PyQt: How to set Combobox Items be Checkable?

To keep the GUI widgets number to minimum I need to find a way to give to user a choice of pull-down menu items that could be used to filter out the displayed in a listWidget items. Let's say the listWidget lists 5 different categories of Items: "Cat A", "Cat B","Cat C","Cat D","Cat E". I could implement the radio or checkboxes for each item category. But then 5 radio buttons or checkboxes would take a lot of GUI space. A combobox with the checkable items seems to be a right choice. Any ideas?

from PyQt4 import QtGui, QtCore
import sys, os


class CheckableComboBox(QtGui.QComboBox):
    def __init__(self):    
        super(CheckableComboBox, self).__init__()

    def flags(self, index):
        return Qt.ItemIsUserCheckable | Qt.ItemIsSelectable | Qt.ItemIsEnabled


class Dialog_01(QtGui.QMainWindow):
    def __init__(self):
        super(QtGui.QMainWindow,self).__init__()

        myQWidget = QtGui.QWidget()
        myBoxLayout = QtGui.QVBoxLayout()
        myQWidget.setLayout(myBoxLayout)
        self.setCentralWidget(myQWidget)

        self.ComboBox = CheckableComboBox()
        for i in range(3):
            self.ComboBox.addItem("Combobox Item " + str(i))

        myBoxLayout.addWidget(self.ComboBox)


if __name__ == '__main__':
    app = QtGui.QApplication(sys.argv)
    dialog_1 = Dialog_01()
    dialog_1.show()
    dialog_1.resize(480,320)
    sys.exit(app.exec_())

This idea of a multi-select combo has come up before, but I'm not sure that its the best solution. Really, all that's needed is a tool-button with a drop-down menu (similar to the history buttons in a web-browser).

Here's a basic demo that illustrates both options (button left, combo right):

PyQt5:

from PyQt5 import QtCore, QtGui, QtWidgets

class CheckableComboBox(QtWidgets.QComboBox):
    def __init__(self, title = '', parent=None):
        super().__init__(parent)
        self.setTitle(title)
        self.view().pressed.connect(self.handleItemPressed)
        self.setModel(QtGui.QStandardItemModel(self))

    def handleItemPressed(self, index):
        item = self.model().itemFromIndex(index)
        if item.checkState() == QtCore.Qt.Checked:
            item.setCheckState(QtCore.Qt.Unchecked)
        else:
            item.setCheckState(QtCore.Qt.Checked)

    def title(self):
        return self._title

    def setTitle(self, title):
        self._title = title
        self.repaint()

    def paintEvent(self, event):
        painter = QtWidgets.QStylePainter(self)
        painter.setPen(self.palette().color(QtGui.QPalette.Text))
        opt = QtWidgets.QStyleOptionComboBox()
        self.initStyleOption(opt)
        opt.currentText = self._title
        painter.drawComplexControl(QtWidgets.QStyle.CC_ComboBox, opt)
        painter.drawControl(QtWidgets.QStyle.CE_ComboBoxLabel, opt)

class Dialog(QtWidgets.QWidget):
    def __init__(self):
        super().__init__()
        hbox = QtWidgets.QHBoxLayout()
        self.comboBox = CheckableComboBox('Categories', self)
        self.toolButton = QtWidgets.QToolButton(self)
        self.toolButton.setText('Categories ')
        self.toolMenu = QtWidgets.QMenu(self)
        for index in range(3):
            self.comboBox.addItem(f'Category {index}')
            item = self.comboBox.model().item(index, 0)
            item.setCheckState(QtCore.Qt.Unchecked)
            action = self.toolMenu.addAction(f'Category {index}')
            action.setCheckable(True)
        self.toolButton.setMenu(self.toolMenu)
        self.toolButton.setPopupMode(QtWidgets.QToolButton.InstantPopup)
        hbox.addWidget(self.toolButton)
        hbox.addWidget(self.comboBox)
        layout = QtWidgets.QVBoxLayout(self)
        layout.addLayout(hbox)
        layout.addStretch()

if __name__ == '__main__':

    app = QtWidgets.QApplication(['Test'])
    dialog = Dialog()
    dialog.show()
    app.exec()
        

PyQt4:

from PyQt4 import QtCore, QtGui

class CheckableComboBox(QtGui.QComboBox):
    def __init__(self, title = '', parent=None):
        super().__init__(parent)
        self.setTitle(title)
        self.view().pressed.connect(self.handleItemPressed)
        self.setModel(QtGui.QStandardItemModel(self))

    def handleItemPressed(self, index):
        item = self.model().itemFromIndex(index)
        if item.checkState() == QtCore.Qt.Checked:
            item.setCheckState(QtCore.Qt.Unchecked)
        else:
            item.setCheckState(QtCore.Qt.Checked)

    def title(self):
        return self._title

    def setTitle(self, title):
        self._title = title
        self.repaint()

    def paintEvent(self, event):
        painter = QtGui.QStylePainter(self)
        painter.setPen(self.palette().color(QtGui.QPalette.Text))
        opt = QtGui.QStyleOptionComboBox()
        self.initStyleOption(opt)
        opt.currentText = self._title
        painter.drawComplexControl(QtGui.QStyle.CC_ComboBox, opt)
        painter.drawControl(QtGui.QStyle.CE_ComboBoxLabel, opt)

class Dialog(QtGui.QWidget):
    def __init__(self):
        super().__init__()
        hbox = QtGui.QHBoxLayout()
        self.comboBox = CheckableComboBox('Categories', self)
        self.toolButton = QtGui.QToolButton(self)
        self.toolButton.setText('Categories ')
        self.toolMenu = QtGui.QMenu(self)
        for index in range(3):
            self.comboBox.addItem('Category %s' % index)
            item = self.comboBox.model().item(index, 0)
            item.setCheckState(QtCore.Qt.Unchecked)
            action = self.toolMenu.addAction('Category %s' % index)
            action.setCheckable(True)
        self.toolButton.setMenu(self.toolMenu)
        self.toolButton.setPopupMode(QtGui.QToolButton.InstantPopup)
        hbox.addWidget(self.toolButton)
        hbox.addWidget(self.comboBox)
        layout = QtGui.QVBoxLayout(self)
        layout.addLayout(hbox)
        layout.addStretch()

if __name__ == '__main__':

    app = QtGui.QApplication(['Test'])
    dialog = Dialog()
    dialog.show()
    app.exec()