WPF Radiobutton (two) (binding to boolean value)

When using MVVMLight and DataContext is set in XAML as:

DataContext="{Binding <Your ViewModel property name>, Source={StaticResource Locator}}" 

BoolInverterConverter causes Stack Overflow second time the window gets opened.

The work around is to remove DataContext from XAML and do it in code in window constructor after InitializeComponent():

DataContext = ServiceLocator.Current.GetInstance<Your View Model class>();

After some testing it was not enough - Stack Overflow error could pop up randomly when clicking on radio button. The solution which worked for me - instead of the converter use another property for other radio button in a group:

public bool Is9to1 { get; set; }
public bool Is1to9 { get { return !Is9to1; } set { Is9to1 = !value; } } 

in XAML:

   <RadioButton GroupName="Is9to1" IsChecked="{Binding Is1to9}"/>
   <RadioButton GroupName="Is9to1" IsChecked="{Binding Is9to1}"/>

Little upgrade of RandomEngy's answer if you want your bool nullable (for no default value/Checked Radiobutton)

public class BoolRadioConverter : IValueConverter
{
    public bool Inverse { get; set; }

    public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
    {
        bool? boolValue = (bool?)value;

        return this.Inverse ? !boolValue : boolValue;
    }

    public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
    {
        bool? boolValue = (bool?)value;

        if (boolValue != null && (bool)!boolValue)
        {
            // We only care when the user clicks a radio button to select it.
            return null;
        }

        return !this.Inverse;
    }
}

and the rest is the same as his answer.

From The answer of Mr-RandomQC everything works fine. But when I click another radio in the same group. Then the opposite radio will show a Red box around the radio button.

I changed the code a little bit from his answer to return Binding.DoNothing instead of return null like this.

public class BoolRadioConverter : IValueConverter
{
    public bool Inverse { get; set; }

    public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
    {
        bool boolValue = (bool)value;

        return this.Inverse ? !boolValue : boolValue;
    }

    public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
    {
        bool boolValue = (bool)value;

        if (!boolValue)
        {
            // Return Binding.DoNothing instead of Return null
            return Binding.DoNothing;
        }

        return !this.Inverse;
    }
}