That same question is already on RG in the link I leave below. I have also found two texts (an article and a dissertation) that may me relevant (attached).
Although not looking specifically at loneliness, you might try to obtain the following article:
Mai-Ly N. Steers, Robert E. Wickham, and Linda K. Acitelli (2014). Seeing Everyone Else's Highlight Reels: How Facebook Usage is Linked to Depressive Symptoms. Journal of Social and Clinical Psychology: Vol. 33, No. 8, pp. 701-731. doi: 10.1521/jscp.2014.33.8.701