Timeline for Comparison of statistical tests exploring co-dependence of two binary variables
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 5, 2020 at 15:31 | comment | added | EdM | @stans-ReinstateMonica thanks, I understand better what you're getting at now and will try to work on that some more. With respect to Wald tests versus LR tests for coefficients in logistic regression, I believe that has to do with the extra calculations required for the LR tests. The curvatures needed for Wald tests come directly from the maximum-likelihood calculations while to get LR coefficient p values and confidence intervals you need to calculate the likelihood profile for each coefficient separately. SAS does offer that as an option. | |
| Feb 5, 2020 at 11:44 | comment | added | stans | ... Both Wald test and LR test make distributional assumptions. Wald test says that the relevant statistic is Gaussian while LR test says that the LR statistic has chi-square distribution. The latter statement is not necessarily true in small and medium-sized samples. Here I am talking about the popular version of the LR test, based on the chi-square approximation and implemented in all statistical packages. I am not referring to the most general set-up by Neyman.... My main question: which test is most powerful in real life? I define codependence as $P(X = 1, Y =1) \neq P(X = 1)P(Y =1)$. | |
| Feb 5, 2020 at 11:37 | comment | added | stans | Thank you for the elaboration. Sadly, asymptotically we all are dead. Yes, the likelihood ratio test is most statistically efficient asymptotically, under certain regularity assumptions, but how does it perform on samples of 30, 100, 200? Kind of samples I work with every day as a statistician. You see, I have not noticed that "the likelihood-ratio test is generally preferred" to Wald test for logistic regression. SPSS and Stata display Wald test for each coefficient as the default. They default to using LR only as the overall, omnibus test for the model... | |
| Feb 3, 2020 at 18:35 | history | edited | EdM | CC BY-SA 4.0 |
caveat about possibility of paired data
|
| Feb 3, 2020 at 17:09 | comment | added | EdM | @stans-ReinstateMonica my point is that to decide whether X and Y are codependent, you need to start with your desired definition of codependence. I've added a couple of paragraphs with respect to contingency-table analysis as done with chi-square or logistic regression. | |
| Feb 3, 2020 at 17:09 | history | edited | EdM | CC BY-SA 4.0 |
added specifics for chi-square and logistic regressions
|
| Feb 2, 2020 at 15:01 | comment | added | stans | ... "The issue of which type of measure makes the most sense in a particular application thus would seem to be more crucial than generic considerations of power..." I politely disagree. I need the power. When deciding between hypotheses [H0: $X$ and $Y$ are independent] and [H1: $X$ and $Y$ are codependent] I need to detect H1 with highest probability when H1 is true... In many parts of finance and other fields, one needs to prescreen the signals first. And then one enters relevant signals into various measures and models, potentially even more flexible than the measures reviewed in Tan et. al | |
| Feb 2, 2020 at 15:01 | comment | added | stans | Thank you for the reference. The paper is interesting in itself. However, it does not answer my exact questions. Instead of explaining how to detect codependent relationships $(X,Y)$ with highest probability, the paper is essentially saying: "Suppose we restrict ourselves only to relationships which are codependent, at least mildly. How do we rank them? How do we systematize numerous metrics for quantifying the strength of the relationship?"... In your post you are stating: ... | |
| Jan 28, 2020 at 18:00 | history | answered | EdM | CC BY-SA 4.0 |