whuber

57,400 reputation

388190

bio	website	quantdec.com
	location	Northeastern US
	age	13
visits	member for	2 years, 9 months
	seen	3 hours ago
stats	profile views	11,351

Consultant (environmental and spatial stats a specialty), expert witness, and teacher.

	57,400 reputation	bio	website	quantdec.com	visits	member for	2 years, 9 months
388190 badges		location	Northeastern US		seen	3 hours ago

summary answers questions tags badges favorites bounties reputation activity

8,021 Comments

suggestions reviews revisions comments badges posts accepts all

3h	comment	Does logistic regression use crosstabs? What is the reason for the upper bound?
9h	comment	Uncertainty from Box–Cox estimation You are correct that the measure of goodness of fit has to be somehow normalized: that's why you want to use some measure of linearity, such as the ever-convenient $R^2$. But that suffers from various problems, too, most importantly its sensitivity to outlying values at the extremes of the independent variables, but conceivably it could lead to tractable and reasonable solutions provided $\lambda$ were constrained to a reasonable range (perhaps around $-1/2$ to $1$, typically).
9h	comment	Does logistic regression use crosstabs? You might want to regress on the counts themselves using Poisson regression.
10h	comment	Uncertainty from Box–Cox estimation It is obvious--but it does not appear statistically meaningful in this context. Using the GM for such normalization appears mathematically ad hoc rather than motivated by a statistical principle. Ordinarily, one uses a Box-Cox transformation for either or both of two reasons: linearization and achieving approximate homoscedasticity. If that's what you're looking for, then rather than rescaling to make it unitless, you might consider optimizing an objective related to those purposes. Two approaches seem appropriate: maximizing likelihood (best) or $R^2$ (both of which are unitless, too).
10h	comment	Uncertainty from Box–Cox estimation It would simplify things to throw out the rescaling by the GM. In practice this will be handled through the estimates of $\alpha$, $\beta$, and $\sigma$ anyway, so the fits will be identical, but for theoretical work the presence of that GM looks terribly complicating. It's rather bizarre that you multiply the $\log(y_i)$ by the GM, by the way. Does that have an interpretation?
13h	comment	Variance of superset from variance of subsets @Glen_b Would you prefer that we migrate your answer into the duplicate thread?
14h	comment	regression and correlation analysis Welcome to our site! Please read our faq concerning how to ask self-study questions. In particular, plain copies of test questions are not appropriate here: we expect you to explain what you have done and identify a specific aspect of the question with which you would like help.
14h	comment	Why is the condition of my design matrix so bad? I'm glad you resolved the issue!
14h	comment	How to define fit robustness? You can determine the "fittability" a priori by studying the chi-squared function. You will immediately see it depends on the data, so at that point you have to make assumptions about what data values you will get: but it's still a prior evaluation. For instance, in your example of a linear+sine term, if you know the data will cover a wider range you can find the fitting is robust. Thus there is no single omnibus data-independent answer to your question.
15h	comment	Why is the condition of my design matrix so bad? Please read through the answers in that thread: they are more nuanced. And the metrics had better change with how the data are expressed: when you recenter the data, for instance, you can make a huge change in the design matrix and its numerical properties. But to get back to your question, what I'm trying to encourage you to do is provide more information about your situation: so far you talk in generalities, but have told us little about the nature of your data (except to hint that some variables might not be continuous) and have given us little to go on to help with your specific problem.
15h	comment	Does logistic regression use crosstabs? Logistic regression does not apply to count outcomes; it only applies to binary outcomes. What are you really doing?
15h	comment	How to define fit robustness? One way is to look at the objective function (which is usually a negative log likelihood or a measure of goodness of fit).
15h	comment	Why is the condition of my design matrix so bad? Could you provide links or specific references? And yes, the condition number is a property of the matrix: when you include one specific parameter, that determines the matrix. The metrics aren't "fickle," but you may have highly collinear data.
16h	comment	Proving stationarity with difference equations Once you prove that stationarity implies the $m^\text{th}$ differences are stationary, you're done. That implication follows inductively by proving that the first differences of a stationary series are stationary. That proof is merely a direct application of your definition of stationary.
16h	comment	Why is the condition of my design matrix so bad? A condition number of $30$ for data with $4000$ rows is unlikely a problem; it certainly is nothing to worry about unless other problems occur, too (such as finding that a variable which ought to be strongly significant is not). A condition number of $30$ for just one parameter is no problem at all. Where did that rule of thumb come from?
17h	comment	Removing borders in R plots for achieving Tufte's axis FWIW, Tufte went further: he showed how in some cases erasing parts of the axes themselves provides additional information, effectively turning each axis into a visual display of the range of data. Inspired by this, in 1989 I wrote software to produce small multiple plots that incorporated this design (among many others inspired by Tufte and Bill Cleveland's group) and subsequently generated several million such graphics. When you have to mine so much data visually, such principles really work.
1d	comment	Logistic model, what is more important: Anova Chi-sq test or significance of coefficients +1 I'm impressed with your rapid progress here in just one month and your ability to provide a well-worked, clear explanation. Thanks for your efforts!
1d	comment	Estimating values of a sequence from observed differences Did you actually read Dougal's reply? It covers everything you suggest that has any theoretical justification: he describes the "noise," writes the system of linear equations, and shows how to use least squares regression ("polynomial" is unnecessary and inappropriate).
1d	comment	Test whether variables follow the same distribution It's all easy to find on Wikipedia through the obvious searches :-). As far as correlation goes, the problem is that variables can be strongly correlated but have totally different distributions; in fact, there exist sequences of distributions that get arbitrarily "far apart" (in an intuitive sense) while the distribution of their correlation coefficient gets arbitrarily close to $1$ in large datasets. This makes the correlation coefficient a poor discriminator of distribution.
1d	comment	what does this +/- of “average” mean? One (rightfully obscure) measure of dispersion of data $x_1,x_2,\ldots,x_n$ is the maximum absolute deviation from the mean, $r = \max_i\{\|x_i-\overline{x}\|\}$ where $\overline{x}$ is their mean. All your data are "valid," by definition, when $r\le .05\overline{x}$. That addresses your first question: yes, there is a statistical measure corresponding to this "validity" criterion.