On 24 Sep 2003 22:02:27 -0700, [EMAIL PROTECTED] (Donald Burrill) wrote: > On Tue, 23 Sep 2003, Rich Ulrich wrote inter alia (concerning > inferences from an ancova in the presence of interaction between the > covariate and the categoircal variables (aka "factors")):
[ snip - about interactions, and regression lines, including all my posted lines. ] DB > > If interaction is present, then the regression lines are not uniformly > the same distance apart vertically (that is, in the direction of the > response variable, which is commonly plotted as the ordinate) at > different values of the covariate (customarily the abscissa). > > If two lines actually cross, there is clearly a region of the covariate > where the lines are not significantly different from each other; and > there may be a region where line A is significantly higher than line B, > and there may be another region (in the other direction from the > crossing) where line B is significantly higher than line A. (I write > "there may be" because the existence of these regions, in the observed > range of the covariate, depends on (1) how sharply the two lines > actually diverge from each other and (2) where, in the observed range of > the covariate, the crossing is. The existence of a significant > interaction would ordinarily lead one to expect that at least one of > these regions exists, on logical grounds.) In this case, as you > observe, the method Kylie reports is clearly applicable. Well, you *can* apply it. I still doubt that I want to do it. I've come up with a simplified example using a Main Effect. Suppose that you have a trend line, showing that Height predicts success at basketball. The population SD for height is 3 inches or so. Let us say that the Success tends to increase by about 0.60 SD for every SD of height; this is a description based on effect size. Clearly, the effect is "0" for "0" increase in height. Now, the Kylie method, adapted, would say that the effect is "statistically significant" for some distance. Either way, in inches or in SD units, I do not like it. Here is a *continuous* effect which is being interpreted discretely. One problem, it seems to me, is that the number depends on the sample size. (Another problem, more technical, is that I don't see a stated basis for prescribing a test; and it seems to *me* that sometimes I would want to be more 'Bayesian' about it, than other times.) [snip, stuff about models] > Rich, you raised this question of "the proper model" in the context of > ANCOVA and interaction involving the covariate. Do you hold the same > opinion, as strongly, where the interaction involves only (some of) the > categorical predictors? If so, I'd like to know your choice of "the > proper model" for the example (the PULSE data set in MINITAB) dealt with > in my White Paper on modelling interactions in multiple regression, on > the Minitab web site (www.minitab.com -- I forget the rest of the > specific URL, but you can get there from the home page by looking for > the section on "white papers"). I rather thought, in that context, that > interaction was a quite reasonable thing to look for, and perhaps even > to expect... In context, there can be reasonable interactions, especially in the statistics. [ I might get to that site, one day, but not yet today.] I can add -- I may have had "inappropriate interactions" on my mind, owing to the origin of this thread. The same person (I believe) started out with asking about skewness, and perhaps ( I wondered) was perpetrating odd transformations on numbers coded as Proportions In fact, we may have to find them and *demonstrate* them, before we can become convinced that the simpler, non- interaction model is therefore reasonable. What is simpler might be different variables, but I think it happens that we can decide to code up the *interaction* as a single term, and 'reify' it. Example -- - If you have two factors that are Male/Female, it is possible to code both main effects as M/F, and the interaction is Same/Opposite (sex). The three dummy variables also work if you enter one main factor as M/F and main factor as Same/Opposite. Can you explain Same/Opposite in the word-story that accompanies your statistical explanation? It seems to me that the interaction instance does not arise all that often, but here is another Main effect example. Whenever two variables are highly correlated, I try to model them as something like (A+B) and (A-B). I don't *need* the same idea in the model, two times, and if the (A-B) term matters, then I would see awkward suppression and weird coefficients, if I did build the model with both. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html "Taxes are the price we pay for civilization." . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
