I used 5-point Likert-type scales as a dependent variables (1 strongly agree, 2 agree, 3 neutral, 4 disagree, 5 strongly disagree), but, as you are aware, using binary logistic regression requires me to create a binary variable from these 5-level responses. So, strongly agree and agree would become category 1, and disagree and strongly disagree would become category 2, while we exclude the neutral response option (although this significantly cuts down my sample size).
One more issue in this regard, my questionnaire has 12 variables and each variable is measured by a group of items. For example, I have education (measured by 7 items), Gender inequality (measured by 6 items), trust (measured by 6 items), career development (measured by 7 items) and so on. Now, and in order to create the binary category do I need to take the high and the low score of each variables and find the mean and standard deviation, and exclude the cases in the middle? but this again will significantly cuts down my sample size?
Finally is it better to use multinomial logistic regression instead of binary logistic regression when dependent variables are measured by 5-point Likert scale, which means there are 5 groups with each variable?