tttjjj/elt_bench huggingface dataset:
(1) Naturally the intercept will change if the functional form changes; (2) Your cubic model posits that the relationship between Leads and ImpA cannot be understood in terms of a single parameter, therefore when interpreting (e.g. predicting a value) you need to combine $\\beta_{ImpA}ImpA$, $\\beta_{ImpA^{2}}ImpA^{2}$, and $\\beta_{ImpA^{3}}ImpA^{3}$; (3) I am not sure if you are asking this, but if you want to know how (for example) my answer used math notation if you click "edit" on a question or answer you can see the underlying markup.
@bart, think of this question: what is the expected value of the height of an American? The only way to know this value exactly would be to ask every single person his height and take the average. That's the expected value---it's a property of the full population. That's really hard. Instead, we get a sample, a subset of our population, ask them their heights and take the average. This is the sample mean---a property of our sample and an estimate of the expected value. As our sample gets larger, we should get a sample mean that gets closer to the true expected value (the law of large numbers).
Thank you for your response, genuinely really appreciate it! So you're suggesting that OLS multiple regression is an adequate way to compare two ordinal variables, as per your second paragraph? I'm not quite sure what you mean by the last sentence of para 2 though? How would i report my beta coefficient?
"*However the pooled variance cannot be used because p1 != pc*" -- not so. Under the appropriate null, the population proportions are equal. It doesn't matter that the null distribution is wrong under the alternative.
This might be a [cs.se] question, but it looks like it's missing a first paragraph to explain what you're trying to achieve: you jumped directly into your failed solution, and I don't understand what you were trying to solve.
Point taken about CW! I made it that way because stats is not my field so I assumed my question would require some correction or extension. Will consider this more carefully next time. Thanks!
Welcome to our site, Kyra!
I think the OP is talking about using a genetic algorithm to extract or engineer features, not to find models.
I'd argue that model misspecification - which seems to be what the OP is talking about, is somewhat distinct from residual confounding. Confounding requires a covariate. You can screw up a regression with *just* the misspecification of an exposure and outcome.
Another relevant question: http://stats.stackexchange.com/questions/2492/is-normality-testing-essentially-useless
@IanBoyd I am not sure it is good practice to accept an answer you do not understand and feel you cannot use - that is not a comment on whuber's answer since I always find them of high quality, but only on how to select an answer!
You've reasonably tagged this "likert" and a quick search shows 174 other questions with this tag, several of which are pertinent including http://stats.stackexchange.com/questions/31598/is-amazons-average-rating-misleading Short answer: You can combine, sure; whether the result is meaningful depends partly on your data. It is common to use the mean of scores, despite much disapproval. A median is the most obvious alternative.
Gaba_p you can see it yourself using the LOOK INSIDE feature on Amazon, jbowman's link will take you there. It's on p.425 as he says. It merely states "As a rule of thumb, $n$ should be large enough so that the expected frequency of each cell is at least 5". It does not cite a paper to substantiate this there or anywhere else that I see. Similar statements of the rule of thumb exist in most intro texts as Macro notes. You could simply cite that book, I think that is what he meant, not that you should buy it.
@Xi'an: I asked about the latter. I think your comment addressed my first part. The second part not yet. Thanks!
I am in agree with chl. Cluster analyses are exploratory approaches and the interpretation of results, for this particular case the optimal number of clusters, depends on your context. For example, in my work is common to used cluster analyses to classify individuals based on several characteristics and sometimes the number of clusters is preset. In this case, our objective is to find the set of classificatory variables that best distinguishes the individuals belonging to different clusters.
This is not about the difference between statisticians and the rest nor is this just about sampling from the right population. Validity is about measuring what you want to measure, and getting the sample wrong is just one way in which you can fail to achieve that goal. More common is to just ask the wrong question or a question that is misunderstood by the respondents. Looking at your data (with more or less advanced statistical techniques) is unlikely to definitively show whether or not you have a problem. Most often you will just need to sit down and think about it to determine it.
That might be sufficient - if I hadn't already voted to keep it open, I would have little concern about doing it now. On the other hand, some people are much more strict about where they draw the line between 'this is a stats/ML question' and 'this is a software question' than I am. You should not take close votes in any way personally, even if it does end up closed or moved to another SE site; this is in part how the site is supposed to work.
All the mentioned mean operations are special cases of the generalized mean operator:
f_s = ((x1^s+...+xn^s)/n)^(1/s). For s = -infinit, -1, 0, 1, +infinite, the generalized
mean f_s becomes: the minimum, harmonic mean, geometric mean, arithmetic mean and the maximum.
Also, f_s depends monotonous on: f_s biases towards larger values for larger s.
@IrishStat Thanks for the information. Naturally you are the absolute authority on what AUTOBOX can do and I most willingly retract that assertion. I take it that a forecast can be based on both "total" and "sample" in OP's terminology. That's useful. I remain a little queasy about overfitting. Using the variable's own history and a covariate sounds like about 5 parameters (or more) for 12 data points.
I would be very suspicious of links to data that require redirecting to other links, especially when R provides the very useful `dput()` function that eliminates any need for doing that. Please provide a reproducible example to receive assistance.
I agree: if $x$ is really continuous then there are too many parameters to be able to estimate them; if not, then it's the same logic as the first pair of models. It would make more sense to test adding a quadratic term in $x$.
Hi there, could you elaborate further on what you mean by "non-uniform" residuals?
In chemometrics the instrument responses are often nonlinear and heteroscedastic.  At a minimum that imposes a certain amount of caution when conducting and interpreting the regression.
Thank you wolfies for this great answer. However, do you know more robust curve fitting method? I haven't tried Tuenter's method, but seems to me that a moment-matching method is less robust than a percentile estimation method, due to the unreliability of the estimation of the moments.
Just as a remark, there are other StackExchange sites which might be better suited for this (I think there are statistic, data collection, as well as programming sites of course). Nevertheless, it's your own choice, and Math has of course a high visiting rate.
@ttnphns, my ultimate goal is a binomial classification task (the Kaggle Titanic comp) as I'm getting familiar with scikit-learn. I've tried a wide variety of feature engineering tasks and different types of models, but I know I'm leaving a few percentage points of accuracy on the table. I wanted to experiment to see if I could generate a small number of clusters (2-3) and improve my overall accuracy by training separate models for each cluster. Unfortunately, because the cluster sizes are so uneven, I don't have enough examples (<150) in the small clusters to generate good models.
Interesting point about the means. I suppose differences between means would suggest that the groups are different in some respect. And empirically I'd expect that where there's large differences between means, there's more likely to be differences in factor structure. Differences in means might also have implications for how the findings regarding the factor structure could be generalised. It might also increase correlations between items in general due to an effect the opposite of range restriction.
College male
(N=143)
1.17 (.77)
1.02 (.79)
.97 (.83)
.47 (.49)
.99 (.83)
.89 (.69)
.79 (.67)
.29 (.27)
I have done some google searches, using my text, other stats sources I have found useful but am still looking for the process - I would like to try to simulate the data if possible (spss, stata or even excel if this is possible).  I appreciated the following post (posted in next comment) which is nearly exactly the same and was hoping that someone may be kind enough to post any helpful tips (or sites) that would guide me.
Thanks! I looked at http://data.princeton.edu/R/glms.html, and the example is pretty much exactly what you describe and what I want. I had just never seen logistic expressed that way. Now I need to dig into the R implementation a bit, and see how the fitting is done!
Michael, because "<" and ">" have special meanings on Web pages, to avoid having large swathes of your text simply disappear from view you it is *essential* that you use $\\TeX$ markup for them in equations (the codes are "\\lt" and "\\gt" respectively). I marked up the two equations that caused this problem for you.  In the future, please read what you post immediately after posting it to make sure people are seeing what you thought they would see, and then feel free to flag your post for moderator attention if there is some problem with the markup.
It's a formula taken from Hubbard's book How to measure anything: EOLF / 1000 * (BB - WB), where EOLF is 15 (based on a EOLF curve and the Relative Threshold factor computed as RT = (C - WB)/(BB - WB)), BB is the Best Bound (25 million) and WB is the worst bound (2.5 million).
Corey, thank you!
It is good to look at how the residuals are distributed.  However, this histogram tells you very little about their apparent "randomness." For that, you need to *compare* the residuals to other data you have, including the dependent variable and any other variables that might not have been involved in the fitting. You want the residuals to look *independent* of all other variables.
Whether or not your pre and post scores are significantly different, without a control group, your inferences regarding the causal relationship of your intervention are more or less meaningless without a control group not receiving the intervention. The test is also different depending on whether there is a control group or not. Can you clarify (1) whether you have a control group, and (2) whether the control group is matched to, or independent of the intervention group?
Not a very good idea - see [here](http://stats.stackexchange.com/questions/68834/what-is-the-benefit-of-breaking-up-a-continuous-predictor-variable).
Interesting.  Could you advise as to what part of linear programming this might come under?  I do actually have the transition probabilities but they're only a guess at best as I didn't observe the process.  Would they help do you think?  Thanks and best regards
abs() for abs(x[1]) changes everything! Thank you.
I personally use Stata for most survey analysis, but Tom Lumley's Survey package for R is excellent:  http://r-survey.r-forge.r-project.org/survey/index.html
See also the resources at the UCLA web site: http://www.ats.ucla.edu/stat/mult_pkg/faq/svy_howtochoose.htm
Var(Xi)=μ=E(Xi)>0. If this were fixed then this would be an error in variables model with variance ratio σ$^2$ $_ro$/μ. It isn't because μ changes with the Xi. I have seen models with non constant variance in Y and models with errors in variables but not this type of model which has errors in variables with non-constant variance.  When the variance in Y is not constant sometimes it is possible to model the variance as a function of the value of the covariate x.  Maybe something like that could be done for the error in X.
Thanks @propofol, that's really helpful.
Why not storing your processed training data in a database?
How is it that you ran this model as both OLS and as a logistic regression? That doesn't make sense. Also, you state that you are adjusting for clustering in the data; that implies that this is a mixed-effects model, in which case it should be GLiMM or LMM, but you don't say anything about that. Can you clarify what the nature of your analysis is?
From another source it has been suggested, that the dataset may be too small (which in my humble opinion still would not warrant a contradiction in results). So here goes some more information: The training set contains 34 data points, the testing set the 4 points used in the example. For the 663 possible predictors it is guaranteed, that each column has 80% values >0 which are spectral counts from a proteomics experiment. Using either the svms from e1071 or ksvm I usually get accuracy values (i.e. the rate of correct predictions) of roughly 80% when doing a 10-fold cross validation.
@conarch I'm not convinced that independent samples tests are right. You should clarify the situation as indicated in my other comment
Are you only interested in how to accurately reflect the random effects in the function call? If so, this Q would belong on [Stack Overflow](http://stackoverflow.com/), rather than here. Alternatively, if you are interested in the statistical issues involved with GLMMs, nesting, etc., the Q should stay. If the latter, please edit to clarify. If the former, flag your Q & we can migrate it for you (*please don't cross-post, though*).
The significance test for r is going to correspond to the confidence interval that's not bootstrapped (the one you would compute using formulas). It seems your question is more about the difference between bias-corrected and percentile bootstrapped confidence intervals.
If you already did some study with it, it could perhaps be rescued by looking at it as binary data (at ceiling/not at ceiling) and analyzing accordingly (contingency table, logistic regression, sign test, etc.) but as a questionnaire, you don't need alpha to say that it is not very good for the population/situation in which you tested it.
Is this a homework problem?  If so, it is considered good practice to mention that fact in the question.  It is also considered good practice to explain what you have tried so far, and how far you have gotten on your own.  We aren't here to do your homework for you.  Read the information on the "homework" tag for more.
How is it any less continuous than a linear regression model?
...maybe Repeated Measures ANOVA could be an option, using replicate level information. We would need to use something that would allow for non-normal data distribution.
What R function are you talking about ?
@B_Miner I might be misunderstanding how HMM works, but it seems that it works as follows: I feed it my input sequence (a b c d e) and it outputs a hidden sequence best matching that, namely (a' b' c' d' e'). I don't think the dummy variables would solve this; I need a true/false classification for the entire sequence.
+1 a large part of the reason why statistical procedures appear questionable is because they are rather counter-intuitive and a historical appreciation of how statistics ended up the way it is, is probably a good approach for the skeptic.
It's not good practice to destroy your post and repost just after. Better to update your question so that this thread remains self-contained. Thanks.
Bootstrap (with replacement) can be used on your training data set, in place of, e.g., (repeated) k-fold cross-validation. See also: [Differences between cross validation and bootstrapping to estimate the prediction error](http://stats.stackexchange.com/q/18348/930), [Understanding bootstrapping for validation and model selection](http://stats.stackexchange.com/questions/14516/understanding-bootstrapping-for-validation-and-model-selection?rq=1).
Is someone's opinion a fault? I'd argue that the failure is trying to draw meaningful conclusions based on a single statistic from only a few data points. As noted by @nico above, Amazon does show a bar graph of all the ratings.
Are you saying that there are no trends in data??
Ratios of 3 & 4 are just rules of thumb--the main point is that it's actually hard to break the ANOVA (the universe is kind to us in this case). As for using the ratio as a formal test, read my answer that I linked above. Note that it is hard to give you any more info about this w/o knowing more about the context.
The link contains the measures. They are predicted number of days (pi) and actual number of days (ai). Maybe that is it in this case as well. Thanks!
Well, collapsing across trial you've done nothing wrong, if that was the implication of your question.  You're supposed to lose that trial information in the ANOVA.  If this is an educational exercise then you're doing it right.  If it was supposed to be you just looking for things in your data then you really probably need to switch to multi-level modelling.  The ez package facilitates that too.
What was the previous question. I don't understand this one.
@Ben Be careful: you are trying to infer something from changes in the p-value in a way that appears to be completely inappropriate. Try to post your real goal!
That's not a correct definition  of pdf, and the question asks for a *physical* meaning in engineering applications, not the actual definition of either term (which the asker already seems aware of). Please address the question that was asked.
How many participants? How many conditions? How many measures per participant? Does each participant get only one condition (as in your sample?)
Thank you for your suggestions for reading. I think it will help me.
Any would do. Thanks.
*(This comment was posted by an anonymous user as an edit to the OP's question I don't know if it was the OP not under his login)*: @Dimitriy V. Masterov: Thanks for your answer. Missing any reference in textbooks/ journals I am unsure how to estimate a type II tobit( heckman selection two stage) with a DiD specification. E.g. how do I implement/ interpret a DiD specification in each stage?
From the plot it appears that you have values greater than $100\\%$. That could be a side-effect of bins being e.g. $[90, 100), [100, 110)$. A model with logit link is indeed likely to work better than ANOVA on this evidence.
+1, re point #1, everyone can sweep faster on day Z and still have X & Z be uncorrelated, but the key is that the rank ordering of sweepers by speed is completely random. That is, although sweeper #17 was the fastest on day X, they are just as likely to be the slowest, or the median sweeper, as they are to be the fastest again on day Z.
+1 I was thinking this would be useful: you saved me having to search for the link!
I don't see where there's a Brownian motion here. Along with the OP, I see a textbook example calling for an unpaired t-test based on the data, not their differences.
When you do imputation within only a subsample of respondents which are qualified to answer (i.e. they were asked those questions), filter out the rest of the sample. MULT IMPUT command honours filtering. Filtered out cases won't be imputed. This issue is irrespective to how you code missing values. (I like to make system-missing only those who weren't asked, and user-missing those who found difficulty to answer.)
Consider abandoning the Markov chain idea, which appears to be an unnecessary and confusing element of the analysis, and focusing on characterizing the multivariate distribution of residence times within each stage.
Have you tried different starting values? Your loss function is non-convex, so different starting values can lead to different solutions.
I mentioned the negative binomial because it is an overdispersed alternative to the Poisson which the poser suggested initially.  Since each respondent has x/10 clues it could be binomial but that for each of the 10 clues there is a fixed probability pi for the ith respondent and the occurrences are independent.  That may nit be the case.
@whuber Typo! I meant (point) 1.
I added an example. Hope it helps. And yes, he is refering to the CV of the residuals.
Agree with @MichaelChernick. I would want to use both the methods (bootstrap and from 'k' moments) to simulate, and compare the results in some way.
@dominic999 And what data do you have now?
Thank you for explaining this in small steps, I now see what is happening.
To get an initial sense of the answers, consider the fraction $f$ of the population that is *not* related to a given ancestor by descent.  Initially $f = (n-1)/n$ for a population of $n$.  With random mixing, $f$ is *squared* after each generation.  In a starting population of $n=10^8$, say, this implies $f$ is almost surely $0$ after $32$ generations (about $600$ - $800$ years).
I don't want to know python either.  I just want help in understanding when to use which rule, and why.
In a way, isn't that similar to false-positives and false-negatives? Or specificity and sensitivity? Is the difference only semantics?
Generally speaking, as I mentioned, I see "subgroup" analysis used to look at a particular group of interest as part of a greater whole. Partitioning the data into a number of mutually exclusive subgroups and comparing them, without any indication of a "whole study" analysis, feels far more like stratification than a subgroup analysis.
@orbital Your modelling task sounds very interesting. I think that the one-off events, particularly the advertising ones, could be modelled as a binary "on-off" variable, as is done in intervention analysis. A reference at hand is: Wichern, D. W. and R. H. Jones (1977). "Assessing the Impact of Market Disturbances Using Intervention Analysis". I think you can do this using ARIMAX models by letting the exogenous explanatory variable(s) be dummy variable(s). Note also that trigonometric terms can also be used to model deterministic seasonal patterns:see Harvey's Time Series Models (1993), p.138.
I mean by simulation drawing samples generated by the system model and observation equations. (I sample the normal deviates of the errors of the system and observation equations.) Thereafter I proceed by predicting the next state and observation (as in filtering) using the corresponding equations. Process (sampling) is repeated at every successive step. So I guess that the answer to your question is yes.
This mean difference is neither small nor large: you simply have no basis for assessing its size.
@John My understanding is this the answer given at http://stats.stackexchange.com/questions/81914/why-is-homogeneity-of-variance-so-important correctly answers that question.
For bootstrap, wouldn't you be sampling WITH replacement? Without replacement you would get the original sample back since the size of each bootstrap sample is equal to the samplle size of x.
Assuming you mean $z =$ (value $-$ mean)/SD, it is just a linear rescaling and requires only that SD is positive. Even that can be caught by $z = 0$ if value is constant, as then $z$ and its mean are one and the same.
Not really. But there are many [algorithms](http://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle) to do that.
I don't see an R package called "omega". I did find a function, [?omega](http://www.personality-project.org/r/html/omega.html), in the `psych` package, & the [Omega Project](http://www.omegahat.org/). Is 1 of those what you're referring to? Can you edit your Q w/ a link to the package &/or function that's confusing you?
If you comments on the above, please let me know as the discussion will really help me! I will accept your answer in a while (just to keep the thread visible). Thanks again!
@Benjamin, thank you too, ;-)