What is causing this error? Coefficients not defined because of singularities

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I'm trying to find a model for my data but I get the message "Coefficients: (3 not defined because of singularities)" These occur for winter, large and high_flow

I found this: https://stats.stackexchange.com/questions/13465/how-to-deal-with-an-error-such-as-coefficients-14-not-defined-because-of-singu

which said it may be incorrect dummy variables, but I've checked that none of my columns are duplicates.

when I use the function alias() I get:

Model :
S ~ A + B + C + D + E + F + G + spring + summer + autumn + winter + small + medium + large + low_flow + med_flow + high_flow

Complete :
          (Intercept) A  B  C  D  E  F  G  spring summer autumn small medium
winter     1           0  0  0  0  0  0  0 -1     -1     -1      0     0    
large      1           0  0  0  0  0  0  0  0      0      0     -1    -1    
high_flow  1           0  0  0  0  0  0  0  0      0      0      0     0    
          low_flow med_flow
winter     0        0      
large      0        0      
high_flow -1       -1      

columns A-H of my data contain numeric values the remaining columns take 0 or 1, and I have checked there are no conflicting values (i.e. if spring = 1 for a case, autumn=summer=winter=0)

model_1 <- lm(S ~ A+B+C+D+E+F+G+spring+summer+autumn+winter+small+medium+large+low_flow+med_flow+high_flow, data = trainOne)
summary(model_1)

Can someone explain the error please?

EDIT: example of my data before I changed it to binary

season  size   flow  A  B   C   D   E   F   G  S
spring small  medium 52 72 134  48 114 114 142 11
autumn small  medium 43 21  98 165 108  23  60 31
spring medium medium 41 45 161  86 177 145  32 12
autumn large  medium 40 86 132  80  82 138 186 16
winter medium  high  49 32 147 189 125  43 144 67
summer large   high  43  9 158  64  14 146  15 71

@JuliusVainora has already given you a good explanation of how the error occurs, which I will not repeat. However, Julius' answer is only one method and might not be satisfying if you don't understand that there really is a value for cases where winter = 1, large=1 and high_flow=1. It can readily be seen in the display as the value for "(Intercept)". You might be able to make the result more interpretable by adding +0 to your formula. (Or it might not, depending on the data situation.)

However, I think that you really should re-examine how your coding of categorical variables is done. You are using a method of one dummy variable per level that you are copying from some other system, perhaps SAS or SPSS? That's going to predictably cause problems for you in the future, as well as being a painful method to code and maintain. R's data.frame function already automagically creates factor's that encode multiple levels in a single variable. (Read ?factor.) So your formula would become:

 S ~ A + B + C + D + E + F + G + season + size + flow

What is causing this error? Coefficients not defined because of , @JuliusVainora has already given you a good explanation of how the error occurs, which I will not repeat. However, Julius' answer is only one  If you ever started to do linear static FEA Analysis, you probably encountered the following singularity error: ERROR [2007]: FACTORIZATION FAILED DUE TO A SINGULARITY AT TRANSLATION-X OF NODE 111 (RANK=5262)

The issue is perfect collinearity. Namely,

spring + summer + autumn + winter == 1
small + medium + large == 1
low_flow + med_flow + high_flow == 1
Constant term == 1

By this I mean that those identities hold for each observation individually. (E.g., only one of the seasons is equal to one.)

So, for instance, lm cannot distinguish between the intercept and the sum of all the seasons' effects. Perhaps this or this will help to get the idea better. More technically, the OLS estimates involve a certain matrix that is not invertible in this case.

To fix this, you may run, e.g.,

model_1 <- lm(S ~ A + B + C + D + E + F + G + spring + summer + autumn + small + medium + low_flow + med_flow, data = trainOne)

Also see this question.

[R] Coefficients: (20 not defined because of singularities), Hi, "singularity" in this case means that your X'X matrix is singular, i.e. you have multicollinearity in your data. A common reasons is selecting  Thanks, Petr. isInterNuclear and zeroSyllToEOP are both binary, and it turns out : isInterNuclear & zeroSyllToEOP == zeroSyllToEOP. On Aug 6, 2006, at 11:23 PM, Petr Pikal wrote:

Some of you variables could be perfectly collinear. Take a look at the variables and how they correlate with each other. You can start inspecting the data with cor(dataset), this will return a correlation matrix of your dataset.

What is the singularity error in linear regression - techniques, Hello, I have run lm in R on some data and got the following output: There is some output like 3 not defined because of singularity. Coefficients: (1 not defined because of singularities) is telling us to beware of perfect colinearity. IIn practice perfect colinearity, mostly occurs when a large number of categorical variables are used as predictors. 12

Linear Models with R, Now although Xhas three columns, it has only rank 2—(!, %1, %2) are not (g) Coefficients: (1 not defined because of singularities) Residual standard error: 61 on In most cases, the cause of identifiability can be revealed with some thought​  I saw Ted's reply and it is certainly sensible. I would wonder whether to model ought to be recast so that the scientific question is more clear? You are obviously studying the effect of different substitutions (F, Cl, Br, I, Me) and different positions around an aromatic ring (meta, para).

Linear Models with R, Second Edition, Coefficients: (1 not defined because of singularities) Estimate Std. Error t value In most cases, the cause of identifiability can be revealed with some thought  This is also seen with the warning: “(1 not defined because of singularities)”. This is good to know, but not revelatory or new; just be aware. When model.matrix goes … differently. Well model.mat already has an intercept, so why not just take out the intercept term with a -1? The model should be the same, right?

[PDF] Linear Models with R - Department of Statistics, Statistics starts with a problem, proceeds with the collection of data, continues with the With observational data, unidentifiability is usually caused by some oversight. Here are some Coefficients: (1 not defined because of singularities). Some of the variables are not defined because of singularity means that the variables are not linearly independent. If you remove the variables that are giving NA in the above summary, you will obtain the same result for the rest of the variables.

Comments
  • Sounds like multicolinearity to me.
  • That is what I want my formula to be! How do I turn them into factors (these store characters and a numeric?) I have tried modelData$flow <- factor(modelData$flow, ordered = TRUE, levels = c(1,2,3)) but I get NA
  • To answer that question I would need to see how the data existed before it was input inot R and what sort of transormation you have done.
  • please see my edit. I didn't 'transform' as such, I manually created variables spring etc and assigned 0 or 1 depending on the season column
  • So presumably you did something like trainOne <- read.table(file="C:/path/filename", header=TRUE). In which case the season, size and flow varaibles are already factors and you wouldn't need to do any of that extra dummy coding. Try that formula that I gave.
  • Oh I didnt think that lm would work on non-numerical... thanks :)
  • I see! I'm reluctant to drop variables as I would have to drop two of my flow/ size variables which are important. I started off with a column 'size' containing small medium or large, is there a way to keep the column as it is and assign a numeric value based on the entry, so the column stores the characters "small" and 1? From this I could do the same to 'flow' and keep the binary season variables
  • @Laura, that's the whole point that right now you actually have too much information and by dropping those three variables from the equation you wouldn't lose anything. I suggest to read those two references (and perhaps some others) to see how the coefficients can be interpreted. Indeed as @42- suggests, you may want to add -1 or +0 as to remove the intercept. In that case, e.g., the coefficient of spring would be relative to the effect of omitted winter. (I added another reference.)