Acts 16:15

And when she was baptized, and her household, she besought us, saying, If ye have judged me faithful to the Lord, come into my house, and abide there. And she constrained us.

And when she was baptized ... As DeWelt observed:

The New Testament conversions all end with the baptism of the convert. Not with their prayer experience but with their baptism; not with their testimony, but with their baptism.[11]

And why was she baptized? Because the commandment thus to obey the Lord was included in the preaching of these who spoke unto her the word of salvation, there being no other reasonable explanation of why she was baptized.

And her household ... The allegation that this household included infants is denied by the earlier statements that the evangelists "spake unto the women that were come together" (Acts 16:13), thus making it mandatory to find Lydia's household in that group of women. The household baptisms of the New Testament afford no support whatever for the notion that infants should be baptized.

She constrained us ... It is not likely that Paul and company would have accepted any casual invitation to accept accommodations provided by the devout Lydia; however, the manner in which she put the invitation, coupled with her insistence upon it, constrained them. They would not long remain, however; for events would shortly occur which would thrust Paul forward on his journey.