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Explanation:

Lets say we have a dataset, df with 'n' columns/variables. Two of 'n' variables are named as Case 1 and Case 2. Case 1 and Case 2 are categorical variables with value levels "Low" and "High".

Logistic regression:

Dependent variable: Case 1 and Case 2

Independent variable: Remaining (n-2) columns

Objective: I want to predict the probability of getting a low and high level based on variable "Case 1" and "Case 2".

Question: What are alternatives to multivariate logistic regression or what is the best way to perform this kind of multivariate logistic regression?

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    $\begingroup$ You can re-code the two levels of each of Case 1 and Case 2 as 4 levels of one variable (all combinations of the 2 levels). Each row will be 1 of the 4 levels, so this is a multinomial logistic regression. $\endgroup$
    – Sycorax ♦
    Commented Jun 1, 2022 at 19:10
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    $\begingroup$ To follow up that comment by @Sycorax, see stats.stackexchange.com/questions/52104. $\endgroup$
    – whuber ♦
    Commented Jun 1, 2022 at 19:10
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    $\begingroup$ You can use ordinal logistic regression if you have ordered categories $\endgroup$
    – Lelouch
    Commented Jun 1, 2022 at 19:52
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    $\begingroup$ @Lelouch Good point--but there is no inherent order when multiple categories are present. $\endgroup$
    – whuber ♦
    Commented Jun 1, 2022 at 20:29

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