I'll try to add some more information regarding my experiment - maybe that would help clear things out. Instead of actually measuring the learning curve (i.e. number of correct responses per block) I created a variable that substract the number of correct answers from the last block with that of the first block. I did the same thing for reward and punishment. I also use the same predictors in both regression models. Until now I just created a new variable - learning vector of reward minus learning vector of punishment. By that I think I measure the difference. I just wanted to know if there's another option to compare a model with same predictors but different dependent variable.
On Thu, Jun 10, 2010 at 12:33 PM, Joris Meys <jorism...@gmail.com> wrote: > This is only valid in case your X matrix is exactly the same, thus > when you have an experiment with multiple response variables (i.e. > paired response data). When the data for both models come from a > different experiment, it ends here. > > You also assume that y1 and y2 are measured in the same scale, and can > be substracted. If you take two models, one with response Y in meters > and one with response Y in centimeters, all others equal, your method > will find the models "significantly different" whereas they are > exactly the same except for a scaling parameter. If we're talking two > different responses, the substraction of both responses doesn't even > make sense. > > The hypothesis you test is whether there is a significant relation > between your predictors and the difference of the "reward" response > and the "punishment" response. If that is the hypothesis of interest, > the difference can be interpreted in a sensible way, AND both the > reward learning curve and the punishment learning curve are measured > simultaneously for every participant in the study, you can > intrinsically compare both models by modelling the difference of the > response variable. > > As this is not the case (learning curves from punishment and reward > can never be made up simultaneously), your approach is invalid. > > Cheers > Joris > > On Thu, Jun 10, 2010 at 9:00 AM, Gabor Grothendieck > <ggrothendi...@gmail.com> wrote: > > We need to define what it means for these models to be the same or > > different. With the usual lm assumptions suppose for i=1, 2 (the two > > models) that: > > > > y1 = a1 + X b1 + error1 > > y2 = a2 + X b2 + error2 > > > > which implies the following which also satisfies the usual lm > assumptions: > > > > y1-y2 = (a1-a2) + X(b1-b2) + error > > > > Here X is a matrix, a1 and a2 are scalars and all other elements are > > vectors. We say the models are the "same" if b1=b2 (but allow the > > intercepts to differ even if the models are the "same"). > > > > If y1 and y2 are as in the built in anscombe data frame and x3 and x4 > > are the x variables, i.e. columns of X, then: > > > >> fm1 <- lm(y1 - y2 ~ x3 + x4, anscombe) > >> # this model reduces to the following if b1 = b2 > >> fm0 <- lm(y1 - y2 ~ 1, anscombe) > >> anova(fm0, fm1) > > Analysis of Variance Table > > > > Model 1: y1 - y2 ~ 1 > > Model 2: y1 - y2 ~ x3 + x4 > > Res.Df RSS Df Sum of Sq F Pr(>F) > > 1 10 20.637 > > 2 8 18.662 2 1.9751 0.4233 0.6687 > > > > so we cannot reject the hypothesis that the models are the "same". > > > > > > On Wed, Jun 9, 2010 at 11:19 AM, Or Duek <ord...@gmail.com> wrote: > >> Hi, > >> I would like to compare to regression models - each model has a > different > >> dependent variable. > >> The first model uses a number that represents the learning curve for > reward. > >> The second model uses a number that represents the learning curve from > >> punishment stimuli. > >> The first model is significant and the second isn't. > >> I want to compare those two models and show that they are significantly > >> different. > >> How can I do that? > >> Thank you. > >> > >> [[alternative HTML version deleted]] > >> > >> ______________________________________________ > >> R-help@r-project.org mailing list > >> https://stat.ethz.ch/mailman/listinfo/r-help > >> PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > >> and provide commented, minimal, self-contained, reproducible code. > >> > > > > ______________________________________________ > > R-help@r-project.org mailing list > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > > and provide commented, minimal, self-contained, reproducible code. > > > > > > -- > Joris Meys > Statistical consultant > > Ghent University > Faculty of Bioscience Engineering > Department of Applied mathematics, biometrics and process control > > tel : +32 9 264 59 87 > joris.m...@ugent.be > ------------------------------- > Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
