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1087 | 2 | null | 152 | 14 | null | There is a nice and reasonably recent discussion of this problem here:
>
Christian P. Robert Multimodality and label switching: a
discussion. Workshop on mixtures, ICMS March 3, 2010.
Essentially, there are several standard strategies, and each has pros and cons. The most obvious thing to do is to formulate the pr... | null | CC BY-SA 4.0 | null | 2010-08-01T13:51:19.667 | 2019-05-30T06:16:09.020 | 2019-05-30T06:16:09.020 | 35989 | 643 | null |
1088 | 2 | null | 114 | 18 | null | In addition to those already mentioned, I like Rob Hyndman's blog:
[http://robjhyndman.com/researchtips/](http://robjhyndman.com/researchtips/)
I guess he's too modest to mention it himself! ;-)
| null | CC BY-SA 2.5 | null | 2010-08-01T14:16:22.900 | 2010-08-01T14:16:22.900 | null | null | 643 | null |
1089 | 2 | null | 726 | 11 | null | >
The true logic of this world is in the calculus of probabilities.
-- James Clerk Maxwell
| null | CC BY-SA 2.5 | null | 2010-08-01T14:21:18.177 | 2010-12-03T04:04:49.117 | 2010-12-03T04:04:49.117 | 795 | 643 | null |
1090 | 2 | null | 726 | 10 | null | A bit obscure this one, but a great quote about subjective probability:
>
... There is no way, however, in which the individual can avoid the
burden of responsibility for his own evaluations. The key cannot be
found that will unlock the enchanted garden wherein, among the
fairy-rings and the shrubs of magic wand... | null | CC BY-SA 3.0 | null | 2010-08-01T14:25:28.323 | 2011-08-15T04:13:32.757 | 2011-08-15T04:13:32.757 | 1381 | 643 | null |
1091 | 2 | null | 575 | 2 | null | There are TWO options for the inferential F-tests In SPSS.
Multivariate does NOT assume sphericity, adn so makes use of a different pairwise correlation for each pair of variables.
The "tests of within subjects effects", including any post hoc tests, assumes sphericity and makes some corrections for using a common co... | null | CC BY-SA 2.5 | null | 2010-08-01T18:14:31.930 | 2010-08-01T18:14:31.930 | null | null | null | null |
1092 | 2 | null | 1082 | 3 | null | Dawy et al. outline an algorithm in [Gene mapping and marker clustering using Shannon's mutual information](http://www.ece.iit.edu/~biitcomm/research/references/Zaher%20Dawy/Zaher%20Dawy%202006/Gene%20Mapping%20and%20Marker%20Clustering%20Using%20Shannon%92s%20Mutual%20Information.pdf) (2006). If you're using R, you m... | null | CC BY-SA 2.5 | null | 2010-08-01T18:41:27.523 | 2010-08-01T18:41:27.523 | null | null | 251 | null |
1093 | 1 | 1098 | null | 3 | 1211 | I'm looking for a distribution to model a vector of $k$ binary random variables, $X_1, \ldots, X_k$. Suppose I have observed that $\sum_i X_i = n$. In this case I do not want to treat them as independent Bernoulli random variables. Instead, I would like something like the multinomial:
$P(X_1=x_1, \ldots, X_k=x_k) = ... | Density function for a multivariate Bernoulli-like distribution | CC BY-SA 2.5 | null | 2010-08-01T22:31:15.863 | 2011-04-29T00:33:52.767 | 2011-04-29T00:33:52.767 | 3911 | 647 | [
"distributions"
] |
1094 | 2 | null | 1093 | 2 | null | Update
In light of your comments, here is an updated answer:
Approach 1: Difficult to implement/analyze
Consider the simple case of $k$ = 3 and $n$ = 2. In other words you toss 3 coins (with probabilities $p_1$, $p_2$ and $p_3$). Then, the required mass function for the above case is:
$p_1 p_2 (1-p_3) + p_1 (1-p_2) p_3... | null | CC BY-SA 2.5 | null | 2010-08-01T22:38:49.430 | 2010-08-02T02:01:37.240 | 2010-08-02T02:01:37.240 | null | null | null |
1095 | 1 | 1721 | null | 2 | 404 | This question concerns an implementation of the topmoumoute natural gradient (tonga) algorithm as described in page 5 in the paper Le Roux et al 2007 [http://research.microsoft.com/pubs/64644/tonga.pdf](http://research.microsoft.com/pubs/64644/tonga.pdf).
I understand that the basic idea is to augment stochastic gradi... | Tonga: low rank approximation of the natural gradient, question regarding Le Roux et al. 2007 | CC BY-SA 2.5 | null | 2010-08-01T22:52:13.423 | 2011-04-29T00:34:34.327 | 2011-04-29T00:34:34.327 | 3911 | 282 | [
"algorithms"
] |
1097 | 2 | null | 181 | 653 | null | I realize this question has been answered, but I don't think the extant answer really engages the question beyond pointing to a link generally related to the question's subject matter. In particular, the link describes one technique for programmatic network configuration, but that is not a "[a] standard and accepted me... | null | CC BY-SA 4.0 | null | 2010-08-02T02:20:30.080 | 2022-08-31T12:09:15.680 | 2022-08-31T12:09:15.680 | 78767 | 438 | null |
1098 | 2 | null | 1093 | 4 | null | The appropriate distribution is [Wallenius's noncentral hypergeometric distribution](http://en.wikipedia.org/wiki/Noncentral_hypergeometric_distributions). Using an urn analogy, the problem is equivalent to picking $n$ of $k$ balls without replacement, where each ball is a different color: the parameters $p$ are analo... | null | CC BY-SA 2.5 | null | 2010-08-02T04:04:13.047 | 2010-08-02T04:04:13.047 | null | null | 647 | null |
1099 | 1 | 1108 | null | 9 | 3233 | I am working on disease infection data, and I am puzzled on whether to handle the data as "categorical" or "continuous".
- "Infection Count"
the number of infection cases found in a specific period of time, the count
is generated from categorical data (i.e. no. of patient tagged as "infected")
- "Patient Bed D... | How to handle count data (categorical data), when it has been converted to a rate? | CC BY-SA 2.5 | null | 2010-08-02T04:40:22.673 | 2020-03-06T23:20:10.997 | 2020-03-06T23:20:10.997 | 11887 | 588 | [
"categorical-data",
"count-data",
"incidence-rate-ratio"
] |
1100 | 2 | null | 886 | 20 | null | I will give an itemized answer. Can provide more citations on demand, although this is not really controversial.
- Statistics is not all about
maximizing (log)-likelihood. That's
anathema to principled bayesians who
just update their posteriors or
propagate their beliefs through an
appropriate model.
- A lot of stati... | null | CC BY-SA 2.5 | null | 2010-08-02T05:16:40.183 | 2010-08-02T05:16:40.183 | null | null | 30 | null |
1101 | 2 | null | 1053 | 3 | null | Survival Analysis: A Self-Learning Text
by Kleinbaum and Klein
is pretty good. It depends on what you want. This is more of a non-technical introduction. It's focused on practical applications and minimizes the mathematics. Pedegocially, it's also intended for learning outside of the classroom.
| null | CC BY-SA 2.5 | null | 2010-08-02T05:49:40.147 | 2010-08-02T05:49:40.147 | null | null | 485 | null |
1102 | 2 | null | 890 | 0 | null | Thannks a lot for this very detailed answer. It does make perfect sense to me. If I have a model know. For example:
```
y = - 2.8 - 1.2 * urban - 3 * forest
```
with the reference category grassland and I would like to predict the model for a new environment.
If I have a point with grassland, the probability of y wou... | null | CC BY-SA 2.5 | null | 2010-08-02T08:14:36.877 | 2010-08-02T08:14:36.877 | null | null | null | null |
1103 | 2 | null | 1063 | 10 | null | To start with what we're talking about here is the standard normal distribution, a normal distribution with a mean of 0 and a standard deviation of 1. The short-hand for a variable which is distributed as a standard normal distribution is Z.
Here are my answers to your questions.
(1) I think there are two key reasons ... | null | CC BY-SA 3.0 | null | 2010-08-02T08:46:38.047 | 2012-08-20T17:02:53.953 | 2012-08-20T17:02:53.953 | 7290 | 215 | null |
1104 | 2 | null | 726 | 19 | null | >
While the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will be up to, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician.... | null | CC BY-SA 2.5 | null | 2010-08-02T08:58:27.830 | 2010-08-02T08:58:27.830 | null | null | 17 | null |
1106 | 2 | null | 1081 | 6 | null | Few opening remarks. In nMDS you have a matrix of dissimilarities $D_{ij}$ (not distances; for instance this can be a per cent of people that said in some poll that i&j are not similar). What you want to obtain is a set of points ($E=[X_i]$) representing objects on M-dim space; having it, you have the matrix of distanc... | null | CC BY-SA 2.5 | null | 2010-08-02T09:58:34.953 | 2010-08-02T11:23:47.897 | 2010-08-02T11:23:47.897 | null | null | null |
1107 | 2 | null | 1099 | 1 | null | From a technical purist point of view, you cannot as your ratio "infection per patient bed days" is not a continuous variable. For example, an irrational value will never appear in your dataset. However, you can ignore this technical issue and do whatever tests that may be appropriate for your context. By way of analog... | null | CC BY-SA 2.5 | null | 2010-08-02T10:03:30.803 | 2010-08-02T10:03:30.803 | null | null | null | null |
1108 | 2 | null | 1099 | 4 | null | For me it does not at all sound appropriate to use a chi-square test here.
I guess what you wanna do is the following: You have different wards or treatments or whatever else kind of nominal variable (i.e., groups) that divides your data. For each of these groups you collected the Infection Count and the Patient Bed Da... | null | CC BY-SA 2.5 | null | 2010-08-02T10:55:30.890 | 2010-08-02T10:55:30.890 | null | null | 442 | null |
1109 | 2 | null | 1099 | 7 | null | I'm not quite sure what your data look like, or what your precise problem is, but I assume you have a table with the following headings and type:
>
ward (categorical), infections (integer), patient-bed-days (integer or continuous).
and you want to tell if the infection rate is statistically different for different w... | null | CC BY-SA 2.5 | null | 2010-08-02T11:24:35.680 | 2010-08-02T11:24:35.680 | null | null | 495 | null |
1111 | 2 | null | 1053 | 6 | null | For a very clear, succinct and applied approach, I highly recommend [Event History Modeling](http://rads.stackoverflow.com/amzn/click/0521546737) by Box-Steffenmeier and Jones
| null | CC BY-SA 2.5 | null | 2010-08-02T13:53:47.847 | 2010-08-02T13:53:47.847 | null | null | 302 | null |
1112 | 1 | 1113 | null | 34 | 53970 | I want to represent a variable as a number between 0 and 1. The variable is a non-negative integer with no inherent bound. I map 0 to 0 but what can I map to 1 or numbers between 0 and 1?
I could use the history of that variable to provide the limits. This would mean I have to restate old statistics if the maximum incr... | How to represent an unbounded variable as number between 0 and 1 | CC BY-SA 2.5 | null | 2010-08-02T14:38:55.070 | 2021-05-21T15:17:22.467 | 2010-09-17T20:29:37.823 | null | 652 | [
"normalization"
] |
1113 | 2 | null | 1112 | 40 | null | A very common trick to do so (e.g., in connectionist modeling) is to use the [hyperbolic tangent tanh](http://en.wikipedia.org/wiki/Tanh) as the 'squashing function".
It automatically fits all numbers into the interval between -1 and 1. Which in your case restricts the range from 0 to 1.
In `r` and `matlab` you get it ... | null | CC BY-SA 2.5 | null | 2010-08-02T14:56:35.277 | 2010-08-03T00:57:51.577 | 2010-08-03T00:57:51.577 | 159 | 442 | null |
1114 | 2 | null | 1112 | 11 | null | Any sigmoid function will work:
- The top half of the logistic function (multiply by 2, subtract 1)
- The error function
- tanh, as suggested by Henrik.
| null | CC BY-SA 2.5 | null | 2010-08-02T15:20:11.690 | 2010-08-02T15:20:11.690 | null | null | 495 | null |
1115 | 1 | null | null | -1 | 4445 | I have computed percentage change from time1 to time2 for several variables.
Can I predict percentage change in earnings from percentage change in produced and percentage changed in price?
When I ran a model with actual data and dummy coded time (time1=1, time2=0), the dummy variable was not statistically significant. ... | Can I predict percentage change in earnings from percentage change in produced and percentage changed in price? | CC BY-SA 3.0 | null | 2010-08-02T16:28:37.277 | 2011-09-28T00:05:47.827 | 2011-09-28T00:05:47.827 | 183 | 474 | [
"regression"
] |
1116 | 2 | null | 1053 | 4 | null | "Survival analysis using SAS: a practical guide" by Paul D. Allison provides a good guide to the connection between the math and SAS code - how to think about your information, how to code, how to interpret results. Even if you are using R, there will be parallels that could prove useful.
| null | CC BY-SA 2.5 | null | 2010-08-02T16:29:37.387 | 2010-08-02T16:29:37.387 | null | null | null | null |
1117 | 2 | null | 1040 | 0 | null | The answer depends on the degree of misspecification and sample size. In small and moderate samples simplified model will fit (in most cases) better to data then the true model.
In moderate and large samples residuals don't have to be normal as due to CLT regression coefficients are normal anyway.
| null | CC BY-SA 2.5 | null | 2010-08-02T16:43:44.403 | 2010-08-02T16:43:44.403 | null | null | 419 | null |
1118 | 2 | null | 1115 | 0 | null | You're likely to have problems with covariance - your model fails to meet the assumption of linear regression that the observations are independent, because a subject in your study will be correlated with itself between time 1 and time 2 (By the way, what are your observations? One for each product type?)
You might wa... | null | CC BY-SA 2.5 | null | 2010-08-02T16:43:49.333 | 2010-08-02T16:43:49.333 | null | null | null | null |
1119 | 2 | null | 1112 | 4 | null | In addition to the good suggestions by Henrik and Simon Byrne, you could use f(x) = x/(x+1). By way of comparison, the logistic function will exaggerate differences as x grows larger. That is, the difference between f(x) and f(x+1) will be larger with the logistic function than with f(x) = x/(x+1). You may or may no... | null | CC BY-SA 2.5 | null | 2010-08-02T16:49:48.093 | 2010-08-02T16:49:48.093 | null | null | null | null |
1120 | 2 | null | 138 | 2 | null | There are some very good learning materials here: [http://scc.stat.ucla.edu/mini-courses/materials-from-past-mini-courses/spring-2009-mini-course-materials/](http://scc.stat.ucla.edu/mini-courses/materials-from-past-mini-courses/spring-2009-mini-course-materials/)
| null | CC BY-SA 2.5 | null | 2010-08-02T16:55:33.157 | 2010-08-02T16:55:33.157 | null | null | null | null |
1121 | 2 | null | 1112 | 1 | null | There are two ways to implement this that I use commonly. I am always working with realtime data, so this assumes continuous input. Here's some pseudo-code:
Using a trainable minmax:
```
define function peak:
// keeps the highest value it has received
define function trough:
// keeps the lowest value it has re... | null | CC BY-SA 4.0 | null | 2010-08-02T16:57:33.557 | 2019-03-20T23:06:17.843 | 2019-03-20T23:06:17.843 | 241755 | 162 | null |
1122 | 2 | null | 534 | 9 | null |
- Almost always in randomized trials
- Almost always in observational study when someone measure all confouders (almost never)
- Sometimes when someone measure some counfounders (IC* algorithim of DAG discovery in Pearl's book Causality)
- In non gaussian linear models with two or more variables but not using corre... | null | CC BY-SA 3.0 | null | 2010-08-02T17:05:49.053 | 2013-06-09T03:50:18.943 | 2013-06-09T03:50:18.943 | 7290 | 419 | null |
1123 | 1 | null | null | 2 | 452 | In many papers I see data representing a rate of success (i.e a number between 0 and 1) modeled as a gaussian. This is clearly a sin (the range of variation of the gaussian is all of R),
but how bad is that sin? Under what assumptions would you say it is tolerable?
| Modeling success rate with gaussian distribution | CC BY-SA 2.5 | null | 2010-08-02T17:08:08.113 | 2010-08-03T19:26:55.673 | 2010-08-03T18:49:43.080 | null | null | [
"distributions",
"normality-assumption"
] |
1124 | 2 | null | 1123 | 1 | null | Could you quote from "many papers" so that we would get some context? Between "Gaussian" and "number between 0 and 1" I see slight conflict as the draws from a Gaussian are not bounded. Maybe you meant p-values?
| null | CC BY-SA 2.5 | null | 2010-08-02T17:15:04.730 | 2010-08-02T17:15:04.730 | null | null | 334 | null |
1125 | 2 | null | 1123 | 1 | null | It depends on the data. While the normal distribution does span the real line do note that nearly 99% of the values are contained within 3 standard deviations of the mean. Thus, if the following conditions hold it may be a reasonable assumption:
(a) the data range is such that 99% of the data falls between [$\mu - 3\si... | null | CC BY-SA 2.5 | null | 2010-08-02T17:15:14.387 | 2010-08-02T17:15:14.387 | null | null | null | null |
1126 | 1 | null | null | 11 | 584 | Joshua Epstein wrote a paper titled "Why Model?" available at [http://www.santafe.edu/media/workingpapers/08-09-040.pdf](http://www.santafe.edu/media/workingpapers/08-09-040.pdf) in which gives 16 reasons:
- Explain (very distinct from predict)
- Guide data collection
- Illuminate core dynamics
- Suggest dynamical ... | Reasons besides prediction to build models? | CC BY-SA 2.5 | null | 2010-08-02T17:29:12.087 | 2010-09-03T03:49:48.030 | null | null | 660 | [
"modeling"
] |
1127 | 2 | null | 1115 | 1 | null | You can do it, but I think that using percentages in a regression framework is likely to lead to a model that has little value. I would try to generalize the model so that the percentage change is a special case, but that more complex behaviour is possible.
| null | CC BY-SA 2.5 | null | 2010-08-02T17:55:23.633 | 2010-08-02T17:55:23.633 | null | null | 187 | null |
1128 | 2 | null | 1126 | 6 | null | >
Reason 17. Write a paper.
Sort-of just kidding but not really. There seems to be a bit of overlap between some of his points (eg 1, 5, 6, 12, 14).
| null | CC BY-SA 2.5 | null | 2010-08-02T17:57:15.127 | 2010-08-02T17:57:15.127 | null | null | 334 | null |
1129 | 2 | null | 1016 | 1 | null | Another vote for Rob's answer.
There are also some interesting ideas in the "relative importance" literature. This work develops methods that seek to determine how much importance is associated with each of a number of candidate predictors. There are Bayesian and Frequentist methods. Check the "relaimpo" package in ... | null | CC BY-SA 2.5 | null | 2010-08-02T18:00:10.207 | 2010-08-02T18:00:10.207 | null | null | 187 | null |
1130 | 1 | null | null | 4 | 2001 | I have data for about 1 year, 100 observations, multiple observations per subject, transactions occur on weekly basis but have 6-12 subjects per week, there is no order to this. There is a policy change in latter half of year, I want to model change in dependent variable due to policy change as a dummy variable: time1=... | Regression-multiple observations per subject | CC BY-SA 3.0 | null | 2010-08-02T18:44:15.063 | 2011-10-10T08:43:36.230 | 2011-10-10T08:43:36.230 | 183 | 474 | [
"regression"
] |
1131 | 2 | null | 1126 | 5 | null | >
Save money
I build mathematical/statistical of cellular mechanisms. For example, how a particular protein affects cellular ageing. The role of the model is mainly prediction, but also to save money. It's far cheaper to employ a single modeller than (say) a few wet-lab biologists with the associated equipment costs... | null | CC BY-SA 2.5 | null | 2010-08-02T18:52:56.510 | 2010-08-02T18:52:56.510 | null | null | 8 | null |
1132 | 2 | null | 1126 | 5 | null | >
For fun!
I'm sure most statisticians/modellers do their job because they enjoy it. Getting paid to do something you enjoy is quite nice!
| null | CC BY-SA 2.5 | null | 2010-08-02T19:16:14.867 | 2010-08-02T19:16:14.867 | null | null | 8 | null |
1133 | 1 | 1210 | null | 14 | 20145 | I have cross classified data in a 2 x 2 x 6 table. Let's call the dimensions `response`, `A` and `B`. I fit a logistic regression to the data with the model `response ~ A * B`. An analysis of deviance of that model says that both terms and their interaction are significant.
However, looking at the proportions of the da... | Multiple Chi-Squared Tests | CC BY-SA 2.5 | null | 2010-08-02T19:19:42.860 | 2016-02-04T08:01:37.070 | null | null | 287 | [
"categorical-data",
"logistic",
"multiple-comparisons",
"chi-squared-test"
] |
1134 | 2 | null | 1126 | 4 | null | >
dimension reduction
Sometimes there can be too much data, so forming an initial model allows for further analysis.
| null | CC BY-SA 2.5 | null | 2010-08-02T19:28:31.653 | 2010-08-02T19:28:31.653 | null | null | 5 | null |
1135 | 2 | null | 1126 | 4 | null | >
regulation
Government agencies require firms to provide reports using certain models. This provides for a degree of standardization in oversight. An example is the use of Value-at-Risk in the financial sector.
| null | CC BY-SA 2.5 | null | 2010-08-02T19:38:11.380 | 2010-08-02T19:38:11.380 | null | null | 5 | null |
1136 | 2 | null | 1126 | 2 | null | This is closely related to some of the others, but:
>
Eliminate human judgement
Human decision making is subject to many different forces and biases. That means that you not only get different answers to the same question, but you can also end up with really suboptimal outcomes. Examples would be the over-confidence... | null | CC BY-SA 2.5 | null | 2010-08-02T19:44:20.117 | 2010-08-02T19:44:20.117 | null | null | 5 | null |
1137 | 2 | null | 1115 | 0 | null | Regress the X1 value for time1 (and any other covariates you want) on the X1 variable for time 2 (your dependent variable). Your regression model will look something like this:
"x1 time 2" = "x1 time1" + x2 + x3 + x4 etc.
Your regression coefficients for x2....xn will be the effect of changes of that variable on "x1 t... | null | CC BY-SA 2.5 | null | 2010-08-02T20:17:03.580 | 2010-08-02T20:17:03.580 | null | null | null | null |
1138 | 2 | null | 1126 | 1 | null | >
Repetitive problems that involve some form of benefit / cost
In my field, we model the same set of variables in different locations, time frame, and magnitudes
| null | CC BY-SA 2.5 | null | 2010-08-02T20:20:52.697 | 2010-08-02T20:20:52.697 | null | null | 59 | null |
1140 | 2 | null | 103 | 4 | null | [EagerEyes ](http://eagereyes.org) by Robert Kosara (~5 posts a month). This blog includes tutorials and discussion articles plus it has a great home page with lots of links to useful information.
| null | CC BY-SA 3.0 | null | 2010-08-02T20:31:22.017 | 2012-10-24T14:53:17.483 | 2012-10-24T14:53:17.483 | 615 | 665 | null |
1141 | 2 | null | 103 | 4 | null | [https://web.archive.org/web/20120102041205/https://datavisualization.ch/](https://web.archive.org/web/20120102041205/https://datavisualization.ch/)
by Benjamin Wiederkehr and others (~15 links a month). If you want heaps of links you can subscribe to their twitter feed twitter slash datavis (~5 links a day)
ahhh... i'... | null | CC BY-SA 4.0 | null | 2010-08-02T20:35:41.460 | 2022-11-29T16:30:03.407 | 2022-11-29T16:30:03.407 | 362671 | 665 | null |
1142 | 1 | null | null | 107 | 82823 | I am working with a large amount of time series. These time series are basically network measurements coming every 10 minutes, and some of them are periodic (i.e. the bandwidth), while some other aren't (i.e. the amount of routing traffic).
I would like a simple algorithm for doing an online "outlier detection". Basica... | Simple algorithm for online outlier detection of a generic time series | CC BY-SA 2.5 | null | 2010-08-02T20:37:27.650 | 2018-08-07T10:50:54.290 | null | null | 667 | [
"time-series",
"outliers",
"mathematical-statistics",
"real-time"
] |
1144 | 2 | null | 1142 | 2 | null | You could use the standard deviation of the last N measurements (you have to pick a suitable N). A good anomaly score would be how many standard deviations a measurement is from the moving average.
| null | CC BY-SA 2.5 | null | 2010-08-02T20:48:01.103 | 2010-08-02T20:48:01.103 | null | null | 666 | null |
1145 | 2 | null | 1123 | 1 | null | It's usually a small sin. In nature, most phenomena can't realistically receive any value in R, but we model them as if they could.
The greater sin is to assume that the rate of success is shaped like a normal distribution if it isn't.
| null | CC BY-SA 2.5 | null | 2010-08-02T20:53:20.623 | 2010-08-02T20:53:20.623 | null | null | 666 | null |
1146 | 2 | null | 1126 | 3 | null | >
Control
A major aspect of the dynamic modelling literature is associated with control. This kind of work spans a lot of disciplines from politics/economics (see, e.g. Stafford Beer), biology (see e.g. N Weiner's 1948 work on Cybernetics) through to contemporary state space control theory (see for an intro Ljung 19... | null | CC BY-SA 2.5 | null | 2010-08-02T20:54:01.713 | 2010-08-02T20:54:01.713 | null | null | 668 | null |
1147 | 2 | null | 1142 | 6 | null | I am guessing sophisticated time series model will not work for you because of the time it takes to detect outliers using this methodology. Therefore, here is a workaround:
- First establish a baseline 'normal' traffic patterns for a year based on manual analysis of historical data which accounts for time of the day,... | null | CC BY-SA 2.5 | null | 2010-08-02T21:23:37.547 | 2010-08-02T21:23:37.547 | null | null | null | null |
1148 | 2 | null | 1142 | 6 | null | Seasonally adjust the data such that a normal day looks closer to flat. You could take today's 5:00pm sample and subtract or divide out the average of the previous 30 days at 5:00pm. Then look past N standard deviations (measured using pre-adjusted data) for outliers.
This could be done separately for weekly and daily... | null | CC BY-SA 2.5 | null | 2010-08-02T21:50:27.147 | 2010-08-02T21:50:27.147 | null | null | 33 | null |
1149 | 1 | 1150 | null | 106 | 51609 | The wiki discusses the problems that arise when [multicollinearity](http://en.wikipedia.org/wiki/Multicollinearity) is an issue in linear regression. The basic problem is multicollinearity results in unstable parameter estimates which makes it very difficult to assess the effect of independent variables on dependent va... | Is there an intuitive explanation why multicollinearity is a problem in linear regression? | CC BY-SA 2.5 | null | 2010-08-02T22:42:32.947 | 2021-05-26T12:01:47.603 | 2021-05-22T15:32:35.887 | 11887 | null | [
"regression",
"multicollinearity",
"intuition",
"faq"
] |
1150 | 2 | null | 1149 | 112 | null | Consider the simplest case where $Y$ is regressed against $X$ and $Z$ and where $X$ and $Z$ are highly positively correlated. Then the effect of $X$ on $Y$ is hard to distinguish from the effect of $Z$ on $Y$ because any increase in $X$ tends to be associated with an increase in $Z$.
Another way to look at this is to ... | null | CC BY-SA 2.5 | null | 2010-08-02T22:59:09.380 | 2010-08-10T06:07:48.497 | 2010-08-10T06:07:48.497 | 159 | 159 | null |
1151 | 2 | null | 1149 | 22 | null | The geometric approach is to consider the least squares projection of $Y$ onto the subspace spanned by $X$.
Say you have a model:
$E[Y | X] = \beta_{1} X_{1} + \beta_{2} X_{2}$
Our estimation space is the plane determined by the vectors $X_{1}$ and $X_{2}$ and the problem is to find coordinates corresponding to $(\beta... | null | CC BY-SA 3.0 | null | 2010-08-02T23:26:02.567 | 2013-09-21T22:18:13.130 | 2013-09-21T22:18:13.130 | 17230 | 251 | null |
1152 | 2 | null | 1130 | 1 | null | If you estimate the policy change as a fixed effects estimation in the context of an OLS regression you'll over-estimate your degrees of freedom because of the repeated measures by subject. If you do not think there is an overall trend of time (beyond the policy shift) then there is no reason to keep all of the observ... | null | CC BY-SA 2.5 | null | 2010-08-02T23:31:46.130 | 2010-08-02T23:31:46.130 | null | null | 196 | null |
1153 | 2 | null | 1142 | 97 | null | Here is a simple R function that will find time series outliers (and optionally show them in a plot). It will handle seasonal and non-seasonal time series. The basic idea is to find robust estimates of the trend and seasonal components and subtract them. Then find outliers in the residuals. The test for residual outlie... | null | CC BY-SA 3.0 | null | 2010-08-03T00:54:56.310 | 2012-02-17T11:27:27.007 | 2012-02-17T11:27:27.007 | 159 | 159 | null |
1154 | 2 | null | 1142 | 16 | null | If you're worried about assumptions with any particular approach, one approach is to train a number of learners on different signals, then use [ensemble methods](http://en.wikipedia.org/wiki/Ensembles_of_classifiers) and aggregate over the "votes" from your learners to make the outlier classification.
BTW, this might b... | null | CC BY-SA 3.0 | null | 2010-08-03T00:56:33.157 | 2012-02-11T08:29:21.253 | 2012-02-11T08:29:21.253 | 2921 | 251 | null |
1155 | 2 | null | 1149 | 2 | null | If two regressors are perfectly correlated, their coefficients will be impossible to calculate; it's helpful to consider why they would be difficult to interpret if we could calculate them. In fact, this explains why it's difficult to interpret variables that are not perfectly correlated but that are also not truly in... | null | CC BY-SA 2.5 | null | 2010-08-03T02:20:32.477 | 2010-08-03T02:20:32.477 | null | null | 672 | null |
1156 | 2 | null | 1149 | 4 | null | My (very) layman intuition for this is that the OLS model needs a certain level of "signal" in the X variable in order to detect it gives a "good" predicting for Y. If the same "signal" is spread over many X's (because they are correlated), then none of the correlated X's can give enough of a "proof" (statistical sign... | null | CC BY-SA 2.5 | null | 2010-08-03T02:28:37.437 | 2010-08-03T02:28:37.437 | null | null | 253 | null |
1157 | 2 | null | 103 | 4 | null | [Chart Porn](http://chartporn.org/)
I find the blog name pretty humorous. Great dataviz.
| null | CC BY-SA 3.0 | null | 2010-08-03T02:45:53.883 | 2012-10-24T14:53:45.140 | 2012-10-24T14:53:45.140 | 615 | 11 | null |
1158 | 2 | null | 103 | 7 | null | It's not a blog, but Edward Tufte has an [interesting forum](http://www.edwardtufte.com/bboard/q-and-a?topic_id=1) on information design including data visualization.
| null | CC BY-SA 2.5 | null | 2010-08-03T02:49:32.377 | 2010-08-03T02:49:32.377 | null | null | 159 | null |
1159 | 2 | null | 1133 | 1 | null | The unprincipled approach is to discard the disproportionate data, refit the model and see if logit/conditional odds ratios for response and A are very different (controlling for B). This might tell you if there's cause for concern. Pooling the levels of B is another approach. On more principled lines, If you're wor... | null | CC BY-SA 2.5 | null | 2010-08-03T02:54:30.290 | 2010-08-03T02:54:30.290 | null | null | 251 | null |
1160 | 1 | null | null | 2 | 467 | R allows us to put code to run in the beginning/end of a session.
What codes would you suggest putting there?
I know of three interesting examples (although I don't have "how to do them" under my fingers here):
- Saving the session history when closing R.
- Running a fortune() at the beginning of an R session.
- I w... | What code would you put before/after your R session? | CC BY-SA 2.5 | null | 2010-08-03T03:02:57.650 | 2010-09-07T20:59:46.453 | 2010-08-03T07:28:24.693 | null | 253 | [
"r"
] |
1161 | 2 | null | 1160 | 5 | null | Some information about how to implement this is provided at `help(.First)` and `help(.Last)`.
| null | CC BY-SA 2.5 | null | 2010-08-03T03:49:10.593 | 2010-08-03T03:49:10.593 | null | null | 159 | null |
1162 | 2 | null | 1126 | 2 | null | >
To take (useful) action.
I'm paraphrasing someone else here, but suppose we built a system of public health around the model that infectious diseases are due to malevolent spirits that spread through contact. The science of microbes may be an infinitely better model, but you could prevent a good number of contagi... | null | CC BY-SA 2.5 | null | 2010-08-03T06:26:47.963 | 2010-08-03T06:26:47.963 | null | null | 251 | null |
1164 | 1 | 1170 | null | 88 | 6844 | When solving business problems using data, it's common that at least one key assumption that under-pins classical statistics is invalid. Most of the time, no one bothers to check those assumptions so you never actually know.
For instance, that so many of the common web metrics are "long-tailed" (relative to the normal ... | Why haven't robust (and resistant) statistics replaced classical techniques? | CC BY-SA 4.0 | null | 2010-08-03T07:49:34.003 | 2022-12-21T10:12:20.553 | 2022-12-21T10:12:20.553 | 110833 | 438 | [
"model-selection",
"nonparametric",
"outliers",
"robust",
"philosophical"
] |
1165 | 2 | null | 1160 | 2 | null | On open, I set R options, load environment variables (eg. global variables, API keys) and open database connections, and then close those connections when exiting. With some of these things, I prefer to do them onLoad of my packages rather than per session.
Regarding how to save your session, use the save command.
| null | CC BY-SA 2.5 | null | 2010-08-03T08:27:13.243 | 2010-08-03T08:27:13.243 | null | null | 5 | null |
1166 | 2 | null | 1164 | 12 | null | I Give an answer in two directions:
- things that are robust are not necessarily labeled robust. If you believe robustness against everything exists then you are naive.
- Statistical approaches that leave the problem of robustness appart are sometime not adapted to the real world but are often more valuable (as a c... | null | CC BY-SA 2.5 | null | 2010-08-03T09:05:56.737 | 2010-08-03T16:51:26.903 | 2010-08-03T16:51:26.903 | 223 | 223 | null |
1169 | 1 | 1171 | null | 5 | 906 | I'm looking to check my logic here.
Say you measure a quantity in group A, and find the mean is 2 and your 95% confidence interval ranges from 1 to 3. Then you measure the same quantity in group B and find a mean of 4 with a 95% confidence interval that ranges from 3.5 to 4.5. Assuming that A & B are independent, what... | CI for a difference based on independent CIs | CC BY-SA 2.5 | null | 2010-08-03T12:20:09.890 | 2010-10-30T12:50:27.890 | 2010-08-13T00:56:41.777 | 364 | 364 | [
"confidence-interval"
] |
1170 | 2 | null | 1164 | 76 | null | Researchers want small p-values, and you can get smaller p-values if you use methods that make stronger distributional assumptions. In other words, non-robust methods let you publish more papers. Of course more of these papers may be false positives, but a publication is a publication. That's a cynical explanation, bu... | null | CC BY-SA 2.5 | null | 2010-08-03T12:22:58.247 | 2010-08-03T12:22:58.247 | null | null | 319 | null |
1171 | 2 | null | 1169 | 10 | null | No, you can't compute a CI for the difference that way I'm afraid, for the same reason you can't use whether the CIs overlap to judge the statistical significance of the difference. See, for example,
"On Judging the Significance of Differences by Examining the Overlap Between Confidence Intervals"
Nathaniel Schenker, ... | null | CC BY-SA 2.5 | null | 2010-08-03T12:30:00.740 | 2010-08-03T12:30:00.740 | null | null | 449 | null |
1172 | 2 | null | 563 | 18 | null | As a medical statistician with no previous knowledge of econom(etr)ics, I struggled to get to grips with instrumental variables as I often struggled to follow their examples and didn't understand their rather different terminology (e.g. 'endogeneity', 'reduced form', 'structural equation', 'omitted variables'). Here's ... | null | CC BY-SA 2.5 | null | 2010-08-03T13:12:04.477 | 2010-08-03T13:12:04.477 | null | null | 449 | null |
1173 | 1 | 1251 | null | 15 | 3729 | In my area of research, a popular way of displaying data is to use a combination of a bar chart with "handle-bars". For example,
The "handle-bars" alternate between standard errors and standard deviations depending on the author. Typically, the sampl... | Alternative graphics to "handle bar" plots | CC BY-SA 3.0 | null | 2010-08-03T13:36:38.303 | 2022-11-30T05:28:30.260 | 2013-12-02T22:54:25.163 | 11633 | 8 | [
"data-visualization"
] |
1174 | 1 | 1212 | null | 50 | 69008 | I know of normality tests, but how do I test for "Poisson-ness"?
I have sample of ~1000 non-negative integers, which I suspect are taken from a Poisson distribution, and I would like to test that.
| How can I test if given samples are taken from a Poisson distribution? | CC BY-SA 3.0 | null | 2010-08-03T13:54:19.897 | 2015-09-03T22:17:07.177 | 2013-05-15T04:10:56.497 | 805 | 634 | [
"hypothesis-testing",
"distributions",
"poisson-distribution",
"goodness-of-fit"
] |
1175 | 2 | null | 1173 | 2 | null | If the data are rates: that is number of successes divided by number of trials, then a very elegant method is a funnel plot. For example, see [this](https://web.archive.org/web/20200928130315/https://qualitysafety.bmj.com/content/11/4/390.2.full) (apologies if the link requires a subscription--let me know and I'll find... | null | CC BY-SA 4.0 | null | 2010-08-03T13:55:22.063 | 2022-11-30T05:28:30.260 | 2022-11-30T05:28:30.260 | 362671 | 495 | null |
1176 | 2 | null | 1173 | 10 | null | Frank Harrell's (most excellent) keynote entitled "Information Allergy" at useR! last month showed alternatives to these: rather than hiding the raw data via the aggregation the bars provide, the raw data is also shown as dots (or points). "Why hide the data?" was Frank's comment.
Given alpa blending, that strikes as... | null | CC BY-SA 2.5 | null | 2010-08-03T13:59:03.973 | 2010-08-03T13:59:03.973 | null | null | 334 | null |
1177 | 2 | null | 1174 | 8 | null | I suppose the easiest way is just to do a chi-squared [Goodness of fit](http://en.wikipedia.org/wiki/Pearson%27s_chi-square_test) test.
In fact here's nice [java applet](http://home.ubalt.edu/ntsbarsh/Business-stat/otherapplets/PoissonTest.htm) that will do just that!
| null | CC BY-SA 2.5 | null | 2010-08-03T14:14:54.700 | 2010-08-03T14:14:54.700 | null | null | 8 | null |
1178 | 2 | null | 1174 | 9 | null | You can use the dispersion (ratio of variance to the mean) as a test statistic, since the Poisson should give a dispersion of 1. [Here is a link](http://www.stats.uwo.ca/faculty/aim/2004/04-259/notes/DispersionTests.pdf) to how to use it as a model test.
| null | CC BY-SA 2.5 | null | 2010-08-03T14:21:43.390 | 2010-08-03T14:21:43.390 | null | null | 378 | null |
1179 | 2 | null | 1173 | 2 | null | I'm curious at to why you don't like these plots. I use them all the time. Without wanting to state the blooming obvious, they allow you to compare the means of different groups and see if their 95% CIs overlap (i.e., true mean likely to be different).
It's important to get a balance of simplicity and information for d... | null | CC BY-SA 2.5 | null | 2010-08-03T14:26:33.223 | 2010-08-03T14:26:33.223 | null | null | 199 | null |
1180 | 2 | null | 1174 | 12 | null | For a Poisson distribution, the mean equals the variance. If your sample mean is very different from your sample variance, you probably don't have Poisson data. The dispersion test also mentioned here is a formalization of that notion.
If your variance is much larger than your mean, as is commonly the case, you might... | null | CC BY-SA 2.5 | null | 2010-08-03T14:39:16.187 | 2010-08-03T14:39:16.187 | null | null | 319 | null |
1181 | 2 | null | 1174 | 15 | null | Here is a sequence of R commands that may be helpful. Feel free to comment or edit if you spot any mistakes.
```
set.seed(1)
x.poi<-rpois(n=200,lambda=2.5) # a vector of random variables from the Poisson distr.
hist(x.poi,main="Poisson distribution")
lambda.est <- mean(x.poi) ## estimate of parameter lambda
(tab.os<-... | null | CC BY-SA 2.5 | null | 2010-08-03T14:52:44.720 | 2010-08-03T14:52:44.720 | null | null | 339 | null |
1182 | 2 | null | 1173 | 7 | null | From a psychological perspective, I advocate plotting the data plus your uncertainty about the data. Thus, in a plot like you show, I would never bother with extending the bars all the way to zero, which only serves to minimize the eye's ability to distinguish differences in the range of the data.
Additionally, I'm fra... | null | CC BY-SA 4.0 | null | 2010-08-03T15:08:16.867 | 2019-08-21T18:48:29.680 | 2019-08-21T18:48:29.680 | 162986 | 364 | null |
1183 | 2 | null | 1173 | 2 | null | I would use boxplots here; clean, meaningful, nonparametric... Or [vioplot](http://cran.r-project.org/web/packages/vioplot/index.html) if the distribution is more interesting.
| null | CC BY-SA 2.5 | null | 2010-08-03T15:19:15.750 | 2010-08-03T15:19:15.750 | null | null | null | null |
1184 | 1 | 1187 | null | 5 | 3085 | Could you recommend an introductory reference to index decomposition analysis, including
- different methods (e.g. methods linked to the Laspeyre index and methods linked to the Divisa index)
- properties of decomposition methods which can be used to compare the different methods
- implementations of methods, e.g. i... | Introduction to index decomposition analysis | CC BY-SA 2.5 | null | 2010-08-03T16:26:48.983 | 2011-07-09T16:47:49.890 | 2011-04-13T08:20:20.310 | null | 573 | [
"index-decomposition"
] |
1185 | 2 | null | 1164 | 30 | null | I would suggest that it's a lag in teaching. Most people either learn statistics at college or University. If statistics is not your first degree and instead did a mathematics or computer science degree then you probably only cover the fundamental statistics modules:
- Probability
- Hypothesis testing
- Regression
... | null | CC BY-SA 3.0 | null | 2010-08-03T17:03:58.947 | 2018-04-19T10:55:00.923 | 2018-04-19T10:55:00.923 | 22047 | 8 | null |
1186 | 2 | null | 1174 | 3 | null | You can draw a single figure in which the observed and expected frequencies are drawn side by side. If the distributions are very different and you also have a variance-mean ratio bigger than one, then a good candidate is the negative binomial. Read the section [Frequency Distributions](http://books.google.com/books?id... | null | CC BY-SA 2.5 | null | 2010-08-03T17:17:31.300 | 2010-08-03T17:17:31.300 | null | null | 632 | null |
1187 | 2 | null | 1184 | 4 | null | This thesis may be a starting place: [A Comparative Analysis of Index Decomposition Methods](https://scholarbank.nus.edu.sg/bitstream/handle/10635/14229/GranelF.pdf?sequence=1), by Frédéric Granel. It should serve as a basic introduction to IDA and the Laspeyre index, but it does not include the Divisa index or any co... | null | CC BY-SA 2.5 | null | 2010-08-03T17:24:56.913 | 2010-08-03T17:30:07.610 | 2010-08-03T17:30:07.610 | 39 | 39 | null |
1188 | 2 | null | 1123 | 1 | null | Are you entirely sure that they're using the normal distribution directly? It's very common to use transformed responses to model success rates, but this involves passing through a link function to move from a Gaussian random variable to a value in [0,1]. A commonly used transform is the probit one, which is just the... | null | CC BY-SA 2.5 | null | 2010-08-03T19:26:55.673 | 2010-08-03T19:26:55.673 | null | null | 61 | null |
1189 | 2 | null | 881 | 4 | null | You can also use Edgeworth series, if your random variable has a finite mean and variance, which expands the CDF of your random variable in terms of the Gaussian CDF. At first glance it's not quite as tidy conceptually as using a mixture model, but the derivation is quite pretty and it gives you a closed form with ver... | null | CC BY-SA 2.5 | null | 2010-08-03T19:37:30.837 | 2010-08-03T19:37:30.837 | null | null | 61 | null |
1190 | 2 | null | 1099 | 1 | null | Chi-square tests do not seem appropriate. As others said, provided there are a reasonable number of different rates, you could treat the data as continuous and do regression or ANOVA. You would then want to look at the distribution of the residuals.
| null | CC BY-SA 2.5 | null | 2010-08-03T19:51:33.140 | 2010-08-03T19:51:33.140 | null | null | 686 | null |
1191 | 2 | null | 1016 | 1 | null | I also like Rob's answer. And, if you happen to use SAS rather than R, you can use PROC GLMSELECT for models that would be done with PROC GLM, although it works well for some other models, as well. See
Flom and Cassell "Stopping Stepwise: Why Stepwise Selection Methods are Bad and What you Should Use" presented at va... | null | CC BY-SA 2.5 | null | 2010-08-03T19:57:01.447 | 2010-08-03T19:57:01.447 | null | null | 686 | null |
1192 | 2 | null | 1174 | 1 | null | Yet another way to test this is with a quantile quantile plot. In R, there is qqplot. This directly plots your values against a normal distribution with similar mean and sd
| null | CC BY-SA 3.0 | null | 2010-08-03T20:00:30.287 | 2013-05-15T12:38:18.147 | 2013-05-15T12:38:18.147 | 686 | 686 | null |
1193 | 2 | null | 726 | 3 | null | A variation on the Fisher quotation given [here](https://stats.stackexchange.com/questions/726/famous-statistician-quotes/739#739) is
>
Hiring a statistician after the data have been collected is like hiring a physician when your patient is in the morgue. He may be able to tell you what went wrong, but he is unlikely... | null | CC BY-SA 2.5 | null | 2010-08-03T20:07:57.437 | 2010-08-07T14:44:30.670 | 2017-04-13T12:44:37.420 | -1 | 686 | null |
1194 | 1 | null | null | 77 | 40283 | Back in April, I attended a talk at the UMD Math Department Statistics group seminar series called "To Explain or To Predict?". The talk was given by [Prof. Galit Shmueli](http://www.rhsmith.umd.edu/faculty/gshmueli/web/html/) who teaches at UMD's Smith Business School. Her talk was based on research she did for a pape... | Practical thoughts on explanatory vs. predictive modeling | CC BY-SA 4.0 | null | 2010-08-03T20:19:57.303 | 2020-01-10T11:53:15.637 | 2018-11-13T20:37:42.233 | 226655 | 11 | [
"predictive-models"
] |
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