In "The Necklace," which type of characterization is predominantly used, direct or indirect? Explain how you know.

In my opinion, the predominant form of characterization in this story is direct.  Direct characterization is when the author of the story directly tells us what a character is like, rather than having us figure it out for ourselves from the character's actions.

Look at the way that the author tells us about Madame Loisel.  He tells us straight out that she is unhappy and why she is unhappy.

She suffered intensely, feeling herself born for every delicacy and every luxury. She suffered from the poverty of her dwelling, from the worn walls, the abraded chairs, the ugliness of the stuffs. All these things, which another woman of her caste would not even have noticed, tortured her and made her indignant.

Later on, he tells us how she feels about the invitation to the ball.

Instead of being delighted, as her husband hoped, she threw the invitation on the table with annoyance,

So what he does in this story is to tell us what she is thinking.  He does not just show her throwing the invitation.  Instead, he tells us why she did it.