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In my study the dependent variable is binary coded as 0 and 1 and independent variables are combination of category variables and variables measured on likert scale on 5 point scale. As per the data i want to perform binary logistic regression but little bit confused how i should treat those independent variables which are measured on likert scale. should these be treated as continuous variables or ordinal variables? As per my knowledge logistic regression deals with only categorical and continuous Independent variables. If variables measured on likert scale are ordinal rather continuous which statistical tool i should apply?

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It is a very debated issue. I suggest you to read the following links. In any case it depends on your research design and on your waitings about the results:

http://www.theanalysisfactor.com/can-likert-scale-data-ever-be-continuous/ https://www.researchgate.net/publication/266212127_Five-Point_Likert_Items_t_Test_Versus_Mann-Whitney-Wilcoxon https://stats.stackexchange.com/questions/86923/effect-of-two-demographic-ivs-on-survey-answers-likert-scale

According to my opinion, it is not possible to consider them like continuous values. Maybe you should ask on this community:

https://stats.stackexchange.com