I feel out of my league responding to a discussion among such an august group of statisticians. But I think I can maybe provide some insight from someone who migrated from SPSS into R and learned R on my own.
I must say that I found it quite confusing to understand why my ANOVA results in R were completely different from those given by SPSS. In retrospect it is obvious, as it must seem to everyone who has R experience, but for people not versed in R, or where to look for help, these types of issues can be extremely frustrating. I figured out the issue eventually, but more through dumb luck and persistence than through any help from R. >From the point of a newbie in R (and let's face it, R is taking over the statistical landscape, which is great, but it also means that from here on out increasing numbers of primary researchers are going to be migrating into R), I think R could make things easier on new users. This is the best example I can think of. When you type in ?anova, the only thing remotely relevant to this confusing issue is: "When given a single argument it produces a table which tests whether the model terms are significant." Not at all helpful given that we do, after all, for better or for worse, live in a world in which "whether the model terms are significant" can mean three different things, depending on whether type I, II, or III sums of squares were used! Is it possible to forward a suggestion? Can the anova function include an option for tests to be "sequential" or "conditional", with default being "sequential"? I suspect the powers that be will not like this. So be it. At the very least, in the help page for anova, could you include just a brief description that the sums of squares produced are "sequential, corresponding to what SAS and other statsitical programs call "type I" sums of squares. If you are interested in conditional, or "type III", sums of squares, packages can be installed that allow for this." This might really help out earnest and eager yet confused R newbies. Barring this, perhaps the final option is to remove the ability for anova to take in a single argument at all - you must include two models which are to be compared. Best, JJ On Feb 7, 2008 6:35 PM, <[EMAIL PROTECTED]> wrote: > Frank Harrell has already added some comments, with which I agree. > > As one of the people who did become rather heated in the discussion, let > me add a few points in a (fairly) calm and considered way. > > 1. The primary objection I had to all of this is that it encourages > people to think of analysis of variance in such a simplistic way, i.e. > in terms of 'sums of squares'. This leads to silly questions like > "Well, if you don't like Type III sums of squares, what type do you > like?" as if the concept of multiple "types" of sum of squares had any > meaning. There is only one type and it represents a squared distance in > the sample space. The real question is how to interpret the vector in > sample space of which any particular sum of squares is a squared length. > For that you need to be very clear about both the null hypothes > implicitly being tested, and the outer hypothesis being assumed. This > issue can become very subtle when interactions are involved, as you > point out. > > 2. Most of the heat came from resentment that SAS should insinuate its > way into the statistical community in such a Microsoft-like way, i.e. > trying to make both its black-box software and defective terminology > some kind of industry standard. > > > Bill Venables > CSIRO Laboratories > PO Box 120, Cleveland, 4163 > AUSTRALIA > Office Phone (email preferred): +61 7 3826 7251 > Fax (if absolutely necessary): +61 7 3826 7304 > Mobile: +61 4 8819 4402 > Home Phone: +61 7 3286 7700 > mailto:[EMAIL PROTECTED] > http://www.cmis.csiro.au/bill.venables/ > > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] > On Behalf Of Bernard Leemon > Sent: Friday, 8 February 2008 7:42 AM > To: r-help@r-project.org > Subject: [R] a kinder view of Type III SS > > A young colleague (Matthew Keller) who is an ardent fan of R is teaching > me > much about R and discussions surrounding its use. He recently showed me > some of the sometimes heated discussions about Type I and Type III > errors > that have taken place over the years on this listserve. I'm presumptive > enough to believe I might add a little clarity. I write this from the > perspective of someone old enough to have been grateful that the stat > programmers (sometimes me coding in Fortran) thought to provide me with > model tests I had not asked for when I carried heavy boxes of punched > cards > across campus to the card reader window only to be told to come back a > day > or two later for my output. I'm also modern enough to know that > anova(model1, model2), where model2 is a proper subset of model1, is all > that I need and allows me to ask any question of my data that I want to > ask > rather than being constrained to those questions that the SAS or SPSS > programmer thought I might want to ask. I could end there, and we would > probably all agree with what I have said to this point, but I want to > push > the issue a bit and say: it seems that Type III Sums of Squares are > being > unfairly maligned among the R cognoscenti. And the practical > ramification of > this is that it creates a good deal of confusion among those migrating > from > SAS/SPSS land into R - not that this should ever be a reason to > introduce a > flawed technique into R, but my argument is that type III sums of > squares > are not a flawed technique. > > In my reading of the prior discussions on this list, my conclusion is > that > the Type I/Type III issue is a red herring that has generated > unnecessary > heat. Base R readily provides both types. summary(lm( y ~ x + w + z)) > provides estimates and tests consistent with Type III sums of squares > (it > doesn't provide the SS directly but they are easily derived from the > output) > and anova(lm(y ~ x + w + z)) provides tests consistent with Type I sums > of > squares. The names Type I and III are dreadful "gifts" from SAS and > others. > I'd prefer "conditional tests" for those provided by summary() because > what > is estimated and tested are x|w,z w|x,z and z|x,w [read these as > "x > conditional on w and z being in the model"] and "sequential" for those > provided by anova(), being x, w|x, and z|x,w. None of these tests is > more > or less valid or useful than any of the others. It depends on which > questions researchers want to ask of their data. > > Things get more interesting when z represents the interaction between x > and > w, such that z = x * w = xw. Fundamentally everything is the same in > terms > of the above tests. However, one must be careful to understand what the > coefficient and test for x|w,xw and w|x,xw mean. That is, x|w,xw tests > the > relationship between x and y when and only when w = 0. A very, very > common > mistake, due to an overgeneralization of traditional anova models, is to > refer to x|w,xw as the "main effect." In my list of ten statistical > commandments I include: "Thou shalt never utter the phrase main effect" > because it causes so much unnecessary confusion. In this case, x|w,xw > is > the SIMPLE effect of x when w = 0. This means among other things that > if > instead we use w' = w - k so as to change the 0 point on the w' scale, > we > will get a different estimate and test for x|w',xw'. Many correctly > argue > that the main effect is largely meaningless in the presence of an > interaction because it implies there is no common average effect. > However, > that does not invalidate x|w,xw because it is NOT a "main" (sense > "principal" or "chief") effect but only a "simple" effect for a > particular > level of w. A useful strategy for testing a variety of simple effects > is to > subtract different constants k from w so as to change the 0 value to > focus > the test on particular simple effects. > > > If x and w are both contrast codes (-1 or 1) for the two factors of a 2 > x 2 > design, then x|w,xw is the simple effect of x when w = 0. While w > never > equals 0, in a balanced design w does equal 0 on average. In that one > very > special case, the simple effect of x when w = 0 equals the average of > all > the simple effects and in that one special case one might call it the > "main > effect." However, in all other situations it is only the simple effect > when > w = 0. If we discard the term "main effect", then a lot of unnecessary > confusion goes away. Again, if one is interested in the simple effect > of x > for a particular level of w, then one might want to use, instead of a > contrast code, a dummy code where the value of 0 is assigned to the > level of > w of interest and 1 to the other level. > > When factors have multiple levels, it is best to have orthogonal > contrast > codes to provide 1-df tests of questions of interest. Products of those > codes are easily interpreted as the simple difference for one contrast > when > the other contrast is fixed at some level. Multiple degree of freedom > omnibus tests are troublesome but are only of interest if we are fixated > on > concepts like 'main effect.' > > gary mcclelland (aka bernie leemon) > colorado > > [[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. > [[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.
