As per my understanding, the method of response should not be affecting the procedure to establish the validity of the scale. Content validity may be established through expert judgment on if the instrument has exhaustively and accurately captured the construct. Concurrent validity may be established by finding if the scores on your instrument correlate with a concurrent measure of the same construct, and predictive validity may be established through correlation with a future measure. You may also find out the convergent and discriminant validity - by simultaneously testing the sample on measures whose scores are theorized to correlate with and to be independent of the scores in your measure.