CODEWITHSUNDEEP
rlogistic-regressionordinal
thezodiac1994
thezodiac1994

Reputation: 31

Understanding format of lrm coefficients in R for ordinal/multiclass regression

I am trying to implement one of the R codes in python from scratch and it involves logistic regression.

As far as I understand logistic regression, (while performing one vs all using gradient descent) I think if there are F features and L labels then the we have M x F coefficients. Basically We have F different vectors for each of M labels and then calculate the sigmoid function for an incoming input X and whichever Vector gives maximum is the class predicted.

The logistic regression function in R: 

try_lrm<-function(datadf, tol=1e-10, maxit=1e6){
  try({ lrm(y~x, data=datadf, penalty=0, x=TRUE, y=TRUE, tol=tol, maxit=maxit) })
}

However on the ordinal regression for the following data-frame: 

    x       y
24.03673    2   
14.63598    2  
26.85079    2  
53.45076    1  
36.8322     1  
42.10773    1  
39.68833    1    
104.64827   0  
114.97038   0   
60.8128     0   
59.67947    0

I get the following coefficients: 

      y>=1       y>=2       x 
131.440196  75.784904  -2.324528

As I am trying to implement everything from scratch, I am trying to use gradient descent.

So how should this be interpreted ? I want to figure out how the sigmoid function should look like but I am not sure why there is just one coefficient for x when I am expecting there to be one x coefficient for every class. And what are those intercepts.

Does it mean that the sigmoid function looks like:

(Lets call the coefficients as k0,k1,k2 which I got for x,y>=1 and y>=2)

for y = 0,
p = 1/(1+e^-(k0 * x))

for y = 1,
p = 1/(1+e^-(k0 * x + k1))

for y = 2,
p = 1/(1+e^-(k0 * x + k1 + k2))

And predict max p class ?

Upvotes: 0

Views: 381

Answers (1)

cmaimone
cmaimone

Reputation: 576

This appears to primarily be a statistics question - there isn't anything obviously wrong with your R code. You should only have one coefficient for x, as is reported. For an example of ordinal logistic regression in R, see https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/. It uses a different package than you are trying to use, but it walks through the statistics as well as R code.

Upvotes: 1

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