Have you considered doing a permutation test on the interaction? Here is an article that gives the general procedure for a couple of algorithms and a comparison of how well they do:
Anderson, Marti J and Legendre, Pierre; An Empirical Comparison of Permutation Methods for Tests of Partial Regression Coefficients in a Linear Model. J. Statist. Comput. Simul., 1999, vol 62, pp. 271-303. -- Gregory (Greg) L. Snow Ph.D. Statistical Data Center Intermountain Healthcare greg.s...@imail.org 801.408.8111 > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r- > project.org] On Behalf Of Iasonas Lamprianou > Sent: Tuesday, September 07, 2010 12:25 AM > To: juan xiong; Dennis Murphy > Cc: r-help@r-project.org > Subject: Re: [R] two questions > > By the way, ordinal regression would require huge datasets because my > dependent variable has around 20 different responses... but again, one > might say that with so many ordinal responses, it is as if we have a > linear/interval variable, right? I just hoped that there would be a > two-way kruskal-wallis or something like that. On the other hand, what > is going to happen if I (1) bootstrap data from all cells of my design > and average the rank ordering of the data of every cell? And then (2) > do the same but using data from a uniform/normal distribution so that I > assume that there is no difference between the cells? From point (1) I > will find the statistical value and from point (2) the expectation and > then with a third step (3) I can run a chi-square on the > observed/expected values. Would this be reasonable? But again, how can > I distinguish between main and interaction effects? > > Dr. Iasonas Lamprianou > > > > > > Assistant Professor (Educational Research and Evaluation) > > Department of Education Sciences > > European University-Cyprus > > P.O. Box 22006 > > 1516 Nicosia > > Cyprus > > Tel.: +357-22-713178 > > Fax: +357-22-590539 > > > > > > Honorary Research Fellow > > Department of Education > > The University of Manchester > > Oxford Road, Manchester M13 9PL, UK > > Tel. 0044 161 275 3485 > > iasonas.lampria...@manchester.ac.uk > > --- On Tue, 7/9/10, Dennis Murphy <djmu...@gmail.com> wrote: > > From: Dennis Murphy <djmu...@gmail.com> > Subject: Re: [R] two questions > To: "juan xiong" <xiongjuan2...@gmail.com> > Cc: "David Winsemius" <dwinsem...@comcast.net>, r-help@r-project.org, > "Iasonas Lamprianou" <lampria...@yahoo.com> > Date: Tuesday, 7 September, 2010, 4:47 > > Hi: > > On Mon, Sep 6, 2010 at 5:26 PM, juan xiong <xiongjuan2...@gmail.com> > wrote: > > Maybe Friedman test > > The Friedman test corresponds to randomized complete block designs, not > general two-way classifications. David's advice is sound, but also > investigate proportional odds models (e.g., lrm in Prof. Harrell's rms > package) in case the 'usual' approach comes up short. It would be > helpful to know the number of response categories and some idea of the > number of cities-of-birth under study, though... > > > HTH, > Dennis > > > > > On Mon, Sep 6, 2010 at 4:47 PM, David Winsemius > <dwinsem...@comcast.net>wrote: > > > > > The usual least-squares methods are fairly robust to departures from > > > normality. Furthermore, it is the residuals that are assumed to be > normally > > > distributed (not the marginal distributions that you are probably > looking > > > at) , so it does not sound as though you have yet examined the data > > > properly. Tell us what the descriptive stats (say the means, > variance, 10th > > > and 90th percentiles) are on the residuals within cells cross- > classified by > > > the gender and city-of-birth variables (say the means, variance, 10th > and > > > 90th percentiles). > > > > > > > > > On Sep 6, 2010, at 4:34 PM, Iasonas Lamprianou wrote: > > > > > > > > >> Dear friends, two questions > > >> > > >> (1) does anyone know if there are any non-parametric equivalents of > the > > >> two-way ANOVA in R? I have an ordinal non-normally distributed > dependent > > >> variable and two factors (gender and city of birth). Normally, one > would try > > >> a two-way anova, but if R has any non-parametric equivalents, that > might be > > >> great. > > >> > > > > > > There is an entire task view page on robust methods if you decide to > press > > > on with this quest. > > > > > > > > > (2) Also, if the interaction of gender and city of birth is > statistically > > >> significant, which post-hoc tests should I run? > > >> > > > > > > How many cities are we talking about? > > > > > > > > > Thanks > > >> > > >> Jason > > >> > > >> > > >> Dr. Iasonas Lamprianou > > >> > > > > > > -- > > > > > > David Winsemius, MD > > > West Hartford, CT > > > > > > > > > ______________________________________________ > > > 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. > > > > > > > [[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. > > > > > > > > [[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.
