tttjjj/elt_bench huggingface dataset:
@flom: thank you for your answer. Yes you understood my question. I also thought about this, but don't you get more detailed results in fitting a model with two independent variables? My problem is, that my results for "testus" are not significant. That's the reason why I tried to predict the probabilities with testus.
If you were my student, I would be concerned about sweeping the conclusions from the CFA under the rug. You can certainly go ahead and just use the scale scores as observed IVs, but this comes the big assumption that they are measured without error. However, it might be that the "standard" CFA is not the "best" model in your particular situation, but it's impossible to say, given your question as it stands. Can you please edit your question to add more detail about your data (how many items, distributed how), and how you estimated your CFA (software, code, specifications)?
Here's a useful formal statement of the definition: Given a sample space $\\langle\\Omega,\\mathcal{F},P\\rangle$ and an unknown parameter $\\theta$, a $1-\\alpha$ *confidence procedure* consists of a pair of functions $L\\leq U:\\Omega\\to\\mathbb{R}$ such that $$P\\big[\\left\\{\\omega\\in\\Omega\\vert [L(\\omega),U(\\omega)]\\ni\\theta\\right\\}\\big]\\approx 1-\\alpha.$$ The left hand side of this expression is the $\\textit{coverage probability}$ (note that this depends on θ) and the RHS is the *nominal confidence level*. If the infimum (over $\\Omega$) of the LHS is equal to the RHS then the procedure is *exact*.
@Sara, if you look at a probability density function http://en.wikipedia.org/wiki/Probability_density_function of the two events fxy then you will get a rectangular distribution if they are independent.
I believe your definition of $g^{-1}$ is incorrect. For any $y\\in [0,1]$, $g^{-1}(y) = 0$ with the definition you've given.
Doing the calculations in R instead of Excel should be preferable because that makes the calculations both _documented_ and _reproducible_.
Well you should know that any distribution that can be written as a member of the regular exponential family must have a conjugate prior.
I am struggling internally to deploy analytical methods at work.  I have run and attempted to deploy logistic models at work, but at the end of the day, the decision is made to use basic averages. it's what they know and are comfortable with.For this reason, I am trying to help bridge the gap internally by translating/combining averages into a weighted average to help with the discussion of why we need to - at a minimum - go the logistic regression route.  I am hoping that this will help the others internalize why other techniques are more robust and accurate
Could you please give a www link how 20/ln(2) is applied? Thanks!
+1 answer. Both `names` and `str` are very useful for poking into structures like that. Unless it's an S4 class (you use an 'foo@bar' instead of 'foo$bar' to access members), in which case you'll need `slotNames`.
What *event* would that be?  And *a priori* and *a posteriori* do have a rather specific meaning in (Bayesian) statistics too.
Hint:  $E[XY]=0$ and $E[XY]=E[X]E[Y]$ _both_ will hold if at least one of $X$ and $Y$ has zero mean.  Also, note that statistically independent random variables for which the expectation is _undefined_ or _does not exist_ (e.g. Cauchy random variables) cannot be said to be uncorrelated or orthogonal since it is not possible to talk of expectations at all.
@MichaelChernick Is it possible to do logit transformation without having the underlying numerator/denominator? My case is similar to what Charlie explains.
@affine you are completely right. I removed the reference.
...and in Stata too! (`xtmixed`, `xtlogit`, `xtpoisson`...)
While script-based tools will help you generate the same chart repeatedly with different data sources, interactive tools are much better for exploration and discovery in a new dataset. When posed with a question, you simply click a button or two to change axis, color scales, clusterings, etc. instead of writing the code to do it. This is a much lower cost, and an undo stack or exploration history view will let you backtrack if you make any mistakes.
This is right in general but in the context of Wald test you always test whether some linear combination is zero.
For LaTeX, enclose terms in $ signs.
If you do your thee pairwise comparisons in a way that's  integrated with your ANOVA, there might be some rationale relating to error variance. The interaction approach I speak about is also a form of "planned contrast".
Assuming you choose category 1 as the base or reference then the reported odds ratios will tell you the effect that university has on being in category 2 vs 1, category 3 vs 1, and category 4 vs 1.  As you can see this probably isn't as intuitive as a simple contingency table.  The contingency table on the other hand is not useful when you wish to partial out the effect of multiple predictors on your outcome.  Try to persuade your supervisor that fancier sounding statistics don't always provide more insightful answers.
@whuber I answered the question because even though it asked about all the diagnostics related to regression I thought that I could give concise answers on what methods are used. As far as providing detailed steps for carrying this out in Excel or Mathematica that probably is not appropriate for a question.  IrishStat provided a detailed description of how to deal with time series modeling assumptions.  I think it is interesting even though I agree that the OP was probably not looking at time series.
Usually, statistical models work by assuming that somewhere really far down the rabbit hole, there is a deterministic quantity and that conditional on that unknown thing, the other stuff in the problem becomes independent and often deterministic. But then the problem is to mathematically encode uncertainty about that rabbit-hole quantity. This idea goes by many different names, hierarchical models, latent variables, exchangeable models, hidden variables, etc. etc. But it's all the same idea: what hidden thing should I condition on to get determinism, and why is it that I cannot know that thing
Depends on your data. Some data can be projected well, because it has much lower intrinsic dimensionality. Time series can easily be plotted, and if your data is a serialized image, visualize it as images? By any means, visualization depends on *your* data, there won't ever be a one-size-fits-all solution.
As you can guess, due to rather big M and N, the matrices of K (and therefore, of H and T) are rather sparse. The current values of M and N are ~1000, and the matrix of K has only ~1% of its elements not equal to zero. I am afraid this sparsity can prevent me from using a lot of the more obvious approaches.
First, thank you so very much for responding. The Chi-squared test part of the class.
For every P, the random variables N and K are independent.
Two discrete random variables X and Y are independent
if Prob(X=x,Y=y) can be expressed as f(x)g(y).
In our case, Prob(N=n,K=k) = binom(1000,k) (1-P)^(n-k) P^k = (1-P)^n * binom(1000,k) (P/(1-P))^k.
Let's say we had 2 samples: weekend transactions and weekday transactions: both on the same inventory of products.
Is there a reason you are not just calculating the MSE of both estimators using bootstrap simulation? If you know the true mean, then repeated re sampling will allow you to better estimate the bias (there should be none) and the variance of the estimator. As you take more boostrap samples, the MSE's will converge to the exact MSE of the empirical distribution (note, not the true MSE..you need an infinite number of data points for that).
It'd probably be helpful to describe the algorithm here instead of referring the readers to an article and letting them figure out what you're talking about.
Thank you!
I have previously only very briefly worked with R, but now I seem to have reason to revisit it!
Also consider what happens to your $\\beta$ if you measure peoples heights in millimeters, or meters.
Have you read all the *other* answers to that post? Only extremely rarely, if ever, does it make sense to do this. That post has lots of good answers; it needn't be re-hashed.
This might even be a duplicate question.
"Hierarchical regression" is dubious phrase. You should write in more precise terms what is on your mind. Regression in blocks, sequential SS decomposition (type I SS), multilevel linear modeling or something else.
The adk package was removed from CRAN. Is there an alternative ?
Currently I am revising the model and thus the parameters too, as I just call the auto.arima function everytime I get more new information. I do not know what is the best approach either to re-estimate the parameters or revise the model. Also my initial training data set size is around n=30, so it is quite low. I could increase the n value a bit more if required
@kbh it's not my financial metric - optimizing for sharpe ratio is very common. One example just at the top of my head http://ssrn.com/abstract=962461 - no exact statistical model is developed but trading rules created to (in very general terms) maximize returns and minimize risk.
@FrankHarrell: yes, at least the naming of the method in the paper is misleading as the final prediction is not continuous. But I understood the mentioning of the paper as showing that the OP did look into literature, and thought that the paper *may* help - which it doesn't.
Okay, added the formula for the knapsack problem. To be 100% clear, I am trying to predict profit values of each item based on past observations of those items. I am facing uncertainty by using an algorithm or statistical method and I would like to try and account for that uncertainty and know how to manage it when picking items for the knapsack.
Almost all mixtures of normal distributions will give a  distribution with multiple local maxima, though extensive sampling would be needed to resolve all the peaks.  In your example, it would seem that most of the $\\mu_i$ are clustered around one value and a few clustered around another value, and yes, lots more sampling will likely give more local peaks; indeed, even the main peak might resolve into two narrower peaks, etc.
@Adam Smith, if you were happy with this answer please consider accepting it. You can do so by ticking the check mark underneath the voting buttons. Writing a good answer takes about 15-20 minutes and it's always nice if this work is appreciated by votes/acceptances. It's only one click :-)
@Tu.2 Can you send me a copy of it to elvis.bistalanouille [at] gmail.com ? I am really curious to see what’s going wrong.
According to the doucmentation i found on the subject it seems that there is the Kappa Method, used for Qualitative Nominal data (with No logical order between scaling categories) and the Intraclass Correlation Coefficient (ICC) Method, used for qualitative Ordinal data (With a logical order between scaling categories. eg Grading).  I wonder if the ICC Method isn't more appropriate for my situation, as i have a logical order  to the categories ...
I'm not an expert in decision trees, but I think your intuition is right and in fact suggests that a tree is inappropriate for nested factors. The task implies fully crossed factors: among them, the strongest predictor is being searched. Imagine Win/Linux strongly differentiate people on the predictand, but can do it only in _part_ of sample - for those using PC. But since you need _all_ the sample to be differentiated at level 1, you _have_ but to prioretize the PC/Phone variable instead, simply because it is the only variable relevant to everybody. The same fallacy repeats on every level.
@sashkello In order to draw a gold sphere
That's a very big question. Entire books have been written on each part of the question. Try (1) Asking a more specific question - what principle of factor analysis are you interested in. (2) Ask one question at a time.  Also, try to explain what you already know, so we know where to start with an answer.
@whuber I was seizing on "roughly equal amount of all 3 colors, to be precise", but Swagatika's latest comment appears to contradict that as spatial homogeneity is now being emphasised. I see no consistent story here.
Glen b, thanks for a very informative answer.  I am not sure if I understand your comments under 2).  Why would variance bows in? I interpret that as large errors near the Mean with smaller errors away from the Mean.  The bit of material I have read on the subject, suggests just the opposite... the bows out thing hourglass shape.  Additionally, how would you define heteroskedasticity?  And, what do you mean by the variance of unobserved errors?  How can you measure those since they are unobserved?
@MichaelChernick, have you considered posting these comments as an answer, rather than listing them under a seemingly unrelated answer?
This is a popular question which has been asked (and answered) in many forms previously.  E.g., search on your key words (such as "dependent +normal +regression") or look at one of the first hits, such as http://stats.stackexchange.com/questions/11256/regression-on-a-non-normal-dependent-variable.  Pay most attention to the *advice* in the replies rather than the details of the circumstances, which vary slightly.
I'm going to try this, I think it will help answer my own questions for myself, but not so sure how it will convince others.  You are spot on with second part, I'm trying to think about how this data informs a future more directed experiment.
Related question: http://stats.stackexchange.com/questions/961/statistical-test-for-n-x-m-contingency-tables
I mean, you should try to see how your variables improve prediction based solely on demographic information. Maybe, a few interaction terms could be added.
@JonyEpsilon I see your point. The KS distribution is unfortunately very difficult. I hope this helps anyway.
Interpolation is a vast subject. The choice of a good method depends on many things, including the statistical and physical nature of the data, expectations about the mathematical and statistical properties of the interpolated function, the geometry of the data locations, how those locations were selected, and the purpose of the interpolation. To make this question sufficiently narrow to be answerable here, please edit it to supply this information.
Very elucidating answer for us non-stats guys/gals.
@user4003: If you base your graph on bands of width 20 then yes, you should divide the 132485 by 5, as it will be 5 bands wide. The density ratio of about 1.6 comes from $\\frac{42246}{400-380} \\div \\frac{132485}{500-400}$
We would normally look for answers on this site to be more extensive that one line. Would you mind editing to expand into a more complete answer, perhaps one designed to help a future user that's more confused than you. Could you also expand CEF to (what I presume is intended to be) *conditional expectation function* on first use, please?
Not exactly "impossible" since among other things, it depends on a specific definition of 'approximately normal' and on the sample size. But if it happens, it's a pretty clear suggestion that the accuracy of the normal approximation on which the CI was based isn't sufficient for your purposes. In some cases truncating the interval is reasonable, but my instinct is usually to abandon it and do something better suited to the situation. It's akin to [CI's for the binomial $p$](http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval) when $p$ is small - normality doesn't really apply.
You might want to try a T-distribution instead since we don't know the variance.
Both might be correct, depending on how the manufacturer's claim is interpreted. Literally, the manufacturer's claim in the problem statement is that the unit uses $6.5$ KW/day, not that it uses that amount or less, so the book at least is consistent. Regardless, how would the choice of $H_0$ affect the agency's test results?  (Answer: not at all.)
@Nick Actually I see a potentially very interesting statistical question--provided I am correctly interpreting it. Imagine two people (or machines) tracing the outline of a feature in an image, recording it as sequence of vertices. Inaccuracies in recognizing the feature boundaries and in specifying the vertices can be viewed as random errors. The problem is the two traces might use completely different (Cartesian) coordinate systems (set up on two digitizing tablets, for instance). The null hypothesis to test is that they represent a common feature. Shakthydoss, am I close?
Glad I could help! It's a subtle gotcha and I sometimes wish The Mathworks were a little more consistent about everything.
So I got x<-c(11,13,13,14,14,14,15,15,17,18)
mean(x)+qt(0.99,df=10-1)*sqrt(var(x))/sqrt(10)
mean(x)-qt(0.99,df=10-1)*sqrt(var(x))/sqrt(10)

[1] 16.19432 [1] 12.60568 . Is this correct?
*All* datasets, regardless of dimensionality, can be described as deriving from some mixture of distributions. Your question needs some refining in order to be answerable: please edit it to give a context and describe what is special about your particular circumstances. Guidance for asking questions appears in our [help].
@StéphaneLaurent What I said goes, mutatis mutandis, for one-sided CIs.  But I was interpreting the question in the same way as gung; perhaps what you're saying is what the OP really wanted to know.
Thank you for the answer, I think it solves my problem. According to it, I'll now correlate the components of $A$ and $B$ that are both orthogonal to $C$.
@question If it (a) is a pattern in which the *mean* residual varies and (b) it would be unacceptable to treat that pattern as random, then--practically by definition--there is nonlinearity.  Some patterns do *not* indicate lack of linearity but suggest other phenomena such as heteroscedasticity, outliers, or high-leverage points, so we shouldn't assume *all* deviations from randomness are evidence of nonlinearity.
Wow, Shane, thanks for the very fast response! I'll look into those references!
Hi @gung, I see your point but I think they're separate :) The other is about the risk of mixed-modelling with multiple correlated variables. This is about how to compare an HLM model with other analytical techniques like OLS regression. I am exploring the relative benefits of the approach, so need an idea of how to compare different models. I'm entirely self-taught and have found it pretty tough getting into the language, so just need some guidance.
this question also has an open bounty ending in 3 days at [mathoverflow](http://mathoverflow.net/questions/97999/inference-on-a-probabilistic-graphical-model-with-observed-continuous-variable)
@rolando2: Outright errors are more likely in earlier printings; so you might be safer with the 7th printing of a 2nd edition (or mature errata) than the 1st printing of a 3rd edition. The inclusion of now-deprecated methods (& omission of modern alternatives) is something I think you have to assess for the particular book in question.
Are we to assume you have *random* friends?
+1 This is more accurate than the accepted answer.  Mata is a relatively recent, matrix-oriented language that supplements Stata's built-in language.  Many (most?) ado files contain little or no actual Mata.
Thanks a lot for the reply. I understand that the specification of the initial model is crucial. In fact, during the model building step of my true dataset (5 regressors) I evidenciated that the coefficient of interest wasn't really robust to the inclusion/exclusion of the other 4 controls.. About the computation of the final bootstrapped standard error, do you find it right? If so I can try to focus on specifying a better initial model to see what happens
If you don't want people objecting to your example (which is unpaired), edit to make a better example - or better, describe your actual situation.
The deviance has the same property.  If we take the same case  of 99% and 1% we get deviance of $-2n(0.99\\log(0.99)+0.01\\log(0.01))=0.112n$.  Similarly for a 50-50 split we have $2n\\log(2)=1.386n$ Which shows the dependence on the marginal distribution.  Same model (constant) gets different deviance.
Thank you very much! The problem is really more complicated than I thought.
Related question:  http://stats.stackexchange.com/questions/11096/how-to-interpret-coefficients-in-a-poisson-regression
These are not the formulas for the distribution: they are formulas for *corrections* to it.  The soliton distribution itself is discussed (with R and Python code) at http://stats.stackexchange.com/questions/37581/how-do-i-generate-numbers-according-to-a-soliton-distribution.
Very low hazard ratio means strong positive effect on typical time to event. Is this unexpected?
If your data come from a multinomial distribution then the Dirichlet distribution is the conjugate prior, which generalizes the Beta distribution to $K$ dimensions. http://en.wikipedia.org/wiki/Dirichlet_distribution#Conjugate_to_categorical.2Fmultinomial
@CarlBenson For a normal distribution the z-value associated with a 95% confidence interval is 1.96. See the wiki link (http://en.wikipedia.org/wiki/1.96) for an explanation. Let me know if the link does not help and I will add further details to my answer.
Do you know how many searches there were for each observation?
Is the confidence interval defined as mean +/- margin of error?
@Matthew I would not advocate using CMs (or any univariate measures of fit) for automated model selection. I don't think the OP was asking about model selection. But as a measure of fit that tells you if a given model puts people in the right buckets, or perhaps on a hold-out sample, CMs can be useful.
However, as a general rule of thumb, downdates are more prone to numerical instability than updates.
So you have 4 likert scales. Are they related? Why did you collect 4?
@DanielVelkov When you bootstrap PCA on a rather noisy data the components are often unstable; this promotes the idea to make one global PCA on the whole available set, what leaks information and is a straight way to spoil the evaluation.
@rolando2, Interactive graphs are still there. The only difference is that they've lost their old looks and editing options; looks and editor is the same as in regular graphs now. Interactive graphs are great, for me, because they support creating categories out of variables (items) - just what I did above.
Mcnemars is great and all...but why not just use logistic regression?
A variable can be in or out? I'm not sure what you mean by that. A variable can range from a - b, in increments of c. So the total number of possible values for a variable is (b-a)/c.
This question seems to contradict itself fundamentally. First it states you chose the transformation to "reconcile with theory" and then immediately it asks why the transformation was chosen. Could you please clarify?
... or - if it doesn't drive you crazy - you could use my suggestion or a slope graph AND include sparklines (a link from Alex's answer).  Sparklines would give you the intragroup comparison you are seeking where as some variant of a regular line chart / slope graph would give you the between groups comparison.
Maybe this article could help, though I'm not sure: http://www.tqmp.org/Content/vol08-1/p023/p023.pdf
Yes, residuals autocorrelation affects the standard error of your predictors (but not the coefficient estimates). There are many resources online referring to the problem. Why wouldn't you want to include a $Y_{t-1}$ predictor in your wind data regression?
I (sort of) know the syntax, I'm just not clear on what the appropriate model is. For example, the one you proposed: will that adequately separate the effect of the two different factors (thresh and season)? My concern is that because they are related (water table is above the threshold much more in the fall) that what seems to be the effect of season will instead be the effect of threshold.
Those might create and *expectation* that it would be rejected, but statistical tests look at the *data*, not biological reasoning or published reports. Rather than get me to download all your data and analyze it (unless you're asking for my consulting services), just draw the two ECDFs... and explain what it is about *the data* that tells you the null ought to be rejected.