This really is not Live Writer specific but is here is how to record a setup log that any setup author can use to debug a problem with setup. This could be used with Windows Live suite setup or even for a Live Writer plug-in.
To enable Windows Installer logging yourself, open the registry with Regedit.exe and create the following path and keys:
If you do not see the Installer key then with the Windows key selected then select the Edit menu, New, Key and name the key Installer.
Next with the Installer selected, select the Edit menu, New, String Value
Rename the key added to Logging and then right click on the key and select Modify. Enter voicewarmupx for the data value.
After you have done this run setup .msi file for the program you are trying to get the log for.
When setup finishes you should have a MSI*.LOG file in your TEMP folder.
After you have captured the log file please delete the key you have added to your registry. If you keep it there it will create a new log every time you install or uninstall software and slow down your machine in the process.