Vue

HTML

<div id="app">
  <div v-for="item in filters">
    <p> {{item.title}} </p>
    <ol>
      <li v-for="filter in item.filterData.variants">
        <label>
          <input type="checkbox" v-model="thisIsStorageForCheckboxesStates[`${item.filterId}-${filter.key}`]">
        </label>
      </li>
    </ol>
  </div>
  <pre>{{ JSON.stringify(selected, null, 2) }}</pre>
</div>

CSS

body {
  background: #20262E;
  padding: 20px;
  font-family: Helvetica;
}

#app {
  background: #fff;
  border-radius: 4px;
  padding: 20px;
  transition: all 0.2s;
}

li {
  margin: 8px 0;
}

h2 {
  font-weight: bold;
  margin-bottom: 15px;
}

del {
  color: rgba(0, 0, 0, 0.3);
}

Vue

new Vue({
  el: "#app",
  data () {
    return {
      thisIsStorageForCheckboxesStates: {},
      "filters": [
        {
          "type": "checkbox",
          "title": "Пол",
          "filterData": {
            "variants": [
              {
                "key": 14,
                "value": "Мужской"
              },
              {
                "key": 15,
                "value": "Женский"
              }
            ]
          },
          "filterId": 1
        },
        {
          "type": "checkbox",
          "title": "num",
          "filterData": {
            "variants": [
              {
                "key": 2,
                "value": "345"
              },
              {
                "key": 1,
                "value": "123"
              }
            ]
          },
          "filterId": 2
        }
      ]
    }
  },
  computed: {
    selected() {
      return Object.entries(this.thisIsStorageForCheckboxesStates).filter(([ k, v ]) => !!v).reduce((acc, [ k ]) => {
        const [ filterId, value ] = k.split('-');
        let f = acc.find(n => n.filterId === filterId);
        if (!f) {
          f = {
            filterId,
            values: []
          };
          acc.push(f);
        }
        f.values.push(+value);

        return acc;
      }, []);
    }
  },
})