Laravel 5 Eloquent Relationship - Has Many Though

It sounds like you have many-to-many relationships between Study->Site and Site->Unit. You can read the Laravel documentation about many-to-many relationships here.

Models

Here are the relevant functions you'll need for Eloquent to recognize the relationships.

class Study extends Model {
    // If you named your table differently (like 'studies'), specify that here
    protected $table = 'studys';

    // This assumes a pivot table named 'site_study', if you named yours
    // differently you can pass in into the belongsToMany() function as the
    // second parameter.
    public function sites() {
        return $this->belongsToMany('App\Site');
    }
}

class Site extends Model {
    protected $table = 'sites';

    public function studies() {
        return $this->belongsToMany('App\Study');
    }

    public function units() {
        return $this->belongsToMany('App\Unit');
    }
}

class Unit extends Model {
    protected $table = 'units';

    public function sites() {
        return $this->belongsToMany('App\Site');
    }
}

Then, to access the Sites belonging to a Study you would do this:

$sites = Study::find(1)->sites;

Pivot Table Migrations

Laravel expects pivot tables to be named like 'alpha_beta' where alpha and beta are the singular model names in alphabetical order. So your migrations for the pivot tables would look like this:

class CreateSiteStudyTable extends Migration {
    public function up() {
        Schema::create('site_study', function(Blueprint $table)) {
            $table->integer('site_id')->unsigned();
            $table->foreign('site_id')->references('id')->on('sites');
            $table->integer('study_id')->unsigned();
            $table->foreign('study_id')->references('id')->on('studys'); // or whatever you named it
            $table->unique(['site_id', 'study_id']);
            $table->timestamps();
        });
    }

    public function down() {
        Schema::drop('site_study');
    }
}

class CreateSiteUnitTable extends Migration {
    public function up() {
        Schema::create('site_unit', function(Blueprint $table)) {
            $table->integer('site_id')->unsigned();
            $table->foreign('site_id')->references('id')->on('sites');
            $table->integer('unit_id')->unsigned();
            $table->foreign('unit_id')->references('id')->on('units');
            $table->unique(['site_id', 'unit_id']);
            $table->timestamps();
        });
    }

    public function down() {
        Schema::drop('site_unit');
    }
}

You can read about Foreign Keys in Laravel here.