Suppose a survey has five items with a six-point Likert scale. It has been rolled out with ill-formed labels:
*the (2) was labelled by "somewhat disagree" instead of "disagree" - and vice versa the (3) was labelled by "disagree"
*analogous ill-forming for (4) and (5): "somewhat agree" and "somewhat disagree" were mixed up
Taken literally, the respondents face a 132546-situation instead of a 123456-situation for some of the items. The begin of the survey was labelled right.
Can this be repaired by a clever and statistically sound repair-procedure as part of the data analysis, if the answered questionnaires should form a basis for structural equation modelling?
From my point of view:
clearly no, the questionnaire must be sent out once again in a sound shape. Even if there is a general conditioning of answering this questionnaire as of the labels were in the right order, "conditioning" is not a 100% concept. So, there are two things we would not know:
how many people took the questionnaire literally and who took it literally.
This introduces a "second noise" to the structural equation model, which uses p-values etc. to quantify "noise". Now, "noise" and "second" noise cannot be separated anymore. Even if we knew the relative amount of conditioned answering, we still did not know, who answered in an unconditioned fashion - ending up with the non-separable "second noise" again.
Normally I am really not that harsh. Thatswhy: any objections to my point of view - is my position too harsh?