Regarding your first question - yes, you can simply reorder the levels and assign 'happiness' as the reference group.

Regarding your second question - I'm a bit confused by the different outputs. The first table you provide includes the full design with results of both predictors included (several showing significant effects); however, the third table shows only a single predictor (emotion type). If there are significant effects with the full model, why run the second model with only one predictor? If you manipulate two features of stimuli in an experiment, trying to assess the effects of just one manipulation is problematic because the two manipulations could interact in some way. Did you test for interactions?

*Parenthetically, statistical significance is an arbitrary decision criteria. It's useful for guiding research questions, but it's not the ultimate determiner of what's scientifically important or relevant. Your hunch may be correct - perhaps the difference is insignificant due to the ceiling effect. That doesn't mean there are not real differences for emotion identification, however.

Thank you Blaine Tomkins for your answer! Regarding the first question, I assume I must include the results of both regression analysis (one with anger as reference and one with happiness as reference) in my paper (e.g. exp(B), B, etc). Regarding the second question, my apologies I am not clear here. In the second question, the emotions refer to pictures representing emotional faces at 100% intensity level. The same categories of emotions are used (anger, happiness, disgust, fear, sadness and surprise), but the gestures of question 1 are no longer used. This is also the bar graph you see. I examine if people can recognize the emotions on the faces in the second question.

Since the levels of the predictor 'emotion' are categorical and have no intrinsic or natural order (* called a discrete categorical variable), which level you choose as a reference is rather arbitrary. This would be different if you had, say, a 'neutral expression' condition - then it would make sense to include this as the reference group, but that is not the case here. In this instance, your choice of reference group doesn't matter. Typically, you would pick a reference that allows you to make the comparison(s) you're most interested in (i.e. the ones you've made predictions about). Reporting multiple regression outputs is unnecessary in my opinion. One model that allows you to test your predictions is enough.

I think I'm still unclear about the design and the stimuli. With reference to the design: is this between-groups, within-groups, mixed? Also, what is meant by 'gesture?'. Could you give an example? Thanks

Thank you for your answer! The model indeed stays the same because the variables stay the same. However, there is one thing I do not get. For example, I want to know the difference between anger and fear (and the other emotions but I take fear as an example now) and between Happiness and fear. If anger is the reference category, all emotions will be compared to anger. For example, the exp(B) and B of fear are in relation to anger. The B of fear displayed in the table is the difference between the actual B of fear and the intercept (anger). If I want to know the difference between Happiness and fear (to keep fear as the example here), I have to re-run the regression in SPSS with happiness as reference. As a result, the exp(B) and B change because now everything is compared to happiness. Should I not also report the exp(B) and B when happiness is the reference next to the exp(B) and (B) when anger is the reference for fear (and the other emotions)?

I have never done a binary regression with a predictor variable with more than two levels.

Study design in the first question: each participant (26 in total) checked every emotion (anger, happiness, disgust, fear, sadness, and surprise). The emotions were presented as gestures. A NAO-robot gestured emotions (e.g. raising its hands when gesturing the emotion happiness). Participants was asked which emotion they thought was gestured by the robot. On top of that, there were two possibilities: the robot gestured the emotions or the robot gestured the emotions while telling a story. In the end, each participant saw 6 video's in which the robot gestured one of the emotions AND 6 video's in which the robot gestured one of the emotions accompanied by a story (26 participants x 6 emotions x 2 gesture conditions)

Design in the second question: every participant saw six pictures with facial expressions (again anger, happiness, fear, disgust, sadness and surprise) with an intensity of 100%. They had to indicate via a multiple choice question which emotion they thought was in the picture (26 participants x 6 pictures).

Thus, the binary outcome variable (in both of my questions 1 and 2) has two values: 0 = the answer to an emotion was wrong (e.g. gesture OR image presented happiness but the participant recognized it as anger) and 1 = answer is correct (e.g. gesture OR image presented happiness and the participant recognized it as happiness).

I hope it is more clear now!

Ok. The design makes sense now. Yes, if you use dummy coding each level of the 'emotion' predictor will be compared to the reference group. It sounds like this is not what you want to do. Rather, you want to be able to make specific comparisons among several levels to each other. Given the number of levels you have, your best bet is to create a custom coding scheme (i.e. contrast matrix) where you can specify which levels you want to compare in the analysis. Unfortunately, I don't know how to do this in SPSS (or if it even can be done in SPSS), but it is fairly easy in R.

The following link includes an example of how to create a contrast matrix (called "user defined coding" in the article) in R. https://stats.idre.ucla.edu/r/library/r-library-contrast-coding-systems-for-categorical-variables/#User

Just by visual inspection of the results, however, apart from 'fear' it doesn't look like there was much difference among the remaining levels. (I wonder if fear was incorrectly identified as disgust?).

Blaine Tomkins, thank you for your answer! I will look into that.

Fear was mostly identified as surprise (followed by disgust).

I also looked a little bit more into the ceiling effect you mentioned earlier and I am afraid my data suffers from that. One of the solutions to solve this could be Bootstrapping, but I still have to examine that a bit more.