search for: reparameterises

I have a question about the basis functions of cubic regression spline in mgcv. Are there some ways I can get the exact forms of the basis functions and the penalty matrix that are used in mgcv? Thanks in advance! Yan [[alternative HTML version deleted]]

ggplot2 ------------------------------------------------------------ ggplot2 is a plotting system for R, based on the grammar of graphics, which tries to take the good parts of base and lattice graphics and avoid bad parts. It takes care of many of the fiddly details that make plotting a hassle (like drawing legends) as well as providing a powerful model of graphics that makes it easy to produce

ggplot2 ------------------------------------------------------------ ggplot2 is a plotting system for R, based on the grammar of graphics, which tries to take the good parts of base and lattice graphics and avoid bad parts. It takes care of many of the fiddly details that make plotting a hassle (like drawing legends) as well as providing a powerful model of graphics that makes it easy to produce

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.

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"

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 <tylermw at gmail.com> wrote: > Hi

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

Hello Tyler, You write that you understand what I am saying. However, I am now at loss about what exactly is the problem with the behavior of R. Here is a script which reproduces your experiments with three variables (excluding the full model): m=expand.grid(X1=c(1,-1),X2=c(1,-1),X3=c("A","B","C")) model.matrix(~(X1+X2+X3)^3-X1:X3,data=m)

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

Hi Arie, I understand what you're saying. The following excerpt out of the book shows that F_j does not refer exclusively to categorical factors: "...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." Since F_j refers to both categorical and numeric variables, the behavior of

Hi Arie, Given the heuristic, in all of my examples with a missing two-factor interaction the three-factor interaction should be coded with dummy variables. In reality, it is encoded by dummy variables only when the numeric:numeric interaction is missing, and by contrasts for the other two. The heuristic does not specify separate behavior for numeric vs categorical factors (When the author of