Solved – Interpreting multinomial logistic regression output in R

logisticmultinomial-distributionrregression

I am trying to perform multinomial logistic regression on my data which is as below(just the header).
enter image description here

"category" is my target variable and all other variables are independent variables. category has values like 1,2,3,4,5,6,7,8,9. My main motive is to predict category from independent variables.
Here is summary of my data set.
summary

I used following command to perform multinomial logistic regression:

> mod=multinom(category~hlen+iplen+ipttl+iptype+tcpsport+tcpdport+tcpsec+tcpack+tcpwindow+tcpchksum+date_time, data=train)

command

I got the following output but i don't know how to interpret it?
enter image description here
What should be the starting point or is there other way to do so? (For example I know how to interpret linear and logistic regression output to create regression equations)

Please right click any image and select view to see it clearly.
Thank you,

Best Answer

Multinomial logistic regression works like a series of logistic regressions, each one comparing two levels of your dependant variable. Here, category 1 is the reference category.

For example, consider the case where you only have values where category is 1 or 5. (Recode that to 0 and 1, so that you can perform logistic regression.) The coefficients of line 5 of your output represent the variable coefficients such a logistic regression would yield.

Multicollinearity

The issue seems to be that colldiag() needs a model parameter, which is not appended to the model fit by default in multinom(). But if you set model = TRUE in the multinom call, the colldiag function should compute without errors.

require(perturb)
set.seed(123)
a <- sample(4, 100, TRUE)
c <- sample(4, 100, TRUE)
a <- as.ordered(a)
c <- as.factor(c)
colldiag(mod = multinom(c ~ a, model = TRUE), scale = FALSE, 
         center = FALSE, add.intercept = TRUE)

Output:

Condition
Index   Variance Decomposition Proportions
         intercept X    
1  1.000 0.002     0.141
2  7.255 0.998     0.859

In regards to the output of perturb, I don't have any good answer as to how to interpret the results. The only comment given in the vignette states that

"If collinearity is a serious problem in the data, then the estimates will be unstable and vary strongly."

Autocorrelation

The dwtest() from {lmtest} should work with multinom() to compute autocorrelation for you, though you will need to convert your factor to a numeric variable.

require(lmtest)
dwtest(multinom(as.integer(c) ~ a))

Output:

      Durbin-Watson test

data:  multinom(as.integer(c) ~ a)
DW = 1.7298, p-value = 0.08517
alternative hypothesis: true autocorrelation is greater than 0

Especially for users of the mlogit function from the {mlogit} package: multinom()from {lmtest} did not work for me, it says in my just downloaded package version that this function doesn't exist. I had to reshape my data from a form fit for the mlogit function to a dataframe form where each item has only one line (instead of the number of potential outcomes per item). Then I could run this code: require(lmtest) dwtest(as.numeric(outcome) ~ predictors, data=dat).

Best Answer

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