Hi, Tom! Actually, this problem is motivated by an application of the Expectation Propagation algorithm, but I'm stuck on constructing a decent approximate distribution on $X$. The $(\\tau_i, \\Gamma_i)$ are computed using EP to approximate the true likelihood function, and I'd like to then incorporate these into updating the beliefs on $X$. I see how to get a Gaussian predictive distribution on $X$ if I choose the prior to be $\\mu \\sim \\mathcal{N}(0, \\Sigma_0)$ if $\\Sigma_0$ is "known", but not how to get a reasonable posterior with both $\\mu$ and $\\Sigma$ unknown. Thanks.
My personal experience made me also very cautious about such sources of overfitting.
Could you explain what the "quadratic form on $b$" is?  (In the question, $b$ is only the coefficient of a *linear* form $b^\\prime X$.)  And what criterion are you using to determine that this form and the form $X^\\prime A X$ are independent?
Hi Glen_b and thank you for your reply. The contingency table with the missing value is an excellent point as it perfectly depicts my issue. The intersection between BLOOD and TISSUE over BLOOD is my measure of similarity. Unfortunately the overlap coeff between BLOOD-A and BLOOD-B would not be directly comparable, the first being calculated with BLOOD-A size in the denominator, the second with TISSUE size (rather than BLOOD-B). The Jaccard index suffers similar issues of non-comparability. A regular percentage doesn't work either, because size(BLOOD-B)/size(TISSUE) > 1. I'm in a deadlock here
@Franceso Good point. When $m=1$ or $m=5$ the formula for the first form is undefined. However, under various assumptions the limit seems to be 1, which is probably what I'd use. If someone wanted to define it as either 1 or 0 for that edge case, it would seem reasonable to me.
I think so, yes. If you have a 1-0 loss function, then the loss is minimised by choosing the most likely class every time. In other words, you're minimising P(error|x) for all x, which just gives you P(error). In other words, if your loss function is chosen as the chance of you being wrong, it minimises the chance of you being wrong!
I believe this is known as a zero-inflation problem, and they're fairly widespread. You need one model that models the "excess zeroes" (when the reading is zero because there cannot be any reading, as opposed to a legitimate reading of zero), then a second-level model that models the rest. For example, the number of customers in a bank: sometimes there actually are none, other times the bank is closed so there can't be any. Or the speed of a car: sometimes it's sitting still with a driver in it, other times it's parked. Etc.
@dikran: I agree with you, and I think his books are troll books.  But I would still lose horribly in a debate against him, in the same way that I would lose against an experienced intelligent design debater.
@BigDataLover, I updated my answer. I am not really sure what you mean by the whole corpus, the feature matrix in initial example is the whole corpus (assuming each phrase is a document), but I hope the update is useful.
Converted to CW because it looks like a bunch of good suggestions will be offered and there is no apparent objective standard to decide a "best" among them.  I hope this will make it easier for readers to vote up lots of the replies, too :-).
Strictly speaking, there is no "redundant" information, unless your initial data were perfectly collinear. One usually sees percentage of variance retained ("we used the first five principal components, which accounted for 90% of the variance"). I'm interested in seeing alternatives.
I'd feel comfortable reading assessing those two ICCs as printed in your comment as indicating differen reliabilities (I'm assuming the group 2 r has a typo and is in fact ~=0.32) -- the overlap is between the confidence interval ends, rather than a given confidence interval and the opposite point estimate, which if these were differences in means would probably correspond to a "significant" t-test result at p < 0.05.
I have formated the answer to make it readable. I urge you, in the most emphatic manner and with all the due respect, to format your answers in order to improve readability. I know that this is a tortuous road but people would be very benefitted from this and I am sure that upvotes would rain on your answers.
I agree, it is a concern. Any idea how to adress it? ;)
+1 Agreed - although what you describe is called statistics.
You need to multiply this answer by the cube of the scale factor, $\\beta^3$.
@Dmitrij, There are two main reasons why I am concerned about bias in the standard errors of the coefficients. The first, as you alluded to, is the creation of prediction intervals. The second is testing for structural breaks in the model, a common question that an economist would be interested in answering. The standard errors generated using a selection procedure should be too small, giving prediction intervals that are too narrow and test statistics that are too large.
Average age of the 28 bears? You'll want to use a finite population correction.
If p-value of J statistics is 0, then either the model or the overrestricting conditions (ie. your choice of instruments and constraints) are rejected. Either way, you shouldn't use the estimated coefficients, they're likely to be quite far from the truth.
There is no statistical question here so I've voted to migrate to stackoverflow. For future reference, you can also type `help(rt)` or `?rt` which takes you to the help page for the function `rt`, which should answer your question completely.
I am not expert on this, but I added the timeseries tag so that people who are expert will see it.
I had applied the tag "statistics" but apparently that is insufficient.  Apparently I'll have to make a duplicate post.  That's unfortunate.
The most common approach to this (there are a number of others!) is known as a chi-square test of homogeneity - generalizing a two sample proportions test. It is akin to ANOVA, in several ways. (You can even partition the chi-squared into orthogonal contrasts, do post-hoc tests of all pairwise comparisons, and so on - but you may not find these readily available in software; they're not hard to compute 'manually' though)
Correct - time 1 refers to the measurement for system 1 and time 2 refers to the measurement for system 2. (The "repeated" part of the question(s) refers to the subject.)
Therefore, based on your response, should I encode the system as additional columns?
As to point (2): That would not be my quote. This quote is more a presentation of a preference of the author for a particular style of doing research. For your concrete application you would have to take into account that many so-called non-parametric test have very low power, so that would represent a real trade-off.
I think aeWiardll is implying that there is a correlation (or some similar structure) in the data. Therefore, the simple assumption of independence of `lm` is probably not what @eWizardll is looking for. I hope the answer to your question would make things clearer.
Also, does this give me probabilities or just relatives scores?
By "significant" I mean what rule should be considered... stronger than the other.
It's not surprising that your model predicts perfectly since you have so many degrees of freedom in your model (overfitting). You could use penalized regression (e.g., package glmnet).
Could you please define $I_0(\\alpha)$?
I see--you forgot some parentheses. Unfortunately, when they are inserted your formula is still incorrect. This is the old socks-in-a-drawer problem: suppose your drawer has two (or $45$) colors of socks. You are getting dressed in the dark, so you will take some socks out of the drawer and carry them into the light. How many must you take in order to be sure of having at least one pair of matching socks? The answer is three (or $(46)$). If you take more than that--such as six--you will still have a matching pair. Your formula therefore should give a value of $1$ in this case, not $0.6875.$
Thanks, @whuber, I somehow mix up row and column all the time (and English is my native language!)
thank you! we had a similar guess, but your suggestions give us additional ground for further experiments.
(+1) If only for your username. Hilarious.
An anonymous user wanted to add the following definition of [homoscedasticity](http://www.wordnik.com/words/homoscedasticity) for those who might be unfamiliar w/ the term: "a property of a set of random variables where each variable has the same finite variance".
Crossvalidated.com deals with exactly this types of questions. I suggest this Q be moved there.
1) is a good point. i guess not something i've encountered much.
@AldousWong  Some additionnal hypotheses are needed that I can't figure out. Or there's a misprint in the paper... Can you put it in some place where we can download it?
Cluster standard errors rely on the iid assumption. Classical panel data models usually assume cross-sectional independence.
Deficiencies in your notation may be causing some confusion. Presumably "$\\delta$" represents the point measure at zero. Don't, however, conflate constants with uniform distributions! For instance, your first "$1/4$" could more explicitly be written as $1/4 I_{[5,7]}(x)$ where $I_A$ is the indicator function for a set $A$.  (This is a guess: I presume you intend $f_x dx$ to be a probability measure.)  When you do this, *the limits of integration do not matter*: all integrals can be viewed as being over the entire Real line.
By the way: moderators, if you think this Q belongs on Stack Overflow then please feel free to migrate it.
Sorry, didn't notice that you want a perfect approximation. Then apparently mgcv is not of much help: stop("Basis only handles 1D smooths") (from https://svn.r-project.org/R-packages/trunk/mgcv/R/smooth.r)
"Some"? Do you want to end up with a fixed number of variables, or do you want to let an algorithm decide on that number based on some statistical criteria?
@naught101: Ah. Two of my three suggestions I've made here are based on what I've learned, but not necessarily well enough to make a good example. I'll try to look for one on the web.
Are the two models run on the same population? Is Y the same? Is X? (it would help to use subscripts on Y and X to distinguish them).
You are probably getting this idea from the delta-method, right? This is a first order approximation, and it only works well when the distribution of $X$ gets tighter as $n\\to\\infty$. If things remain $O(1)$, this expression fails miserably; think about $X\\sim N(0,10)$ and $g(X)=\\exp[X]$. The correct expression is $E[g(X)] = \\exp( \\mu + \\sigma^2/2 ) = \\exp( 5 ) = 148.41$; your first order approximation gives $\\exp(0) + \\frac12 \\cdot 10 \\cdot \\exp(0) = 1 + 5 = 6$.
@IrishStat I think your question is rhetorical.  If a model can have a simple recursion to update the model it can't have all the complexities that you describe. Sometimes it is more important to get a correct answer rather than a quick answer that is poor.  That is why in my answer I said to only do it if the model fits the data well!
Isn't it a little pointless use "all men ever" as a population? I mean, there's not even a consensus as to how old *homo sapiens* is, or whether *homo neanderthalensis* were a separate species, let alone whether males of the stone-tool using *homo habilis* count as "men". Presumably the same problems will face us in the future, too.
Statistics is not as unified as other disciplines: often different words are used for the same thing and the same word for different things. I suspect that @FrankHarrell is right, but it really depends on the exact context in which you found these words. So can you tell us where you found references to these models and why you think that they are different?