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Can the odds ratio be calculated for a continuous dependent variable using logistic regression? If yes, kindly explain the procedure in SPSS. Further, can we apply logistic regression to an dependent variable when it is a scale without dichotomizing it? Since I need to report the odds ratio after adjusting for multiple variables to an outcome that is continuous, I have dichotomized it and have applied logistic regression, but I want to do the same for it in its continuous form (I need to report the odds ratio for both the models, i.e., continuous and dichotomous). If this is possible kindly explain.

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I don't use SPSS but yes you can use a proportional odds ordinal logistic model on continuous $Y$. Don't use any grouping/dichotomization of $Y$. The R rms package orm function handles this efficiently for up to 6000 distinct $Y$-values (i.e., up to 5999 intercepts in the model). A case study appears here.

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