Having been begotten again (anagegennēmenoi). Perfect passive participle of anagennaō, which see in 1Pe 1:2.
Not of corruptible seed (ouk ek sporās phthartēs). Ablative with ek as the source, for phthartos see 1Pe 1:18, and sporās (from speirō to sow), old word (sowing, seed) here only in N.T., though sporos in Mar 4:26., etc. For “incorruptible” (aphthartou) see 1Pe 1:4; 1Pe 3:4.
Through the word of God (dia logou theou). See Jam 1:18 for “by the word of truth,” 1Pe 1:25 here, and Peter’s use of logos in Act 10:36. It is the gospel message.
Which liveth and abideth (zōntos kai menontos). These present active participles (from zaō and menō) can be taken with theou (God) or with logou (word). In 1Pe 1:25 menei is used with rēma (word). Still in Dan 6:26 both menōn and zōn are used with theos. Either construction makes sense here.