According to Thayer’s Lexicon, the word hós as used in Eph 5:1 refers to a quality which belongs to a person or thing (Strong’s 5613). The word hós in Eph 5:1 appears to function as a sentential adverb, describing an entire clause rather than an individual verb. As such it is "closely related to conjunctions" (unfoldingWord). In Eph 5:1, hós implies that the quality of our being imitators of God is or should be characterized by our being his beloved children.
The word kathos (Strong’s 2513) is an adverb meaning “according to the manner in which, in the degree that, just as, as.” In Eph 5:2, kathos implies that we should love one another in the manner that Christ loved us.
In context, the word “hós” in Eph 5:1 is actually situated between two “kathos”, one in Eph 4:32 and the other in Eph 5:2. The change from kathos (4:32) to hós (5:1) and back to kathos (5:2) again suggests a chiastic structure. I’ve arranged the words to show that structure as follows:
just as (kathos) God in Christ also has forgiven you.
Therefore be imitators of God,
as (hós) beloved children;
and walk in love,
just as (kathos) Christ also loved you and gave Himself up for us.
– Eph 4:32 to 5:2 NASB
From this arrangement, we can see how the reality of our being God’s beloved children is key. In other words, God’s love for us is the source and center (cf 1 Jn 4:7, 19). To be imitators of God then is to walk in love. In other words, we are called to imitate God’s love for us. Furthermore, God’s example of love has two distinct aspects: 1) the love of God in forgiving us in Christ and 2) the love of Christ in offering himself as a sacrifice for us to God (cf Lk 6:36, Jn 13:34). The chiastic structure serves to bring these two aspects and everything in between together as one.