If we are running monthly cross sectional regressional, where we regress excess stock returns on their the stock characteristics like market capitalization, B$/$M plus a new factor for example "twitter factor", for all companies in a given month. Then we fetch monthly betas for twitter factor, and we use that twitter factor beta and regress that on fama french factors and get significant alpha $-$ to me this means additional premium associated with the Twitter factor that is not explained by the allready existing factors.

Question: If we now want to analyse if this twitter factor is compensation for some risk, for example default risk which we represent as the atlman z score, what appraoch we can use $?$

Use Altman Z score for each company, for each month as control variable in regression $1,$ and then again fetch monthly betas for twitter factor and regress on existing factors to see if alpha is still significant.

Or Use Altman Z score for each company, for each month as control variable in regression $1,$ and then again fetch monthly betas for twitter factor and regress on existing factors but also include agregate Altman Z score for all firms in regression $2$ as well to see if alpha is still significant.

Thank you