In the movie Inside Out, I noticed that in Riley's mom the Sadness emotion was quite the one leading or managing the other emotions while in Riley's dad, the Angry emotion was the one leading the group and Lastly, in Riley's own brain, it was Joy that was leading the group. Would that mean whichever emotion is leading that's the person's personality? Is there any explanation for this?
As noted in that other question:
First, the parents' emotions are due to both emotional development and story and acting flow:
I [Director Docter] remember, we talked to John and he said, ‘Well, I thought you did it because, as adults, we become more kind of set in our ways. As a kid, you can... anywhere is possible.’
Notice that all of the emotions for other characters are pretty homogenous. They are similar, and in the case of the Bus Driver, it's 5 shades of Anger. We don't see much of the Dad or Mom, but we can tell that the Mom isn't chronic Depressed, nor is the Dad a Rage-aholic. The Dad specifically seems pretty Joyful for the most part. What we do see is the the emotions are working together. One emotion may take the figurative lead, as Inside Out represents a figurative view of the mind, but the emotions are a team.
Riley, as the Protagonist has the added bonus of variations for her emotions, for the audience's benefit, but at the same time, we see how her emotions evolve over time. As a baby, she first had Joy, then Joy and Sadness. The emotion console was a single button. As she got older, she gained more emotions, the five main emotions the film presents, and the console got bigger, a bit more complex, yet it's still manned by a single emotion at a time. Anyone that has dealt with children growing up knows how one-track minded children's emotions are. They tend to only express a single one at a time (yes, this is a simplified view of child psychology).
The film's plot and climax results in Riley working out an emotional conflict of leaving her old home while at a tender age, where emotions start to branch out and human expression becomes more complex. At the end, we see that new memories start to become multi-faceted. Instead of a single color memory, only joyful, or disgust, or anger, it's a mix of them. The film lampshades this with the upgraded emotion console, complete with full curse board and a puberty button. As we saw with Mom and Dad, Riley's upgraded emotion console now has to be controlled by all of the emotions at the same time instead of one by one.
In the end, the upgraded console (adult or adult lite) reflects a truer adult personality then the single faceted child personality. There is no single emotional personality, it's a mix of them all. Of course, the visual cues were simplified for the same reason as the emotions were for anyone not Riley, it made the story easier to flow.