Hello Tyler, I rephrase my previous mail, as follows:
In your example, T_i = X1:X2:X3. Let F_j = X3. (The numerical variables X1 and X2 are not encoded at all.) Then T_{i(j)} = X1:X2, which in the example is dropped from the model. Hence the X3 in T_i must be encoded by dummy variables, as indeed it is. Arie On Thu, Nov 2, 2017 at 4:11 PM, Tyler <tyle...@gmail.com> wrote: > Hi Arie, > > The book out of which this behavior is based does not use factor (in this > section) to refer to categorical factor. I will again point to this > sentence, from page 40, in the same section and referring to the behavior > under question, that shows F_j is not limited to categorical factors: > "Numeric variables appear in the computations as themselves, uncoded. > Therefore, the rule does not do anything special for them, and it remains > valid, in a trivial sense, whenever any of the F_j is numeric rather than > categorical." > > Note the "... whenever any of the F_j is numeric rather than categorical." > Factor here is used in the more general sense of the word, not referring to > the R type "factor." The behavior of R does not match the heuristic that > it's citing. > > Best regards, > Tyler > > On Thu, Nov 2, 2017 at 2:51 AM, Arie ten Cate <arietenc...@gmail.com> wrote: >> >> Hello Tyler, >> >> Thank you for searching for, and finding, the basic description of the >> behavior of R in this matter. >> >> I think your example is in agreement with the book. >> >> But let me first note the following. You write: "F_j refers to a >> factor (variable) in a model and not a categorical factor". However: >> "a factor is a vector object used to specify a discrete >> classification" (start of chapter 4 of "An Introduction to R".) You >> might also see the description of the R function factor(). >> >> You note that the book says about a factor F_j: >> "... F_j is coded by contrasts if T_{i(j)} has appeared in the >> formula and by dummy variables if it has not" >> >> You find: >> "However, the example I gave demonstrated that this dummy variable >> encoding only occurs for the model where the missing term is the >> numeric-numeric interaction, ~(X1+X2+X3)^3-X1:X2." >> >> We have here T_i = X1:X2:X3. Also: F_j = X3 (the only factor). Then >> T_{i(j)} = X1:X2, which is dropped from the model. Hence the X3 in T_i >> must be encoded by dummy variables, as indeed it is. >> >> Arie >> >> On Tue, Oct 31, 2017 at 4:01 PM, Tyler <tyle...@gmail.com> wrote: >> > Hi Arie, >> > >> > Thank you for your further research into the issue. >> > >> > Regarding Stata: On the other hand, JMP gives model matrices that use >> > the >> > main effects contrasts in computing the higher order interactions, >> > without >> > the dummy variable encoding. I verified this both by analyzing the >> > linear >> > model given in my first example and noting that JMP has one more degree >> > of >> > freedom than R for the same model, as well as looking at the generated >> > model >> > matrices. It's easy to find a design where JMP will allow us fit our >> > model >> > with goodness-of-fit estimates and R will not due to the extra degree(s) >> > of >> > freedom required. Let's keep the conversation limited to R. >> > >> > I want to refocus back onto my original bug report, which was not for a >> > missing main effects term, but rather for a missing lower-order >> > interaction >> > term. The behavior of model.matrix.default() for a missing main effects >> > term >> > is a nice example to demonstrate how model.matrix encodes with dummy >> > variables instead of contrasts, but doesn't demonstrate the inconsistent >> > behavior my bug report highlighted. >> > >> > I went looking for documentation on this behavior, and the issue stems >> > not >> > from model.matrix.default(), but rather the terms() function in >> > interpreting >> > the formula. This "clever" replacement of contrasts by dummy variables >> > to >> > maintain marginality (presuming that's the reason) is not described >> > anywhere >> > in the documentation for either the model.matrix() or the terms() >> > function. >> > In order to find a description for the behavior, I had to look in the >> > underlying C code, buried above the "TermCode" function of the "model.c" >> > file, which says: >> > >> > "TermCode decides on the encoding of a model term. Returns 1 if variable >> > ``whichBit'' in ``thisTerm'' is to be encoded by contrasts and 2 if it >> > is to >> > be encoded by dummy variables. This is decided using the heuristic >> > described in Statistical Models in S, page 38." >> > >> > I do not have a copy of this book, and I suspect most R users do not as >> > well. Thankfully, however, some of the pages describing this behavior >> > were >> > available as part of Amazon's "Look Inside" feature--but if not for >> > that, I >> > would have no idea what heuristic R was using. Since those pages could >> > made >> > unavailable by Amazon at any time, at the very least we have an problem >> > with >> > a lack of documentation. >> > >> > However, I still believe there is a bug when comparing R's >> > implementation to >> > the heuristic described in the book. From Statistical Models in S, page >> > 38-39: >> > >> > "Suppose F_j is any factor included in term T_i. Let T_{i(j)} denote the >> > margin of T_i for factor F_j--that is, the term obtained by dropping F_j >> > from T_i. We say that T_{i(j)} has appeared in the formula if there is >> > some >> > term T_i' for i' < i such that T_i' contains all the factors appearing >> > in >> > T_{i(j)}. The usual case is that T_{i(j)} itself is one of the preceding >> > terms. Then F_j is coded by contrasts if T_{i(j)} has appeared in the >> > formula and by dummy variables if it has not" >> > >> > Here, F_j refers to a factor (variable) in a model and not a categorical >> > factor, as specified later in that section (page 40): "Numeric variables >> > appear in the computations as themselves, uncoded. Therefore, the rule >> > does >> > not do anything special for them, and it remains valid, in a trivial >> > sense, >> > whenever any of the F_j is numeric rather than categorical." >> > >> > Going back to my original example with three variables: X1 (numeric), X2 >> > (numeric), X3 (categorical). This heuristic prescribes encoding X1:X2:X3 >> > with contrasts as long as X1:X2, X1:X3, and X2:X3 exist in the formula. >> > When >> > any of the preceding terms do not exist, this heuristic tells us to use >> > dummy variables to encode the interaction (e.g. "F_j [the interaction >> > term] >> > is coded ... by dummy variables if it [any of the marginal terms >> > obtained by >> > dropping a single factor in the interaction] has not [appeared in the >> > formula]"). However, the example I gave demonstrated that this dummy >> > variable encoding only occurs for the model where the missing term is >> > the >> > numeric-numeric interaction, "~(X1+X2+X3)^3-X1:X2". Otherwise, the >> > interaction term X1:X2:X3 is encoded by contrasts, not dummy variables. >> > This >> > is inconsistent with the description of the intended behavior given in >> > the >> > book. >> > >> > Best regards, >> > Tyler >> > >> > >> > On Fri, Oct 27, 2017 at 2:18 PM, Arie ten Cate <arietenc...@gmail.com> >> > wrote: >> >> >> >> Hello Tyler, >> >> >> >> I want to bring to your attention the following document: "What >> >> happens if you omit the main effect in a regression model with an >> >> interaction?" >> >> >> >> (https://stats.idre.ucla.edu/stata/faq/what-happens-if-you-omit-the-main-effect-in-a-regression-model-with-an-interaction). >> >> This gives a useful review of the problem. Your example is Case 2: a >> >> continuous and a categorical regressor. >> >> >> >> The numerical examples are coded in Stata, and they give the same >> >> result as in R. Hence, if this is a bug in R then it is also a bug in >> >> Stata. That seems very unlikely. >> >> >> >> Here is a simulation in R of the above mentioned Case 2 in Stata: >> >> >> >> df <- expand.grid(socst=c(-1:1),grp=c("1","2","3","4")) >> >> print("Full model") >> >> print(model.matrix(~(socst+grp)^2 ,data=df)) >> >> print("Example 2.1: drop socst") >> >> print(model.matrix(~(socst+grp)^2 -socst ,data=df)) >> >> print("Example 2.2: drop grp") >> >> print(model.matrix(~(socst+grp)^2 -grp ,data=df)) >> >> >> >> This gives indeed the following regressors: >> >> >> >> "Full model" >> >> (Intercept) socst grp2 grp3 grp4 socst:grp2 socst:grp3 socst:grp4 >> >> "Example 2.1: drop socst" >> >> (Intercept) grp2 grp3 grp4 socst:grp1 socst:grp2 socst:grp3 socst:grp4 >> >> "Example 2.2: drop grp" >> >> (Intercept) socst socst:grp2 socst:grp3 socst:grp4 >> >> >> >> There is a little bit of R documentation about this, based on the >> >> concept of marginality, which typically forbids a model having an >> >> interaction but not the corresponding main effects. (You might see the >> >> references in https://en.wikipedia.org/wiki/Principle_of_marginality ) >> >> See "An Introduction to R", by Venables and Smith and the R Core >> >> Team. At the bottom of page 52 (PDF: 57) it says: "Although the >> >> details are complicated, model formulae in R will normally generate >> >> the models that an expert statistician would expect, provided that >> >> marginality is preserved. Fitting, for [a contrary] example, a model >> >> with an interaction but not the corresponding main effects will in >> >> general lead to surprising results ....". >> >> The Reference Manual states that the R functions dropterm() and >> >> addterm() resp. drop or add only terms such that marginality is >> >> preserved. >> >> >> >> Finally, about your singular matrix t(mm)%*%mm. This is in fact >> >> Example 2.1 in Case 2 discussed above. As discussed there, in Stata >> >> and in R the drop of the continuous variable has no effect on the >> >> degrees of freedom here: it is just a reparameterisation of the full >> >> model, protecting you against losing marginality... Hence the >> >> model.matrix 'mm' is still square and nonsingular after the drop of >> >> X1, unless of course when a row is removed from the matrix 'design' >> >> when before creating 'mm'. >> >> >> >> Arie >> >> >> >> On Sun, Oct 15, 2017 at 7:05 PM, Tyler <tyle...@gmail.com> wrote: >> >> > You could possibly try to explain away the behavior for a missing >> >> > main >> >> > effects term, since without the main effects term we don't have main >> >> > effect >> >> > columns in the model matrix used to compute the interaction columns >> >> > (At >> >> > best this is undocumented behavior--I still think it's a bug, as we >> >> > know >> >> > how we would encode the categorical factors if they were in fact >> >> > present. >> >> > It's either specified in contrasts.arg or using the default set in >> >> > options). However, when all the main effects are present, why would >> >> > the >> >> > three-factor interaction column not simply be the product of the main >> >> > effect columns? In my example: we know X1, we know X2, and we know >> >> > X3. >> >> > Why >> >> > does the encoding of X1:X2:X3 depend on whether we specified a >> >> > two-factor >> >> > interaction, AND only changes for specific missing interactions? >> >> > >> >> > In addition, I can use a two-term example similar to yours to show >> >> > how >> >> > this >> >> > behavior results in a singular covariance matrix when, given the >> >> > desired >> >> > factor encoding, it should not be singular. >> >> > >> >> > We start with a full factorial design for a two-level continuous >> >> > factor >> >> > and >> >> > a three-level categorical factor, and remove a single row. This >> >> > design >> >> > matrix does not leave enough degrees of freedom to determine >> >> > goodness-of-fit, but should allow us to obtain parameter estimates. >> >> > >> >> >> design = expand.grid(X1=c(1,-1),X2=c("A","B","C")) >> >> >> design = design[-1,] >> >> >> design >> >> > X1 X2 >> >> > 2 -1 A >> >> > 3 1 B >> >> > 4 -1 B >> >> > 5 1 C >> >> > 6 -1 C >> >> > >> >> > Here, we first calculate the model matrix for the full model, and >> >> > then >> >> > manually remove the X1 column from the model matrix. This gives us >> >> > the >> >> > model matrix one would expect if X1 were removed from the model. We >> >> > then >> >> > successfully calculate the covariance matrix. >> >> > >> >> >> mm = model.matrix(~(X1+X2)^2,data=design) >> >> >> mm >> >> > (Intercept) X1 X2B X2C X1:X2B X1:X2C >> >> > 2 1 -1 0 0 0 0 >> >> > 3 1 1 1 0 1 0 >> >> > 4 1 -1 1 0 -1 0 >> >> > 5 1 1 0 1 0 1 >> >> > 6 1 -1 0 1 0 -1 >> >> > >> >> >> mm = mm[,-2] >> >> >> solve(t(mm) %*% mm) >> >> > (Intercept) X2B X2C X1:X2B X1:X2C >> >> > (Intercept) 1 -1.0 -1.0 0.0 0.0 >> >> > X2B -1 1.5 1.0 0.0 0.0 >> >> > X2C -1 1.0 1.5 0.0 0.0 >> >> > X1:X2B 0 0.0 0.0 0.5 0.0 >> >> > X1:X2C 0 0.0 0.0 0.0 0.5 >> >> > >> >> > Here, we see the actual behavior for model.matrix. The undesired >> >> > re-coding >> >> > of the model matrix interaction term makes the information matrix >> >> > singular. >> >> > >> >> >> mm = model.matrix(~(X1+X2)^2-X1,data=design) >> >> >> mm >> >> > (Intercept) X2B X2C X1:X2A X1:X2B X1:X2C >> >> > 2 1 0 0 -1 0 0 >> >> > 3 1 1 0 0 1 0 >> >> > 4 1 1 0 0 -1 0 >> >> > 5 1 0 1 0 0 1 >> >> > 6 1 0 1 0 0 -1 >> >> > >> >> >> solve(t(mm) %*% mm) >> >> > Error in solve.default(t(mm) %*% mm) : system is computationally >> >> > singular: >> >> > reciprocal condition number = 5.55112e-18 >> >> > >> >> > I still believe this is a bug. >> >> > >> >> > Best regards, >> >> > Tyler Morgan-Wall >> >> > >> >> > On Sun, Oct 15, 2017 at 1:49 AM, Arie ten Cate >> >> > <arietenc...@gmail.com> >> >> > wrote: >> >> > >> >> >> I think it is not a bug. It is a general property of interactions. >> >> >> This property is best observed if all variables are factors >> >> >> (qualitative). >> >> >> >> >> >> For example, you have three variables (factors). You ask for as many >> >> >> interactions as possible, except an interaction term between two >> >> >> particular variables. When this interaction is not a constant, it is >> >> >> different for different values of the remaining variable. More >> >> >> precisely: for all values of that variable. In other words: you have >> >> >> a >> >> >> three-way interaction, with all values of that variable. >> >> >> >> >> >> An even smaller example is the following script with only two >> >> >> variables, each being a factor: >> >> >> >> >> >> df <- expand.grid(X1=c("p","q"), X2=c("A","B","C")) >> >> >> print(model.matrix(~(X1+X2)^2 ,data=df)) >> >> >> print(model.matrix(~(X1+X2)^2 -X1,data=df)) >> >> >> print(model.matrix(~(X1+X2)^2 -X2,data=df)) >> >> >> >> >> >> The result is: >> >> >> >> >> >> (Intercept) X1q X2B X2C X1q:X2B X1q:X2C >> >> >> 1 1 0 0 0 0 0 >> >> >> 2 1 1 0 0 0 0 >> >> >> 3 1 0 1 0 0 0 >> >> >> 4 1 1 1 0 1 0 >> >> >> 5 1 0 0 1 0 0 >> >> >> 6 1 1 0 1 0 1 >> >> >> >> >> >> (Intercept) X2B X2C X1q:X2A X1q:X2B X1q:X2C >> >> >> 1 1 0 0 0 0 0 >> >> >> 2 1 0 0 1 0 0 >> >> >> 3 1 1 0 0 0 0 >> >> >> 4 1 1 0 0 1 0 >> >> >> 5 1 0 1 0 0 0 >> >> >> 6 1 0 1 0 0 1 >> >> >> >> >> >> (Intercept) X1q X1p:X2B X1q:X2B X1p:X2C X1q:X2C >> >> >> 1 1 0 0 0 0 0 >> >> >> 2 1 1 0 0 0 0 >> >> >> 3 1 0 1 0 0 0 >> >> >> 4 1 1 0 1 0 0 >> >> >> 5 1 0 0 0 1 0 >> >> >> 6 1 1 0 0 0 1 >> >> >> >> >> >> Thus, in the second result, we have no main effect of X1. Instead, >> >> >> the >> >> >> effect of X1 depends on the value of X2; either A or B or C. In >> >> >> fact, >> >> >> this is a two-way interaction, including all three values of X2. In >> >> >> the third result, we have no main effect of X2, The effect of X2 >> >> >> depends on the value of X1; either p or q. >> >> >> >> >> >> A complicating element with your example seems to be that your X1 >> >> >> and >> >> >> X2 are not factors. >> >> >> >> >> >> Arie >> >> >> >> >> >> On Thu, Oct 12, 2017 at 7:12 PM, Tyler <tyle...@gmail.com> wrote: >> >> >> > Hi, >> >> >> > >> >> >> > I recently ran into an inconsistency in the way >> >> >> > model.matrix.default >> >> >> > handles factor encoding for higher level interactions with >> >> >> > categorical >> >> >> > variables when the full hierarchy of effects is not present. >> >> >> > Depending on >> >> >> > which lower level interactions are specified, the factor encoding >> >> >> > changes >> >> >> > for a higher level interaction. Consider the following minimal >> >> >> reproducible >> >> >> > example: >> >> >> > >> >> >> > -------------- >> >> >> > >> >> >> >> runmatrix = expand.grid(X1=c(1,-1),X2=c(1,-1),X3=c("A","B","C"))> >> >> >> model.matrix(~(X1+X2+X3)^3,data=runmatrix) (Intercept) X1 X2 X3B >> >> >> X3C >> >> >> X1:X2 X1:X3B X1:X3C X2:X3B X2:X3C X1:X2:X3B X1:X2:X3C >> >> >> > 1 1 1 1 0 0 1 0 0 0 0 >> >> >> > 0 0 >> >> >> > 2 1 -1 1 0 0 -1 0 0 0 0 >> >> >> > 0 0 >> >> >> > 3 1 1 -1 0 0 -1 0 0 0 0 >> >> >> > 0 0 >> >> >> > 4 1 -1 -1 0 0 1 0 0 0 0 >> >> >> > 0 0 >> >> >> > 5 1 1 1 1 0 1 1 0 1 0 >> >> >> > 1 0 >> >> >> > 6 1 -1 1 1 0 -1 -1 0 1 0 >> >> >> > -1 0 >> >> >> > 7 1 1 -1 1 0 -1 1 0 -1 0 >> >> >> > -1 0 >> >> >> > 8 1 -1 -1 1 0 1 -1 0 -1 0 >> >> >> > 1 0 >> >> >> > 9 1 1 1 0 1 1 0 1 0 1 >> >> >> > 0 1 >> >> >> > 10 1 -1 1 0 1 -1 0 -1 0 1 >> >> >> > 0 -1 >> >> >> > 11 1 1 -1 0 1 -1 0 1 0 -1 >> >> >> > 0 -1 >> >> >> > 12 1 -1 -1 0 1 1 0 -1 0 -1 >> >> >> > 0 1 >> >> >> > attr(,"assign") >> >> >> > [1] 0 1 2 3 3 4 5 5 6 6 7 7 >> >> >> > attr(,"contrasts") >> >> >> > attr(,"contrasts")$X3 >> >> >> > [1] "contr.treatment" >> >> >> > >> >> >> > -------------- >> >> >> > >> >> >> > Specifying the full hierarchy gives us what we expect: the >> >> >> > interaction >> >> >> > columns are simply calculated from the product of the main effect >> >> >> columns. >> >> >> > The interaction term X1:X2:X3 gives us two columns in the model >> >> >> > matrix, >> >> >> > X1:X2:X3B and X1:X2:X3C, matching the products of the main >> >> >> > effects. >> >> >> > >> >> >> > If we remove either the X2:X3 interaction or the X1:X3 >> >> >> > interaction, >> >> >> > we >> >> >> get >> >> >> > what we would expect for the X1:X2:X3 interaction, but when we >> >> >> > remove >> >> >> > the >> >> >> > X1:X2 interaction the encoding for X1:X2:X3 changes completely: >> >> >> > >> >> >> > -------------- >> >> >> > >> >> >> >> model.matrix(~(X1+X2+X3)^3-X1:X3,data=runmatrix) (Intercept) X1 >> >> >> >> X2 >> >> >> X3B X3C X1:X2 X2:X3B X2:X3C X1:X2:X3B X1:X2:X3C >> >> >> > 1 1 1 1 0 0 1 0 0 0 >> >> >> > 0 >> >> >> > 2 1 -1 1 0 0 -1 0 0 0 >> >> >> > 0 >> >> >> > 3 1 1 -1 0 0 -1 0 0 0 >> >> >> > 0 >> >> >> > 4 1 -1 -1 0 0 1 0 0 0 >> >> >> > 0 >> >> >> > 5 1 1 1 1 0 1 1 0 1 >> >> >> > 0 >> >> >> > 6 1 -1 1 1 0 -1 1 0 -1 >> >> >> > 0 >> >> >> > 7 1 1 -1 1 0 -1 -1 0 -1 >> >> >> > 0 >> >> >> > 8 1 -1 -1 1 0 1 -1 0 1 >> >> >> > 0 >> >> >> > 9 1 1 1 0 1 1 0 1 0 >> >> >> > 1 >> >> >> > 10 1 -1 1 0 1 -1 0 1 0 >> >> >> > -1 >> >> >> > 11 1 1 -1 0 1 -1 0 -1 0 >> >> >> > -1 >> >> >> > 12 1 -1 -1 0 1 1 0 -1 0 >> >> >> > 1 >> >> >> > attr(,"assign") >> >> >> > [1] 0 1 2 3 3 4 5 5 6 6 >> >> >> > attr(,"contrasts") >> >> >> > attr(,"contrasts")$X3 >> >> >> > [1] "contr.treatment" >> >> >> > >> >> >> > >> >> >> > >> >> >> >> model.matrix(~(X1+X2+X3)^3-X2:X3,data=runmatrix) (Intercept) X1 >> >> >> >> X2 >> >> >> X3B X3C X1:X2 X1:X3B X1:X3C X1:X2:X3B X1:X2:X3C >> >> >> > 1 1 1 1 0 0 1 0 0 0 >> >> >> > 0 >> >> >> > 2 1 -1 1 0 0 -1 0 0 0 >> >> >> > 0 >> >> >> > 3 1 1 -1 0 0 -1 0 0 0 >> >> >> > 0 >> >> >> > 4 1 -1 -1 0 0 1 0 0 0 >> >> >> > 0 >> >> >> > 5 1 1 1 1 0 1 1 0 1 >> >> >> > 0 >> >> >> > 6 1 -1 1 1 0 -1 -1 0 -1 >> >> >> > 0 >> >> >> > 7 1 1 -1 1 0 -1 1 0 -1 >> >> >> > 0 >> >> >> > 8 1 -1 -1 1 0 1 -1 0 1 >> >> >> > 0 >> >> >> > 9 1 1 1 0 1 1 0 1 0 >> >> >> > 1 >> >> >> > 10 1 -1 1 0 1 -1 0 -1 0 >> >> >> > -1 >> >> >> > 11 1 1 -1 0 1 -1 0 1 0 >> >> >> > -1 >> >> >> > 12 1 -1 -1 0 1 1 0 -1 0 >> >> >> > 1 >> >> >> > attr(,"assign") >> >> >> > [1] 0 1 2 3 3 4 5 5 6 6 >> >> >> > attr(,"contrasts") >> >> >> > attr(,"contrasts")$X3 >> >> >> > [1] "contr.treatment" >> >> >> > >> >> >> > >> >> >> >> model.matrix(~(X1+X2+X3)^3-X1:X2,data=runmatrix) (Intercept) X1 >> >> >> >> X2 >> >> >> X3B X3C X1:X3B X1:X3C X2:X3B X2:X3C X1:X2:X3A X1:X2:X3B X1:X2:X3C >> >> >> > 1 1 1 1 0 0 0 0 0 0 1 >> >> >> > 0 0 >> >> >> > 2 1 -1 1 0 0 0 0 0 0 -1 >> >> >> > 0 0 >> >> >> > 3 1 1 -1 0 0 0 0 0 0 -1 >> >> >> > 0 0 >> >> >> > 4 1 -1 -1 0 0 0 0 0 0 1 >> >> >> > 0 0 >> >> >> > 5 1 1 1 1 0 1 0 1 0 0 >> >> >> > 1 0 >> >> >> > 6 1 -1 1 1 0 -1 0 1 0 0 >> >> >> > -1 0 >> >> >> > 7 1 1 -1 1 0 1 0 -1 0 0 >> >> >> > -1 0 >> >> >> > 8 1 -1 -1 1 0 -1 0 -1 0 0 >> >> >> > 1 0 >> >> >> > 9 1 1 1 0 1 0 1 0 1 0 >> >> >> > 0 1 >> >> >> > 10 1 -1 1 0 1 0 -1 0 1 0 >> >> >> > 0 -1 >> >> >> > 11 1 1 -1 0 1 0 1 0 -1 0 >> >> >> > 0 -1 >> >> >> > 12 1 -1 -1 0 1 0 -1 0 -1 0 >> >> >> > 0 1 >> >> >> > attr(,"assign") >> >> >> > [1] 0 1 2 3 3 4 4 5 5 6 6 6 >> >> >> > attr(,"contrasts") >> >> >> > attr(,"contrasts")$X3 >> >> >> > [1] "contr.treatment" >> >> >> > >> >> >> > -------------- >> >> >> > >> >> >> > Here, we now see the encoding for the interaction X1:X2:X3 is now >> >> >> > the >> >> >> > interaction of X1 and X2 with a new encoding for X3 where each >> >> >> > factor >> >> >> level >> >> >> > is represented by its own column. I would expect, given the two >> >> >> > column >> >> >> > dummy variable encoding for X3, that the X1:X2:X3 column would >> >> >> > also >> >> >> > be >> >> >> two >> >> >> > columns regardless of what two-factor interactions we also >> >> >> > specified, >> >> >> > but >> >> >> > in this case it switches to three. If other two factor >> >> >> > interactions >> >> >> > are >> >> >> > missing in addition to X1:X2, this issue still occurs. This also >> >> >> > happens >> >> >> > regardless of the contrast specified in contrasts.arg for X3. I >> >> >> > don't >> >> >> > see >> >> >> > any reasoning for this behavior given in the documentation, so I >> >> >> > suspect >> >> >> it >> >> >> > is a bug. >> >> >> > >> >> >> > Best regards, >> >> >> > Tyler Morgan-Wall >> >> >> > >> >> >> > [[alternative HTML version deleted]] >> >> >> > >> >> >> > ______________________________________________ ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel