从mysql中选择填充optgroup和选项的表单错误

Question

我已经创建了一个包含来自mysql的optgroups和选项的选择列表。当我尝试以下代码时，虽然optgroup正确，但是出现此错误，但选项显示错误。有人可以帮我解决吗？感谢。

<select id="lr-cat" name="category">
            <option value="0"></option>
            <?php

            $mysqli = new mysqli("localhost", "root", "password", "database");
            $results = $mysqli->query('SELECT subcat_id, subcat_name, subcategories.cat_id, cat_name FROM subcategories INNER JOIN categories ON subcategories.cat_id=categories.cat_id');

            $categories = array();
            while ($row = $results->fetch_assoc()) {
                $cat_name = $row['cat_name'];
                if (!array_key_exists($cat_name, $categories)){
                    $categories[$cat_name] = array();}

                $categories[$cat_name][] = array($row['subcat_id'], $row['subcat_name']);
            }

            mysqli_close($con);
            ?>
            <?php foreach ($categories as $cat_name => $subcategories): ?>

                <optgroup label="<?php echo htmlentities($cat_name); ?>">

                    <?php foreach ($subcategories as $subcat_name): ?>

                        <option value=$subcat_id><?php echo htmlentities($subcat_name); ?></option> <!--line 128-->

                    <?php endforeach; ?>

                </optgroup>

            <?php endforeach; ?>
        </select>

错误

  

警告：htmlentities（）期望参数1为字符串，给定数组   在第128行