Modification of an existing custody arrangement is permissible only upon a showing that there has been a change in cir*744cumstances such that modification is necessary to ensure the best interests of the child (see Matter of Tobar v Velez-Molina, 95 AD3d 1224 [2012]). The court must consider the totality of the circumstances (id.). In this regard, the court should consider whether the alleged changed circumstances indicate that one of the parties is unfit, the nature and quality of the relationships between the child and the parties, and the existence of a prior agreement (id. at 1224-1225). Since custody determinations turn in large part on assessments of the credibility, character, temperament, and sincerity of the parties, the Family Court’s determination should not be disturbed unless it lacks a sound and substantial basis in the record (see Eschbach v Eschbach, 56 NY2d 167, 173-174 [1982]). Here, the Family Court’s determinations that there had been a change in circumstances since the issuance of the order awarding the parties joint custody of the subject children, and that an award of sole custody of the subject children to the father would be in the their best interests, have a sound and substantial basis in the record and, thus, should not be disturbed (see Matter of Tobar v Velez-Molina, 95 AD3d at 1225; Matter of Francis v Cox, 57 AD3d 776, 777 [2008]).
The new facts that the attorney for the subject children sets forth on appeal do not demonstrate that the record before us is no longer sufficient for determining the best interests of the subject children (see Matter of Michael B., 80 NY2d 299, 318 [1992]).
Contrary to the mother’s contention, she failed to establish, by a fair preponderance of the evidence (see Family Ct Act § 832), that the father committed the family offense of menacing in the third degree (see Penal Law § 120.15; Matter of Sharyn PP. v Richard QQ., 83 AD3d 1140, 1141-1142 [2011]; People v Nwogu, 22 Misc 3d 201, 204 [2008]; People v Stephens, 100 Misc 2d 267, 267-268 [1979]; see also Family Ct Act § 812 [1]). Accordingly, the Family Court properly denied her family offense petition. Skelos, J.P., Balkin, Lott and Miller, JJ., concur.