I have a question with 12 options. Respondents are allowed to choose multiple options. Among these 12 options, 6 are correct responses and 6 are not. I want to penalize the respondent if an incorrect response was chosen. How to go about this?
You may grade your test using a 3-parameter item response theory. Then, you are fine as the guessing parameter will be incorporated into your students' scores.
What is your opinion on negative marking for dichotomous (yes/no) questions? Suppose there are 10 yes/no questions, and the respondent answers 6 correctly and 4 incorrectly, can I calculate the final score as follows with negative marking, as we do with multiple choice questions? This essentially subtracts the number of incorrect responses from the correct ones.
score = number of correct responses - number of incorrect responses (1/ number of options -1)
It is a good idea to consider negative marking in your scoring. However, you should have literature to justify any routine you use in the scoring process.