Timeline for What is a contrast matrix?
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Sep 15 at 16:04 | comment | added | Tomas | Again, super complicated answer, I was asking for simple definition... | |
| Sep 2, 2021 at 1:33 | history | edited | kjetil b halvorsen♦ | CC BY-SA 4.0 |
added 193 characters in body
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| S Nov 30, 2020 at 15:53 | history | suggested | user253642 | CC BY-SA 4.0 |
This hyperlink is outdated 'http://www.ats.ucla.edu/stat/data/hsb2.csv'. Replaced with new hyperlink 'https://stats.idre.ucla.edu/stat/data/hsb2.csv'.
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| Nov 30, 2020 at 14:46 | review | Suggested edits | |||
| S Nov 30, 2020 at 15:53 | |||||
| Jun 11, 2020 at 14:32 | history | edited | CommunityBot |
Commonmark migration
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| Feb 3, 2020 at 21:30 | history | edited | ogustavo | CC BY-SA 4.0 |
Updated to clarify that the discussion of contrasts is one possible approach to ANOVA with non-full-rank X
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| Feb 3, 2020 at 21:05 | comment | added | ogustavo | @fabiob technically, ANOVA is not GLM. But, I think I understand your question. When you have an overparameterized model you can: i) reparameterize the model to get a full-rank matrix; ii) define side conditions (which gives you a full-rank matrix); or iii) work with the model as is and define lin. comb. of the parameters that are unique and can be estimated (these are called contrasts). Since the question is about a contrast matrix, I used iii). However, we also have ANOVA cases where X is full-rank. I updated my answer to clarify that I'm talking about the special non-full-rank case. | |
| Jan 28, 2020 at 10:32 | comment | added | fabiob | I do not understand the sentence "Now, for the ANOVA case, we have that X is not full-rank anymore". Isn't an ANOVA a GLM, so one can write down a full rank design matrix? | |
| Jul 10, 2016 at 21:45 | history | edited | amoeba | CC BY-SA 3.0 |
typos and "modified X"
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| Jul 10, 2016 at 8:02 | history | bounty ended | Glen_b | ||
| Jul 9, 2016 at 22:23 | comment | added | ogustavo | @Curious I'm sorry to hear that. But I believe that my conclusion, along with Amoeba's answer (and the discussion that follows it) should clarify this concept. | |
| Jul 9, 2016 at 22:14 | history | edited | ogustavo | CC BY-SA 3.0 |
added 8415 characters in body
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| Jul 8, 2016 at 15:53 | comment | added | Tomas | Thank you for this answer, but I will probably never be able nor have time to understand it. And I studied maths :-) I expected some very simple definition as an answer :-) | |
| Jul 8, 2016 at 14:23 | comment | added | amoeba | @ttnphns: $i$ is indexing group (there are two groups in Example 1), $j$ is indexing data point inside each group. $\mu$ is a constant and $\alpha_i$ are constants for each group such that $\mu+\alpha_i$ are group means (so $\mu$ can be total mean and $\alpha_i$ can be deviation of the group means from the total mean). Columns of $X$ are constant term and two dummies, yes. | |
| Jul 8, 2016 at 9:58 | comment | added | ttnphns | I'm having troubles with understanding starting right from Example1. What is $i$ an $j$ in your notation $y_{ij}$? What is $a_i$ and what do the columns od $X$ represent? Is that Constant term (column of ones) and the two dummy variables? | |
| Jul 8, 2016 at 0:17 | comment | added | amoeba | Thanks a lot for such a big update. I removed some of my comments above that were obsolete by now (you can remove some of yours, e.g. the first one). However, by now it is clear to me that "contrast matrix" in your (and Monahan's) sense is something entirely different from "contrast matrix" in the sense it's used in this R manual and also in the original question here (what ttnphns calls C-matrix). I think it would make sense if you make a note somewhere in your answer about this difference. | |
| Jul 7, 2016 at 23:57 | history | edited | ogustavo | CC BY-SA 3.0 |
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| Jul 6, 2016 at 10:07 | comment | added | Tomas | please do not restrict this answer just to anova if possible. The [anova] tag was added by @amoeba by the time when you answered my question, but I don't want the answer to be restricted just to anova. | |
| Jul 4, 2016 at 17:44 | history | edited | ogustavo | CC BY-SA 3.0 |
finished tidying latex code (bf -> mathbf), corrected minor typos, rephrased and added/removed sentences for clarity
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| Jul 4, 2016 at 17:33 | history | edited | ogustavo | CC BY-SA 3.0 |
finished tidying latex code (bf -> mathbf), corrected minor typos, rephrased and added/removed sentences for clarity
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| Jul 4, 2016 at 16:11 | history | edited | amoeba | CC BY-SA 3.0 |
started tidying latex code (bf->mathbf) but did not finish (yet)
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| Jul 2, 2016 at 23:17 | history | answered | ogustavo | CC BY-SA 3.0 |