Apart from the 4 examples you completely overlooked no
We've played 16 games at home since October (including cup games) 4 of those games we've scored second half goals. We've won 6 including games against Arsenal, Chelsea and Tottenham, drawn 2 (one against Leicester), lost 8 including games against Man it's, Man City, Chelsea, West Ham.
Given that the stat I just heard about the defending Champions having not scored at home in open play for 700+ minutes and Man City losing at home today, Chelsea losing last time out 2-5 to West Brom, it may just be that the season home records are a bit skewed.