converting 7 point likert scale to Dichotomous question

[SHIKHA GARG]

Greetings to everyone

In my research I am planning to study SEM through SmartPLS. 

A dichotomous question was asked in the questionnaire and  it was decided that only 'Yes' responses will be kept for further analysis and 'No' will be dropped.

That question represent my Independent variable which is again asked on 7 point Likert Scale and is represented by 4 items.

It was believed that if a respondent marks Yes to dichotomous question then her responses will be more towards agree side. But when I looked at the responses I found that there are some respondents who have marked yes to the dichotomous question but in four statements they are on disagreement side.

So in order to use proper data for my study I am thinking of finding out mean of all the statements for all the respondents and keep only those responses which have agreed to it. 

Please guide me if I am doing it correctly. 

If yes, pls suggest some papers which I can cite in my research to justify my action.

if no, pls suggest some alternatives.

Thanks and regards