Multinomial and Ordinal Logistic Regression

In this section we extend the concepts from Logistic Regression where we describe how to build and use binary logistic regression models to cases where the dependent variable can have more than two outcomes. Using such models the value of the categorical dependent variable can be predicted from the values of the independent variables.

We first address the categorical case where there is no order to these outcomes (multinomial logistic regression). We then turn our attention the situation  where there is order (ordinal logistic regression).


25 Responses to Multinomial and Ordinal Logistic Regression

  1. Fatimah says:

    Dear Charles,

    IF the Model fitting is not significant, should I proceed?
    If yes, what does it mean for the model fitting to be not significant while the parameter estimates
    is significant?

    Model Fitting Information
    Model Fitting Criteria
    -2 Log Likelihood
    95.673 90.756
    Likelihood Ratio Tests
    Intercept Only Final
    Chi-Square df
    IF the Model fitting is not significant, should I proceed?
    If yes, what does it mean for the model fitting to be not significant while the parameter estimates is significant?

  2. Sam says:

    Dear Sir,
    Please help me, I’m a newbie about this problem.
    Well, I’m now completing a research study about the relationship between narcissism (IV) and cyberbullying (DV) to instagram user. My independent variable has low-mid-high (interval data) and my dependant variable has a categorical data which consist of cyberbullying perpretator-cyberbullying victim-and the unidentified one.
    Yesterday, i tried a multinomial logistic regression analysis in SPSS, and it gave me a warning:

    “There are 1 (11,1%) cells (i.e., dependent variable levels by subpopulations) with zero frequencies.
    Unexpected singularities in the Hessian matrix are encountered. This indicates that either some predictor variables should be excluded or some categories should be merged.
    The NOMREG procedure continues despite the above warning(s). Subsequent results shown are based on the last iteration. Validity of the model fit is uncertain.”

    What’s the warning means ? I don’t understand
    And is a multinomial logistic regression analysis that i’ve choosen right to be analysed in my research ?

    Thankyou, Sir

    • Charles says:

      From your description, multinomial logistic regression analysis seems to be a good choice, except for the warning. You should pay attention to warning “There are 1 (11,1%) cells (i.e., dependent variable levels by subpopulations) with zero frequencies.” You can ignore the rest of the warning.
      I don’t use SPSS and so I can’t comment further about the warning message, but I suspect that your sample is very small with not enough data to find a fit for the logistic regression model.

  3. Dennis says:

    Is it possible to use your resource pack for conditional logisitic regression? Think of analyzing which horse will win a given horse race relative to the other horses….Thanks!

  4. Ashik says:

    Please help me with this notification i am very new to real statistic package while i am trying to perform multinomial logistic regression its saying “last column of input range must contain all the values 0,1,2,…, and only these values where r=max value in the last column of input range (r must be <25). How can i solve this problem ?

  5. sarah kolshuk says:

    Hi Dear Dr. Zaiontz,
    Im am completing a research study looking to see if there is an association between rates of hypotension (yes/no) during surgery (primary outcome) and use of a certain blood pressure medication (given /held prior to surgery). I have multiple regressors / confounding variables that I am trying to account for. Some are binary in nature (0,1) and some are continuous (ex. blood pressure readings). Someone had suggested I split my regression analysis: 1) do a multi nominal analysis for comparing my independent variable and nominal data, 2) do a multivariate linear regression for comparing independant variable with continuous regressors. What is your opinion on the above advise? What type of test do you feel would be most appropriate?

    • Charles says:

      These approaches could be useful, but I would need to have a more complete picture of the situation before I could definitively answer your question.

  6. AGHA says:

    My Independent variables are gender and academic achievements in term of CGPA. While my DV is Emotional intelligence EI. What type of tests i will do to prove that gender has relationship with EI, and Academic achievements predict EI.

  7. Hamad says:

    Dear Dr. Zaiontz,

    I am planning on using Conjoint Analysis to measure preference for new products. As you know, it uses a multinomial logit model. However, I have found special softwares to conduct such analysis but they are very expensive. Do you know if Conjoint Analysis could be performed using Excel, or are there other ways of doing it? (I have been told that I could find free codes to use it on R, but I got lost when I saw those). Any help is greatly appreciated.

  8. Hossein Jamaly says:

    Hi Prof. Zaiontz
    I appreciate if you kindly help me in doing multinomial logistic regression between my categorical phenotypic data (as dependent variables) and genotypic data (both binary and allelic states as independent variables).
    FYI, I am analysing my data in a panel of 143 barley genotypes for association mapping in barley. I have used GLM and MLM models for my quantitative and ordinal phenotypic data in TASSEL software(

  9. Iresha says:

    Dear sir,
    Can u tell me, when we have Categorical variable for both dependent & Independent variables, How we will do the regression analysis

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