exampleModule.js

function MyModule() {}

module.exports = function(_params) {
  // Could even do things in here for pre-init
  
  return new MyModule(_params);
}

// Implementation:
var module = require("mymodule")();

moreExplicit.js

function MyModule() {}

exports.init = function(_params) {
  return new MyModule(_params);
}

// Implementation:
var module = require("mymodule").init();